P.M.S. HACKER
Throughout its long history metaphysics has been variously conceived. At its most sublime, it has been taken to be the study of the super‐sensible, in particular of the existence of a god, the nature of the soul, and the possibility of an afterlife. Hardly less sublimely, it has been thought to concern itself with the essence of all things and the ultimate categories of being (ontology). It is not surprising that once physics had started to trespass on this terrain, metaphysics had to be differentiated from the natural sciences that were successfully investigating the nature of things. So metaphysics was held to be the most general investigation into the nature of reality – the conclusions of which are presupposed by all the particular sciences. This conception was duly sharpened and refined. Meta‐physicists laid claim to investigate not the empirical nature of things, but rather the necessary nature of the world – as it were, its scaffolding. So, it was held, the natural sciences investigate empirical questions, study the contingencies of the world, its inessential, quasi‐accidental features, whereas metaphysics investigates the essential, great, and universal features of reality.
When the young Wittgenstein entered the lists, it was entirely reasonable to conceive of metaphysics in this manner. Its subject matter was held to be the language‐independent and thought‐independent de re necessities of the world. Moreover, the truths it strives to attain are synthetic a priori. They are not analytic: the predicate is not contained in the concept of the subject (as Kant put it) nor are they true in virtue of explicit definitions and the laws of logic (as Frege put it). They are synthetic – substantive truths concerning the world. But they are a priori – can be known independently of experience. They are established by rational argument, not by empirical observation, hypothesis‐formation, and experimental confirmation. Kant had decried transcendent metaphysics. The question he posed was “How is metaphysics as a science possible?” His answer was that its synthetic a priori truths are presupposed for the possibility of conceptualized experience and hence for empirical knowledge of nature. Metaphysics is limited to the domain of possible experience. The young Wittgenstein’s route was different. He moved not from the conditions of the possibility of empirical knowledge to their transcendental idealist roots, but rather from logic and the necessary truths of logic to their metaphysical presuppositions. His concern was with the presuppositions of the possibility of representation in general, and with the presuppositions of logic in particular.
In his first surviving writing on philosophy, the “Notes on Logic” of September 1913, he wrote, “Philosophy gives us no pictures of reality, and can neither confirm nor confute scientific investigations,” so “the word ‘philosophy’ ought always to designate something over or under, but not beside, the natural sciences” (NL 93; cf. TLP 4.111). “Philosophy,” he added, “consists of logic and metaphysics, the former its basis” (NL 93). This was a fundamental commitment while writing the Tractatus.
By the time he wrote his second surviving piece six months later, the “Notes Dictated to G.E. Moore in Norway,” Wittgenstein had arrived at the deepest commitment of his first masterwork, namely the distinction between what can be said, and what can only be shown, by language (NM 107). It is of this that he wrote to Russell in August 1919:
Now I’m afraid that you haven’t really got hold of my main contention, to which the whole business of logical prop[osition]s is only a corollary. The main point is the theory of what can be expressed (gesagt) by prop[osition]s – i.e. by language – (and, which comes to the same, what can be thought) and what cannot be expressed by prop[osition]s, but only shown (gezeigt); which, I believe, is the cardinal problem of philosophy.
(Letter to Russell, 19 August 1919)
A consequence of this “main contention” was that the truths of metaphysics, which concern the essential forms of the world, cannot be stated or described by any proposition, but only shown – by every proposition. The reason for this lies in the nature of any system of representation. As he explained to Moore:
Logical so‐called propositions show [the] logical properties of language and therefore of [the] Universe, but say nothing. [Cf. TLP 6.12]
This means that merely by looking at them you can see these properties; whereas, in a proposition proper, you cannot see what is true by looking at it. [Cf. TLP 6.113]
It is impossible to say what these properties are, because in order to do so, you would need a language, which hadn’t got the properties in question, and it is impossible that this should be a proper language. Impossible to construct [an] illogical language.
In order that you should have a language which can express or say everything that can be said, this language must have certain properties; and when this is the case, that it has them can no longer be said in that language or in any language.
(NM 107)
So the truths of metaphysics, as well as the metaphysical truths about the essence of language, can become apparent by careful logical analysis of language, but they cannot be stated.
Every real proposition shows something, besides what it says, about the Universe: for, if it has no sense, it can’t be used; and if it has a sense, it mirrors some logical property of the Universe.
(NM 107)
Metaphysical truths, therefore, are shown by the logical properties of language.
By January 1915, Wittgenstein had come to the following conclusion:
My whole task consists in explaining the nature of the proposition.
That is to say, in giving the nature of all facts, whose picture the proposition is.
In giving the nature of all being.
(NB 22.1.15)
From the essential nature of the proposition, he thought to derive the essential nature of logic, of logical propositions, and of logical necessity. This would show the essential nature of the world. For the “all‐embracing world‐mirroring logic” forms “the great mirror” (NB 22.1.15; cf. TLP 5.511). A year and a half later, he noted with satisfaction, “Indeed, my work has extended from the foundations of logic to the essence of the world” (“Ja, meine Arbeit hat sich ausgedehnt von den Grundlagen der Logik zum Wesen der Welt,” NB 2.8.16).
The Tractatus is dominated by three problems: first, the nature of logic and logical necessity (cf. Chapter 21, NECESSITY AND APRIORITY); secondly, the essence of the proposition and hence the characterization of the general propositional form (cf. Chapter 17, LOGIC AND THE TRACTATUS); and thirdly, the intentionality (pictoriality) of the proposition (and of thought) (cf. Chapter 32, WITTGENSTEIN ON INTENTIONALITY and Chapter 8, THE PICTURE THEORY). The latter is presented as “the mystery of negation,” that is: how can a proposition be false yet meaningful? – a problem that needs considerable clarification before it can even be apprehended, let alone associated with intentionality.
These three problems are interwoven. To grasp the nature and necessity of the propositions of logic, one must grasp the essence of the proposition, of propositional representation, and of truth‐functional propositional combination. To grasp the essence of the proposition, one must resolve the mystery of negation. In the course of resolving these great problems, the metaphysical presuppositions of logic and of representation in general are brought to light. Once the nature of representation is laid bare, the limits of language are revealed and the theory of what cannot be said but only shown is evident. Metaphysics, mathematics, ethics, aesthetics, and religion all belong beyond the bounds of possible description. Hence, in a final, but appealing, paradox, the very sentences of the Tractatus are manifestly attempts to say what cannot be said but can only be shown. Once one has apprehended the intentions of their author in writing these meticulously crafted and intentionally ill‐formed sentences, one will be able to apprehend in language – in the forms of well‐formed, fully analyzed propositions of language – the essence and nature of all that is there mirrored. One will have attained a correct logical point of view. Thenceforth, the sole task of philosophy will be analysis of propositions and the curbing of the metaphysical impulse to transgress the limits of language.
Although the order of presentation in the Tractatus moves from ontology to representation, from representation in general to propositional representation, and from propositional representation to the nature of the propositions of logic, the ordo cognoscendi is from reflection on the nature of logic to its ontological presuppositions. It should be no surprise that the initially proposed title for the book was Der Satz (The Proposition). It was by examining the nature of representation, in particular representation by means of propositions (sentences with a sense) that Wittgenstein came to construct an ontology – a metaphysical account of the essential constituents and forms of the world, and a corresponding metaphysics of symbolism, as presuppositions of the possibility of representation and of logic. Later, in June 1916, he added an obscure metaphysics of subjectivity, advancing what seems to be a form of transcendental solipsism conjoined with empirical realism.
Unlike his predecessors, Frege and Russell, Wittgenstein did not think that logic was the most general of the sciences. Nor did he think that the mark of a proposition of logic is complete generality. Frege had thought that logic is the science of thoughts, that its laws are descriptions of the topic‐neutral relationships between thoughts, and that all the laws of logic are generalizations. Russell had thought that logic is the science of the most general facts in the universe, and its task is to catalog their logical forms. Wittgenstein denied these claims. Essential generality is not a mark of the propositions of logic at all. Rather it is essential validity, i.e., necessity, that characterizes them. The proposition “Either it is raining or it is not raining” is a logical truth, and not, as Frege and Russell thought, merely an instantiation of the essentially general logical truth that every proposition is either true or false. (Indeed, he argued, “Every proposition is either true or false” is not even a proposition.) What precisely is a proposition of logic? If it does not describe relationships between thoughts, or the most general facts of the universe, what does it describe? If a mark of the propositions of logic is necessity, what explains this necessity and how can we recognize it? What is presupposed by logic? Frege and Russell would have said that logic presupposes the truth of its self‐evident axioms. Wittgenstein did not think that logic rests on self‐evidence, or that it presupposes axioms. But that does not mean that it does not have presuppositions.
The conclusions at which Wittgenstein arrives are bold. All propositions are truth‐functional combinations of elementary propositions (the principle of extensionality). Elementary propositions (propositions containing only simple names, and no logical connectives or quantifiers) are logically independent of each other. They consist of logically proper names, combined in accordance with logical syntax. Such logically simple names have both form and content. Their form consists in their logico‐syntactical combinatorial possibilities. Their content consists in their meaning, which is the simple object (thing, entity) in reality for which they stand. The objects for which these names stand must be beyond existence and inexistence – otherwise sense, which is presupposed by any statement, would depend upon the facts, and analysis would have no terminus. What simple objects there are is for analysis to disclose. But pro tempore, we might imagine these objects as minima sensibilia, such as shades of color and such like, and perhaps also spatiotemporal points (since space and time are the forms of all objects, TLP 2.0251). Such entities (things, objects) are obviously prima facie candidates for sempiternalia and for concatenation without the glue of a relation to connect them (as in Fa and aRb). So the question that exercised Bradley and Russell of how an object that stands in a relation to another object is related to the relation cannot arise.
The form of a name is represented in a logically perspicuous notation by a variable, the values of which are the various objects that share the same form. So, for example, the words “color” and “sound” signify forms of visual and auditory objects respectively. If presented explicitly as variables, e.g., “( )c” and “( )s,” it is obvious that what appears to be a necessary metaphysical proposition, e.g., “red is a color,” is not a well‐formed proposition at all, since it contains an unbound variable: “red ( )c.” So it is a mere nonsense. But that red is a color is shown by the form of the word “red,” i.e., by the combinatorial possibilities it shares with all other names of the same ontological category, i.e., color names. All names that are intersubstitutable in a well‐formed sentence salva significatione belong to the same ontological category. It is this that shows that red, green, orange, etc., are colors.
Elementary propositions have a sense. They describe, or depict, a possibility (a state of affairs) in reality, namely that the meanings of their constituent names are combined in reality as the names are combined in the proposition, given the conventions of representation. If “a” is the name of a, and “xRy” is the name of the relation “larger than,” and “b” the name of b, then “aRb” describes the state of affairs that a is larger than b, whereas “bRa” describes the state of affairs that b is larger than a. With different conventions, “Rab” might describe the former, and “Rba” the latter. So simple names have the same logical form as the simple objects in reality that are their meanings. A proposition, which is essentially a description of a state of affairs, is an abstract, logical, picture or model of what it depicts. Simple names are representatives of simple objects. Relations represent relations (it is not simply “R” that represents standing‐in‐the‐R‐relation, but rather that ‘R’ is flanked by two simple names). And facts represent facts. For what represents in a proposition such as “aRb,” what makes it possible for the sequence of signs to represent what it represents, is the fact that they are arranged as they are, given the conventions of this method of representation.
Names are connected to reality by lines of projection. The method of projection is: thinking the sense of the sentence. To think the sense of the sentence is to mean, by the sentence, the state of affairs it depicts (TLP 3.11), and hence too, to mean by the names conjoined in the sentence the objects the concatenation of which is a possibility in reality. It is of the nature of possibilities that they may obtain, i.e., be actualized, or fail to obtain, i.e., not be actualized. The actualization of a possibility is a positive fact. Its non‐actualization is a negative fact. What an elementary proposition describes is a possibility. What it says, is that it obtains (is actualized). If things are in fact as the proposition depicts them as being, then the proposition is true. If they are not, then it is false.
Truth and falsity are not objects, and propositions are not names of anything, let alone of a pair of logical objects (the True and the False, as Frege held). They are not, as both Frege and Russell had supposed, on the same level, like black and white, but are more akin to a shape and a space into which it fits (truth has priority). For a proposition to be true is for things to be as the proposition describes them as being. For a proposition to be false is for things not to be as the proposition describes them as being. So a deflationary (disquotational) account of truth (“‘p’ is true” = “p”) is taken for granted. A true proposition agrees with the possibility that obtains, and disagrees with the non‐obtaining of that possibility. Conversely, a false proposition disagrees with what is actually the case, and agrees with what is not the case. The sense of a proposition is its agreement and disagreement with the possibility of the obtaining and non‐obtaining of states of affairs (TLP 4.2).
With this apparatus, the “mystery” of negation dissolves, and the intentionality of thought and proposition becomes perspicuous. The problem is produced by the following compelling consideration. If a proposition is true, then what it depicts is what is the case. If a proposition is false, then what it depicts is not what is the case. But what a proposition depicts is the same, no matter whether it is true or false. How can this be? Or to put the problem slightly differently: how can a proposition be false but meaningful? For if it is true then what it depicts is what is the case. But if it is false, what it depicts is not what is the case. But what‐is‐not‐the‐case is nothing. Yet the false proposition depicts something, not nothing. How can this be? The picture theory of the proposition, together with the attendant ontology resolves the predicament. For the proposition depicts a possibility, and says that it obtains. If what it says is true then the possibility is actualized and what it says is indeed what is the case. If what it says is false, it is not. But the proposition says the same, no matter whether it is true or false. It describes reality “give or take a Yes or No.” The Tractatus’ metaphysics, its modal realism, provides (or seemed to provide) the key with which to unlock the mystery of negation and the puzzle of the intentionality of proposition (and thought).
It is the essence of a proposition not merely to be bivalent (either true or false) but to be bipolar (to be capable of being true and capable of being false). This follows from the proposition’s having a sense, i.e., being essentially a picture of a possibility that may or may not obtain. It also gives a further reason why metaphysical propositions, such as “One is a number” or “Red is a color” are nonsense. They are not bipolar, and they are not pictures of reality. (One cannot picture red’s being a color, but this is shown by the proposition “A is red.”) The bipolar nature of the proposition mirrors the nature of states of affairs, since it is of their nature to obtain or not to obtain. The world consists of facts, not of things. It is everything that is the case, i.e., the totality of facts. This is shown by a complete statement of the facts being a complete world‐description. A complete list of objects, by contrast, would not be a world‐description at all, but a catalogue of the substance of all possible worlds. Simple objects are the substance of the world – that which persists through all change. Change consists in the combination and separation of objects. Destruction consists in decomposition of complexes. What objects actually furnish the universe is a matter for experience to disclose. What the facts are is an empirical matter. But what logic presupposes, is this: namely, that there are simple objects and that the world consists of the obtaining and non‐obtaining of states of affairs. No elementary proposition can be a logical truth, since it is of the essence of the elementary proposition to be bipolar. But it is of the essence of a logical proposition to be necessary, so it must be unipolar. So all the propositions of logic result from combining elementary propositions. (For the sake of brevity and simplicity, I bypass Wittgenstein’s account of quantified propositions.) So logic presupposes that names have meaning and that elementary propositions have sense (TLP 6.124). So it presupposes that objects are the substance of the world, that they are constituents of states of affairs, and that the world consists of facts.
Logical propositions are combinations of elementary propositions by means of truth‐functional logical connectives. Contrary to what Frege thought, these are not names of properties (e.g., negation is not a property of a proposition) or of relations (alternation, conjunction, and conditionality are not relations between propositions). There are no such logical entities or “logical constants.” This Wittgenstein announces, is his Grundgedanke (TLP 5.4). The whole of logic flows from the essential nature of the elementary proposition. With its bipolarity, negation is given. From the possibility of successive assertion, conjunction is given. If negation and conjunction are given, then all forms of logical combination are given. The logical connectives are not function names, as Frege had thought, rather they signify combinatorial operations by means of which we generate various nonelementary propositions out of a given stock of elementary ones. If we are given two elementary propositions “p” and “q,” for example, we can generate four truth‐possibilities (TT, TF, FT, FF), and 16 different truth functions. Of all the possible truth functions, there are two limiting cases, namely, when the combination is true no matter what the distribution of truth values, and when it is false no matter what the distribution of truth values. These are limiting cases in as much as they say nothing: they are true come what may (tautologies), or false come what may (contradictions). So they give us no information about how things stand. So they are senseless (not nonsense, since they are well formed). They are necessarily true, or necessarily false. The former are the propositions of logic. The price that tautologies pay for their necessity, so to say, is their vacuity. They say nothing. They delimit reality in no way: for a tautology is compatible with any state of affairs whatsoever – it makes no difference. “p & (q v ~ q)” = “p.” But any tautology can be transformed into the form of a modus ponens, and so is correlative to an inference rule. All the propositions of logic say the same, to wit – nothing. So logic does not describe sempiternal relations between thoughts (propositions), as Frege supposed. Nor does it describe the most general truths in the universe, as Russell supposed. The propositions of logic describe nothing whatsoever. So there is no logical knowledge. So there can be no science of logic (there cannot be a science all the propositions of which say nothing). Logic is a calculus, and logical truths are not descriptions of anything. But they show the logical properties of the world.
The Tractatus advances a bold, elegant, and schematic logical atomist ontology of facts, sempiternal objects, and de re possibilities. It is schematic in as much as the book is a treatise on logic. So only so much is laid bare as is necessary to clarify the essential nature of logical combinatorics and to explain the nature of logical necessity and of the propositions of logic. What belongs to the analysis of elementary propositions themselves is of no concern to logic (all logic presupposes, as we have seen, is that names have meanings and elementary propositions have sense). For all logical propositions are consequences of truth‐functional combination, irrespective of the content of the elementary propositions thus combined. The analysis of the inner forms of elementary propositions belongs to the application of logic, which is not the concern of the book. It is striking that it was precisely to this that Wittgenstein turned when he resumed work in philosophy in 1929. It was then that he wrote “Some Remarks on Logical Form,” which gives us some idea of what he meant by analysis of elementary propositions. Notoriously, it was this paper that led to the collapse of the whole system of the Tractatus, and to a profound anti‐metaphysical turn.
The metaphysics adumbrated in the Tractatus, Wittgenstein thought, was required for the possibility of representation and for the possibility of logic. Things must be so, otherwise we could not represent things by means of language, and there could be no truths of logic. Side by side with this ontology, we have a metaphysics of symbolism, according to which only simple names can represent simple objects, only relations can represent relations, and only facts can represent facts. Conjoined with the metaphysics of symbolism, we have an array of metalogical principles linking language to reality. Language must be connected to reality – otherwise propositions could not “reach right up” to it. Propositions must agree and disagree with how things stand – otherwise they would lack sense. So propositions must be bipolar – otherwise they would not be able to do what they do, describe truly or falsely how things are. All these “musts” and “cans” Wittgenstein would later characterize as “dogmatism.”
On top of the ontology, the metaphysics of symbolism, and the metalogical principles Wittgenstein added, late in 1916, a bizarre form of transcendental solipsism conjoined with empirical realism (TLP 5.6–5.621). Space does not permit its description here (but cf. Chapter 30, WITTGENSTEIN ON “I” AND THE SELF; also Hacker, 1986, ch.IV). This was to evolve into the methodological solipsism of Philosophical Remarks, and thence to the brilliant demolition of solipsism and idealism in the “Blue Book” and the Investigations.
Two broad features distinguish the metaphysics of the Tractatus from previous metaphysical systems. First, Wittgenstein derived his metaphysical system from the (apparent) requirements of logic and representation by means of language, rather than from epistemological considerations. Secondly, these metaphysical sentences, by reference to the very doctrines propounded in the book, transgress the bounds of sense – for three interconnected reasons:
Consequently, as the paradoxical penultimate remark of the book explains, the sentences of the book serve as elucidations, i.e., clarifications (the expression “elucidation” is not a term of art, but the common or garden notion of making something clear). For anyone who understands their author will recognize them as deliberate nonsense. The nonsensical sentences of the book are, of course, not intelligible nonsense (that is an oxymoron). Rather it has been made intelligible that and why they are nonsense. The comprehending reader will have come to understand the limits of language and to apprehend what is shown by language but cannot be said. He will then see the world from a correct logical point of view.
Wittgenstein, as he wrote in the preface, believed himself “to have found, on all essential points, the final solution of the problems.” He viewed his work as the culmination, correction, and the perfection of the great tradition of Western philosophy. He had indeed made room for high metaphysics, but had demonstrated that its truths cannot be described in putatively metaphysical sentences. In that sense, they are ineffable. On the other hand they not only can be expressed or made manifest, they are inevitably expressed or made manifest, since they are shown by the forms of fully analyzed sentences of natural language.
The Tractatus ends with paradox. As Ramsey remarked, it is like the small child who, when instructed to say “breakfast,” replies “Can’t say ‘breakfast.’” Russell too found the doctrine of the ineffability of essences implausible: “after all, Mr Wittgenstein manages to say a good deal about what cannot be said” (TLP, Introduction). Carnap thought that Tarski’s methods of metalinguistic ascent showed how to circumvent it. In fact, none of them understood clearly why the propositions of the Tractatus are, according to the Tractatus itself, nonsense. But Wittgenstein, after 1929, patiently dismantled the Tractatus, showing what was right and what was wrong about it. It was not, he later remarked to Anscombe, just a pile of old junk, but a clock that didn’t work. As we shall see, in the 1930s he assigned a wholly different role to apparent metaphysical truths, namely as grammatical propositions that are actually norms of representation, i.e., rules for the use of words, in the guise of descriptions. And he gave a completely different account of the drive to construct metaphysical systems and of the consequent metaphysical confusions, namely as implicitly hankering after alternative forms of representation, as being mesmerized by the model of the natural sciences and their method of inference to the best explanation, and as illicitly crossing different forms of representation. We shall examine this below.
In recent decades, a new interpretation of the Tractatus has been vigorously propounded in the United States by a group of philosophers, led by Cora Diamond and James Conant. They became known as the New Wittgensteinians or American Wittgensteinians, and amusingly described themselves as “austere” and “resolute” in their puritanical interpretation of the nonsense of the Tractatus. Actually, their interpretation was not austere New England puritanism, but merely a postmodernist malaise of the time. Alas, when America sneezes, Britain catches cold, and the New Wittgensteinian interpretation severely infected some university departments in Britain too. Other British philosophers, in the traditional spirit of the British foreign office, tried to find a compromise between right and wrong by splitting the difference (cf. Chapter 10, RESOLUTE READINGS OF THE TRACTATUS and Chapter 11, INEFFABILITY AND NONSENSE IN THE TRACTATUS).
According to the New Wittgensteinian interpretation, one must resolutely embrace the penultimate sentence of the book, and not pretend that some nonsense (the nonsense of the Tractatus) makes more sense than any other nonsense. The simple fact, they insisted, which no reader of the Tractatus had yet been bold and resolute enough to confront, is that the book is simply gibberish, albeit written with the wit of a Zen master or a Kierkegaardian pseudonymist, in order to curb our natural desire to advance metaphysical pronouncements. Nonsense is nonsense, they austerely insisted. There can be no illuminating nonsense or elucidatory nonsense that deliberately tries to say what can only be shown.
But all this is mere postmodernist nonsense. It is an internally inconsistent interpretation. It violates every exegetical principle known to philosophical hermeneutics. It pays no attention to Wittgenstein’s remarks about what he was doing when composing the book. It pays no attention to everything Wittgenstein later wrote about the book. It pays no attention to what Wittgenstein later said to friends and pupils about the book. We shall deal with it briefly (for more detailed discussion, see Hacker, 2000, 2001b).
First, it is internally inconsistent in as much as the only reasons for thinking that metaphysical propositions are nonsense is given by metaphysical propositions concerning the essential nature of all possible methods of representation. If these are simply gibberish, then there is no reason at all for considering non‐tautologous necessary truths like “The world is everything that is the case” or “Red is a color” to be nonsense.
Secondly, the author’s preface to the Tractatus asserts that the book will be understood by some readers, namely by those who have had similar thoughts (which cannot be said about Edward Lear’s nonsense poems). It also presages the final sentence of the book in saying in advance that “what we cannot talk about we must pass over in silence” (TLP, preface). So there are things that cannot be said (which, as he later said to Russell, is the cardinal point of the book). The preface concludes with the bold assertion that the truth of the thoughts set forth in the book seems to the author “unassailable and definitive” and that he believes himself to have found, “on all essential points, the final solution to the problems.” Indeed, he wrote to both Russell and Keynes, that he believed that he had solved the problems they had been working on (and he did not mean either that their problems or that his solutions were gibberish).
Thirdly, in the body of the book, quite apart from the metaphysics, metalogic, and metaphysics of symbolism, Wittgenstein advanced a large number of highly compressed but immensely powerful criticisms of Frege and Russell, that are unquestionably meaningful (on the early Wittgenstein on Frege, see Hacker, 2001a; also Chapter 4, WITTGENSTEIN AND FREGE; on Russell, see Hacker, 1986, ch.II; also Chapter 5, WITTGENSTEIN AND RUSSELL). But, according to the New Wittgensteinians, Wittgenstein thought that these criticisms are just more gibberish.
Fourthly, while composing the book in 1916, as we noted, Wittgenstein remarked that his researches had led him from the foundations of logic to the essence of the world. So he cannot then have realized that he was writing carefully composed gibberish – that must have come later!! But, as we have seen, the distinction between what can be said and what cannot be said but only shown had already occurred to him back in 1914, when it became clear to him that internal relations cannot be expressed in propositions, but are shown by the symbols themselves (NM 115).
Fifthly, among the permanent achievements of the book, are deep insights into the nature of logic, supported by extensive argument, such as
that the propositions of logic are not descriptions of anything;
that they are not essentially characterized by generality, but by necessity;
that the tautologies of logic say nothing, but are correlative to rules of inference;
that the logical connectives are not names of logical functions (i.e., logical properties and relations), but are operators;
that all the logical connectives can be reduced to the single operation of joint negation, and all the truth functions can be generated by that operation;
that the truth tables provide a decision procedure for the propositional calculus;
that the T/F notation eliminates the need for any connectives in the propositional calculus, thus demonstrating their status.
All these insights are perfectly true and immensely important. They transformed our understanding of logic. But, according to the New Wittgensteinians, Wittgenstein held that all this is mere gibberish, supported only by pseudo‐argument (which it took six years to produce!).
Sixthly, in a very large number of later writings about the Tractatus and about what he wrote in it, Wittgenstein speaks of what he used to think, what mistakes he made and why, and of what he should have said. But, according to the New Wittgensteinians, he never did think that what he said in the book was true; he thought it was just plain nonsense (not mistake).
The Tractatus, as its author came to realize in 1929–1930, is not a consistent book. For the New American Wittgensteinians to try (unsuccessfully, as we have seen) to save its consistency by reducing it to intentional gibberish is not a licit hermeneutical method. It is merely a postmodernist one, which is neither austere nor resolute. What needs to be done is what the author of the Tractatus did between 1929 and 1945: to recognize the “grave mistakes” in his first book (as he confessed in the preface to the Investigations), to explain what they are and why he was tempted to make them, to strive to see clearly what he had seen only through a glass darkly, and to salvage from the wreck what was still valuable, even if it had to be cleaned up and repaired.
The tapestry of the Tractatus began to unravel in 1929 because of the color exclusion problem (cf. Chapter 1, WITTGENSTEIN’S PHILOSOPHICAL DEVELOPMENT). What this showed was that not all logical relations are consequences of truth‐functional composition. “A is red,” for example, entails that “A is not green (yellow, blue, etc.).” But this logical relation is not a consequence of any inner complexity or truth‐functional compositionality of “A is red.” This undermined the idea that the whole of logic is given with the mere idea of the essence of the elementary proposition as such. Once Wittgenstein pulled at this little dangling thread of determinate exclusion, the whole fabric came apart. Over the next two years, he came to realize that there are, and can be, no simple objects, as he had conceived of them. Whatever legitimate needs called simple objects into apparent existence are fully met by
Logic is indeed a calculus, but it is not a calculus that underlies every possible language. It is rather a grid that we can place over certain patterns of sentence‐sequences and derivations in natural language to determine formal validity. The world does not consist of facts, Wittgenstein now realized. (Rather, a description of (any part of) the world consists in a statement of facts.) Facts are not spatiotemporal denizens – they have no spatiotemporal location. Facts do not consist of objects in concatenation – they don’t consist of anything. So the ontology of the Tractatus was both incoherent and, as we shall see, unnecessary.
There are no elementary propositions, as he had conceived them. There are no simple names standing for simple objects. The meaning of a name is not an object it stands for. Sentences are not concatenations of names. They are not composed of names alone. Propositions are not facts, and a proposition does not say what it says in virtue of being a fact. So the metaphysics of symbolism had to be jettisoned. So the picture theory of representation had to be rejected. Names are not connected to reality by lines of projection, and meaning something by a sentence and by its constituent names is not the method of projection. There are no sense‐endowing or meaning‐endowing connections between language and reality. The sense of a sentence is not its agreement and disagreement with possibilities of the existence and nonexistence of states of affairs. The meaning of an expression is, in most cases, its use, and its use is given by an explanation of meaning. An explanation of meaning is a rule for the use of the expression explained. So there are no metalogical connections between language and reality, and there are no metalogical truths presupposed by any form of representation.
The calculus conception of language that characterized the Tractatus was swept away. As the spell was broken, the illusory metaphysical foundations disappeared. What had appeared to be wondrous jewels set in a golden crown was just a pile of old stones and rusty iron. Language is a human institution, a practice of communicative interaction in the stream of human life. It is indeed rule‐governed, but not in the manner of a calculus (cf. Chapter 24, RULES AND RULE‐FOLLOWING). The meaning‐determining rules for the use of words constitute the grammar of a language (cf. Chapter 14, GRAMMAR AND GRAMMATICAL STATEMENTS). Grammatical rules, unlike the previously envisaged rules of logical syntax, are not hidden – awaiting discovery by means of depth‐analysis. Rather they are visible to all in the practices of explaining the meanings of expressions, in correcting mistakes and in the practice of going by the rules. They are often open‐ended, dealing with cases that actually arise, not (impossibly) with all possible cases. The concept of a proposition is a family‐resemblance one, and propositions have no essence. In particular, a proposition is not essentially a logical picture, nor is it essentially a description of a possibility. Indeed, it is not even essentially a description. What had seemed to be the general propositional form, “This is how things are,” is merely a device for anaphoric reference to something already said, no different in principle from “That is how the cookie crumbles” (which plumbs no metaphysical depths). Bipolarity is indeed an important feature of many kinds of proposition, but not of all. Propositions of arithmetic and geometry, of ethics, aesthetics, and religion are indeed not bipolar, but they are perfectly well‐formed propositions for all that, and they belong to the family of propositions. So too, as we shall see in a moment, are “grammatical propositions,” which bring out into the light what good metaphysics saw only in the dark.
There are no metalogical concepts, and there are no metalogical connections between language and reality. So the problem of the intentionality of thought and language has to be confronted afresh. And so it is. In the Tractatus the problem was solved by means of the picture theory of meaning and a metalogical relation between word and world. Now Wittgenstein resolves it in terms of intra‐grammatical relationships between alternative descriptions without recourse to isomorphism between language and reality. The proposition does indeed “reach right up to reality,” for if it is true, what it says or describes is indeed what is the case. It is perfectly correct to say that if it is false then what it says is not what is the case. And it is also true that what it says is the same, no matter whether it is true or false. But although what it says when it is true is what is the case, it is not the same as what is the case, insofar as this means that one is dealing with one and the same entity. We must not confuse the relative Wh‐pronoun with the interrogative Wh‐pronoun. The question “What does the true proposition say?” and “What is the case?” have the same answer. Shared logical form does not enter the tale. The expression “the proposition that p” and the expression “the proposition made true by the fact that p” are simply two different ways of referring to the same proposition. The same goes for the two expressions “the proposition that p” and “the proposition made false by the fact that not‐p.” So, of course, it is one and the same proposition that is made true by the fact that p and is made false by the fact that not‐p. The harmony between language and reality is orchestrated in language, not between language and reality (cf. Chapter 15, THE AUTONOMY OF GRAMMAR). So what seemed like a metalogical relation between language and reality is no more than the grammatical coordination of two different ways of speaking of the same proposition.
So what is the fate of metaphysics? To be sure, we think of metaphysical propositions as necessary. However, the questions to confront are not “What is the source of their necessity?” and “How do we recognize it?,” but rather “Why do we conceive of them as necessary?” and “What is their role – how are they used, and to what purpose?” What appear to be necessary truths describing de re necessities, such as “Red is a color,” “One is a number,” “Nothing can be red and green all over,” “Red is more like orange than it is like yellow,” are in fact expressions of rules. Wittgenstein called them “grammatical propositions.” They are rules for the use of their constituent expressions in the guise of descriptions of reality. Of course, for anyone who actually knows what the constituent words of a grammatical proposition mean, such sentences convey nothing new. For those who do not, such sentences give partial explanations of the meaning, the use, of these words. Some are, in effect, inference rules. If you have three cushions, one red, one orange, and one yellow, then you may infer, without more ado, and without looking, that color‐wise the first cushion is more like the second than it is like the third. If you know that something is red all over, you may infer, without more ado, that it is not green all over. And so forth. Such propositions are rules of grammar, not descriptions of necessities in nature and, so too, not synthetic a priori metaphysical truths.
Such propositions are humdrum affairs. But their truth has long puzzled philosophers, since they are obviously “necessary truths” and, equally obviously, they are not true in virtue of the laws of logic and explicit definitions. So they seemed to be “synthetic a priori propositions.” The supposition that they describe de re necessities seemed irresistible – until Wittgenstein showed that they are expressions of norms, not statements of metaphysical fact. Of course, rules are not true or false. But there is nothing unusual about saying of the statement of a rule that it is true (e.g., that it is true that the chess king moves one square at a time). To say of a grammatical proposition that it is true is simply to say that a rule of grammar runs thus. But what of more general and august examples that have captured the attention of meta‐physicists throughout the ages, such as the principle of causality, “Every event has a cause”? This principle, insofar as we do actually accept it, is the expression of commitment to a very general norm of representation to the effect that it always makes sense to ask of any event what caused it, and that it never makes sense to say that nothing caused it. It is doubtful, despite Kant, whether we are committed to this rule of representation. However, one might argue, as Collingwood did, that it was a commitment of Newtonian physics.
The “must” of such apparently metaphysical propositions is indicative not of a de re necessity, but of a commitment to a rule of use. The rule, of course, is not necessary – there are no necessary or contingent rules (cf. Chapter 21, NECESSITY AND APRIORITY and Chapter 15, THE AUTONOMY OF GRAMMAR). But the appearance of an objective necessity in nature is the shadow which the rule of grammar casts upon the world. What follows, according to a rule that is partly constitutive of the meaning of its constituent expressions, appears to be an objective necessity in nature. If something is red, then it must be colored; if something is red all over, it cannot also be green all over; if something is red, then it must be darker than anything pink; and so on through the geometry of color that determines its internal relations. But the “must” adds nothing to the “follows” of “If A is red all over, it follows that it is not green all over.” And this “follows” is indicative of a rule: in this system of representation, this may be inferred from that.
Most grammatical propositions, once stripped of their metaphysical finery, are obvious to any speaker of the language. After all, they are partly constitutive of the meanings of words familiar to us all. They express inference patterns and combinatorial possibilities we employ daily. They are news from nowhere, and if they were really news, they would be nonsense (e.g., that colors are merely ideas in the mind; that no material object is really colored). Nevertheless, it is false that grammatical propositions are always immediately obvious. For the mastery of the use of ordinary (i.e., nontechnical) words, which is possessed by all competent speakers, does not imply mastery of their comparative uses or awareness of all analogies and disanalogies with the uses of other words. In the Investigations, Wittgenstein shows us that there cannot be a private ostensive definition, i.e., an analogue of a public ostensive definition, but which uses a recollection of a sense‐impression as a sample (see Chapter 28, PRIVACY AND PRIVATE LANGUAGE). He then goes on to show that there cannot be a private language, that is, a language the names of which refer to experiences that only the subject has and that only he knows. These claims look as if they are making metaphysical statements about what cannot be the case, i.e., disclosing hitherto unknown impossibilities in nature. But these kinds of proposition are grammatical propositions. “There cannot be” amounts to “there is no such thing as” (not: “Try as you may, you will not…,” but rather “There is nothing to try!”). And “there is no such thing as a private ostensive definition (or private language)” amounts to this: the word sequence “private ostensive definition” (or “private language”) makes no sense, has no use, and is excluded from the language. It is correct that these propositions are anything but obvious. They are the upshot of reductio ad absurdum arguments, each step of which, when properly laid forth, is indeed obvious. In this respect they are similar to the reductio ad contradictionem arguments characteristic of impossibility proofs in mathematics. The conclusion of such reductio ad absurdum arguments may well be an unobvious grammatical proposition (e.g., there can be no transparent white glass = there is no such thing as transparent white glass = the string of words “transparent white glass” is excluded from our language).
What is left of metaphysics, what can be salvaged from its castles in the air, are merely rules for the use of expressions in our language. Does metaphysics not deal with the objective, language‐independent natures and essences of all things? No, the a priori nature of things is determined by grammar (PI §§371–3), and grammar itself is autonomous. Grammar is not answerable to reality in the currency of truth. It is not a mirror of the scaffolding of the world, but the scaffolding from which we describe the world. The world has no scaffolding, and what looks like scaffolding is merely the shadow of grammar. Is metaphysics not concerned with the essential, great, and universal features of reality? No, there are no such features – only the illusion of such features (BT 407). What is left of the majesty of metaphysics are merely rules for the use of very general or very important expressions in our language, such as “substance” and “property,” “cause” and “effect,” “space” and “time,” “mind” and “body,” and “I” (cf. Chapter 29, THE INNER AND THE OUTER; Chapter 30, WITTGENSTEIN ON “I” AND THE SELF; and Chapter 37, WITTGENSTEIN ON CAUSATION AND INDUCTION). Descriptive metaphysics, as Peter Strawson used this expression, is just more linguistic (grammatical) analysis, at a high level of generality.
Does this mean that the great metaphysical systems of the past are all mere nonsense? – That the whole endeavor was worthless? No. Wittgenstein remarked to Drury:
Don’t think I despise metaphysics. I regard some of the great philosophical systems of the past as among the noblest productions of the human mind. For some people it would require a heroic effort to give up this sort of writing.
(Drury, 1973/96, p.105)
Philosophical systems of the past often contain great conceptual insights, seen through a glass darkly. They raise deep problems that need to be confronted. Their mistakes are great mistakes from which there is much to be learnt. But “this sort of writing” must indeed be given up. For it is now clear that metaphysics, conceived as an investigation into de re necessities and impossibilities, is an illusion. To be sure, to those who are accustomed to pursuing this holy grail, renouncing it may be as difficult as holding back one’s tears, or as giving up an addiction.
At one stage, when he was contemplating the second book that he wanted to write in repudiation of his earlier vision, Wittgenstein remarked that it seemed to him that it would be right to begin his book with remarks on metaphysics as a kind of magic. Of course, he added, the depth of this magic must be preserved. After all, is it not deep magic that gets us to believe that nothing is really colored, that material objects are not really solid, that one cannot really know whether the sun will rise tomorrow, and that a person is really his brain? (And, of course, when a meta‐physicist says that things are really thus‐and‐so, that means that they really aren’t.) Breaking the spell of metaphysics is a major task of philosophy, and this too involves a kind of magic (MS 110, p.177).
So it was that Wittgenstein, in the early 1930s came to think that one of his major tasks was to hunt metaphysics down in all its hidden lairs. What then is the mark of metaphysical propositions? The essential thing about metaphysics, he thought, is that it obscures the distinction between factual and conceptual investigations. Metaphysics characteristically gives the appearance of being concerned with factual problems: What are the fundamental constituents of reality? What is the nature of substance? Are colors real? – whereas in fact all the problems are conceptual (see Z §458). The pseudo‐empirical air is deceptive, for it is not as if the results of metaphysics are amenable to empirical confirmation or refutation. No experiment could prove that there are universals; or that falling trees on uninhabited desert islands make no sound; or that there is something (“inexpressible”) that it is like to be a bat. Equally deceptively, the meta‐physicist presents the results of his super‐physics as necessary: their negation is, he insists, impossible. Things must be so, for the contrary is unimaginable or inconceivable. So metaphysical propositions seem to be substantial truths about the world, but nevertheless a priori. Of course they do, Wittgenstein explained:
The avowal of adherence to a form of expression, if it is formulated in the guise of a proposition dealing with objects (instead of signs) must be ‘a priori’. For its opposite will really be unthinkable, inasmuch as there corresponds to it a form of thought, a form of expression, that we have excluded.
(Z §78)
This requires clarification.
When Berkeley declares that there are no material objects, that reality consists only of ideas and spirits, he does not mean that the chair on which he is about to sit will not hold his weight. When Hume declares that people are but bundles of perceptions, he does not mean that one cannot talk to them, fall in love with them, merrily dine and wine together with them. The great metaphysical systems of the past purport to tell for the first time what the world is really like, but in fact, nothing changes (a solipsist still calls for a doctor when his wife is ill). For what looks like an insight into the essential nature of the world, is actually the expression of an inchoate dissatisfaction with our existing grammar or form of representation, and a confused recommendation of an alternative grammar. Meta‐physicists purport to make geographical discoveries, whereas all they are actually doing, at best, is redrawing the administrative boundaries in the landscape (BB 57). Nevertheless, it would be misleading to say that alternative forms of representation make no difference. They make no difference to the facts, but they make a difference to the way in which we view the facts. The difference between two distinctly tailored suits makes no difference to the form of the body they clothe. But they make a great deal of difference to the way it looks.
Now, there is nothing amiss in wanting to draw new boundaries: it amounts to recommending different concepts and inference patterns in a given domain of thought. What is amiss is to think that one is rejecting false boundaries, and discerning the real boundaries (the real Devonshire, the meta‐physicist proclaims, is not where you think it is at all, it is over here, where I say it is (BB 57)). What is even more misguided is to proclaim that real boundaries are not administrative conventions at all – they are adamantine herms “set in an eternal foundation, which our thought can overflow, but never displace” (Frege, 1893, p.xvi). Worst of all is to suppose that our existing concepts that are part of our present conceptual scheme, really signify the new boundaries that the meta‐physicist purports to have discovered. For then one crosses two different grammars, and produces news from the Metaphysical Times: nothing is really solid; colors are really ideas in the mind; only I really exist; the past does not really exist.
What explains this intellectual malaise? The dissatisfaction with our existing grammar typically rests upon the distorted apprehension of a genuine feature of grammar. It is perfectly true that the first‐person pronoun is not used in the same way as the other personal pronouns: there is here no such thing as reference‐failure or misidentification. So the meta‐physicist (e.g., Descartes) concludes that it is a super‐referring expression that never fails to hit its target, namely: one’s self. On rebound from this, unable to find anything in experience to which “I” refers (no “self” to be encountered in introspection), another meta‐physicist (Hume) concludes correctly that we are not selves, and incorrectly that we are no more than a bundle of perceptions. Whereas the simple fact is that “I” is not a referring expression at all; or, if you prefer, it is a limiting, degenerate, case of a referring expression (as a point is a limiting case of a conic section). The meta‐physicist (e.g., Descartes) correctly notes that perceptual statements are not incorrigible, and that when we are unsure of what we perceive, we can always withdraw to “It sensibly seems to me just as if…” He then jumps to the conclusion that the latter kinds of statement (Cartesian “thoughts,” Lockean ideas, or sense‐datum statements) are certain, infallible, and incorrigible and that they constitute the foundations of empirical knowledge; that they are the causal effects of objects; that they are the grounds for inferences to the best explanation (the causal theory of perception). On rebound from this unverifiable principle, other meta‐physicists (idealists) conclude that what we take ourselves to perceive (e.g., material objects) are really mere collections of seemings, of ideas in the mind. Yet others (phenomenalists) conclude that material things are logical constructions out of sense‐data. The solipsist observes correctly that self‐ascription of experience is wholly unlike other‐ascription, notes that in one sense he cannot have another’s experience, and concludes that all experience is his experience. He fails to see that in the sense in which it is correct that I can’t have your experience, I can’t have my experience either. (For “my experience” = “the experience I have”; so “I have my experience” = “I have the experience I have” – which, far from expressing a deep metaphysical insight, says nothing at all.)
Dissatisfied with the existing grammar of some segment of our language, typically misconstrued, the meta‐physicist presents us with the “ultimate hidden truth” about reality. But his revelations are, in effect, no more than recommendations, typically mangled and incoherent, to adopt a new system of representation. So the phenomenalist tells us that the world consists of nothing but sense‐data; but what this actually amounts to is that we should abandon a material object language in favor of a sense‐datum language. But this is incoherent, because a sense‐datum language is essentially a fragment of our existing grammar, and is unintelligible when severed from it (like chess without the king). The solipsist, impressed by the use of the first‐person pronoun, asserts “Only I really exist!,” “I am the center of the world,” or “Only my experience exists.” But “I” belongs to the same grammatical system as “you,” “he,” and “she.” If it makes no sense to ascribe experience to others, then it makes no sense to ascribe it to oneself. We can imagine a language in which “I” has no privileged role. It would be a language without any personal pronouns at all. Instead of Jack saying “I have a pain,” he would say “There is pain,” and instead of “Jill has a pain,” one would say “Jill is behaving as Jack behaves when there is pain.” In such a language, no one could be said to have a pain. But doctors would not go out of business, and people would still need analgesics.
A feature of metaphysics is the tendency to idealize ordinary expressions, and to give them a “special metaphysical sense,” which is typically no more than a special philosophical confusion. So, in the true sense of “certainty,” we are informed, only the propositions of mathematics are really certain; in the proper sense of “know,” one cannot know the future; in the real meaning of “name,” what are ordinarily called “names” are not really names at all – the only real names are “this” and “now.” So too, the meta‐physicist discovers, as Frege announced he had, that truth and falsehood are really a pair of coordinate logical objects that are values of functions for arguments. Or he discovers that there really are no vague propositions: that apparent vagueness disappears on analysis; or that it is merely an epistemic defect; or that what seem to be vague concepts (e.g., the concept of a Christian) are not really concepts at all. And he discovers that “exists” is not really a predicate: it really is a second‐level function name – and that is why one cannot meaningfully say things we all say, e.g., that God does (or does not) exist, that Moses really did (or did not) exist.
So a further task for philosophy, Wittgenstein suggested, is to bring ordinary words back from their metaphysical use to their normal, everyday use (PI §116). We need to be reminded that it is no part of our ordinary use of “knowledge” that something counts as knowledge only if all possible doubts have been excluded – all we need do, before we claim to know something, is to ensure that all actual doubt has been excluded. We should remind ourselves that “I” is much more like “now” than it is like “he” – and that “now” does not refer to, but signals, a time. We must bear in mind the fact that the simultaneous occurrence of an eclipse of the moon and a court case is not, pace Frege, an object, just as knowing something is not what we call “being in a certain mental state” (pace Williamson), and understanding something is not a process. If it is said that these are special philosophical uses of “know,” “name,” “object,” “mental state,” and that the philosopher has as much right to introduce new technical terms for the purpose of a philosophical theory as scientists do, then we must show that this is a muddle. For scientists construct verifiable or falsifiable theories that are tested against experience, experiment, and observation. But metaphysics produces no testable hypotheses. The propositions of metaphysics are not confirmable or refutable by experience or experiment. Its putative theories are pseudo‐theories. There are no theories in philosophy in the sense in which there are theories in science. The purported “special technical terms” are no more than misconstruals of ordinary terms. This is a consequence of misunderstanding the workings of our conceptual scheme, and projecting our own misunderstanding onto the grammatical forms that we misconstrue. Of course, none of this means that philosophers may not introduce special technical terms for purposes of philosophical classifications and typologies.
The main inspiration for metaphysics typically lies in the culture of the day. It is therefore unsurprising to find Wittgenstein observing that the main seedbed for metaphysics in our times is science. Our culture is, overwhelmingly, a scientific, technological culture. If there is a serious problem, then, we are prone to think, it must have or will have, a scientific answer. So we turn to science to tell us whether the world is really multicolored or whether colors are mere illusion. And it tells us that nothing is actually colored. We are baffled at the nature of the mind. So we turn to science, and are told that the mind is really the brain. We wonder whether our will is free, and neuroscientists tell us that the motor centers of the brain are active 350 milliseconds before we even felt a decision or an intention to act. We are puzzled by the nature of morality and its dictates. So we turn to evolutionary sociobiologists, who advise us to study the morality of chimpanzees. Science is ill equipped to combat such scientism. The task of showing that it is nonsense, and to explain why it is nonsense, falls to the philosopher who has understood how to break the spells of intellectual illusion. That task is of capital importance.
Metaphysics, Wittgenstein showed, is not a science. It is not even a legitimate part of philosophy. The criticism of metaphysics is a part of the dialectic of philosophy, of the logic of illusion. The task of good philosophy is to curb the metaphysical impulse, to dispel its beguiling magic, and to expose its legerdemain.