The Megarians and the Stoics
1 Introduction
In the opinion of Carl Prantl, the nineteenth century historian of logic, the Stoics were no logicians at all, but merely confused plagiarists who peddled second-rate versions of Peripatetic and Megarian doctrines. Chrysippus of Soli, touted by many as the greatest logician of the Hellenic age, was a special target of Prantl’s baleful attacks, as witness the following assessment of his logical skills:
Chrysippus created nothing really new in logic, for he only repeated details already known to the Peripatetics or pointed out by the Megarians; his activity consisted in this, that in the treatment of the material he descended to a pitiful degree of dullness, triviality, and scholastic quibbling. … It is to be considered a real stroke of luck that the works of Chrysippus were no longer extant in the Middle Ages, for in that extensive morass of formalism, the tendency (weak as it was) toward independent investigation would have been completely eliminated.1
Although Chrysippus may have borne the main thrust of Prantl’s assault, there is no doubt that his criticisms were meant to have general application among the philosophers of the Stoa.
It is difficult to discern the motivation behind Prantl’s ad hominem attacks on the Stoics in general and on Chrysippus in particular, and one has to look back to Plutarch’s polemic in De communibus notitiis and De Stoicorum repugnantiis to find anything remotely similar in tone. On the other hand, it is not so difficult to see, as Mates argues [Mates, 1953, pp. 87–88], that one can safely discount virtually all of Prantl’s judgements on Stoic logic, not only because there is lacking any argument to substantiate them, but also because Prantl himself seems to have had little understanding of what the Stoics were about (cf. Boche
ski 1963, 5). Unfortunately, Prantl’s estimation of Stoic logic, echoed by Eduard Zeller with somewhat more scholarly decorum, but with little more skill and understanding, was to remain for the most part unchallenged until late in the first half of the twentieth century when it was called into question, first, by Jan Łukasiewicz, and later, by Benson Mates.
Prantl’s work, according to Łukasiewicz, although “indispensable … as a collection of sources and material,… has scarcely any value as an historical presentation of logical problems and theories” [Łukasiewicz, 1967, p. 67]. Moreover, since neither Prantl, nor Zeller, nor any other of the older historians of logic, had any understanding of the difference between the logic of terms, which was Aristotle’s logic, and the logic of propositions, which was the logic of the Stoa, there exists no history of the logic of propositions, and thus, no complete understanding of the history of formal logic. For this reason, “the history of logic must be written anew, and by an historian who has fully mastered mathematical logic” [Łukasiewicz, 1967, p. 67].
In the interest of setting the historical record straight, one cannot help but endorse this project, and we ought to be ever grateful not only to Łukasiewicz, but also to Mates, Bocheski, the Kneales, and others for their contributions toward this end. It should be noted, however, that there is a danger that the historian of logic possessing this requisite mastery of mathematical logic may allow his or her familiarity with the discipline to obscure, or even distort, the historical enterprise. When viewing the past from the perspective of contemporary doctrines, it is sometimes all too easy to succumb to the appeal of a ‘convergence’ theory of history, and to assume that one’s predecessors, if only they had got it right, would have come to the same place we now occupy. At any rate, there seems to have been a tendency toward such a view among several modern commentators. These writers seem to presume that the Stoics had in mind to develop a formal logic along the lines of the modern propositional calculus, and their respective appraisals of Stoic logic might be seen as dependent on their estimates of the degree of success to which this goal was carried through.
It must be admitted, however, that there are some texts which would seem to justify such a presumption; on the other hand, all of these texts can be, and have been, called into question. To consider two examples, there are texts which may be taken to indicate that, in general, the Stoics defined those logical constants having a role in their syllogistic as binary connectives; other texts may be taken to support the view that Stoic logic was a formal logic—formal, that is, in the specialised sense in which mathematical logic is formal, namely, the substitutional sense.
As to the first of these suppositions, it is surely false that the logical connectives which appear in the Stoic syllogisms were in general defined as binary connectives. In particular, consider 
, which is evidently the notion of disjunction occurring in the fourth and fifth Stoic syllogisms.2 This disjunction, represented at the linguistic level by the connective particle 
(or 
), is assumed by not a few writers to be the ‘exclusive’ disjunction defined by the matrix 0110.3 The reason for this assumption, according to some writers at least,4 is that an inclusive notion of disjunction will not support both the fourth and fifth Stoic syllogisms, whereas the exclusive disjunction will. It can be shown, however, that 
, the Greek notion of disjunction which validates both the fourth and the fifth syllogisms, is not the exclusive disjunction of modern logic in which the connective is defined as a binary operator satisfying the matrix 0110.
Now it is not at all clear whether the Stoics viewed 
as a purely truth-functional notion of disjunction, but it seems evident from the texts which mention a disjunction consisting of more than two disjuncts that if the Stoic disjunction were to be characterized truth-functionally, then the general truth condition (i.e. the truth condition for the occurrence of two or more disjuncts) would be that it is true whenever exactly one of its clauses is true.5 On the other hand, it can be shown by means of a simple inductive proof that the general truth condition for the modern exclusive disjunction is that an odd number of disjuncts be true. As a consequence of this result, it is apparent that even if the Stoic disjunction is given a truth-functional interpretation, its truth will coincide with that of the 0110 disjunction only in the two-disjunct case.
It seems evident, then, that we can rule out the assumption that the Stoic disjunction and the modern exclusive disjunction are identical; hence, we can not take their alleged identity as evidence for the conclusion that the Stoic disjunction was viewed as a binary connective. Furthermore, there seems to be nothing in the texts to force the interpretation of 
as even having a fixed ‘arity’,6 and in particular, nothing to force the interpretation that it has arity two. But if a Stoic disjunction has no fixed arity, then we are not required—indeed, we are not allowed—to treat an n-term disjunction as a two-term disjunction by the use of some bracketing device. This proscription has consequences for the idea that Stoic logic was formal in the substitutional sense, an issue which we shall take up later on in this article.
If it is neither true that the logical connectives occurring in the Stoic syllogisms are in general binary operators, nor that Stoic logic is a formal system in the substitutional sense of formal, then the modern historians and commentators who have affirmed the contrary have misunderstood and misrepresented Stoic logic no less than have the earlier historians of logic, such as Prantl and Zeller. The obstacle for both the later and earlier writers, it seems to us, is that they have allowed their preconceptions to obscure their understanding. It is obvious from their writings that Prantl and Zeller held to the general conviction of their era that the intellectual achievements of the Hellenic period in Greece were few indeed. And no doubt this view would have affected their ability to provide a balanced account of Stoic philosophy in general, and Stoic logic in particular. As for the writers who published in the early and middle years of this century, they no doubt were influenced by the tendency, experienced at some time or other by most of us familiar with modern formal logic, to suppose that there really is no other notion of logic.
Be that as it may, we are nevertheless indebted to these logicians and historians of logic for having rescued the logic of the Stoa from the lowly status to which it was relegated at the hands of Prantl and his contemporaries. That having been said, it needs also to be said that we ought now to move out from the shadows of Łukasiewicz, Bochenski, and Mates, and attempt an interpretation of Stoic logic less coloured by a reverence for modern formal systems, and more in harmony with what the texts seem to indicate as being the place of logic in the Stoic system as a whole. This point of view is well expressed by Charles Kahn:
We may not have an accurate picture of Chrysippus’ enterprise in “dialectic” if we see it simply as a brilliant anticipation of the propositional calculus. No doubt it could not be accurately seen at all until it was seen in this way, again by Lukasiewicz and then more fully by Mates. But now that their insights have been assimilated, I think it is time to return to a more adequate view of Stoic logic within the context of their theory of language, their epistemology, their ethical psychology, and the general theory of nature [Kahn, 1969, p. 159].
The elements of Stoic philosophy mentioned by Kahn— epistemology, theory of language, ethical psychology, and a general theory of nature—are just the elements viewed as extraneous to the logician’s enterprise by the early modern commentators. Indeed, the creation of contemporary formal logic by Frege required, in the words of Claude Imbert, “[the] gradual and piecemeal disintegration of a logical structure built by or borrowed from the Stoics” [Imbert, 1980, p. 187]. On this account, it seems evident that any attempt to understand Stoic logic as a formal calculus must fail; moreover, it would seem that anyone wishing to provide an adequate understanding would be constrained to do so as part of a reconstruction of the logical edifice built by the Stoics. The present essay is one attempt to formulate such an interpretation.
Leaving aside the matter of setting straight the historical record, one might ask what the worth of studying an ancient logic such as that of the Stoics might be. The answer to this question, it seems to us, lies in how one views the nature of Stoic logic itself. For our part, we believe that Stoic logic developed out of a desire to provide an account of the inferences one could make concerning the natural course of events, such inferences depending on premisses based in the perceptual knowledge of the occurrence of particular events or states of affairs, and in a general knowledge of relationships discovered in nature between events or states of affairs of certain types.
The relationships between events or states of affairs which the Stoics referred to as ‘consequence’ 
and ‘conflict’ 
, are represented in the Stoic syllogistic in the major premisses of four of their five basic inference schemata. Particular events or states of affairs are represented in the minor premisses. Knowledge of these relationships and particular events is based on certain perceptual structures called ‘presentations’ 
. Associated with these presentations as their content are conceptual structures called pragmata 
, and associated with the pragmata are ‘propositional’ structures called lekta 
. According to the Stoic theory, we proceed from language and thought to the world, and to language and thought from the world, through the media of these various structures.
This theory suggests a different paradigm from that of present-day formal logic. It would seem to imply an understanding of logic as a human linguistic practice—a theory of inference rather than of inferability. Given the difficulties encountered so far in attempts to develop automated inference systems based on the paradigm of modern formal logic, it may be worthwhile to attempt a formalisation of the Stoic semantic theory in the hope that such a formalisation would provide a more successful alternative. The first step in such an enterprise would be to try to develop as clear an understanding of the Stoic theory as is possible.
2 Historical Survey
On the assumption that more than a few readers will be unfamiliar with early Stoic philosophy, and since this essay is an interpretation of certain logical doctrines of the Old Stoa, it would seem appropriate to present first a brief historical sketch of the Stoic School, and, in particular, of the philosophers of the early Stoa.
2.1 The influence of Stoicism
The first Stoic was Zeno of Citium who founded the school some time near the turn of the century between the third and fourth centuries B.C. The last Stoic, according to Eduard Zeller [Zeller, 1962, p. 314], was Marcus Aurelius, the Roman emperor who died in 180 A.D. Of course, as J. M. Rist points out [Rist, 1969c, p. 289], one ought to understand this claim not in a literal sense, for there were Stoics who came after Aurelius, but rather in the sense that with his passing the school came to an end as a recognisable entity. Hence the Stoic School was extant for a period of almost five hundred years, a remarkable achievement by any standard. But it is not only the longevity of the school which would seem exceptional, for it might be claimed, as at least one scholar has done, that “Stoicism was the most important and influential development in Hellenistic philosophy” (A. A. Long [1986], 107). The basis for this claim lies in part at least in the far-reaching domain of Stoic doctrines. For according to Long, not only were Stoic teachings prevalent among a large segment of the educated population in the Hellenic era, but also their influence is apparent in various intellectual spheres during the early post-Hellenic period as well as from the Renaissance up to fairly recent times. The tenets of Christian philosophy, for example, exhibit certain evidence of Stoic bias, as do the moral precepts of Western civilisation in general. Moreover, the manifestations of such influence would seem apparent in the realm of secular literature and thought as well, reaching a peak, according to Long, between 1500 and 1700 (1986, 247). One scholar even perceives the presuppositions of Stoic logical principles at work in the writings of the Alexandrian novelists and poets (Claude Imbert [1980]). In later philosophy, according to Long, Stoic canons are evident in the writings of men as diverse in their beliefs as the religious philosopher Bishop Butler and the metaphysicians, Spinoza and Kant (1986, 107). And according to Imbert: “[The] gradual and piecemeal disintegration of a logical structure built by or borrowed from the Stoics was a necessary preliminary to Frege’s formulation of a sentential calculus and to the conception … of such a calculus as an independent system” [Imbert, 1980, p. 187].
But if Stoicism has indeed found expression in such widespread and various areas of thought, then why, one might ask, does it seem that in the English-speaking world at least, Stoic philosophical theories have been so little studied in recent times as compared with the treatises of Plato and Aristotle—aside, that is, from the chiefly moralistic writings of the later Stoics such as Marcus Aurelius. The answer no doubt lies, at least in part, in the fact that virtually none of the records of the early Stoics has survived the vagaries of time. We are fortunate to have mined in their extant writings an abundant source from which we may develop a deep appreciation of the philosophical thought of Plato and Aristotle, but there is no mother lode of philosophical literature from which to develop a rich understanding of Stoic thought. Those direct sources which have survived consist in a few badly damaged papyri salvaged from the ruins of Herculaneum. For the most part, however, one must rely on the reports of various commentators of uneven reliability, authors such as Sextus Empiricus,7 Diogenes Laërtius,8 Galen, Cicero, Stobaeus, Plutarch, Alexander of Aphrodisias, and Aulus Gellius, to name a few. Many of these reports are presented in the form of doxography, and many are second-hand; some, however, possess the merit of having direct quotations appearing in them, and it is from these quotations that the most reliable information can be gleaned. But even having quotations available is no guarantee that one is getting an unbiased account. For much of the commentary by authors such as Plutarch, Alexander, Sextus Empiricus, Cicero, and to some extent, Galen, is polemical in tone and clearly inimical to various Stoic doctrines. Hence, one suspects that quotations are often chosen not to illustrate a point in a positive mode, but rather to show up perceived absurdities and inconsistencies in Stoic thought. Given problems of this kind, it is clear that the road to an understanding of Stoicism could not be as free from impediment as that to an understanding of Plato and Aristotle.
A further reason why Stoic philosophy has been by comparison so little studied in recent times might be the bad press it received at the hands of the nineteenth century historians of philosophy, Prantl and Zeller.9 Prantl apparently took to heart Kant’s pronouncement that “since Aristotle … logic has not been able to advance a single step, and is thus to all appearance a closed and completed body of doctrine.”10 Hence, in his Geschichte der Logik, he was especially critical of Stoic logical doctrines, attacking with a vehemence curiously out of place in what is supposed to be a scholarly work, not only these doctrines themselves, but also the men who authored them. Nor did Stoic logic fare much better at the hands of Zeller, although it must be admitted that his critique lacks to some extent the intense personal animosity characteristic of Prantl’s writings. According to Zeller, “no very high estimate can be formed of the formal logic of the Stoics” [Zeller, 1962, p. 123], and “the whole contribution of the Stoics in the field of logic consists in … clothing the logic of the Peripatetics with a new terminology” [Zeller, 1962, p. 124]. But it was not only the field of Stoic logic that received such negative assessment from Zeller, for in his judgement the Hellenistic era was characterised by a general decline in the quality of intellectual life, and by the particular decline in the virtue of the philosophical enterprise (cf. Long [1986, p. 10; 247]). There would seem to be little doubt, according to Long, that the estimates of Prantl and Zeller in favour of Platonic and Aristotelian philosophy and against Hellenistic philosophy carried a good deal of weight among succeeding historians of the subject [Long, 1986, p. 10]. Perhaps no further reason than this need be sought to account for the want of a general interest in Stoic philosophy in the modern era.
2.2 The philosophers of the Early Stoa
Traditionally, the Stoic era has been divided into three periods: the Early Stoa (often the Old Stoa), which begins with Zeno and ends with Antipater; the Middle Stoa, which covers the leadership of Panaetius and Posidonius; and the Late Stoa, which is represented by Seneca, Epictetus, and Marcus Aurelius.11 Since this essay will be concerned mainly with the logical doctrines of the Early Stoa, and in particular the doctrines of Zeno, Kleanthes, and Chrysippus, we shall have little to say in this introduction about the Middle and Late periods of Stoic history; indeed, given these restrictions, we shall not have much to say about those Stoics such as Diogenes of Babylon, Antipater of Tarsus, and several others, who came after Chrysippus but yet belong to the Old Stoa. Furthermore, the scope of this introduction will not permit more than a cursory glimpse of the lives of Zeno and his two immediate successors, nor will it allow more than a brief and somewhat arbitrary survey of their philosophical doctrines.
Zeno (333–261 B.C.)
As mentioned above, the Stoic School was founded by Zeno, a native of Citium on the island of Cyprus. Born around 333/2 B.C., Zeno is reported to have arrived in Athens at about the age of twenty-two and to have begun his teaching about 300/301 B.C.12 By way of establishing himself as a teacher, he chose to discourse with his followers in the ‘Painted Colonnade’ (Stoa Poikilē), where Polygnotus’ paintings of the Battle of Marathon were displayed. Hence, his followers, known first as the ‘Zenonians’, came to be known as ‘the men of the Stoa’ or ‘the Stoics’ (DL 7.5).
In the period between his arriving in Athens and his starting the Stoic School, Zeno engaged in the development of his formal philosophical education. He apparently began this training by studying with the Cynic philosopher Crates (DL 7.4), but though it would seem fairly certain that Zeno’s first formal training in philosophy was in the doctrines of the Cynics, it is possible that he had prepared himself for the study of philosophy by reading the many books on Socrates which his father, a merchant, had brought home from his trips to Athens (DL 7.31). After the period of study with Crates, Zeno became a pupil of the Megarian philosopher Stilpo and of the Dialectician Diodorus Cronus (DL 7.25). As well, he “engaged in careful dispute” with the Dialectician Philo of Megara, who was also a student of Diodorus Cronus (DL 7.16). He is further reported to have studied with the Academic philosophers Xenocrates and Polemo (DL 7.2), but given the chronology cited above, there is some doubt that he actually did study with the former (cf. Zeller [1962, 37n1]). On the other hand, there is confirmation that he was a pupil of Polemo, for Cicero explicitly states that this was so (de fin. 4.3), and Diogenes Laërtius attests that he was making progress with Diodorus in dialectic when he would enter Polemo’s school (7.25). It may be, however, that his attendance at Polemo’s lectures was somewhat surreptitious, for according to Diogenes, Polemo is said to have reproached him thus: “You slip in, Zeno, by the garden door—I am quite aware of it—you filch my doctrines and give them a Phoenician make-up.”13 However that may be, it is in light of Cicero’s further testimony that Zeno’s association with Polemo is significant, for he maintains that Zeno had adopted Polemo’s teaching on the primary impulses of nature (de fin. 4.45), as well as on the doctrine that the summum bonum is ‘to live in accordance with nature’ (de fin. 4.14).
There is some controversy among modern scholars whether the Peripatetics had any influence on Zeno’s philosophical education, and, assuming they did have, in what it might have consisted. Some commentators propose that there was such influence,14 but it would seem that such proposals should be regarded as conjecture, for unlike the situation with the Cynics, the Megarians, the Dialecticians, and those from the Academy, “there is no ancient evidence concerning Zeno’s relationship with Theophrastus or other Peripatetics” Long [1986, p. 112].15 In addition, many writers insist that certain Stoic doctrines must have developed either as an extension of Aristotelian theories, or, as a reaction to them, and underlying this contention is the assumption that the early Stoics must have had available, and made a close study of, the corpus of Aristotelian literature which we have available to us.16 In his monograph “Aristotle and the Stoics,” F.H. Sandbach conducts a careful study of these claims and of the assumptions which underlie them. He contends that this investigation supports the theory that, barring a few exceptions, this corpus of Aristotle’s works (which he refers to as the ‘school-works’) was not available to the early Stoics [Sandbach, 1985, p. 55]. On the other hand, where certain Stoic doctrines are similar in content to passages in the school-works, this similarity may be explained by the hypothesis that an analogous passage occurred in an ‘exoteric work’,17 and some Stoic had read it there. Alternatively, the early Stoics may have come across these teachings in oral form, either as explicitly attributed to Aristotle or as recognised Peripatetic doctrine. Another possibility, one apparently acknowledged by few, if any, writers, is that the Stoics may simply have thought of these doctrines independently of Aristotle [Sandbach, 1985, p. 55]. Sandbach concludes that for the most part the evidence will not support the probability, let alone the certainty, that Aristotle was an influence on the origin of Stoic doctrines [Sandbach, 1985, p. 57]. Moreover, he quite forcefully expresses the view that “it is a mistake to proceed on the a priori assumption that the Stoics must have known the opinions expressed in his school-works, must have understood his importance sub specie aeternitatis, and must therefore have been influenced by him” [Sandbach, 1985, p. 57]. It is important to see that Sandbach is not ruling out the possibility of Aristotelian or Peripatetic influence, but rather urging a more careful and less biased approach to the question.
As might be expected, the foundations for many of the central tenets of Stoicism can be discerned in the philosophical education of Zeno, and though it would be interesting to trace the sources of the full range of Stoic doctrines, such pursuits will be restricted in this introduction to considering those influences which would seem likely to have affected the origins of Stoic logical theory. Probably Zeno’s most significant contribution to Stoic logic is his work in epistemology.
It has been widely accepted among modern commentators that Zeno received his education in logical techniques directly from the Megarians, and in particular, from Diodorus Cronus (cf. Long [1986, p. 111]; Mates [1953, p. 5]; Kneale and Kneale [1962a, p. 113]; Rist [1978, p. 388]). An article by David Sedley, however, would seem to raise some doubt that this assumption can be maintained. What is called into question is not whether Zeno was indeed a student of Diodorus, for this would seem to be beyond dispute, but rather whether Diodorus himself can be established as belonging to the Megarian School.
The Megarian School was founded by Euclides, a pupil of Socrates (DL 2.47) and a native of Megara on the Isthmus (DL 2.106). He was succeeded as head of the school first by Ichthyas and later by Stilpo, also a native of Megara in Greece (DL 2.113). Evidently, since Diodorus can trace his philosophical lineage back to Euclides through Apollonius Cronus and Eubulides (DL 2.110-11), it has been generally thought that he also was a member of the Megarian school; hence, the Megarian connection with respect to the source of Zeno’s logical doctrines would seem assured. Sedley, however, has presented what seems to us a convincing argument to the effect that Diodorus belonged rather to a rival school which was called the Dialectical School (Sedley, [1977, pp. 74–75]; cf. Sandbach, [1985, p. 18]).
At 2.106 Diogenes reports that the followers of Euclides were called Megarians after his birthplace. Later they were called Eristics, and later still, Dialecticians. Sedley argues for the possibility that these remarks should not be interpreted, as they usually are, to mean that this was one and the same school known at different times by different names, but rather that these names designated splinter groups whose raisons d’être were different enough from that of the Megarian School to warrant viewing them as distinct schools [Sedley, 1977, p. 75]. According to Sedley, several sources inform us that the Dialecticians recognised Clinomachus of Thurii, a pupil of Euclides, as the founder of their school [Sedley, 1977, p. 76]. However, since the name ‘Dialectician’ was first coined for the school by Dionysius of Chalcedon (DL 2.106), an “approximate” contemporary of Diodorus (Sedley [1977, p. 76]), it seems more likely not that Clinomachus actually founded the school, but rather that he was recognised by its members as the source of the ideas foremost in their teachings [Sedley, 1977, p. 76]. As Sedley points out, practically nothing is known of Clinomachus’ doctrines, except for the fact, reported by Diogenes Laërtius (2.112), that he was the first to write about axiōmata18 
and predicates 
. But this fact is of “utmost significance” [Sedley, 1977, p. 76], for both of these notions, as will become apparent in the sequel, are fundamental constituents of the conceptual apparatus in Stoic logic.
The Dialectician Diodorus and his pupil Philo apparently engaged in a famous debate about the criterion according to which the consequent of a conditional axiōma (proposition) ‘follows’ from the antecedent (PH 110–12; AM 112–17).19 The controversy between these logicians was apparently of interest not only to themselves, for Sextus Empiricus reports that Challimachus, who served in mid-third century B.C. as the chief librarian at the great library in Alexandria, wrote to the effect that even the crows on the rooftops, having repeatedly heard the debate, were cawing about the question which conditional axiōmata are sound (AM 1.309-10). The debate was extended by the introduction of two additional accounts, one of which is attributed to Chrysippus on fairly strong evidence (e.g., Gould, [1970, pp. 74–76]), but the other not attributed to any particular philosopher or even to any particular school. Given Zeno’s association with Diodorus and Philo it seems fairly certain he would have taken part in the debate; moreover, he wrote a book On Signs 
(DL 7.4), and a ‘sign’ is defined by the Stoics as “the antecedent axiōma in a sound conditional, capable of revealing its consequent” (AM 8.245). Hence he would have had an interest in the criterion for a sound conditional axiōma, perhaps even offering a view of his own. We will argue in the sequel (see page 142) that given his motivation and particular interests in logic, it is unlikely that he would have opted for the view of either Diodorus or Philo. And since the third account can be attributed to Chrysippus with some certainty, one may conjecture that Zeno supported the fourth view. Furthermore, if Long and Sedley are correct, there may be no significant difference between the third and fourth statements of the criterion [Long and Sedley, 1990, 1.211], so that one might suppose, as long as we are in the realm of speculation, that the third criterion represents a tighter version of the fourth account.
Evidently, then, there is some reason to believe that Zeno was influenced by Diodorus and Philo through a familiarity with these ideas, and that it was the Dialectic School rather than the Megarian School which was the important inspiration for the development of Stoic logic (Sedley [1977, p. 76]). It may be, nevertheless, that Stilpo played some part as an influence on Zeno’s logical education, and indeed, there may be some overlap in certain areas, for after all, if what has been argued above is correct, the source of the logical doctrines of both the Megarians and the Dialecticians is, for the most part, one and the same.20 Given that Stilpo was one of those who came to listen to Diogenes the Cynic (DL 6.76), it is possible, as Sandbach submits [Sandbach, 1975, p. 22], that it was not Stilpo’s logical tutoring but rather his moral teachings which attracted Zeno to the Megarian School, for these instructions were probably not unlike those of the Cynics. On the other hand, J.M. Rist puts forward the hypothesis that Zeno became dissatisfied with Cynic ethical doctrine and its rather circumscribed concept of ‘life according to nature’, and so was looking to develop an account of nature with a basis in physical theory—any such account being rejected by the Cynics [Rist, 1978, pp. 387–88]. The difficulty in such an undertaking is summed up by Rist as follows:
In Zeno’s time and before … the problems confronting a philosopher who has come to the conclusion that he must embark on the study of nature … is that Parmenides and his Eleatic successors had attempted to rule out such study altogether, and before it could be taken up, philosophers deemed it desirable to propose ways by which Parmenides’ ban could be overcome [Rist, 1978, p. 388].
Hence “for the would-be 
the acquisition of a certain familiarity with Eleatic procedures would be a sine qua non” [Rist, 1978, p. 388]. According to the testimony of Diogenes Laërtius, Euclides “applied himself to the writings of Parmenides” (2.106), and since Stilpo was a pupil of Euclides (or at least, of one of Euclides students) (2.113), he would no doubt be familiar with the arguments of Parmenides; hence, it is possible that Zeno was attracted to him for this reason. And certainly in the Stoic theory of a coherent and continuous universe held together by a pervasive pneuma immanent in all matter, (e.g., Alexander de mixtione 216.14–17) there is some evidence that Zeno took up Parmenides’ thesis of the unity of being.
Another possibility, not necessarily an alternative, is that Zeno was attracted by Stilpo’s fame in the posing of logical problems and fallacies. One account has it that Zeno once paid twice the asking price for seven dialectical forms of the ‘Reaper Argument’, so great was his interest in such things (DL 7.25). Probably of more reliability, we have Plutarch’s testimony that Zeno would spend time solving sophisms and would encourage his pupils to take up dialectic because of its capacity to assist in this endeavour (de Stoic repugn. 1034e). Furthermore, Stilpo is reported by Diogenes Laërtius to have “excelled all the rest in the invention of arguments and in sophistry” (DL 2.113). The story goes that during a banquet at the court of Ptolemy Soter he addressed a dialectical question to Diodorus Cronus which the latter was unable to solve. Because of this failure, Diodorus was reproached by the king and subsequently received the derisive name ‘Cronus’. This caused him so much anguish that he wrote a paper on this logical problem and “ended his days in despondency” (DL 2.112). Even taking into account the likelihood that this story might be somewhat apocryphal, it probably can be taken as a reliable indicator of Stilpo’s skill as an inventor of logical arguments and puzzles. As an aside, recalling Sedley’s argument cited above, it would also seem to point to a certain tension between Stilpo and Diodorus, a tension that one would not normally expect if they had been members of the same school.
Another logical doctrine in which Zeno may have been influenced by Stilpo is that concerning his rejection of the ‘forms’ or ‘ideas’. According to Diogenes Laërtius, Stilpo used to demolish the forms or universals, saying that whoever asserts the existence of Man refers to nothing, for he neither refers to this particular man nor to that; hence, he refers to no individual man (DL 2.119). And according to the testimony of Stobaeus. similar opinions were held by Zeno, for he and his followers relegated such ‘ideas’ or ‘concepts’ 
to a sort of “metaphysical limbo”, referring to them as ‘pseudo-somethings’ 
(eclog. 1.136.21). It should be noted that this stance does not represent a rejection of all those things which we refer to as ‘universals’. Common nouns such as ‘man’ or ‘horse’ were taken to refer to the essential quality – and all qualities are corporeal – which made something either a man or a horse (DL 7.58). It is if we were to use the term ‘man’ to refer to the genetic material which differentiates us from other creatures.
Kleanthes (331-232 B.C.)
After the death of Zeno in 261/2 B.C., Kleanthes, a native of Assos on the Troad, became head of the Stoic School (DL 7.168). According to the historian Antisthenes of Rhodes, Kleanthes was a boxer before taking up philosophy (DL 7.168). Upon his arrival at Athens he fell in with Zeno and was introduced to Stoic teachings which, in spite of having no natural aptitude for physics and of being extremely slow (DL 7.170), he studied “right nobly”, remaining faithful to the same doctrines throughout (DL 7.168). Zeno compared him to those hard waxen tablets which are difficult to write on but which retain well the characters written on them (DL 7.37). Kleanthes was perhaps the most religious of the Stoics, as witness his well-known Hymn to Zeus.21 He was acclaimed for his industry and perseverance (DL 7.168), for it was said that he came to Athens with only four drachmas in his possession (DL 7.168), and so was forced to work drawing water for a gardener by night in order to support himself while studying philosophy by day (DL 7.169). Apparently he never got far beyond this impecunious state, for the story goes that he was too poor even to buy paper, and so used to copy Zeno’s lectures on oyster shells and the blade-bones of oxen (DL 7.174). At some point, however, he must have gained access to a supply of writing material, for Diogenes has compiled a list of his writings which includes about sixty books.
Of these sixty books catalogued, a series of four is listed under the title Interpretations of Heraclitus (DL 7.174). A connection with Heraclitus is also indicated by the report of Arius Didymus to the effect that Kleanthes, comparing the views of Zeno with those of other natural philosophers, says that Zeno’s account of the soul or psychē 
is similar to that of Heraclitus (fr. 12 DK; DDG 470.25–471.5). Other than a book under the title Five Lectures on Heraclitus attributed to the Stoic Sphaerus, a pupil of Kleanthes (DL 7.178), there is little other direct evidence to support the hypothesis of the influence of Heraclitus on Stoicism and on Zeno in particular. This hypothesis is expressed, for example, in the following statement by A.A. Long: “Heraclitus’ assumption that it is one and the same logos which determines patterns of thought and the structure of reality is perhaps the most important single influence upon Stoic Philosophy” [Long, 1986, p. 131]. It is also expressed by G.S. Kirk, but with reservations:
Although Zeno must have based his physical theories particularly upon Heraclitus’ description of fire, he is never named in our sources as having quoted Heraclitus by name; while Kleanthes evidently initiated a detailed examination of Heraclitus with a view to the more careful foundation of Stoic physics upon ancient authority. … and there is reason to believe that he made some modification of Zeno’s system in the light of his special knowledge of the earlier thinker … [Kirk, 1962, pp. 367–68].
It is not a straightforward matter to see what can be made out from these circumstances. What seems likely is that Zeno tacitly appealed to Heraclitus in formulating his views on physics and cosmology, and that it was left to Kleanthes to make explicit this appeal, modifying the theory where it seemed appropriate to do so.
We can also look to the catalogue of Kleanthes’ writings reported by Diogenes Laërtius for assistance in giving an account of Kleanthes’ contribution to Stoic logical theory. There is a set of three books under the title 
(DL 7.175) which one might take to be about logic, especially since Hicks translates this title as Of Logic. It seems to us, however, that Of the Logos would be equally possible. In light of Kleanthes’ interest in Heraclitus, and in light of the apparent debt—pointed out by Long in the passage above—which the Stoics owe to Heraclitus for their concept of the logos, it seems less likely that these books of Kleanthes are about logic than that they are about the logos. There are three other titles, however, which would appear to be uncontroversially on logical topics. These are: Of Dialectic, Of Moods or Tropoi, and Of Predicates (DL 7.175). As to the first title, not much can be said, for there is little in the sources to indicate Kleanthes’ particular thoughts on dialectic as such. However, more can be said about the subjects of the other two books, for it is of some interest that Kleanthes wrote about them.
Concerning the book about tropoi, Galen reports that logicians (dialektikoi) call the schemata of arguments by the name ‘mode’ or ‘tropos’ 
. For example, for the argument which Chrysippus calls the first indemonstrable 
and which we would call modus ponens, the mode or tropos on the Stoic account is as follows” If the first, the second; but the first; therefore, the second (inst. log. 15.7). Now according to Galen, since the major premisses (
)22 
of the minor premisses 
, Chrysippus and his followers call such a proposition or axiōma not only determinative but also tropic 
.23 What is of interest here is that Kleanthes’ concern with tropoi may be an indication that he had some knowledge of the so-called indemonstrables, that is, the five argument schemata which Chrysippus took as the basis of the Stoic theory of inference.24 As to the book about predicates 
, we also have a passage of Clement of Alexandria which maintains that Kleanthes and Archedemes called predicates lekta 
(strom. 8.9.26.3-4). According to Michael Frede, this testimony indicates that Kleanthes was the first philosopher to use the term ‘lekton’ ([Frede, 1987b], 344). This innovation is quite significant, for the concept of the lekton is well recognised as possibly the most fundamental notion in Stoic semantic theory. Frede suggests, however, that this passage is evidence that the concept may have been introduced by the Stoics in the ontology of their causal theory rather than in their philosophy of language ([Frede, 1987a, p. 137]; cf. Long and Sedley [1990, 2.333]). At any rate, one might conjecture that Kleanthes had some hand in the development of this concept.
We have the testimony of Epictetus of a book on a logical topic written by Kleanthes but not recorded by Diogenes. Although he does not give its name, this work, according to Epictetus, was on the so-called ‘Master Argument’ of Diodorus Cronus (disc. 2.19.9). The Master Argument was apparently posed by Diodorus in order to establish his definition of the possible (disc. 2.19.2; cf. Alexander in an. pr. 184.5), this definition being ‘The possible is that which either is or will be’ (
(in an. pr. 184.1).25 A definition of the possible attributed to the Stoics both by Diogenes Laërtius (7.75) and by Boethius (in de interp. 234.27) is that the possible is ‘that which admits of being true and which is not prevented by external factors from being true’ (DL 7.75). Now both Kleanthes and Chrysippus rejected Diodorus’ interpretation of the Master Argument (Epict. disc. 2.19.6) and presumably, therefore, would have also rejected his account of the possible, and since the Stoic characterisation given by Diogenes and Boethius is not attributed to any specific Stoic, it is open to debate whether to credit it to Chrysippus or to Kleanthes. There is, however, a passage in Plutarch which would seem to indicate that Chrysippus warrants the attribution (de Stoic repugn. 1055d-e). However that may be, it is evident that Kleanthes had an interest in questions about modality and no doubt gave some account of the possible and the necessary.
Chrysippus (circa 282-206 B.C.)
Chrysippus of Soli26 succeeded Kleanthes in 232 B.C. to become the third leader of the Stoic School (DL 7.168; 1.15–16). There is not much information on his early life. Hecato, the Stoic, says that he came to philosophy because the property he had inherited from his father had been confiscated by the king (DL 7.181). And there is a story that he was a long distance runner before taking up philosophy as a pupil of Kleanthes (DL 7.179). Even as a student he seemed to possess a good deal of confidence in his abilities, especially in logic, for he used to say to Kleanthes that he needed to be instructed only in the doctrines; the proofs he would discover himself (DL 7.179). His relationship with Kleanthes was somewhat troublesome to him at times. On the one hand, he showed a great deal of respect for Kleanthes, deflecting to himself the attacks of certain presumptuous dialecticians who would attempt to confound Kleanthes with their sophistical arguments. Chrysippus would reproach them not to bother their elders with such quibbles, but to direct them to his juniors (DL 7.182). On the other hand, he himself would sometimes contend with Kleanthes, and whenever he had done so, would suffer a good deal of remorse (DL 7.179).
Chrysippus apparently left the Stoic school while Kleanthes was still alive, becoming a philosopher of some reputation in his own right (DL 7.179), and on the authority of the historian Sotion of Alexandria, Diogenes tells us that he also studied philosophy for some period under Arcesilaus and Lacydes at the Academy (DL 7.183). This would explain, according to Diogenes, his arguing at one time for common experience (
),27 
, as well as a series of seven books under the title In Defence of Common Experience 
(DL 7. 198). In this regard, according to Cicero, some later Stoics complained against him for providing Carneades and the Academy with arguments with which to assail against the whole of common experience, as well as against the senses and their clarity and against reason itself (acad. 2.87; cf. Plutarch de Stoic repugn. 1036b-c).
Chrysippus was an extremely prolific writer. Diogenes Laërtius reports that in all he wrote seven hundred and five books (DL 7.180), of which three hundred and eleven were on logic (DL 7.198). And Diogenes provides an inventory of about three hundred and seventy five of them, the majority of these being books on logic (DL 7.189-202). Diogenes also cites the testimony of Diocles Magnes who claims that Chrysippus wrote about five hundred lines a day (DL 7.181). It would seem, however, that in the opinion of many, such a profusion of material did not come without a price, for the ancients, according to Zeller, were unanimous in putting forward a litany of complaints against the literary style of these texts [Zeller, 1962, pp. 47–48]. However, this criticism is somewhat mitigated by Zeller’s comment that “with such an extraordinary literary fertility, it will be easily understood that their artistic value does not keep pace” [Zeller, 1962, p. 47]. But whatever are the merits of these criticisms, one cannot help but speculate on how different would have been our understanding of Hellenistic philosophy had even a few of these works survived.
With the death of Kleanthes, Chrysippus returned to Stoicism to become leader of the school. In that capacity he was, “in the opinion of the ancients, … the second founder of Stoicism” Zeller, [1962, p. 45], for it was said, according to Diogenes Laërtius, that “if there had been no Chrysippus, there would have been no Stoa” (DL 7.183). Gould takes this to refer to the belief that Chrysippus “revived the Stoa after the crushing blows dealt it by Arcesilaus and other Academics” [Gould, 1970, p. 9]. He continues:
In antiquity, then, even outside the school, Chrysippus was regarded as an eminently capable philosopher, as an extraordinarily skilful dialectician, and as one who came to the defense of the Stoa in a crucial moment, namely, when it was about to encounter its death blow from a rival school in Athens, the Academy, which had then become the stronghold of scepticism [Gould, 1970, p. 9].
It was no doubt his skill as a dialectician which enabled Chrysippus to defend so well the doctrines of the Stoa, for he was considered by many to have been one of the foremost logicians of Hellenic Greece. In fact, according to Diogenes Laërtius, he was so renowned for his logical acumen “that it seemed to most people, if dialectic was possessed by the gods, it would be none other than that of Chrysippus” (DL 7.180). Perhaps there would be no more fitting way to conclude this section on Chrysippus than to quote the words of Long and Sedley in their source book The Hellenistic Philosophers: “In the period roughly from 232 to 206 [Chrysippus] was to … develop all aspects of Stoic theory with such flair, precision and comprehensiveness that ‘early Stoicism’ means for us, in effect, the philosophy of Chrysippus” [Long and Sedley, 1990, 1.3].
3 Preliminaries
Several of our sources attest to a tripartite division of philosophy by the Stoics. These branches are logic, physics, and ethics (DL 7.39; Aëtius plac. DDG 273.11; Plutarch de Stoic repugn. 1035a). According to Diogenes Laërtius, Zeno of Citium, in his book On Discourse 
, was the first of the Stoics to make this division (DL 7.39). Diogenes also informs us that Zeno arranged these topics with logic first, physics second, and ethics third (DL 7.40), although it is somewhat unclear whether the standard for this arrangement is according to intrinsic importance or according to teaching priorities. Perhaps what it reflects is the relationship between these parts as it is represented in one of the many similes that the Stoics drew upon for illustration. Their philosophical system, they said, is like a fertile field with logic as the surrounding wall, physics as the soil or trees, and ethics as the fruit (DL 7.40). It is clear on this conception that logic is given the task of protecting the system from external threats—the first line of defence, as it were, and the aspect of logic emphasised is skill in dialectic in the sense of mustering counter-arguments and solving sophisms (cf. Plutarch de Stoic repugn. 1034e). But there is another aspect of logic in which the sense of dialectic stressed is that in which it signifies “the testing of hypotheses and the quest for ultimate principles or true definitions, which are the essential procedures of every metaphysician” (Long and Sedley 1.189). In The Discourses, Epictetus surmises that the reason why the philosophers of the Old Stoa put logic first in the exposition of their doctrine is that it is in the study of logic that one comes to understand the criterion by which one judges in other pursuits what is true. So it is, according to Epictetus, that:
… in the measuring of grain we put first the examination of the measure. And if we should neither first define what a modius is, nor first define what a scale is, how shall we be able to measure or weigh anything? So with the subject of logic, how shall we be able to investigate accurately and understand thoroughly anything of other subjects if we neither thoroughly understand nor accurately investigate that which is the criterion of other subjects and that through which other subjects are thoroughly understood? (disc. 1.17.7-8)
In the first part of this section, we explore the hypothesis that the development of the Stoic system as it is discernible in the philosophical education of Zeno followed the reverse order to that envisaged above: it evolved from a primary interest in ethics and thence to physics and logic. And the aspect of logic cultivated in this succession is that characterised both in the quotation from Long and Sedley and in the quotation from The Discourses: that is, logic as concerned with truth, knowledge, definitions, and other elements of reason, and, as Zeno says, with understanding “what sort of thing each of them is, how they fit together and what their consequences are” (Epictetus disc. 4.8.12). Given this understanding of Zeno’s development of the Stoic system, we shall suggest, in the second part of this section, an interpretation of Stoic logical doctrines which may be perceived as being motivated by this evolution, doctrines propounded either by Zeno himself or by his successors.
3.1 Stoic Ethics: the Motivational Basis
From Crates and the Cynic School Zeno doubtless inherited the foundation for his moral theories. But the Cynics apparently devoted themselves only to ethics, choosing to do away with the topics of logic and physics (DL 6.103). Zeno, on the other hand, clearly did not reject these topics, for it is uncontroversial that he laid the foundations not only for Stoic ethics, but for physics and logic as well. It would seem evident, therefore, that at some point he broke ranks with the Cynics, choosing a philosophical curriculum richer than that of his mentors.28 The point on which Zeno diverged from the Cynic path is the premiss described by Long and Sedley as “the bastion of Stoic ethics,” that is, “the thesis that virtue and vice respectively are the sole constituents of happiness and unhappiness” [Long and Sedley, 1990, 1.357].29 
) nor harm 
: they are neither necessary nor sufficient for a virtuous—which is to say a moral—life, and thus can have no effect on one’s eudaimonia; hence, they are called ‘indifferent’ 
(DL 7.102–03). This thesis was undoubtedly an endowment to Zeno from the Cynics, for we learn from Diogenes Laërtius that for the Cynics virtue is sufficient in itself to secure happiness (DL 6.11), so that “the end for man is to live according to virtue” 
, a credo that was echoed by the Stoics (DL 6.104; cf. Stobaeus eclog. 2.77.9). We also learn from Diogenes that the Cynics count as ‘indifferent’ whatever is intermediate between virtue and vice (DL 6.105).
The Cynic stance toward the ‘indifferents’ can perhaps best be understood by considering the views of Ariston of Chios, a pupil of Zeno’s whom we might call a ‘neo-Cynic’, since he “greatly simplified Stoicism, so that it was hardly distinguishable from the attitude of the Cynics” (Sandbach [1975, p. 39]; cf. Rist [1969c, pp. 74–80]). Ariston recommended complete indifference to everything between virtue and vice, recognising no distinctions among them and treating them all the same, for the wise man, according to Ariston, “is like a good actor, who can play the part of both Thersites and Agamemnon, acting appropriately in each case” (DL 7.160). A problem for this credo is summarised by Cicero, who is setting out the opinions of the Stoic Cato:
If we maintained that all things were absolutely indifferent, the whole of life would be thrown into confusion, as it is by Aristo, and no function or task could be found for wisdom, since there would be absolutely no distinction between the things that pertain to the conduct of life, and no choice need be exercised among them (de fin. 3.50; trans. Rackham).
This criticism, which was no doubt a standard reproach among the ancients, might be expressed by the observation that “[Aristo’s] position robbed virtue of content” [Sandbach, 1975, p. 38]. It is unclear whether Zeno himself subscribed to this assessment; however, it would seem likely that he did. He was, after all, in attendance at Polemo’s lectures, and there he would no doubt have become familiar with the view, ascribed by Cicero to Xenocrates as well as to his followers, that the ‘end of goods’ (finis bonorum) is not limited to virtue alone, but includes just those things which belong to the class which the Cynics and Ariston held to be ‘indifferents’ (de fin. 4.49; Tusc. disp. 5.29–30).30
At any rate, although he may have agreed with this critique of Cynic views to the extent of granting that such things as “health, strength, riches, and fame” (de fin. 4.49) have some value, Zeno was nevertheless unwilling to depart from Cynic tenets to the point of admitting that any of the indifferents were required for eudaimonia. His solution to this dilemma was to introduce a classification of the indifferents distinguishing those which are ‘according to nature’ 
, those which are ‘contrary to nature’ 
, and those which are neither (Stobaeus eclog. 2.79.18). Indifferents which are according to nature (ta kata physin) are such things as health, strength, sound sense faculties, and the like (eclog. 2.79.20). All indifferents which are kata physin have ‘value’ 
, whereas those contrary to nature have ‘disvalue’ 
(eclog. 2.83.10). A categorisation of indifferents which would seem to coincide with this division is that which distinguishes them according to those which are preferred’ 
, those ‘rejected’ 
, and those neither preferred nor rejected (DL 7.105; Cicero de fin. 3.51; Stobaeus eclog. 2.84.18). According to Diogenes Laërtius, the Stoics teach that those indifferents which are preferred (ta proēgmena) have value (axia), whereas those rejected have ‘disvalue’ (apaxia) (7.105). Thus it would appear that the class of those indifferents which are ‘kata physin’ is coextensive with ‘ta proēgmena’.
Value is defined by the Stoics as having three senses, only two of which are relevant in this context.31 Foremost, it is the property of contributing to a harmonious life, this being a characteristic of every good 
(DL 7.105). However, since no goods are among the preferred (Stobaeus eclog. 2.85.3), this connotation of axia must refer only to goods and not to the preferred, and hence designates value in an absolute sense; indeed, the things which have value in this sense are called 
(eclog. 2.83.12), which may be rendered as ‘value per se’ (cf. Cicero de fin. 3.39 and 3.34). The second sense is that of some faculty or use which contributes indirectly 
to life according to nature (DL 7.105). Things which have value according to this sense of axia are ‘selected’ 
, in Antipater’s phrase, on which account, when circumstances permit we choose these particular things rather than those: for example, health against illness, life against death, and wealth against poverty (Stobaeus eclog. 2.83.13). The notion of value among those indifferents having ‘preferred’ status, as well as the responsibility of the moral agent with respect to these notions, is well summarised by Long and Sedley in the following passage:
This ‘selective value’, though conditional upon circumstances (contrast the absolute value of virtue), resides in the natural preferability of health to sickness etc. That is to say, the value of health is not based upon an individual’s judgement but is a feature of the world. The role of moral judgement is to decide whether, given the objective preferability of health to sickness, it is right to make that difference the paramount consideration in determining what one should do in the light of all the circumstances. In the case of those indifferents of ‘preferred’ status, there will be ‘preferential’ reason for selecting these ‘when circumstances permit’. It is up to the moral agent to decide, from knowledge of his situation, whether to choose actions that may put his health at risk rather than preserve it, but the correctness of sometimes deciding in favour of the former does not negate the normal preferability of the latter [Long and Sedley, 1990, 1.358].
The hypothesis of ta kata physin as a sub-class of the indifferents, then, will permit Zeno to maintain the thesis that only virtue is good, and at the same time provides a content for his ethics. A concomitant result of this hypothesis will be to lead to the reinstatement of physics and logic as legitimate components of a philosophical education. The theory may be represented as positing three levels of maturation in the moral agent (Cicero de fin. 3.20–21; 4.39; Aulus Gellius 12.5),32 so that ta kata physin contribute content for Zeno’s theory in accordance with the level of moral development of the agent (cf. Edelstein and Kidd, 155–57). In each stage of development ta kata physin are associated with a category of acts to which Zeno has given the name ‘appropriate acts’ 
(DL 7.108). At the first level, instanced by babies and young children in whom the faculty of reason or logos 
has not yet evolved, the agent is concerned with ‘primary’ things according to nature 
(Stobaeus eclog. 2.80.7; Aulus Gellius 12.5.7). These are the things toward which natural impulse 
inclines us in order to preserve and enhance our own constitution (Cicero de fin. 3.16; Seneca epist. 121.14). Hence at this level an appropriate act would be just to carry out those desires which impulse urges that we do; moreover, such acts would entail no consequences for morality, since moral choice and responsibility requires rationality.
At the second stage, subsequent to the emergence of the faculty of reason in the agent, ta kata physin are the base (proficiscantur ab initiis naturae) (Cicero de fin. 3.22) and the impetus or archē 
(Plutarch comm. not. 1069e) for those acts which reason convinces us to do, or those for which, when done, a reasonable justification can be given (DL 7.108; Stobaeus eclog. 2.85.14). Ta kata physin are themselves still the objects of appropriate acts, but now it is logos rather than hormē (impulse) which is active in the agent, directing his choices (Cicero de fin. 3.20). Concomitantly with the emergence of logos, comes the capability to form ‘conceptions’ or ennoiai 
. The gradual accumulation of the appropriate stock of ennoiai will, in the end, endow the agent with the capacity to discern the order and harmony in nature and to act in accordance with them (de fin. 3.21).
Having reached this state, the agent is at the threshold of the third stage of moral development. At this third level, ta kata physin are no longer the impetus for choice, but are merely the ‘material’ or hyle 
of ta kathēkonta (Plutarch comm. not. 1069e; cf. Cicero de fin. 3.22–23 and Galen SVF 3.61.18); moreover, the object of ta kathēkonta at this level is not the attainment of ta kata physin, but rather wisdom of choice, which is, in effect, choice in accordance with virtue (de fin. 3.22); hence, it is the moral character of the agent that determines the appropriateness of the act (de fin. 3.59; Sextus Empiricus AM 11.200; Clement SVF 3.515). Thus, even though there may be “a region of appropriate action which is common to the wise and unwise” (Cicero de fin. 3.59), the appropriate acts of the wise man, unlike those of the unenlightened, are consistently motivated by reason. Appropriate acts at this stage are ‘perfect’ and are referred to as ‘right actions’ 
, since they contain all that is required for virtue (de fin. 3.24; Stobaeus eclog. 2.93.14).
It is evident, given the above characterisation of a ‘perfect’ kathēkon or ‘right action’ (katorthōma), that the Stoic sage will be the only one to reach the third level of moral development, for only the wise man performs right actions (Cicero de fin. 4.15). It would seem, therefore, that a function or task for wisdom, the lack of which was seen as a shortcoming of the Cynic view as represented by Ariston (see page 416), is found in the choices the wise man makes among ta kata physin. Where this Stoic version of moral preference differs from what might be called the ‘common sense’ account is that the object of such choices is not the attainment of particular things which accord with nature—things such as health, strength, wealth, and so on—but rather the attainment of a virtuous disposition which functions consistently in the making of such choices (Cicero de fin. 3.22; 3.32). Thus, even though this feature of the Stoic position was much maligned in ancient times (e.g., de fin. 4.46–48; Plutarch comm. not. 1060e), there is no doubt that Zeno’s innovation provided the improvement he desired over Cynic doctrine (Cicero de fin. 4.43).
A related shortcoming of the Cynic view is the doctrine to the effect that “virtue needs nothing except the strength of a Socrates” and that “virtue is concerned with deeds, requiring neither a host of rules nor education” (DL 6.11). One might suspect that for Zeno the difficulty with this credo would have been the problem that it rendered the content of virtue as quite arbitrary, dependent only on the will of the wise man;33 moreover, one might also surmise that Zeno would have questioned how the ordinary person, not endowed by nature with the strength of a Socrates, would be supposed to go about improving himself with respect to moral rectitude. This difficulty was evidently addressed by the thesis that virtue is the outcome of a developmental process. The latter premiss suggests that it should be possible to learn to be virtuous, and, indeed, the idea that virtue is or can be taught is explicitly reported as Stoic doctrine in several places (DL 7.91; Clement SVF 3.225). Now although Zeno is not mentioned as advocating this view, both Kleanthes and Chrysippus are; hence, there would seem to be no good reason not to attribute it to Zeno as well. The details of the Stoic account of how virtue is learned may be inferred from the sources;34 what is relevant here, however, is the contrast between this thesis and the preceding description of Cynic doctrine.
Given the account of moral development outlined above, it would seem that Zeno would have been in a position to augment the Cynic dictum reported by Diogenes Laërtius that ‘the telos for man is to live in accordance with virtue’ (see page 416). The right actions or katorthōmata performed by the wise man are mentioned in several places by Stobaeus as being actions performed according to ‘right reason’ 
(eclog. 2.66.19; 93.14; 96.18); moreover, right reason is described by numerous sources as being equivalent to virtue (Plutarch de virt. mor. 441c; Cicero Tusc. disp. 4.34; Seneca epist. 76.11). Hence, the virtue of the wise man consists in the perfection of his rationality with respect to the choices he makes among ta kata physin (Seneca epist. 76.10; Cicero de fin. 3.22). These choices are made in accordance with his own rational nature and in accordance with the logos of the universe, the rationality of which he shares (DL 7.87–88; Cicero de nat. deorum 1.36–39; 2.78; 133; 154; Seneca epist. 124.13–14).
According to Diogenes Laërtius, Zeno’s position concerning the summum bonum was that “the telos for man is to live harmoniously with nature” 
(DL 7.87); Stobaeus, however, reports that this formulation is due to Kleanthes, whereas Zeno’s statement is simply that the telos is “to live harmoniously” 
. This means to live in accordance with a single harmonious logos, since those who live in conflict with this are not eudaimones (eclog. 2.75.6–76.6). Chrysippus’, on the other hand, said that the telos is “to live in accordance with experience of what happens by nature” 
(eclog. 2.76.6–8). There would seem to be no good reason to suppose that these definitions are incompatible in any way, for according to Stobaeus, the augmentations to Zeno’s statement were proposed not because Kleanthes and Chrysippus disagreed with him, but rather because they assumed that his formulation was an ‘incomplete predicate’ (eclog. 2.76.2–3) and they wished to make it clearer (eclog. 2.76.7).35
Cicero reports a further statement which the Stoics declared to be equivalent to Zeno’s representation. It asserts that the telos is “to live in the light of a knowledge of the natural sequence of causation” (vivere adhibentem scientiam earum rerum quae natura evenirent) (de fin. 4.14). The justification for this equivalence can evidently be inferred from several passages in the sources. First, the Stoics called the natural sequence of causation ‘heimarmenē’ 
, usually translated as ‘fate’ or ‘destiny’ (Cicero de div. 1.125–26; Aulus Gellius 7.2.3). In addition, Stobaeus reports that heimarmenē is the logos, or rational principle of the universe (kosmos). It is “the logos according to which past events have happened, present events are happening, and future events will happen”; furthermore, Stobaeus informs us that the rational principle, in addition to being called the logos, is also referred to as ‘truth’ (
), ‘explanation’ (
), ‘nature’ (
) or ‘necessity’ 
(eclog. 1.79.1–12; cf. Alexander de fato 192.25). The identification of heimarmenē with logos, the rational principle of the kosmos, and the fact that this principle is also referred to as physis, would seem to establish the basis for the equivalence in question.
Thus Zeno’s interpretation of the Cynic doctrine that the end for man is to live according to virtue can be formulated first by the statement that the telos is ‘to live according to right reason’, since virtue and right reason are taken to be equivalent. What this means, given the account of the development of the virtuous man, is that the end for man is ‘to live in accordance with his own rational nature and in accordance with the logos of the universe’. This latter version can be summarised in turn by the statement that the telos for man is ‘to live harmoniously with nature’, or equivalently, ‘to live in the light of a knowledge of the natural sequence of causation’.
Evidently, if someone thought that to be a wise man one ought to live according to nature in the sense of living according to a knowledge of the natural sequence of causation, then he most likely would also think that the study of physics and logic would be a requirement of a philosophical education. It is quite probable, therefore, that Zeno’s concept of the telos would have led him to adopt a philosophy in which physics and logic were as much a part of the curriculum as was ethics. The discussion in the last few paragraphs would seem to show that the development of Zeno’s notion of the telos is a result of his doctrine of ta kata physin. This doctrine represented a major break with his Cynic roots inasmuch as it required that some things which the Cynics had classified as absolutely morally ‘indifferent’, be classified instead as ‘preferred’, in the sense that they are ‘according to nature’. Hence it would seem not only that Zeno’s notion of ta kata physin itself represented an important break with Cynic doctrine, but also that this notion led to a further breach inasmuch as it induced him to include physics and logic in his philosophical curriculum, contrary to the Cynics.
If the philosopher is to be educated in the study of physics and logic, the question arises concerning the scope and content of his knowledge in these subjects. A passage from Seneca and one from Diogenes Laërtius will be helpful here. Seneca tells us that “the wise man investigates and learns the causes of natural phenomena, while the mathematician follows up and computes their numbers and their measurements” (epist. 88.26) In a passage with a similar theme, Diogenes Laërtius tells us that the part of physics concerned with causation is itself divided between the investigation of such things as the hēgemonikon 
—that is, the ‘leading part’ of the soul or psychē 
, of what happens in the psychē, of generative principles, and of other things of this sort. This is the province of the philosopher. On the other hand, the mathematician is concerned with such things as the explanation of vision, the cause of an image in a mirror, the origins of weather phenomena, and similar things (DL 7.133). These passages would seem to suggest that scope of the wise man’s knowledge of physics would probably not be of particular data, but rather of general principles.36
As to the question concerning the nature of the logical theory that the philosopher would need, we take it that the motivation for such a theory would be the requirements of the ethical doctrine outlined above.37 Thus, given that the wise man’s aim is to live in harmony with a knowledge of the natural sequence of causation, he will need to make correct judgements about the relations between particular states of affairs, based on his knowledge of the general principles governing such connections; moreover, he will need to comprehend the patterns of inference which will allow him to effect such judgements. Evidently, these general principles will be manifestations of the universal logos, and as such, given that logos is another name for anankē (necessity) (Stobaeus eclog. 2.79.1–12; Alexander de fato 192.25), they will be embodied by necessary connections in nature; moreover, one can surmise that the patterns of inference which emerge will consist in part of representations of such necessary connections.
3.2 Inference and Akolouthia
At 7.62, Diogenes Laërtius reports that, according to Chrysippus, dialectic is about ‘that which signifies’ and ‘that which is signified’ 
. It is clear from the context that ‘that which signifies’ is a meaningful utterance. Presumably, then, ‘that which is signified’ is the significatum of such an utterance. Diogenes does not elaborate on what belongs to this class, except to say that the doctrine of the lekton is assigned to the topic of ‘that which is signified’.38 
but for the present it will be sufficient to understood the meaning as ‘what is said’ or ‘what can be said’ (cf. Long [1971], 77); in any case, what is of immediate interest is the reported Stoic classification of lekta, and in particular, the type of lekton called the axiōma.
Axiōmata have two characteristic properties which differentiate them from the other lekta: first, they are the significata of declarative sentences, and second, they are the only lekta which can be true or false (DL 7.68; cf. AM 8.74). Thus, it seems apparent that axiōmata are somewhat in accord with what we call propositions (I have already used that term to refer to them in the discussion above); there are, however, several characteristics with respect to which axiōmata differ from propositions, so that they cannot be merely identified with them (cf. Kneale and Kneale [1962a], 153–57). It may be, as Long and Sedley propose (1.205), that ‘proposition’ is the least misleading of the possible translations for axiōma; nevertheless, we propose to avoid using ‘proposition’ and to merely transliterate the term.
Having introduced the notion of an axioma, Diogenes goes on to report that several Stoics, including Chrysippus, divided axiomata into the simple and the non-simple. Simple axiomata, on this account, are those consisting of one axioma not repeated (for example: ‘It is day’), whereas non-simple are those consisting either of one axioma repeated (for example: ‘If it is day, it is day’) or of more than one axioma (for example: ‘If it is day, it is light’) (DL 7.68–69). Of the non-simple axiomata, the first introduced is the ‘conditional’, an axioma constructed by means of the connective ‘if’ 
(DL 7.71). The Greek word is 
, which might be better rendered ‘connexive’ in accordance with its etymology; however, even leaving etymological questions aside, translating synēmmenon as ‘conditional’ is somewhat misleading. It seems evident that the Stoic use of the connective 
was technical, and hence there are some uses of this connective in ordinary Greek which seem not to be captured by the Stoic understanding of the term.
One problem with taking ‘conditional’ as the translation of ‘synēmmenon’ is that there is a temptation to suppose, as the Kneales seem to do, that what the Stoics had in mind was to give an account of the occurrence in language of the connective 
which would be “satisfactory as a general account of all conditional statements” (Kneale and Kneale [1962a, p. 135]). It seems to us that this interpretation gets the matter wrong. The term ‘synēmmenon’ denotes a complex axioma, and according to the description of Diogenes Laërtius at 7.66, this is just to say that it denotes a complex state of affairs; moreover, this complex state of affairs is signified by the predication of the relation of following between the states of affairs which are the constituents of the complex axioma. What the Stoics had in mind was to give an account of the inferences that could be made given the knowledge that some particular type of event or state of affairs folIowed from some other particular event or state of affairs. It seems plausible that they chose 
as the syntactic representation of the relation of following because it is suggestive of that relation, as the arrow is suggestive of the relation of implication in modern syntactic accounts. Hence they chose expressions of the form ‘If A, B’ to be the canonical representation in their patterns of inference. They might, however, have chosen to express this relation by saying ‘B follows from A’ rather than ‘If A, B’, for although they would not recognise the schema ‘B follows from A; but A; therefore B’ as a proper syllogism of their logical system, they were nevertheless willing to view it as being equivalent to the syllogistic schema ‘If A, B; but A; therefore B’, which was an authentic syllogism of their system (Alexander in an. pr. 373.29–35). And if they had chosen so to represent it, then no one, we assume, would be tempted to view their characterisation of 
as an attempt to give a general account of conditional statements. Having said all this, we will nevertheless carry on the tradition of translating ‘synēmmenon’ as ‘conditional axiōma’, just so long as it is understood that by so doing we do not assume that in giving a characterisation of ‘synēmmenon’ the Stoics supposed themselves to be providing a general account of conditionals.
Now although the Stoics did not use expressions of the form ‘B follows from A’ as the canonical expression of the relation denoted by ‘synēmmenon’, this notion of ‘following’ in a conditional was of primary importance in their theory of inference, for their fundamental criterion of a valid argument was based on this concept. This canon is the so-called conditionalisation principle (cf. Mates [1953, pp. 74–77]). As it is framed by the Stoics, this principle states that an argument is conclusive39 whenever its corresponding conditional is sound (
: PH 2.137) or true (
: AM 8.417):40 that is, the conditional which has the conjunction of the premisses as antecedent and the conclusion of the argument as consequent. Now Sextus Empiricus writes that “the ‘dialecticians’41 all agree that a conditional is sound whenever its consequent ‘follows’ its antecedent” (AM 8.112; cf DL 7.71). In effect, then, one can say that for the Stoics, an argument is valid (conclusive) just in case its conclusion ‘follows’ from its premisses, as the consequent follows from the antecedent in a sound or true conditional. In noting this criterion, however, Sextus also outlines a difficulty, for it seems that although the ‘dialecticians’ were agreed on the standard for a true conditional, there was a controversy as to how the notion of ‘following’ was to be characterised (AM 8.112; PH 2.110). There were apparently four competing views,42 only two of which, we shall suggest, would have provided a criterion consistent with the role of inference in Stoic philosophy: the first of these, advocated by those who spoke of ‘connexion’ (
), required that the contradictory of the consequent ‘conflict’ 
with the antecedent; while the second, advocated by those who spoke of ‘implication’ 
, required that the consequent be ‘potentially contained’ 
in the antecedent (PH 2.111–12).43
The Greek terms used in these contexts are 
, either of which has the sense of ‘to follow upon’ or ‘to be consequent upon’. Now although ‘to follow logically’ is no doubt one way in which these terms were understood, it also seems evident that this meaning is not the only one they carried. But even if it had been, that fact would not warrant the assumption that for the Stoics ‘to follow logically’ meant quite what it does in a modern setting. For, given the hypothesis outlined earlier in this section of a motivation for logic grounded in ethics, we take it that the role of logic in Stoic philosophy is primarily to determine the inferential relations between states of affairs and only derivatively (if at all) between sentences of the language. The view we put forward has much in common with that expressed by A.A. Long in the following passage ([Long, 1971], 95):
The human power of drawing inferences from empirical data presupposes an ennoia akolouthias, an idea of succession or consequence. … And endiathetos logos, internal speech (reason), is described as ‘that by which we recognise consequences and contradictions’ 
But akolouthia is not confined to what we would call ‘logical consequence’. The sequence of cause and effect is explained by reference to it, for fated events occur 
[according to order and consequence] or 
[according to the following of causes]. This use of a common term is exactly what we should expect in view of Chrysippus’ methods of inference from actual states of affairs.
Given that the world operates according to a strict causal nexus one of the roles of logic, perhaps its major role in Stoicism, is to make possible predictions about the future by drawing out consequences from the present. The cardinal assumption of the Stoics is that man can put himself in touch with the rational course of events and effect a correspondence between them and his own actions and intentions. This assumption provides the ethical aim of living homologoumenōs [harmoniously]. More particularly, ethics is connected with logic and physics by akolouthia and its related words.
If this is an accurate characterisation of the role of logic in Stoic philosophy, then in order that such predictions might be carried out, the Stoic conditional will need to represent the logical as well as the nomic connections, not only between actual events or states of affairs, but also between mooted events or states of affairs. Such connections will need to be manifest in the relation between the content of the antecedent and that of the consequent.
In describing these constraints on akolouthia in the above quotation, Long refers to Chrysippus’ “methods of inference from actual states of affairs” (1971, 95). In a similar vein, J.B. Gould states that “as Chrysippus maintains, one may generalise and amrm that if events of a particular sort occur, then other events of a specified sort will occur. Such generalisations may be expressed in conditional propositions. … These kinds of generalisations, then, are true only when they denote connections between things or events in nature” ([Gould, 1970], 200–201). Along the same lines, Michael Frede asserts that “the Stoics seem to regard consequence and (possibly various kinds of) incompatibility as the relations between states of affairs or facts in terms of which one can explain that something follows from something” ([Frede, 1987d], 104). We propose to take seriously this talk of ‘states of affairs’ and ‘facts’ in order to present an interpretation of the notion of ‘following’ or ‘consequence’ in the Stoic system of inference.
If the conception of consequence or ‘following from’ as expressed in the conditional is a notion of a relation between states of affairs, then to say that a sound conditional is such that the contradictory of the consequent ‘conflicts with’ the antecedent, as in the ‘connexion’ theory, or that the consequent is ‘potentially contained’ in the antecedent, as in the ‘containment’ theory, would seem to suggest that these conceptions of conflict and of potential containment are also notions of a relation between states of affairs. How is this to be understood? In particular, how are we to understand this talk of ‘states of affairs’ and the notion of one state of affairs being ‘in conflict with’ or being ‘potentially contained in’ another? Unfortunately, there is so little information in the texts about the containment criterion that we cannot attempt to give more than a speculative account of this definition. On the other hand, there are fairly clear indications in the texts about what was meant by ‘conflict’. As to the first part of this question, answering it will be the burden of our interpretation of Stoic semantic theory. Interpreting Stoic semantics is in effect to provide an understanding of the theory of the lekton. Moreover, since there is a clear indication in the texts of the dependence of lekta on ‘rational presentations’ 
(e.g. AM 8.70: DL 7.63), it would seem that an understanding of the lekton will require an interpretation of this relation in particular, and of the theory of presentations in general; indeed, it seems to us that there is evidence enough to indicate that one cannot give an adequate account of Stoic logical theory without taking into consideration the theory of phantasiai. Such reflections will no doubt entail some involvement in epistemological questions, and though some writers have ruled out concern with such questions as being ‘extra-logical’ (e.g., Mates [1953, pp. 35–36]; Kneale and Kneale [1962a, p. 150]; Mueller [1978, p. 22]), others see them as an essential component of an understanding of Stoic logical theory (e.g., Imbert [1978, p. 185]; Gould [1970, pp. 49–50]; Kahn [1969, p. 159]).
Our suggestion is that the ‘states of affairs’ which stand in the relation of conflict or containment in a sound conditional can be thought of as abstract semantic structures the constituents of which correspond to individuals, properties, and relations. They are the objective content of rational presentations as well as of axiōmata and other types of lekta, and as such are the designata of the Stoic term ‘pragmata’.
4 Semantics
4.1 Epistemology: phantasiai and lekta
The connection between the theory of the lekton and the Stoic doctrine of presentations is well documented in the texts. Parallel passages in Sextus Empiricus and in Diogenes Laërtius explicitly refer to this connection. The passage written by Sextus at AM 8.70 is somewhat more complete:
[The Stoics] say that the lekton is that subsisting 
coordinately with a rational 
presentation, and that a rational presentation is one in which it is possible that what is presented be exhibited by means of discourse.44
The corresponding passage in Diogenes Laërtius is at 7.63: “They (sc. the Stoics) assert that the lekton is that subsisting coordinately with a rational presentation.”45 The Stoics used forms of the verb 
to indicate a ‘mode of being’ which is something less than the being that material bodies possess (see page 462); hence, the use of 
to describe the being of the lekton, makes it seems evident that one can take the lekton as somehow dependent for its being on the corresponding rational presentation. On this understanding of the relationship between the lekton and the presentation, it is evident that an exploration of the semantic role of the lekton cannot leave the doctrine of presentations out of account. As we understand the theory, that which is presented 
in a rational presentation, and which is capable of being exhibited by means of discourse, is a pragma 
. Moreover, we take it that the term ‘pragma’ is used in Stoic semantics to mean a ‘state of affairs’ which is the unarticulated objective content of a rational presentation. And since we also understand the axiōma to be what is said in the assertion of a pragma, it would seem necessary to refer to the Stoic theory of presentations in order to present a characterization of the notion of akolouthia as a relation between axiōmata.
From the point of view of some modern logicians and historians of logic, this proposal presents a difficulty inasmuch as it implies a merging of epistemological (and psychological) concerns with logical concerns. Benson Mates, for example, states in his Stoic Logic that “the criterion for determining the truth of presentations … is an epistemological problem and not within the scope of this work” [Mates, 1953, pp. 35–36]. According to the Kneales, “the theory of presentations belongs to the epistemology rather than the logic of the Stoics” [Kneale and Kneale, 1962a, p. 150]. And Mueller expresses the view that considerations of the possibility of knowledge of “necessary connections between propositions” (which, we take it, are a component of the theory of presentations) “would take us outside the domain of logic and into epistemology” [Mueller, 1978, p. 22]. In other words, there seems to be a strong bias among some contemporary commentators in favour of the supposition that epistemological considerations could have had no part in the logic of the Stoa, and that those who cultivated Stoic logic shared this aversion in common with those who developed the propositional calculus. But not all present-day commentators agree with this assessment. Some believe, in the words of Claude Imbert, that “the ancients… judged matters differently” [Imbert, 1980, p. 185].
Josiah B. Gould, for example, cites textual evidence from Sextus Empiricus and from Epictetus to support the claim that the Stoics placed their epistemological theory “squarely within the confines of logic” ([Gould, 1970], 49–50). In his treatise against the logical doctrines of ‘the dogmatists’, Sextus tells us that the logical branch of Stoic philosophy includes the theory of criteria and proofs (AM 7.24).46 According to this theory, things which are evident can be apprehended directly, either through the senses or through the intellect, in accordance with a criterion of truth.47 Things non-evident, on the other hand, can be apprehended only indirectly through the means of signs and proofs by inference from what is evident (DL 7.25). The inclusion of such a theory—which, as Gould points out [1970, p. 49], is that of Chrysippus himself—in the logical division of their philosophy seems clearly to commit the Stoics to consideration of epistemological concerns within the purview of their logic. As for Epictetus, according to him the philosophers of the Old Stoa held that logic “has the power to discriminate and examine everything else, and, as one might say, to measure and weigh them” (disc. 1.17.10). Thus it is “the standard of judgement for all other things, whereby they come to be known thoroughly” (disc. 1.17.8). This power, it seems to him, is the reason why these philosophers put logic first in the development of their doctrine (cf. AM 7.22; DL 7.40). In Gould’s estimation [Gould, 1970, p. 49], these comments of Epictetus seem to provide further evidence of a close relationship between logic and knowledge in early Stoic philosophy.
As the quotation above would appear to indicate, Claude Imbert is another recent commentator who thinks we have evidence that the Stoics took epistemological questions to be within the province of logic. She cites the passage at 7.49 in Diogenes Laërtius to support this thesis. In an earlier passage Diogenes has presented a summary of the Stoic logical doctrine (7.39–48), and he proposes now to give in detail what has already been covered in this introductory treatise. He begins with a quotation from the book Synopsis of the Philosophers by Diocles of Magnesia, the passage cited by Imbert:
The Stoics accept the doctrine that the account of presentation and sensation 
be ranked as prior [in their logical theory], both inasmuch as the criterion by which the truth of states of affairs 
is determined is of the genus presentation, and inasmuch as the account of assent 
, apprehension 
, and the process of thought 
, although preceding the rest [of their logical theory], cannot be framed apart from presentation. For presentation comes first, then thought, being capable of speaking out, discloses by means of discourse that which is experienced through the presentation (DL 7.49).
This passage, according to Imbert, indicates that “however obscure it may seem to modern logicians, it is undeniable that the Stoics derived their methods of inference from certain presentational structures” [Imbert, 1980, p. 185]. Moreover, since it indicates that the criterion of truth is itself a presentation, it also implies that Stoic logical theory contains an epistemological component.
The difference of opinion among these scholars concerning the content of Stoic logic is no doubt a reflection of a more fundamental disagreement about its general nature. Some writers seem to view the Stoic system as an attempt to develop a calculus of propositions with a truth-functional semantics in accordance with the model of the propositional calculus which emerged in the twentieth century. For such writers the inclusion of epistemological (or psychological) components in a logical system would no doubt be seen as a flaw, a reason to discount such a system as a genuine logic and to view the attempt at its development as misguided. And of course, if Stoic logic really were an attempt to develop such a calculus, they would be right. Other writers, however, seem to proceed with no such presuppositions about the nature of the Stoic system, or at least, with different ones. This latter approach is well summarised by C.H. Kahn in a passage which we cited in the introductory section (see page 400). According to Khan, our picture of Stoic logic will be distorted if we see it merely as a precursor to the propositional calculus. A more adequate view would require that we take into account the relationship in Stoic philosophy between ‘dialectic’ (logic) and their epistemology, semantics, ethical psychology, and general theory of nature [Kahn, 1969, p. 159]. Since we are in agreement with this assessment of what is required to construct an adequate interpretation of Stoic logic in general, we could perhaps appeal to these remarks as independent justification for including the doctrine of presentations in an interpretation of the notion of akolouthia. However, assuming that akolouthia is a relation between axiōmata, it would seem that the connection outlined above between axiōmata, lekta, and rational presentations is sufficient in itself to justify this inclusion.
4.2 Phantasiai
‘Presentation’ 
, according to Stoic doctrine, is an ‘impression’ 
on the soul or psychē 
(AM 7.228). Sextus Empiricus attests that this doctrine was put in place by Zeno himself (AM 7.2.30; 36), but that it was interpreted somewhat differently by Kleanthes and Chrysippus (AM 7. 2.28–31). Kleanthes apparently took the meaning of the term ‘impression’ quite literally, understanding it in the sense that a signet-ring makes an impression in wax (AM 7.228). Chrysippus objected to this interpretation, arguing that not only would this model make simultaneous impressions impossible, but also it would imply that more recent impressions would obliterate those already in place. Since experience would seem to show that various impressions can occur simultaneously, and that prior impressions can coexist with more recent ones, this model cannot be correct (AM 7.228–30). The model to which Chrysippus appealed was that of the air in a room, which, when many people speak at once, receives many different impacts and undergoes many alterations (AM 7.231). The model is apt, as we shall see, since the soul, according to Chrysippus, is composed of pneuma or ‘natural breath’. Accordingly, he defined phantasiai as ‘alterations’ or ‘modifications’ occurring in the psychē, revealing both themselves and that which has caused them:48 more specifically, they are modifications of the hēgemonikon 
, the ‘governing part’ of the psychē (AM 7.233).49
We are informed by several sources that the psychē itself has eight parts.50 Aside from the hēgemonikon already mentioned, it consists in the five senses, the faculty of speech 
, and the generative or procreative faculty.51 In the account of Diogenes Laërtius, the term 
does not appear; instead, he uses the term 
, i.e., the intellectual faculty, “which is the mind itself” (DL 7.110).52 The suggestion implicit in this passage is that we can understand the hēgemonikon to be the mind itself; moreover, this interpretation is verified by Sextus Empiricus in the passage at AM 7.232: “[Presentations occur] only in the mind or governing part of the psychē.”53 Thus it would seem that presentations, according to the Stoics, are modifications or alterations of (or in) the mind. In the parlance of present-day philosophy of mind, we (at least some of us) would refer to presentations as ‘mental states’ and associate them with corresponding ‘brain states’. But for the Stoics there was no need to postulate this kind of dualism (cf. Sandbach [1971b, p. 10]). For according to them, the psychē is constituted by ‘pneuma’ or ‘breath’ 
, itself composed of the elements fire and air “which are blended with one another through and through” (Galen SVF 2.841).54 It seems evident on this account that since fire and air are material elements par excellence, the soul must also be a material entity.
The Stoics held that there are two principles 
in the universe: the passive 
, which is substance without quality 
, or prime matter 
, and the active 
, which is the logos inherent in matter, or God (DL 7.134). By the nature of the properties ascribed to the pneuma, it would appear that the active principle is embodied in it. First, the pneuma is the force which maintains the universe as a unity. Chrysippus, for example, holds that “the whole of substance is unified because it is entirely pervaded by a pneuma, by means of which the universe is held together, is maintained, and is in sympathy with itself.”55 Second, the pneuma invests with qualities the undifferentiated matter in which it inheres (Plutarch de Stoic repugn. 1054a–b). And third, the pneuma is constitutive of the souls of human beings. According to Chalcidius, Zeno and Chrysippus put forward similar arguments for this thesis. Chrysippus argues thus: “It is certain that we breathe and live with one and the same thing. But we breath with natural breath (naturalis spiritus). Therefore we live as well with the same breath. But we live with the soul. Therefore, the soul is found to be natural breath” (SVF 2.879).56
According to the Stoics, then, the psychē, is corporeal, and hence just as much a material entity as is the substantial body of which it is a part. Further arguments for this thesis are set out both by Kleanthes (SVF 1.518) and by Chrysippus (SVF 2.790); moreover, there is no doubt that they followed Zeno in this view (SVF 1.137; 138; 141). The details neither of these arguments nor of the underlying physical theory need concern us here; what is of interest, however, is the implication that when the Stoics speak of modifications or changes in the mind, they are not speaking metaphorically. A modification of the mind would appear to be a determinate change of state of the mind-substance or pneuma 
. Hence a presentation, since it is such an alteration, would be a physical event (cf. [Sandbach, 1971a, p. 10]), as much a physical entity as the pneuma itself.57
At 7.51, Diogenes Laërtius provides evidence that the Stoics observed a distinction among presentations between those which are sensory 
and those which are non-sensory 
. “Sensory impressions,” according to Diogenes’ account, “are those which are apprehended 
through one or more of the sense organs; non-sensory, on the other hand, are those which apprehended through thought or by the mind 
, such as those of the incorporeals 
and other things apprehended by reason (DL 7.51). We take it that this distinction is designed to describe presentations in accordance with the character of their immediate sources. Obviously, a sensory presentation is one whose immediate source is an actual state of affairs, and this state of affairs is also its cause. It is somewhat unclear what the immediate source of non-sensory presentations might be, but since they are “apprehended through thought,” perhaps the most likely candidate would be another presentation. Moreover, there would seem to be nothing to stand in the way of this second presentation’s being the cause of the first, for presentations, as was noted above, are ‘bodies’ (sōmata) and hence can enter into causal relationships (Stobaeus eclog. 138.24; AM 9.211). Indeed, there would seem to be no reason why one could not envisage a sequence of presentations forming a causal chain.
Ultimately, however, there must be a presentation whose cause is not another presentation, but rather some external state of affairs. This requirement would not be a problem in the case of some non-sensory presentations: for example, the Stoics hold that “it is not by sense-perception 
but by reason 
that we become cognizant of the conclusions of demonstrations, such as of the existence of the gods and of their providence” (DL 7.52). Presumably, since the gods themselves are evidently corporeal entities,58 it would be as a result of their actions that one would become cognizant of their existence, and the presentation in which one apprehends that existence would have its cause in the gods themselves. But in the case of other non-sensory presentations, such as those of the incorporeals, there is a difficulty in seeing how to give an account of the causal basis of such a presentation. For the Stoics hold that the class of incorporeals, which includes lekta, void, place, and time (AM 10.218), are asōmata (literally ‘without body’) and hence cannot enter into causal relationships (AM 8.263). A plausible solution to this difficulty is suggested by Long and Sedley, who propose that “perhaps we should connect [this relation between asōmata and presentations] with ‘transition’ 
, a method by which incorporeals are said to be conceived” ([Long and Sedley, 1990], 1.241). They go on to suggest that “this refers … to the mind’s capacity to abstract, e.g., the idea of place from particular bodies” [Long and Sedley, 1990, 1.241]. In an earlier work, however, Long renders metabasis as “a capacity to frame inferences” [Long, 1971, p. 88], and there are several texts which would seem to confirm this reading.59 Presumably, such a capacity would be seated in the mind (hēgemonikon) or intellectual faculty (dianoētikon) and thus ultimately in the soul itself (cf. DL 7.110).
According to Iamblichus as quoted by Stobaeus, “those philosophers who follow Chrysippus and Zeno and all those who conceive of the soul as body, bring together the powers 
of the soul as qualities in the substrate 
and posit the soul as substance 
already underlying the powers” (eclog. 1.367.17). Moreover, there are several texts which report that the Stoics characterise qualities as corporeal,60 and at least one passage specifically reports that they describe the qualities of the psychē as such (Alexander de anima 115.37). Given their corporeal nature, one might suppose that the various capacities of the psychē would have causal powers, and this supposition gains credence from a passage in which Zeno is reported to hold that prudence 
is the cause of ‘being prudent’ 
, and temperance 
is the cause of ‘being temperate’ 
(Stobaeus eclog. 1.138). Thus one might plausibly conjecture that the Stoics could give an account of the causal basis of non-sensory presentations, such as those of the incorporeals, by invoking, presumably along with the data of experience, the causal powers associated with metabasis. And one might further suppose that some such account would throw light on the Stoic explanation that “presentations are formed because of [the incorporeals] and not by them,”61 and that they are perceived not by the senses, “but in a certain manner by the senses” (sed quodam modo sensibus) (Cicero acad. 2.21). If so, then we would not have to suppose with Long and Sedley that these explanations represent an attempt by the Stoics “to find a relationship other than causal to fit the case” [Long and Sedley, 1990, 1.241].
Whatever may be the difficulties involved in providing a causal basis for non-sensory presentations, no comparable problems exist for sensory presentations, for the source of such presentations is an actual state of affairs. We can probably take a passage of Aëtius to imply that sensory presentations are the primary means by which a person develops the stock of conceptions which comprise the content of memory and experience.
When a man is born, the Stoics say, he has the commanding-part of his soul like a sheet of paper ready for writing upon. On this he inscribes each one of his conceptions 
. The first method of inscription is through the senses. For by perceiving something, e.g., white, they have a memory of it when it has departed. And when many memories of a similar kind have occurred, we then say we have experience 
. For the plurality of similar impressions is experience. Some conceptions arise naturally in the aforesaid ways and undesignedly, others through our own instruction and attention. The latter are called ‘conceptions’ only, the former are called ‘preconceptions’ 
as well. Reason, for which we are called rational, is said to be completed from our preconceptions during our first seven years.62
Another distinction among presentations which is relevant at this point is that between presentations which are rational 
and those which are irrational 
. Rational presentations, according to Diogenes Laërtius, are those of rational creatures. They are processes of thought (DL 7.51), and they have an objective content which can be expressed in language (AM 8.70). It looks as though the ‘preconceptions’ mentioned in the quotation from Aëtius are those which ‘arise naturally’ from sensory presentations. Since these preconceptions are a requisite for rationality, it is apparent that our first sensory presentations are preconceptual and hence non-rational. Evidently, rational presentations are possible only when a person has acquired the preconceptions which go to make up the content of such presentations. Since the preconceptions would seem to provide a fairly basic conceptual apparatus (e.g., colour concepts), the rational presentations based on them would also be fairly basic. Diogenes Laërtius lists several ways that more complex conceptions may be brought about.
Of these [complex conceptions] some are acquired by direct experience, some by resemblance, some by analogy, some by transposition, some by composition, and some by contrariety. … Some things are conceived by inference 
, such as lekta and place. The conception of what is just and good comes naturally. And some things are conceived by privation, such as the idea of being without hands (DL 7.52–53).
Sextus Empiricus gives a similar list of ways by which conceptions are grasped, and it is notable that he precedes this list with the comment, apparently having its basis in Stoic doctrine, that “in general it is not possible to find in conception that which someone possesses not known by him in accordance with direct experience” (AM 8.58). Of the rational presentations which are primary, an important sub-class are those presentations which are called ‘apprehensive’ or ‘cognitive’ 
. We follow F.H. Sandbach in rendering 
as ‘cognitive presentations’ [Sandbach, 1971a, p. 10]. Presentations belonging to this class play a central role in the Stoic theory of knowledge.
The material nature of the mind in Stoic psychology is an important component in what seems to us a plausible interpretation of the notion of an ‘apprehensive’ or ‘cognitive’ presentation. The interpretation we have in mind is that presented by Michael Frede in his essay “Stoics and Skeptics on Clear and Distinct Impressions” [Frede, 1987e, 151–76]. Cognitive presentations (Frede calls them ‘cognitive impressions’) were deemed by the Stoics to be “the criterion of truth” 
(DL 7.54), and as such played a foundational role in the Stoic account of the development of an individual person’s knowledge of the world. According to the definition given both by Sextus Empiricus (AM 7.248) and by Diogenes Laërtius (7.46), cognitive presentations arise only from that which is real and are imaged and impressed in accordance with that reality.63 In his account, Sextus Empiricus adds a third condition to this definition: a cognitive presentation cannot have its source in that which is not real (AM 7.248). This last condition was apparently added to forestall certain objections of the Academics. According to Sextus (AM 7.252), the Stoics thought that a cognitive presentation would possess a distinctive feature 
by which it could be distinguished from all other presentations, such a feature reflecting a corresponding distinction in the object from which the cognitive presentation arises. The Academics, on the other hand, denied that any presentation could have such a feature. According to them, a false presentation can always be found which is similar in all respects to any given presentation (AM 7.402–10). According to Frede, both the Stoic and Academic schools probably agreed that cognitive presentations, “in order to play the role assigned to them by the Stoics, would have to satisfy the third condition too” [Frede, 1987e, pp. 165–66].
A problem for the Stoics, then, is to give an account of how one could tell that a presentation satisfied this condition, or, as Sandbach expresses it, “How could the bona fides of a cognitive presentation be established?” [Sandbach, 1971a, p. 19]. The difficulty is that any sort of test one might make to determine whether a given presentation is cognitive will itself depend on a presentation. But then a test will be required to determine whether the latter presentation is cognitive, and so on. Evidently such a process will lead to an infinite regress, a criticism expressed by Sextus Empiricus (AM 7.429), and probably derived from the early Academics, Arcesilaus and Carneades (cf. Long and Sedley, [1990, 1.249]).
One sort of reply to this criticism is that proposed by Sandbach: “There must be a point to call a halt. There must be some presentations that are immediately acceptable, that are self-evidently true. That is what constitutes a cognitive presentation. It is the attitude of common sense that most presentations are of this sort” [Sandbach, 1971a, p. 19]. It is not clear how far this reply will go to convince the sceptic. At any rate, if there were to be such self-evidently true presentations, it seems a plausible supposition that they would be sensory presentations having fairly basic conceptions as content. From these basic cognitive presentations the corresponding conceptions would be derived, and from these, in turn, more complex presentations. Thus, through the development of more and more complex notions, a complete grasp of things would eventually be gained, such grasp being expressed in general conditionals such as this: “If a thing is a human being, it is a rational mortal animal” (Si homo est, animal est mortale, rationis particeps). This seems to be the developmental process envisaged by Antiochus in his defence of Stoic epistemology (Cicero acad. 2.21). Frede conveys the idea with the remark that “the Stoics take the view that only perceptual impressions are cognitive in their own right. Thus other impressions can be called cognitive only to the extent that they have a cognitive content which depends on the cognitive content of impressions which are cognitive in their own right” [Frede, 1987e, p. 159].
Frede suggests that these basic presentations which are self-evidently true are so because they possess a causal feature which acts on the mind “in a distinctive way” thus bringing about recognition of the veridicality of the presentation [Frede, 1987e, p. 168]. “It is in this sense,” according to Frede, “that the mind can discriminate cognitive and noncognitive impressions” [Frede, 1987e, p.168]. The plausibility of this suggestion, it seems to us, depends in no small measure on the material nature of the mind in Stoic psychology. Previously in this section we saw that the pneuma which pervades all substance is also constitutive of the minds of human beings. Now according to the Stoics, causal interactions between bodies occur either through spatial contact (Simplicius in cat. 302.31) or through the medium of the pneuma (Aëtius plac. 1.11.5, DDG 310). Hence, the feasibility of a causal interaction between the mind and some distinctive feature of a state of affairs is not prima facie out of the question; moreover, such an interaction would evidently result in a unique presentation.
5 Lekta
Traditionally, one of the more celebrated texts providing evidence for Stoic semantic theory is that presented by Sextus Empiricus at AM 8.11–12. Just before this passage he has given an account of a controversy between the Epicureans and the Stoics as to whether the true is that which is perceptible only to the senses or only to the intellect. He continues:
Such, then, is the character of the first disagreement concerning what is true. But there was another controversy according to which some located both the true and the false in that which is signified, some in the utterance, and some in the process of thought. The Stoics, moreover, put forward the first opinion, saying that three things are connected: that which is signified 
, that which signifies 
, and the subject of predication 
. Of these, that which signifies is the utterance 
, for example, ‘Dion’. That which is signified, that is, what is indicated 
by the utterance, is the state of affairs itself 
which we apprehend as subsisting coordinately with 
our thought, but which the Barbarians, although hearing the utterance, do not comprehend. The subject of predication is the external substrate 
as, for instance, Dion himself. And of these (three things) they say that two are corporeal, namely, the utterance and the subject of predication; whereas one is incorporeal and spoken, or able to be spoken 
, namely, the state of affairs 
signified, precisely that which also becomes 
true or false. And these (pragmata which are spoken or can be spoken) are not all of a kind, but some are incomplete 
, while others are complete 
. And of the complete, one is called axiōma, which they also describe by saying “The axiōma is that which is true or false.”
The above passage provides a point of reference for the discussion of various questions which play a central role in the interpretation of Stoic semantic theory. It is our intention that an understanding of this theory will emerge as a result of discussing these various issues. Since we will frequently refer to this passage in what follows, it will be convenient for such reference to call it ‘Passage A’.
Sextus informs us in this passage that the Stoics develop their theory of what is true or false by distinguishing three kinds of items which are connected. These are ‘that which signifies’ 
, ‘that which is signified’ 
, and ‘the subject of predication’ 
. He goes on to provide a more specific delineation of each of kind of item. That which signifies (to sēmainon) is characterised as ‘the utterance’ 
. The term 
is standardly rendered as ‘sound’ or ‘speech’, but it seems to us that in certain contexts it has a somewhat more ambiguous meaning for the Stoics, this meaning being better captured by the indeterminate sense that ‘utterance’ has as it is used in modern philosophy. For instance, ‘utterance’ on this account would encompass writing as well as speech (cf. DL 7.56). As an example of to sēmainon, Sextus provides the utterance of the name ‘Dion’. This example, it seems to us, is not only completely inappropriate for the context, but is also inappropriate at a more fundamental level. We shall have more to say about this problem presently. That which is signified (to sēmainomenon), that is, what is indicated by the utterance, is characterised as ‘the state of affairs itself’ 
.64 Sextus implies that on hearing the utterance a Greek speaker will apprehend the pragma as ‘subsisting coordinately with thought’, but the Barbarian or non-Greek-speaker will not apprehend the pragma, even though he hears the same utterance. Recalling that rational presentations are ‘processes of thought’ (DL 7.51) having an objective content which can be expressed by discourse (AM 8.70), this sounds very much like a description of how a rational presentation would be induced in the mind of the Greek speaker by the utterance, with the content of the presentation being the state of affairs signified by the utterance.
To return to the problem of Sextus’ example ‘Dion’, the context of Passage A is an account of what it is to which the Stoics ascribed the property of having a truth value, and we are told that it is to sēmainomenon. We are also told that to sēmainomenon is the pragma or state of affairs indicated by the utterance. Now it seems evident that the utterance of ‘Dion’ will not indicate a state of affairs which is either true or false. Hence, the example seems to be inappropriate in the context of the discussion. A more suitable example would be something like the utterance of the sentence 
(Dion is walking).65
At a more fundamental level, the example is problematic inasmuch as it seems to suggest that in Stoic semantics a proper name signifies a ‘meaning’ or ‘sense’ and refers to the object named. According to Diogenes Laërtius, however, Diogenes the Babylonian defined a name as a part of speech 
indicating an individuating quality 
(DL 7.58). This teaching would appear to have its basis in certain epistemological and metaphysical concerns, in particular, in the doctrine of cognitive presentations, in the principle of the identity of indiscernibles, and in the theory of change and identity. Recall that one of the functions of the pneuma in Stoic philosophy is to invest undifferentiated matter 
with qualities (see page 430). Certain of these qualities serve not only to differentiate portions of prime matter from the rest, but also to individuate them as unique entities. The matter invested with an ‘individuating quality’ 
, along with the quality itself, together comprise ‘that which is individually qualified’ 
, that is, the uniquely qualified individual which serves as the substrate for further qualities and for the predication of attributes (Simplicius in cat. 48.11). An essential feature of this doctrine is that although the substance 
of which an individual entity is comprised is constitutive of that entity, it is not identical with it (Stobaeus eclog. 1.178.21–179.17). Thus, the Stoics were able to defend the idea of something which remains constant and serves as the basis for change, for although the substance of which an entity is comprised might undergo constant ‘alteration’ 
and so never be the same from moment to moment, the individuating quality remains constant (Stobaeus eclog. 1.177.21–178.21; Plutarch comm. not. 1083c). As well, this notion of a uniquely qualified individual is no doubt the basis of the Stoic thesis of the identity of indiscernibles which held that “no hair or grain of sand is in all respects the same as another hair or grain” (Cicero acad. 2.85), and which served in the defence of the theory of cognitive presentations (acad. 2.83–85).
According to this doctrine, then, the utterance of ‘Dion’ signifies the portion of pneuma individuating that part of the substrate 
which is constitutive of the qualified individual 
, Dion. And even when Dion has died and it is no longer possible to refer to him by means of a demonstrative, it is still possible to refer to him by name (Alexander in an. pr. 177.31), since the name picks out not the substance of Dion, but the individuating quality. At any rate, the point is that the Stoics already have an adequate theory of signification for names which links the utterance of the name directly to what it signifies, and there is no need, therefore, to posit an incorporeal ‘meaning’ or ‘sense’ as the signification of a name.
Returning to Sextus’ account of the three connected items, the ‘subject of predication’ 
is characterised as ‘the external substrate’ 
. According to Simplicius, the Stoics, as well as earlier philosophers, held that the substrate is twofold: primarily it is unqualified matter 
, which is what Aristotle named it; and secondly, it is that which is commonly or individually qualified 
. In this latter case, the qualified substrate serves as the substrate for further qualities and as the subject of predication (in cat. 48.11–16). Since it seems evident that the utterance signifies the pragma and predicates a property or quality of the external substrate, we have translated 
as ‘the subject of predication’.66
Having given this more specific characterisation of the three connected items, Sextus then reports the Stoic doctrine that two of these items are ‘corporeals’ 
, which is to say, bodies or material entities, while the other is ‘incorporeal’ 
, literally, ‘without body’. It seems obvious that the Stoics would have classed the external substrate as corporeal. Moreover, since they viewed the utterance as a body, it seems clear that they would also have classed it as corporeal. It is Stoic doctrine that whatever produces an effect is a body; hence, the utterance is evidently a body, for it produces an effect as it proceeds from the speaker to the hearer (DL 7.55–56). In addition, since a written utterance 
–which, according to Diogenes the Babylonian, is speech 
(DL 7.56)—is also capable of producing an effect, they no doubt would have counted it as corporeal as well. On the other hand, given that the Stoics held that “bodies alone are existents” (Plutarch comm. not. 1073e), the conception of the pragma as incorporeal does seem to be problematic, for, as Gerard Watson puts it, “incorporeal” is an extraordinary concept in a materialist universe” [Watson, 1966, p. 38]. We shall have more to say about the ontological status of the pragma or lekton in Subsection 5.5. For the moment, however, we discuss the semantic considerations which might have prompted the Stoics to posit such an item.
At the end of Passage A Sextus makes it clear that there are several different types of complete pragmata, and in a later passage (AM 8.70–74) he provides a list of them. In this later text, however, he does not write, as he does in Passage A, of complete pragmata which are spoken or can be spoken 
but rather of complete lekta. It would appear, therefore, that we can take complete lekta to be complete pragmata which are spoken or can be spoken. From what was said earlier in Passage A, the lekton is the signification of an utterance, and from discussion in the text at AM 8.70–74, as well as in the text of Diogenes Laërtius at 7.65–68, the type of the lekton is evidently determined by the type of speech act which is its signifier. One type of lekton, for example, is signified by the utterance of a command, another type, by the utterance of a question (DL 7.66; AM 8.71). The axiōma, as one might expect, is apparently signified by an assertion, which is to say, the utterance of a declarative sentence (DL 7.65–66).
Now it would seem that a difficulty becomes manifest when one asks what is the character of the lekton, or, as it might be expressed, what is the character of ‘that which is signified’. This difficulty is relevant to every type of lekton, but one can get a general idea of the problem by considering the axiōma in particular. At the beginning of Passage A Sextus informs us that the Stoics rejected the view that the true and the false are in the utterance, as well as the view that they are in the process of thought. They themselves put forward the thesis that the true and the false are located in ‘that which is signified’ 
. At the end of Passage A, we are told that of the various types of complete lekta, the axiōma is the one which the Stoics say is true or false, and according to Diogenes Laërtius (7.65–66), the axiōma is signified by an assertion. Hence, according to the Stoics, when someone makes an assertion, i.e., utters a declarative sentence, he signifies an axiōma, and the axiōma is either true or false. The problem, then, which in general can be expressed as ‘What is the nature of “that which is signified”?’, can be expressed with respect to the axiōma as ‘What is the nature of “that which is true or false”?’.
It might be helpful at this point to consider how the Stoics define something as being true. Sextus reports in one place, for example, that they hold the definite axiōma ‘This man is sitting’ or ‘This man is walking’ to be true 
whenever the predicate ‘to sit’ or ‘to walk’ corresponds to the attribute falling under the demonstrative (AM 8.100).67 Similarly, Diogenes Laërtius relates that on the Stoic account, someone who says ‘It is day’ seems to make a claim that it is day, and the axiōma set forth is true 
just in case it really is day, otherwise, it is false 
(DL 7.65).68
Now suppose that someone utters the sentence ‘Dion is walking’, and suppose further that Dion really is walking. Evidently, on the above account, what is signified by the utterance would be true, and it seems tempting in such a situation to think that what is signified is the actual state of affairs, which, on the Stoic view, could be described as Dion’s hēgemonikon in a certain state. And since the hēgemonikon, which part of the soul, is constituted by pneuma and so is corporeal (see page 430), what would be signified on this understanding would be something corporeal, and hence unproblematic for Stoic materialism.69 Suppose, however, that someone utters the sentence ‘Theon is walking’, and that Theon is actually sitting at the Stoa listening to Zeno’s lecture. Evidently, what is signified by the utterance in this case will be false; moreover, there is no temptation to think that what is signified is an actual state of affairs consisting in the non-walking Theon. Nevertheless, the utterance is significant, and whether Theon is actually walking or not, a Greek speaker who hears the utterance of the sentence 
will experience in either case a rational presentation according to which he will apprehend the same pragma signified and spoken. In other words, what will be signified by the utterance will be the same in either case. It seems evident, therefore, that what is signified is not the actual state of affairs. What is suggested by this commentary is that the Stoics were persuaded by theoretical considerations to admit items into the ontology of their theory of language for which they could not give a materialist account.
It may be, however, that because of reflections on their theory of causality, the lekton, or at least, the incomplete lekton, had already been admitted as an item in their ontology. Although the weight of evidence adduced by many modern commentators would seem to support the view that the lekton was posited by the Stoics in their semantic theory, Michael Frede has recently proposed that “it is not clear … that the notion of a lekton was introduced by the Stoics in the context of their philosophy of language rather than their ontology” [Frede, 1987a, p. 137]. The evidence for this proposal comes from a passage in Clement’s Stromata (8.9.4) in which it is claimed that Kleanthes called predicates 
lekta. As far as we know, according to Frede, this is the first use by a Stoic of the term ‘lekton’ [Frede, 1987a, p. 137]. In order to bring out the significance of this passage with respect to the present concern, it will be necessary to consider briefly the role of the predicate (katēgorēma) in the Stoic theory of causality.
It would seem that for the Stoics “the canonical representation of the causal relation was … as a three-place relation between a body and another body and a predicate true of [the second] body” (Frede [1987a, p. 137]). Thus a knife (or a scalpel) is the cause for flesh of being cut 
(AM 9.211; Clement strom. 8.9.30.3), and fire is the cause for wood of burning 
(AM 9.211). In representing the causal relation in this manner the Stoics were no doubt influenced by their conception of the universe as a dynamic continuum. Such a view would seem to presuppose a theory of causality in which events rather than particular entities are seen as the effects of causes. For on this conception, the universe just is the totality of events which occur as the result of causal interactions between bodies (sōmata), either through spatial contact or through the medium of the pneuma.70 According to Sextus Empiricus, the Stoics characterise such interactions as follows: “Every cause is a body which becomes responsible to a body of something incorporeal” (AM 9.211).71 Thus an effect, on this account, is something which happens to a body as a result of some action of another body. This ‘something which happens’, however, is not itself a body, but is something ‘incorporeal’, that is, a predicate. We shall return to the topic of the predicate and its role in Stoic semantic theory, but for the moment we intend to give some consideration to the various other types of lekta recognised by the Stoics.
In the last part of Passage A, Sextus writes that the pragmata which are signified by the utterance are not only incorporeal, but also spoken or able to be spoken 
. They are differentiated first of all between those which are ‘complete’ 
and those which are ‘incomplete’ 
. Of the complete pragmata, one is called the axiōma, and it is this which is either true or false. In similar texts strongly suggestive of a common source, Sextus and Diogenes Laërtius each render an account of the various kinds of complete pragmata (AM 8.70–74; DL 7.65–68). In these passages, however, they write of lekta rather than of pragmata which are spoken or can be spoken. In the text at AM 8.70, Sextus reiterates some of the things he mentioned in Passage A. In particular, he tells us that the Stoics maintain in common that the true and the false are in the lekton. He goes on to report that according to them, the lekton subsists coordinately with a rational presentation, and that a rational presentation is one in which it is possible that what is presented be exhibited in discourse. Further on, he also mentions again that the Stoics call some lekta incomplete, and others, complete. He then provides a list of several different kinds of complete lekta (AM 8.71–73).
Diogenes Laërtius, after relating that Chrysippus takes the subject of dialectic to be that which signifies 
and that which is signified 
, also reports that the lekton is that which subsists coordinately with a rational presentation. He provides a brief summary of the doctrine of the lekton, saying that this theory is arranged under the topic of pragmata and sēmainomena, and includes complete lekta, such as axiōmata and syllogisms, as well as incomplete lekta, namely predicates 
, both direct 
and indirect 
(DL 7.63).72 He then gives an account of incomplete lekta, or predicates (7.63–65), which leads into a summary of the various kinds of complete lekta (7.65–68). He begins this synopsis with the following characterisation of the axiōma:
An axiōma is that which is either true or false, or a complete pragma 
such as can be asserted 
in itself. Thus Chrysippus says in his Dialectical Definitions, “An axiōma is that such as can be asserted in itself, as, for example, ‘It is day’, ‘Dion is walking’” (DL 7.65).73
There is some question concerning the meaning of 
in this passage. Hicks renders it ‘capable of being denied’, but Mates argues that this adjective is derived from 
, not from 
, and so should be translated as ‘asserted’ or ‘capable of being asserted’ [Mates, 1953, p. 28]. In accord with Mates’ view, Diogenes writes, just after the text quoted above, that the term 
is derived from the verb 
This has the meaning ‘to be asserted’ or ‘to be claimed’.74
As for the other kinds of complete lekta, both authors present a similar catalogue. There are discrepancies, however, inasmuch as some kinds of lekta appear on one list but not on the other, and inasmuch as some kinds are not denoted by the same terminology on both lists. What we report here is inclusive of both lists and ignores the differences in terminology. This comprehensive list includes questions of two kinds: interrogations 
, i.e., those which require only a ‘yes’ or ‘no’ reply, and inquiries 
, i.e., those which require an explanatory reply. It also includes imperatives 
, prayers 
and curses 
, oaths 
, hypotheticals 
, vocatives 
, declaratives 
, a kind of rhetorical question 
, and finally, a lekton which Diogenes calls a quasi-axiōma 
(DL 7.67). For example, although the sentence ‘Priam’s sons are like the cowherd’ signifies an axiōma, the sentence ‘How like to Priam’s sons the cowherd is!’ signifies a quasi-axiōma; or, as Sextus puts it, “something more than an axiōma, but not an axiōma” (AM 8.73). We have noted that these texts would seem to suggest that the type of lekton is determined by the type of speech act which is its signifier, and it is tempting to conjecture that there is some parallel with the speech act theories of Searle, Hare, and Austin. At any rate, we shall say more about this possibility in the next subsection.
Not much textual information has come down to us concerning the Stoic treatment of these various kinds of lekta other than axiōma. We do know, however, that Chrysippus had an interest in developing a theory of at least some of them, for he is reported by Diogenes Laërtius to have written a series of books on imperatives and questions under the general heading of Logical Topics Concerning Lekta (DL 7.191); moreover, in a damaged papyrus discovered at Herculaneum we have a discussion by Chrysippus on the relationship between predicates, statements, and imperatives.75 Nevertheless, aside from these examples and some isolated entries in the texts of a few commentators “most of the attention was given to propositions” [Frede, 1987b, p. 345], and virtually all of the extant writing by the ancient commentators on the topic of the lekton is about the axiōma.
5.2 Lekta and rational presentations
In the passage from Sextus Empiricus quoted above (AM 8.70), we are told that “the lekton is that which subsists in accordance with a rational presentation” and that “a rational presentation is one in which it is possible that what is presented 
be set forth in language.” Another passage, this one from Diogenes Laërtius, informs us that “those presentations which are rational are processes of thought”76 (DL 7.51). If one compares these texts with the text of Passage A, where Sextus implies that the pragma is that which subsists coordinately with thought, this comparison would seem to indicate that there is some sort of correspondence between the terms ‘pragma’ and ‘lekton’ in these contexts. Confirmation for this correspondence is provided by a comparison of the discussion at the end of Passage A with what Sextus reports at AM 8.70 concerning complete and incomplete lekta. In Passage A, Sextus writes that the pragmata which are spoken or can be spoken 
differ inasmuch as some are complete, whereas others are incomplete. At AM 8.70, however, he writes that lekta are differentiated in that some are complete while others are incomplete. What would seem to be the case, then, is that lekta are pragmata which are spoken or can be spoken. If this judgment is correct, then it is evident that in the text at AM 8.70 one could substitute ‘pragma which is spoken or can be spoken’ for ‘lekton’ and thus interpret Sextus’ remark as ‘the pragma which is spoken or can be spoken is that which subsists coordinately with a rational presentation’. It also seems plausible that in the kinds of contexts under consideration the qualifying phrase ‘spoken or capable of being spoken’ could be dropped. This possibility seems to be realised, for example, in Passage A, where the pragmata referred to are sēmainomena, and hence, one would suppose, spoken. At any rate, by dropping the qualifying phrase, and substituting just the term ‘pragma’ for the term ‘lekton’ in the text at AM 8.70, one could simply say that ‘the pragma is that which subsists coordinately with a rational presentation’. However, ‘pragma’ should always be understood as ‘pragma spoken’ or ‘pragma which can be spoken’.
Possibly a relevant text here is that of Diogenes Laërtius in which he writes that under the general heading of dialectic, the doctrine of the lekton is arranged under the topic of pragrnata and sēmainomena (7.63). These remarks seem to indicate that lekta belong to a differentia of pragrnata and of sēmainomena. That lekta are a species of sēmainomena seems unproblematic, and we shall argue in the sequel that not all sēmainomena are lekta. It is not clear, on the other hand, what the other differentiae of pragmata would be. However, given the understanding of ‘pragmata’ as ‘states of affairs’, it is plausible to suppose that the Stoics did not think that all states of affairs are spoken or capable of being spoken.
Another section of the text at AM 8.70 to consider is the remark that a rational presentation is one for which it is possible that what is presented 
be exhibited by means of discourse. There is some controversy concerning the interpretation of 
in this passage. Mates writes that 
is “the objective content of the presentation,” and equates it with 
(1953, 22). In criticising this view, Long says that “the presented object” (sc. 
) is what a phantasia reveals, a ‘thing’ not a lekton. If I see Cato walking I am presented with an object which can be denoted in a complete lekton” [Long, 1971, 109m33]. We would reply that what I am presented with is not merely Cato, but Cato walking, which we take to be not merely an object, but a state of affairs. We would agree with Long, however, that 
should not be equated with 
. It seems to us that 
should be understood simply as ‘that which is presented’, and the text should be taken as setting out a necessary and sufficient condition for a presentation to be rational. On this reading, we take it that the condition is fulfilled if and only if 
is a 
, that is, a state of affairs which is spoken or can be spoken. On the other hand, the condition is not fulfilled if τ
is not a 
.77 At any rate, we take it that Sextus’ remark can be rephrased thus: “A rational presentation is one in which what is presented is a pragma which is spoken or can be spoken.”
The following quotation from Diogenes Laërtius indicates that the Stoics appear to have drawn a distinction which is of relevance to the present discussion. They seem to have differentiated discourse from both mere utterance and speech, and to have referred to discourse as ‘speaking pragmata’.
Mere utterance 
and speech 
differ inasmuch as mere utterance is sometimes just noise, whereas speech is always articulate 
. And speech also differs from discourse 
inasmuch as discourse is always significant 
; hence, though speech (lexis) is sometimes meaningless, as for instance the word 
, discourse is never so. And discourse or ‘speaking’ 
also differs from mere utterance, for whereas sounds are uttered, states of affairs 
are spoken: and such states of affairs, in fact, happen to be lekta (DL 7.57).
This notion of ‘discourse’ as ‘speaking pragmata’ is elaborated by Sextus Empiricus in a passage in which he is reports that “to speak 
, according to the Stoics themselves, is to utter sounds capable of signifying the state of affairs 
apprehended” (AM 8.80). Thus one might say that to engage in discourse, that is, to speak pragmata, is to utter articulate sounds which signify the state of affairs apprehended in a rational presentation.
Other passages which seem relevant are those recorded by Diogenes Laërtius at 7.66–67. Here he informs us that, according the Stoics, an axiōma “is a [state of affairs] which we assert to be the case when we speak it” (7.66).78 we take it that what this means is that when one ‘speaks a pragma’79 by asserting it, the lekton, that is, what is said, is an axiōma: to put it another way, what is said when one asserts that some state of affairs holds or is the case is an axiōma or proposition. It might be instructive to compare Diogenes’ account of the lekton called an imperative 
: “An imperative is a pragma which we command to be the case when we speak it” (DL 7.67).80 Thus, when one speaks a pragma by commanding it, the lekton, or what is said, is a prostaktikon: in other words, what is said when one commands that some state of affairs be the case is a prostaktikon or imperative. Similarly, when one speaks a pragma by asking it, the lekton is a query or interrogation 
. According to Diogenes, the sentence ‘It is day’ signifies an axiōma whereas the sentence ‘Is it day?’ signifies an interrogation. What this example would seem to indicate is that the same pragma or state of affairs—in this case, its being day—can function as the content of various types of lekta, depending on the speech act involved.
Brad Inwood plausibly suggests that this conception is comparable to the idea familiar in the speech act theories of Searle and Hare, that is, the idea of a “distinction between content and mode of assertion” [Inwood, 1985, p. 93].81 It is similar, for example, to the distinction made by Searle “between the illocutionary act and the propositional content of the illocutionary act” (Searle, [1969, p. 30]). By ‘illocutionary acts’ he means acts of “stating, questioning, commanding, promising, etc.” [Searle, 1969, p. 24], and by ‘propositional content’ he seems to mean (in the case of asserting or stating, for example) “what is asserted in the act of asserting, what is stated in the act of stating” [Searle, 1969, p. 29]. Thus according to Searle, uttering the sentence ‘Sam smokes habitually’ constitutes the performance of a different illocutionary act than uttering the sentence ‘Does Sam smoke habitually?’ or ‘Sam, smoke habitually!’, but although the ‘mode of assertion’ differs in each case, the propositional content, which might be represented by the complex {Sam, smokes habitually}, is the same. Inwood has reservations about this comparison, however, writing that “for the analogy to a speech act theory like Hare’s or Searle’s to be complete, it would have to be the case that the Stoics isolated a subject-predicate complex from its mode of assertion. And they appear not to have done this” ([Inwood, 1985], 95). We shall attempt to develop an interpretation to the contrary, an interpretation in which the complete pragrna 
is just such a complex.
At 7.49, Diogenes Laërtius details an order of priority between presentation and discourse. He writes that according to the Stoics, “presentation is first, then thought, which is capable of speaking out, discloses by means of discourse that which is experienced through the presentation.” At 7.57, Diogenes also writes that pragmata are spoken and that discourse is to speak pragmata. If one interprets ‘τò λε
τóν’ to mean ‘that which is spoken or can be spoken’, an interpretation we shall argue for in the sequel, then one can render the text at AM 8.70 as ‘that which is spoken or can be spoken is that subsisting coordinately with a rational presentation’. Since ‘that which is spoken’ is the pragma, the foregoing interpretation becomes ‘the pragma is that subsisting coordinately with a rational presentation’. Hence, the pragma will also be prior to discourse, since it subsists coordinately with the rational presentation. And of course, if the pragma is what is spoken, it would seem to be prior to discourse in any case. This priority, we take it, along with the passage at DL 7.66–67 in which Diogenes characterises each type of lekton as a pragma spoken in a certain mode, is a strong indication that the Stoics isolated the pragma from its ‘mode of assertion’.
The question arises as to the nature of the pragma, or more particularly, of the complete pragma. The simplest procedure for setting out an account of this item will be to consider an example of a sensory presentation which is a presentation of a real feature of the world. A general characterisation of the pragma might be that it is an abstract structure which is the result of a mental process whereby the mind interprets the actual state of affairs apprehended in the presentation. This structure is assembled from the appropriate conceptions selected from those stored in the mind’s stock of conceptions,82 and it is this interpretation which allows what is perceived to be represented in language. Pragmata, then, are abstract structures which correspond, on the one hand, to the language used to represent them, and on the other hand, to the actual states of affairs or situations which engender the presentations of which they are the content. This latter correspondence, however, only holds in the case of veridical presentations.83
Consider an example. Suppose we see Dion walking. What there is, according to the Stoics, and hence, what is perceived, is the individually qualified substance of Dion in a certain state 
, that is, possessing the attribute ‘walking’ 
.84The mind seaches its stock of conceptions, and if the conception of Dion and of the attribute ‘walking’ are among them, then it possesses the necessary components for constructing the pragma. In general, for a simple example such as this, the components of the pragma could be thought of as an ordered pair of items, of which the first is either an individuating quality 
or a common quality 
, and second is a predicate 
. For a particular pragma, the first of these components would be signified by either an individual name or a common name, and the second, by a nominalised infinitive verb. For convenience, we shall represent such a structure by first writing down a left brace, then the name signifying the individuating quality, then a comma, then the nominalised infinitive verb signifying the predicate (AM 9.211; Clement strom. 8.9.30.3), and last, a right brace. Hence, for the example under consideration, the pragma will be represented thus: 
. In English this will be: {Dion, to walk}.85
We take those passages at AM 8.80 and DL 7.66–67 to indicate that to ‘speak a pragma’ is to perform what Searle defines as an ‘illocutionary act’ (24). According to these texts, the result of speaking a pragma in a certain mode is a certain type of lekton. Obviously, ‘lekton’ (or, more strictly, 
) will have the sense in these contexts of ‘pragma spoken’. An axiōma, on this account, is the result of speaking a pragma by asserting it, a prostaktikon is the result of speaking a pragma by commanding it, and a similar account can be given for the other types of lekta. Moreover, an axiōma is what is asserted in the act of asserting, a prostaktikon is what is commanded in the act of commanding, and so on. One can probably think of the lekton as an abstract structure which will include the elements of the associated pragma, but which will have a richer structure in that it will contain items not part of the pragma. For example, lekta will obviously have moods, and probably tenses as well. At any rate, as the Kneales point out, axiōmata will have tenses [Kneale and Kneale, 1962a, p. 153]. There may be items corresponding to various sentence operators, such as operators for negations and questions. In addition, there may be items corresponding to connectives and articles (cf. DL 7.58). Although We will need to look at axiōmata which involve items corresponding to connectives, we do not intend to give an analysis of the structure of lekta in general; hence, for the most part, we will simply represent a lekton by writing down its signifying sentence and enclosing it with a pair of braces. For example, one way in which one could speak the pragma Dion, walking would be to utter the sentence ‘Dion is walking’. The axiōma associated with this utterance would be represented thus: {Dion is walking}.
At this point, there are some observations which should be made. First, it is evident that the pragma is what might be called the ‘propositional content’ of a rational presentation, but we would as soon avoid using this expression. Some commentators who speak of the ‘propositional content’ of a rational presentation seem to suppose that this content is a proposition (e.g., Frede [1987e, p. 154]). However, the only item which could be compared to a proposition in Stoic semantics is the axiōma, and we do not see why, supposing that the content of a rational presentation is a lekton, it should be an axiōma rather than some other type of lekton. Second, the formation or construction of the pragma would appear to be a constituent of the perceptual process. According to Chrysippus, a presentation reveals itself and that which caused it (AM 7.230; Aëtius plac. 4.12.1, DDG 401). Thus one is conscious of the mental process which is the presentation, as well as the external state of affairs (in the case of a sensory presentation) which caused the presentation. Sandbach writes that the presentation thus “gives information about the external object” [Sandbach, 1971b, p. 13]. But clearly, without the pragma, which we take to be the mind’s interpretation of the external state of affairs, there can be no information received, and hence, no perception. Third, it was suggested above that a presentation is rational if and only if there is a pragma subsisting coordinately with it. This would be a lekton in the sense of a ‘pragma which can be spoken’. We do not think that there is necessarily a lekton subsisting coordinately with the presentation in the sense of a pragma spoken. This result would seem to be indicated by the priority of the presentation with respect to discourse (see page 428).
It is clear that this account of the lekton is fairly rudimentary at best. For example, we have said nothing of how this interpretation will function for non-sensory presentations. Although we will need to address this topic in particular and expand certain other aspects of the account as well (aspects such as axiōmata involving connectives, already mentioned above), we believe that what has been said so far will serve as a basis for developing a characterisation of the role of the axiōma in the theory of inference.
5.3 Incomplete lekta
Another relevant point not brought out in Passage A but mentioned just after, is the distinction among lekta drawn by the Stoics between those lekta which are ‘complete’ 
and those which are ‘incomplete’ 
. This distinction is confirmed by Sextus in another passage (AM 8.70–74) and also by Diogenes (7.65–68). Incomplete lekta, according to Diogenes, are those for which the signifying expression is also incomplete. For example, ‘He writes’ 
, although a grammatically complete expression, signifies an incomplete lekton, presumably because it lacks a definite subject, and hence, does not signify a complete state of affairs. A complete lekton, on the other hand, is one signified by a complete expression, for example, ‘Socrates writes’ 
(7.63). At 7.58 Diogenes reports that a verb 
signifies an uncombined predicate, and at 7.64 he gives a characterisation of a predicate 
as “an incomplete lekton which has to be combined with a nominative case 
in order to form a complete lekton.” Given that the expression ‘Socrates writes’ signifies a complete lekton these two passages would seem to suggest that the significatum of a noun such as ‘Socrates’ occurring in the subject position of a sentence such ‘Socrates writes’ is, according to the Stoics, a nominative case 
(DL 63–64). Moreover, no matter how odd or even obscure it might seem to us, what is further suggested is that for the Stoics the cases (hai ptōseis) are not understood primarily in a grammatical sense.
From what has been said above, it is clear that an isolated verb such as ‘writes’ can signify an incomplete lekton. An issue which arises is the question whether isolated nouns can also signify incomplete lekta. Many commentators seem to think that they can,86 and they seem to think so for one or both of two closely connected reasons. One reason is the example given by Sextus Empiricus in Passage A. Recall that Sextus informs us in this passage that the Stoics distinguish among three things: that which signifies (to sēmainon), i.e., the utterance (hē phōnē); that which is signified (to sēmainomenon), i.e., the lekton; and the subject of predication (to tynchanon), i.e., the external existent (to ektos hypokeimenon). As an instance of that which signifies he cites the utterance ‘Dion’. Given this example it seems natural to suppose that there is a lekton associated with this expression and that one may take this lekton to be something like its sense or meaning; one may suppose, moreover, that the referent of this meaning is the object picked out, i.e., Dion himself. All this seems to suggest a Fregean semantic analysis of the lekton, and this is the course which some authors appear to take.87
There is a difficulty with this approach, however, and it involves the fact that in Passage A Sextus is giving an account of a controversy over what it is that is true or false. According to him, the Stoics locate truth and falsity in ‘that which is signified’, which, as we have seen, is the axiōma. But we have also seen that an axiōma is signified by the utterance of a declarative sentence. Hence one would expect that Sextus would give a declarative sentence as an example of an utterance which is ‘that which signifies’. Whatever else it might be, the utterance ‘Dion’ seems clearly not to be the utterance of a declarative sentence. Hence it is not the significans of an axiōma, and thus not the significans of anything either true or false. The inappropriateness of Sextus’s example is emphasised by consideration of a passage from Seneca’s Epistulae Morales. The content of this passage would seem to parallel that of Passage A.
I see Cato walking. The sense (of sight) reveals this (state of affairs), the mind believes it. What I see is an object, toward which I direct both (my) sight and (my) mind. Then I say: “Cato is walking.” What I say now, according to them, is not an object, but something declarative about an object: this (that I say) some call ‘effatum’, others ‘enuntiatum’, and others ‘dictum’.88 Thus when we say ‘wisdom’ we understand something material; when we say ‘He is wise’, we say (something) about an object. It makes a great deal of difference, therefore, whether you indicate the object or say something about it (3: 117.13).
It is apparent that something like Seneca’s example ‘Cato is walking’ is needed, and this requirement is all the more apparent when one considers the examples given by Chrysippus as quoted by Diogenes Laërtius, i.e., ‘It is day’, ‘Dion is walking’ (DL 7.65). One proposal for clearing up this problem is the suggestion that uttering ‘Dion’ may be taken as “equivalent to asserting the true proposition ‘this man is Dion’” [Long, 1971, p. 77, 107n11]. Whatever are the merits of this particular suggestion, it seems that something of this sort must be posited, for we have another passage similar in context to Passage A in which Sextus also mentions the expression ‘Dion’ as being the significans of an “incorporeal lekton” (AM 8.75). Hence we cannot simply write off the example as an aberration in Sextus’s account (cf. Frede [1987b, p. 349]). Be that as it may, we think that the infelicity of Sextus’s example for the point it is meant to illustrate renders it questionable as evidence that Stoics viewed isolated nouns as significantia of lekta.
Recall that, according to Passage A, the Stoics suppose that the sign (to sēmainon) and the object of reference (to tynchanon) are both corporeal 
, whereas the lekton is incorporeal 
. We wish to discuss an assumption made by some authors which is based on the posited immaterial nature of the lekton. This assumption leads to the second reason for an affirmative reply to the question whether isolated nouns can signify an incomplete lekton. This is the assumption that since the lekton is incorporeal, whatever are its constituents must also be incorporeal. Hence, since the significatum of a noun such as ‘Socrates’ can be a constituent of a complete lekton–for example, the lekton signified by the expression ‘Socrates walks’–it would seem to follow that the significatum of the expression ‘Socrates’ is incorporeal. But if it is, then it must be a lekton of some sort, since it could hardly be an incorporeal belonging to any one of the other classes of immaterial entities. Now it seems clear that the expression ‘Socrates’ will not signify a complete lekton; therefore, it seems natural to conclude that this expression signifies an incomplete lekton, and that, in general, isolated nouns can signify incomplete lekta.
Given the Stoic view cited above that nouns signify cases 
, it would seem to follow from the argument in the last chapter that a case is an incomplete lekton and hence something incorporeal. On the other hand, if one assumes that “the ptōsis is definitely conceived of as something incorporeal” [Graeser, 1978b, p. 91], then it would seem to follow that a case is an incomplete lekton. Either way we get the conclusion that isolated nouns can signify incomplete lekta. One attractive feature of this argument is that it fits in rather well with the example ‘Dion’ presented by Sextus Empiricus in Passage A; indeed, some writers conclude that the supposed incorporeal nature of the cases provides confirmation of the legitimacy of Sextus’s example (cf. Graeser [1978b, p. 91]), whereas others conclude that Sextus’s example provides confirmation that the Stoics viewed the cases as incorporeal.89
We have already suggested that Sextus’s example is suspect as evidence that isolated nouns signify lekta, and this would seem to count against the view that the Stoics thought of the cases as incorporeal. However, there are two other objections to these theses which would seem to be somewhat stronger. The first is based on the fact that in any discussion of this subject in the sources, only predicates are ever mentioned as being incomplete lekta (cf. Frede [1987b, p. 347]; Long [1971, pp. 104–05]; Graeser [1978b, p. 91]). The other is based on the report of Diogenes Laërtius (7.58) to the effect that the Stoics assumed that the significata of names and common nouns are, respectively, individual qualities 
and common qualities 
. Now there is no doubt that the Stoics assumed that the qualities of material objects were themselves material;90 hence, if proper nouns and common nouns signify qualities, and qualities are corporeal, there would seem to be a difficulty for anyone wishing to maintain the view either that nouns signify incomplete lekta, or that cases are incorporeal.91
One might suppose that this should resolve the matter, but at least two more complications arise. The first complication involves two passages in Clement of Alexandria’s Stromateis in which it is claimed that “a case is incorporeal … and … agreed to be incorporeal” (Frede [1987b], 350). As for the claim that a case is incorporeal, Frede has argued convincingly that non-Stoics of later periods in Greek philosophy would use the term ‘case’ with the conviction that cases are incorporeal “because they did not share the Stoic view that qualities are bodies” ([Frede, 1987b], 350). As for the claim that cases are agreed to be incorporeal, he argues that the examples cited by Clement are examples of things which would no doubt be agreed to be incorporeal by the Stoics, but which would not be agreed by them to be examples of cases. So much then for the difficulties raised by the passages of Clement.
The second complication involves interpreting a passage of Stobaeus (SVF 1.65) in such a way that common qualities, at least, are shown to be incorporeal (cf. Rist [1969a, p. 165]). This passage, which is described by Frede as “notoriously obscure and difficult” [Frede, 1987b, p. 348]), is as follows:
Zeno <and his followers> say that concepts 
are neither somethings 
nor qualified things 
, but are mere images in the mind—only quasi-somethings or pseudo-qualified things 
. These (sc. concepts) are called ideas by the ancients. For the ideas are (ideas) of the things falling under 
the concepts, such as of men, or of horses, or, speaking more generally, of all living things, and of any other things which they say are ideas. The Stoic philosophers say that these (sc. concepts) are non-existents, and that whereas we participate 
in the concepts, the cases, which they call prosēgoria, we possess 
.
Following Frede [1987b, pp. 348–49], we take it that the substance of this passage is claim that the Stoics from Zeno on refused to grant the Platonic Forms or Ideas, which they called ‘concepts’, any existential status at all—not even the existential status of the incorporeals such as lekta, void, place, and time. However, there are things which, because they ‘fall under’ 
the concepts, are called ‘cases’ 
by the Stoics, and which are contrasted with the concepts, the contrast being that corporeal objects merely participate in the latter, whereas the cases they possess.
Now according to Frede [1987b, p. 348], the Platonists assumed that in addition to the transcendental forms or ideas, there are immanent forms which are embodied in concrete particulars. He suggests that the immanent forms of the Platonists correspond to the Aristotelian forms, and that both are qualities of some kind. Thus the Platonists differentiate between the transcendental form wisdom, which the Stoics would call the concept wisdom, and the embodiment of the form in Socrates himself, i.e., Socrates’ wisdom. On the Stoic view, according to Stobaeus, Socrates’ wisdom would be a case (ptosis), because it falls under (hypopiptein) the concept wisdom. Moreover, Socrates would merely participate in the transcendental form wisdom, whereas he would possess the embodiment of that form. Hence the Stoic cases appear to correspond to the embodied forms of the Platonists and the Aristotelians, and like them, appear to be qualities of some kind. As such, they would be corporeal on the Stoic view, although they would be incorporeal on the Platonic or Aristotelian conception.
This interpretation of Stobaeus’s passage seems to us to capture the substance of the Greek. Unfortunately, not all commentators agree. Rist, for example, thinks that we can deduce from this passage that it is the common qualities of the Stoics which correspond to the Platonic Forms, and hence, that such qualities must have been given the same ontological status as the Forms—which is to say, they were thought of as non-existents ([Rist, 1969a, p. 165]; cf. Reesor [1954, p. 52]). It is not difficult to see how one might arrive at this interpretation, for there would seem to be some confusion created inasmuch as the common nouns such as ‘man’ and ‘horse’, which, on the Stoic view, signify common qualities (DL 7.58), are used by the commentators to refer to the ideas or concepts. Thus, since the term ‘horse’ is used to talk about both the quality common to all horses and the concept ‘horse’, it should not be surprising that the concept and the common quality are taken to be identical. Now it may be that the Stoics themselves are to blame for at least some of this confusion, for it is easy enough to be careless about the distinctions one draws. On the other hand, given the view that the cases are qualities, and given the distinction between cases and concepts—both of which are integral to Frede’s interpretation of Stobaeus’s passage—there is no reason to suppose that the Stoics did not intend to maintain the distinction between concepts and common qualities. But if this distinction is observed, then there would seem to be no basis for maintaining that common qualities are not corporeal.
It should be noted that the distinction between concepts and cases is mentioned in other ancient texts. Simplicius, for example, using language similar to that of Stobaeus, reports that the Stoics called the concepts 
(which may be translated as particibilia (cf. Frede [1987b, p. 348]), because they are participated in 
and the cases ‘possessibles’, because they are possessed 
(in cat. 209.12–14).
Predicates
At 7.63 Diogenes Laërtius comments that the class of incomplete lekta includes all predicates 
and if we are correct in rejecting the significata of isolated nouns from this class, then it includes only predicates. A predicate, according to Diogenes, is “that which is said about something, or a pragma constructed from one or more elements, or (as we have already noted above) an incomplete lekton which must be joined on to an nominative case 
in order to yield an axiōma” (DL 7.64). The first two of these characterisations are attributed to the Stoic Apollodorus and the passage is translated by Hicks as if they were in conflict with the last one. But it seems to us that the versions of Apollodorus are compatible with the third one and that the three are merely alternatives. Given what has been said above about complete lekta, we take the sense of the first of these alternatives to be the idea that in order to signify a complete lekton one must make some attribution to an object, and what is attributed is a property or attribute. Corresponding to this property at the level of lekta, is a predicate or incomplete pragma, and, at the level of language, a verb. In the example of the above paragraph, writing has been asserted about Socrates to form the axiōma ‘Socrates writes’. But it would seem that one could also form the interrogative 
‘Is Socrates writing?’ by asking of Socrates whether he is writing (cf. DL 7.66). In either case we take it that 
is ‘that which is said’ about Socrates.
The second alternative seems to reflect an ambiguity in the Stoic use of the term katēgorēma which we are rendering as ‘predicate’. This ambiguity has been noted by Michael Frede in his article “The Origins of Traditional Grammar” [Frede, 1987b, pp. 338–59]. According to Frede, the Stoics made a distinction between those predicates which are simple and those which are complex [Frede, 1987b, p. 346]. There seems to be good reason to take the latter to be the result of combining a ‘direct predicate’ 
(DL 7.64) with an oblique case 
. Such complex predicates, according to Diogenes, must be constructed in this way so as to be capable of combining with a nominative case to produce a complete lekton. The examples cited by Diogenes are signified by verbs such as ‘hears’, ‘sees’, and ‘converses’, and these are contrasted with those signified by such verbs as ‘thinks’ and ‘walks’ (DL 7.64). Now we know that for the Stoics a verb 
is “a part of speech signifying an uncombined 
predicate” (DL 7.58). Hence, it seems to be the case that some uncombined predicates (e.g., those cited as instances of direct predicates) cannot as they stand be joined with other elements to produce a complete lekton, the reason being that there is a sense in which the verbs signifying such predicates must first be combined with other parts of speech before they can be joined with a name or common noun in the nominative case to produce a complete thought. For example, in comparison with ‘Dion is thinking’ or ‘Dion is walking’, it seems plausible that the sentence ‘Dion is seeing’ or the sentence ‘Dion is hearing’ requires a complement in order to express a complete thought. To recapitulate, there are, it would seem, some uncombined predicates which are required to be joined with other elements before they can partake in the production of a complete lekton. On the other hand, there are some which can partake in the production of a complete lekton just as they stand. Frede calls the former ‘syntactic predicates’ and the latter ‘elementary predicates’ ([Frede, 1987b], 346). We shall adopt this terminology in the sequel.
Given this ambiguity in the term katēgorēma, one can think of the third alternative characterisation of a predicate as a recipe for constructing an axiōma from either an elementary predicate or a syntactic predicate. On the one hand, an incomplete lekton which is an elementary predicate can be combined with a nominative case to produce an axiōma without further ado. On the other hand, an incomplete lekton which is a syntactic predicate must first be combined with other elements before it can be joined with a nominative case to form an axiōma.
It is perhaps appropriate at this point to make explicit what is suggested in the preceding discussion concerning the ‘construction’ of an axiōma: that is, the notion of a syntax of lekta.92 A good way to introduce this task is to notice that the Greek noun from which the English word ‘syntax’ is derived, is itself derived from the Greek verb 
and that various forms of this verb are used by Diogenes in the passages from 7.63 to 7.74 to indicate the notion of ‘putting together’ various kinds of elements to form a lekton (cf. Frede [1987c, p. 323, 246]; Elgi, in Brunschwig [1978, p. 137]). Furthermore, we have evidence that Chrysippus, at least, was interested in such a notion, for among the more that seven hundred books he is reported to have written (DL 7.180), the following titles appear: (2) On the Syntax of What is Said, four books 
, and (3) Of the Syntax and Elements of What is Said, to Philip, three books 
(DL 7.193).93 Now according to A.A Long, the expression ‘τò λεγóμενoν’, which may be rendered as ‘what is said’ or as ‘that which is said’, is extremely difficult to distinguish in sense from to lekton ([Long, 1971], 107n13); moreover, as Frede points out, the passage at DL 7.57 indicates that ‘what is said’ is in fact a lekton. These writings of Chrysippus seem to reinforce what is implicit in Diogenes’ report of the Stoic characterisation of a predicate at DL 7.64 and in the whole discussion from DL 7.63 to DL 7.74: that is, that the Stoic theory of the lekton included the conception that lekta were analysable into various elements and that there was a set of syntactic principles whereby such elements were to be joined together to form a lekton.
5.4 Lekta and parts of speech
The Stoics seem to have thought that one constructs a lekton, and in particular an axiōma, by combining the elements of the corresponding declarative sentence in the right way. This amounts to putting together the elements of the sentence in such a manner that the structure of the corresponding axiōma is syntactically correct, its elements being combined in accordance with the syntax of lekta (cf. Frede [1987c, p. 324]). The supposition that the Stoics entertained some such notion of a relation between the elements of a sentence and the elements of the corresponding lekton is suggested by the remaining two titles in the sequence of four mentioned above. These are: (1) On the Elements of Speech and on Things Said, five books 
, and (4) On the Elements of Speech, to Nicias, one book 
) (DL 7.193). Note that (1) and (4) are concerned not only with the parts of speech but also with the elements of lekta, and that (2) and (3) are concerned not only with the elements of lekta but also with the syntax of lekta. The placement of these titles in this particular sequence seems to point to “a systematic connection between parts of speech, elements of lekta, and the syntax of lekta” [Frede, 1987c, p. 324]; moreover, such a connection would be explained by assuming that the Stoics envisaged the production of a lekton to take place in accordance with the theory outlined above.
As for the connection between the parts of speech and the elements of lekta, we have a text of Diogenes Laërtius which seems to suggest that this connection is a relation of signification. Both Chrysippus and Diogenes the Babylonian,94 according to this text, stated that there are five parts of speech: these are individual name, common name, verb, conjunction, and article. Diogenes, in his treatise On Language, associates at least the first three of these with the corresponding elements of lekta. An individual name 
, according to him, is a part of speech indicating 
an individual quality 
(e.g., Diogenes, Socrates); whereas a common name is a part of speech signifying 
a common quality 
(e.g., man, horse). A verb 
is a part of speech signifying an uncombined predicate (as we have already seen). A conjunction 
is an indeclinable part of speech, binding together the parts of a sentence, and an article 
is a declinable element of a sentence, determining the genders and numbers of nouns (DL 7.58). The relation outlined in this passage between the elements of speech and the elements of lekta seems clear with respect to the first three parts of speech on the list. It also seems clear what the corresponding element at the level of lekta is for each of these parts of speech. If we take the participle ‘δηλoν’ to mean ‘signified’ in this context, then we can suppose that for the Stoics there is a relation of signification respectively between individual names, common names, and verbs at the level of parts of speech, and individual qualities, common qualities, and predicates at the level of lekta.
The passage is not so clear, however, about the elements of lekta which are supposed to correspond to conjunctions or articles. One assumes, given what has been said about the other three parts of speech, that whatever the nature of these elements of lekta might be, the connection between each of them and the corresponding part of speech should also be one of signification. But it is difficult to tell from the text, for conjunctions and articles are defined grammatically rather than by their signification at the level of lekta. In addition, as Frede points out [Frede, 1987c, p. 331], there is a difficulty inasmuch as the Stoics think that the class of conjunctions includes both conjunctions proper and prepositions, and that the class of articles includes both articles proper and pronouns. Thus it is not at all transparent how one is to envisage an element of a lekton which can be the significate both of conjunctions and of prepositions, or one which can be the significate both of articles and of pronouns.
5.5 Ontological concerns
In this section we intend to consider briefly some issues concerning the ontological status of the lekton. The first of these is the problem of how one ought to interpret the meaning of the term ‘lekton’. The question presents some difficulty inasmuch as it seems to be connected with ontological concerns. The other topic is the question whether the lekton was conceived by the Stoics as merely a construct of the mind, or as something having a more tangible status.
The interpretation of ‘λεκτóν’
The substantive expression ‘τò λετóν’ is derived from the neuter nominative of the verbal adjective ‘λετóζ’, which in turn is derived from the verb 
, to say or to speak. Since lektos is one of those adjectives having the sense both of the perfect passive participle and of the notion of possibility, to lekton is probably best understood either as ‘that which is said’ or as ‘that which can be said’. Now it is true that one way in which the Stoics characterise the lekton is to say that it is ‘that which is signified’ 
by a significant utterance (e.g. AM 8.11–12), and some writers take it that to lekton ought therefore to be rendered, either exclusively or primarily, as ‘what is meant’.95 This interpretation, which gains further credence from the fact that Liddell and Scott list ‘to mean’ as one of the senses of legein, is then taken to imply that a lekton was thought of by the Stoics as some kind of ‘meaning’ or ‘sense’, whatever such may be (e.g., Graeser [1978b]).
There are at least two difficulties with this reading. One is the question whether the Stoics did in fact take 
and 
to be synonymous. From the fact that they called lekta sēmainomena, it does not follow that all significata of significant utterances are lekta. Indeed, there is a passage in Diogenes Laërtius (7.58) which seems to make it clear that this is so. According to this passage, what is signified by a name is an ‘individual quality’ 
, and by a common noun, a ‘common quality’ 
. Now since the qualities of corporeal bodies are, according to the Stoics, as much material as the bodies themselves (cf. Simplicius in cat. 217.32), and since lekta are not material entities, what seems to be suggested is that ‘what is signified’ by a name or common noun is not a lekton. In other words, 
is not coextensive with ‘λετóν’.
The other problem with reading to lekton as ‘what is meant’ is that there is more than a little evidence supporting the idea that one species of lekton, the axiōma, had the role in Stoic semantic theory as that which is true or false. Hence, if one interprets the lekton as being in general a ‘meaning’ or ‘sense’, then one seems to commit the Stoics to saying that such things as ‘meanings’ or ‘senses’ are the sorts of things which can be true or false. We think that one would be hard pressed to find textual evidence for such a commitment. Thus it would appear that however else they may have thought of the axiōma, it is unlikely that the Stoics could have viewed it as such a thing as a meaning or sense. It seems to us rather that the Stoics would have agreed with Austin in his contention that “we never say ‘The meaning (or sense) of this sentence (or of these words) is true’” (“Truth” in Phil. Papers, 87); hence, it seems unlikely that the Stoics could have viewed the axiōma as such a thing as a meaning or sense. But if it is improbable that the Stoics thought of the axiōma as a meaning or sense, then since the axiōma is a kind of lekton, it is not clear that one can legitimately promote an interpretation of the lekton as being in general a meaning or sense. From the point of view of the interpretation we are suggesting, rendering ‘to lekton’ as a meaning or sense cannot do justice to the various roles the concept plays in Stoic semantics (cf. [Long, 1971, p. 77]).
But even supposing we interpret ‘to lekton’ as ‘what is said’, there is still some controversy whether we should also interpret it as ‘what can be said’. The problem is summarised by Andreas Graeser as follows:
For taking lekton to mean “that which can be said” may seem tantamount to committing oneself to the position that the lekton exists regardless of whether it is being expressed or not, whereas taking lekton to mean “what is said” seems rather to entail that the very entity in question exists only as long as the expression that asserts it [Graeser, 1978b, pp. 87–88].
This worry is reiterated later in Graeser’s essay when he asks “Did the Stoics hold that the axiōmata or lekta respectively exist in some sense whether we think of them or not?” [Graeser, 1978b, p. 95], and it is echoed by A.A. Long when he wonders whether “ lekta only persist as long as the sentences which express them” [Long, 1971, p. 97]. In giving expression to this problem both Graeser and Long are concerned to reply to an assertion made by the Kneales to the effect that axiōmata “exist in some sense whether we think of them or not” [Ksneale and Kneale, 1962a, p. 156]. The context in which this claim is made is an iteration of the various similarities and dissimilarities perceived by the Kneales between axiōmata and propositions. We shall not comment on the arguments adduced by the Kneales concerning this issue, nor on the counter-arguments presented by Graeser and Long. Indeed, we intend to develop an interpretation of the lekton which will require an understanding of the meaning of the term ‘to lekton’ as being systematically ambiguous. On such a reading this controversy would seem to be of less concern. We do, however, wish to note that saying “lekta only persist as long as the sentences which express them” does not seem to render their existence any less mysterious or problematic than saying that they “exist in some sense whether we think of them or not.”
The passage in Diogenes Laërtius at 7.66, discussed in the last section, would seem to suggest that the axiōma is the significatum of some actual utterance of a particular type, i.e., an assertion. Similarly, each of the other kinds of lekta is the significatum of the appropriate type of utterance (i.e., command, question, and so on). It seems apparent that on this account the question whether axiōmata “exist in some sense whether we think of them or not” should not arise, for the subsistence of the axiōma is clearly dependent upon the existence of an act of assertion. Obviously this dependent status will apply to the lekta corresponding to the various other types of illocutionary acts. We suggested in the last section that one ought to understand ‘lekton’ in these contexts as a generic term denoting the content of a speech act; hence, it seems appropriate in such cases to take ‘to lekton’ to mean ‘what is said’.
On the other hand, there would seem to be room in the Stoic theory for lekta which subsist independently of any particular utterance. When one asserts, for example, that the state of affairs {Dion, walking} is a fact, or commands that it become a fact, or questions whether it is a fact and so on, what gets said, or exhibited 
in language, in such an utterance is the unarticulated objective content 
of the rational presentation, that is, the 
{Dion, walking} (cf. AM 8.70). We have proposed that ‘lekton’ is sometimes used to denote the pragma which is the unarticulated content of a rational presentation. In such contexts, it seems appropriate to understand ‘to lekton’ to mean ‘what can be said’.
The lekton and ontology
There is a tradition among ancient commentators that the Stoics posited a summum genus 
which they called ‘the something’ 
(AM 8.32; PH 2.86; Seneca epist. 58.13–15), and under which they included not only material bodies or ‘corporeals’ 
, but also a set of items ‘without body’ which they called ‘incorporeals’ 
(AM 10.218).96 We are informed by Sextus Empiricus that under the class of incorporeals were included lekta, void, place, and time 
(AM 10.218).97 Now inasmuch as the Stoics thought that “bodies alone are existents,”98 it is apparent that they did not take ‘to be something’ necessarily to mean the same as ‘to exist’ in the sense that material bodies exist.
In addition to material bodies and incorporeals, the class of somethings appears to have included a collection of items containing both fictional beings and theoretical constructs, particulars such as Centaurs (Seneca epist. 58.15) and limits (Proclus SVF 2.488; DL 7.135). Although it might seem natural to assume that these particulars ought to have been classified among the incorporeals, there is no evidence to support the view that the Stoics did so, for none of the texts providing a list of the incorporeals include such items in the list. The fact that the members of this class of ‘mental constructs’ are included among the ‘somethings’ but are never included among the incorporeals, would seem to indicate that the genus of ‘the something’ was differentiated into three subclasses: the class of material bodies or ‘corporeals’; the class of ‘incorporeals’ which included lekta, void, place, and time; and the class of fictions or mental constructs (cf. Long and Sedley [1990, 1.163–66]). At least one respect in which such a tripartite differentiation would be significant is to give lie to the claim made by some modern commentators that the incorporeals were viewed by the Stoics as merely ‘constructs of the mind’ (e.g., Watson, [1966, pp. 38–39]). We believe that the commentary of Long and Sedley is sufficient to show that the Stoics did indeed propose this tripartite division of the genus of ‘the something’. But granting this division as a component of Stoic ontology, the question occurs as to the basis for differentiating between fictional or theoretical constructs and the incorporeals. Since an adequate treatment of this problem is beyond the scope of this essay, we can only give a suggestion here of the reason.
It seems fairly clear, at least with respect to void, place, and time, that the Stoics needed these items in their ontology in order to develop their physical and cosmological theories. A consideration of the roles envisaged for these items makes it also seem clear that although these incorporeals fell short of having the real existence that substantial bodies have, it is unlikely that the Stoics viewed them merely as mental constructs. Similar reasons can be adduced on behalf of the lekton, supposing that Frede is correct in his suggestion that the concept of the lekton was first introduced in the ontology of Stoic causal theory [Frede, 1987a, p. 137]. On the other hand, the connection between the lekton and the immanent logos, a feature of its role as the pragma which is the content of a presentation, would seem to provide further reason why it is unlikely that the lekton was viewed merely as a mental construct.
Recalling our suggestion that for the Stoics ‘to be something’ did not seem to mean the same as ‘to exist’, the question naturally arises as to what ‘to be something’ did mean. It has been suggested that for the Stoics ‘to be something’ meant “to be a proper subject of thought and discourse” (Long and Sedley [1990, 1.164]). This idea is developed with the observation that since the Stoics thought that expressions such as ‘Centaur’ and ‘limit’ “are genuinely significant, they are taken to name something, even though that something has no actual or independent existence” [Long and Sedley, 1990, 1.164]. It is not obvious, however, what the force of the expression “genuinely significant” is supposed to be in this context. This shortcoming, however, can probably be filled out by a consideration of what is excluded from the genus of the something. We have a passage from Stobaeus (eclog. 1.136.21 = SVF 1.65) which would seem to indicate that the Stoics did not include what ‘the ancients’ 
called ‘ideas’ 
in the class of somethings. Michael Frede plausibly suggests that these ‘ideas’ which the Stoics called ‘concepts’ 
, are the transcendental Ideas or Forms of Plato ([Frede, 1987b], 348). According to Stobaeus, ‘concepts’ such as ‘Man’ or ‘Horse’ were referred to by Zeno and his followers as ‘pseudo-somethings’ 
. A possible reason why these items might have been refused the ontological status of somethings can be gleaned from a passage of Sextus Empiricus. Clearly presenting Stoic doctrine, Sextus argues at AM 7.246 that the genera of which the particular instances may be of this kind or that kind cannot themselves be of either kind. Thus the generic ‘Man’ is neither Greek nor Barbarian, for if he were Greek, then all particular men would have been Greek, and, conversely, if he were Barbarian, then all particular men would have been Barbarian. We take the general point of this argument to be the idea that it is not possible to ascribe to the ennoēmata any of the attributes one may ascribe to the particulars which fall under them. But if one cannot say of the universal ‘Man’ that he is either Greek or Barbarian, young or old, tall or short, cowardly or brave, and so on, then the term ‘man’ would seem to lack ‘genuine significance’ when it is used in this way. Hence the force of the expression “genuinely significant” might be understood to specify a contrast between terms such as ‘Centaur’ and ‘limit’, which are taken to name items to which one can ascribe certain appropriate attributes, and terms such as ‘Man’, which are taken to name items to which one can not ascribe such attributes. Thus, although it makes sense to say ‘A Centaur has four legs’, it does not make sense to say “Man” has two legs’. Hence, the Stoics might have thought that an item such as a Centaur or a limit could be said to be something, which is to say “the proper subject of thought and discourse,” but it was evidently not part of their ontological commitment to think that an item such as the universal ‘Man’ could also be so.99
The terms which the Stoics standardly used in their characterisations of the incorporeals were various forms of the verbs 
(AM 8.70; DL 7.63),100 and 
(AM 8.12; Simplicius in cat. 361.10). These terms, which are both customarily translated as ‘to subsist’ (e.g., Long and Sedley [1990], 1.196, 162–66), are contrasted with the verb 
(e.g., Stobaeus eclog. 1.106.20) which, on at least one of its senses, can be translated as ‘to exist’. This distinction, referred to by Galen as ‘splitting hairs’ (SVF 2.322), was, needless to say, the source of much critical commentary (cf. also Alexander in topica 301.19). We shall not attempt here to discuss this criticism, since it has, in any case, already been adequately addressed by A.A. Long [1971, pp. 84–90]. It seems clear, however, that the Stoics used this distinction to indicate the ontological status of the incorporeals as ‘somethings’, although not necessarily as existents. It has been suggested that the Stoic usage of the terms “seems to capture the mode of being that Meinong called bestehen and Russell rendered by ‘subsist’” (Long and Sedley [1990, 1.165]). The parallel is perhaps even closer inasmuch as the Stoics also seemed to count ‘fictions’ or ‘mental constructs’ such as surfaces and limits as belonging to the class of ‘somethings’ and to use forms of these verbs to refer to them (Proclus SVF 2.488; DL 7.135). It would be wrong, though, to infer from this that they classed incorporeals as fictions, the views of some modern commentators notwithstanding.
6 Axiōmata
It is evident that in some respects axiōmata have a character similar to that of propositions. For one thing, several texts confirm the judgment that the Stoics attributed to axiōmata the property of being true or false.101 There is some question, however, whether axiōmata were true or false in ‘the basic sense’. This question arises because the Stoics assigned the terms ‘true’ and ‘false’ not only to axiōmata, but also to arguments 
and to presentations 
. An argument was said to be true whenever it was conclusive 
and had true premisses (PH 2.138; DL 7.79), and, according to Sextus, “a true presentation is one from which it is possible to produce a true predication 
102 such as this in the present circumstances: ‘It is day’, or this: ‘It is light’” (AM 7.244).103 The consensus among modern commentators, however, seems to be that “the basic application was probably to propositions” [Long, 1971, p. 92]. In addition to being the primary items to which the terms ‘true’ and ‘false’ are applied, axiōmata are like propositions in that they are signified by declarative sentences.104 According to the Kneales, two further ways in which axiōmata are similar to propositions, is that “they are abstract, or, as the Stoics perhaps rather unhappily put it, incorporeal; and they exist in some sense whether we think of them or not” [Kneale and Kneale, 1962a, p. 156]. We have discussed the latter thesis in Subsection 5.5. As for the former, it may be that we can plausibly think of axiōmata as ‘abstract’; it would seem, however, that we can criticise the Stoics for calling them ‘incorporeal’ instead of ‘abstract’ only if we are certain that they meant ‘abstract’ and not ‘incorporeal’.
At any rate, however many of these characteristics of propositions one wants to apply to axiōmata, there are several differences which, according to the Kneales, indicate that axiōmata cannot simply be identified with propositions [Kneale and Kneale, 1962a, pp. 153–56]. For one thing, axiōmata appear to have certain ‘grammatical’ characteristics which we usually do not associate with propositions, but rather with the sentences which express them. For another thing, lekta obviously have moods. For another, lekta in general, and hence axiōmata in particular, have tenses. This is indicated by the titles of a series of four books written by Chrysippus and reported by Diogenes Laërtius. These titles are Temporal Lekta105, τωo βooς 
and Axiōmata in the Perfect Tense, two books 
(DL 7.190). There are reports as well that predicates, which are major constituents of axiōmata, were distinguished according to voice (DL 7.64-65) and number (Chrysippus SVF 2:99.38-100.1). Michael Frede, in his discussion of the origins of traditional grammar, has suggested that for the Stoics the notion of syntax was applied primarily to lekta and only derivatively to parts of speech and sentences ([Frede, 1987b], 345-47). Hence, distinctions which we would expect to be made at the level of expressions are made by the Stoics at the level of lekta, and the features at the level of expressions which correspond to certain features distinguished at the level of lekta, take their names from these latter features ([Frede, 1987b], 345). If Frede is correct, then it should come as no surprise that axiōmata differ from propositions in these ways.
Another difference between axiōmata and propositions, is that axiōmata can change truth value. As the Kneales point out, this feature is what might be expected since axiōmata have tenses [Kneale and Kneale, 1962a, pp. 153–54]. Finally, axiōmata may cease to exist.106 The evidence for this latter property is a passage of Alexander of Aphrodisias (in an. pr. 177.25–178.1). He reports that according to Chrysippus, the axiōma ‘This man is dead’ (indicating Dion demonstratively) is impossible when Dion is alive but is ‘destroyed’ 
when Dion has died (177.31). On the other hand, the axiōma ‘Dion has died’ which is possible when Dion is alive is apparently still possible when Dion has died (178.21-22). This result is what one would expect, given that a demonstrative must indicate the individually qualified substrate 
, that is, the qualified substance of Dion, whereas the name signifies the individuating quality 
(DL 7.58). When Dion has died, the individually qualified substrate ceases to exist as such, and thus can no longer be indicated demonstratively; the individuating quality, however, can still be referred to by the name.
According to Sextus Empiricus, the ‘dialecticians’ (i.e., the Stoics) declare that the first and most important distinction among axiōmata is that between those which are ‘simple’ 
and those which are ‘complex’ 
(AM 8.93). Sextus reports that even though axiōmata are constructed of other elements, they are called ‘simple’ if they do not have axiōmata as constituents. Thus a simple axiōma is one which is neither constructed from a single axiōma taken twice 
, nor from different axiōmata by means of one or more conjunctions 
(AM 8.94). The following, for example, are simple axiōmata, as is every axiōma of similar form: ‘It is day’, ‘It is night’, ‘Socrates is conversing’ (AM 8.93). Complex axiōmata, on the other hand, are those constructed from a single axiōma taken twice, for example, ‘If it is day, it is day’; or those constructed from different axiōmata by means of a conjunction, for example, ‘If it night, it is dark’. Further examples of complex axiōmata are such as the following: ‘Both it is day and it is light’, ‘Either it is day or it is night’ (AM 8.95). The content of these passages should be compared with the similar content of the text of Diogenes Laërtius at 7.68–69. Each author goes on to discuss the various kinds of simple and complex axiōmata, but we shall refer to Diogenes’ text for this information.
Simple axiōmata, according to Diogenes, are classified as follows: ‘negative’ 
, ‘negatively assertoric’ 
, ‘privative’ 
, ‘assertoric’ 
, ‘demonstrative’ 
, and ‘indefinite’ 
(7.69).107 In the passage at 7.70, Diogenes provides some details about these various kinds of simple axiōmata. A negative axiōma is constructed with a negative particle and an axiōma, e.g., ‘Not: it is day’. A negatively assertoric axiōma is produced from a negative constituent and a predicate, e.g., ‘No one is walking’. A privative axiōma is constructed with a privative constituent and a possible axiōma 
, e.g., ‘This man is unkind’. An assertoric axiōma is constituted by a nominative case and a predicate, e.g., ‘Dion is walking’. A demonstrative axiōma is constructed with a demonstrative nominative case and a predicate, e.g., ‘This man is walking’. An indefinite axiōma consists of one or more indefinite constituents and a predicate, e.g., ‘Someone is walking’. Diogenes makes a special note of the ‘double-negative’ axiōma 
. This is a negative axiōma constructed with a negative particle and a negative axiōma, e.g., ‘Not: not: it is day’. Such an axiōma, according to Diogenes, is assumed to have the same meaning as the axiōma ‘It is day’ (DL 7.69).
Of the complex axiōmata described by Diogenes, we will consider only those which have a role in the Stoic syllogistic system.108 These are the ‘conditional axiōma’
, the ‘disjunctive axiōma’ 
, and the ‘conjunctive axiōma’ 
. The conditional axiōma is constructed by means of the conditional connective ‘if ‘
.109 This connective ‘guarantees, 
that the second constituent of the conditional axiōma follows 
from the first, as, for example, ‘If it is day, it is light’ (DL 7.71). A disjunctive axiōma is constructed by means of the connective ‘or’ 
. This connective guarantees that one or the other of the constituent axiōmata is false, for example, ‘Either it is day or it is night’ (DL 7.72). A conjunctive axiōma is constructed by means of a ‘conjunctive’ connective, such as the particle 
in this example: ‘It is day and it is light’ 
(DL 7.72).
A topic of interest at this point might be that concerning the truth conditions for the various types of complex axiōmata. We shall discuss the truth conditions for the conditional in the section on inference, but for the moment we intend to consider some questions about axiōmata in relation to what has been written about presentations and pragmata. One of the distinctions among presentations recorded by Diogenes Laërtius is that between sensory 
and non-sensory 
presentations (DL 7.51). He writes that “sensory presentations are those apprehended through one or more sense-organs, whereas non-sensory presentations are those perceived through the mind itself, such as those of the incorporeals and of other things apprehended by reason” (DL 7.51).110 In Passage A Sextus implies that a Greek speaker, on hearing a significant utterance in Greek, will apprehend the pragma signified and subsisting coordinately with thought, whereas the non-Greek-speaker will not apprehend the pragma (AM 8.12). We interpreted this as a description of how a rational presentation would be induced in the mind of the Greek speaker by the utterance. The content of the presentation would be the pragma signified by the utterance.
We take it that such a presentation, although induced by a sound sensed through the hearing organs, or perhaps by the marks on a papyrus or a stone sensed through the organ of sight, would, nevertheless, be classified as a non-sensory presentation. For in order that a presentation be a sensory presentation, it seems evident that not only must it be apprehended through one or more of the sense organs, and hence have its cause in some portion of the qualified substrate, but also it must have a content in which either that portion of the qualified substrate is itself signified by a demonstrative, or the quality which individuates it is signified by a name. It is apparent that in the normal course of events, a presentation caused by an utterance may satisfy the first requirement, but it will not satisfy the second, for the content of such a presentation, as is indicated by the discussion in the preceding paragraph, is the pragma signified by the utterance, and not any feature of the utterance itself.
There is evidence that the Stoics viewed certain thought processes as some sort of ‘internal discourse’ 
.111 Such thoughts can no doubt be considered as ‘utterances’, and as such, will induce presentations in the mind. Clearly the presentations produced by such utterances will be non-sensory. Hence it would seem that a non-sensory presentation may be induced in one’s mind either by someone (else) speaking a pragma, or by one speaking a pragma in thought. The pragma spoken 
might be an axiōma signified by an assertion, but it might also be prostaktikon signified by a command, or an erōtēma signified by a query, or some other type of lekton. No doubt we not only sometimes make assertions to ourselves in thought, but also sometimes ask ourselves questions or exhort ourselves to action. This latter notion of speaking imperatives to ourselves in thought seems to be a necessary feature of Brad Inwood’s interpretation of the Stoic theory of action [Inwood, 1985, pp. 59–60 86–87]. Interesting as it might be to follow up on these other classes of lekta, axiōmata, however, are the lekta which are of interest in the present context.
We take it that the presentation induced by someone uttering a declarative sentence, or by someone uttering a declarative sentence in thought, will have a pragma as content which has a structure isomorphic to that of the axiōma signified. We are using ‘isomorphic’ here to suggest a structure preserving correspondence between the elements of the pragma and the elements of the axiōma. Thus, if we see Dion walking and so have a sensory presentation of Dion walking, the pragma accompanying this presentation can be represented by the simple structure {Dion, to walk}; however, if someone were to say to us ‘Dion is walking’ so that we have a non-sensory presentation of Dion walking at the present time, the attendant pragma, although representable on some level by the same structure, would seem to require a representation which includes an element to signify the present tense. One might, for example, portray this pragma as follows: {Dion, to walk: now}. However, since it is beyond the scope of this work to develop a detailed account of how such representations might be handled, we will resist the temptation. We have chosen to characterise the axiōma by merely enclosing its signifying sentence in braces, and although there are probably good reasons to develop distinct modes of representation for the pragma and the axiōma, we have chosen to depict the pragma by the same method.
To consider a more complex example, suppose that someone says to one ‘Dion was walking about in Athens at noon yesterday’. It seems evident that the pragma which accompanies the presentation induced by this utterance will reflect the structure of the axiōma, and hence have as constituents not only the individuating quality signified by the name ‘Dion’ and the predicate signified by the verb ‘walking’, but also temporal components and the individuating quality signified by the name ‘Athens’. We shall represent both the pragma and the axiōma as follows: {Dion was walking about in Athens at noon yesterday}. It is worth emphasising that we shall represent the pragma in this way only when it is the content of a presentation induced by an utterance.