§1.1: the question of a priority
‘A priori’ (from the Latin word which gives us prior, or before) contrasts with ‘a posteriori’ (posterior, or after); the terms are used to mark a central fissure in epistemology. In contemporary discussion, ‘a priori’ is used to designate a putative non-empirical source of justification.1 Debates surrounding the existence and nature of the a priori thread through the history of philosophy, connecting with and underlying various other questions, issues, and debates. Broadly speaking, the many varieties of rationalists believe in some or other version of the a priori, as do many moderate empiricists. In contrast, the very idea of non-empirical justification is dismissed as, at worst, incoherent, or, at best, unhelpful, by many proponents of radical empiricism, naturalism, and skepticism.
At first pass, something is justified a priori if and only if the grounds for believing it do not depend on sensory evidence. A plausible candidate for being justified a priori is:
1. One cannot steal one’s own property.
To determine whether one is justified in believing that [1] is true, one need not take a poll to find out how many people agree, or devise a variety of experiments to test whether one could succeed in stealing one’s own property.2 One’s justification for believing [1], it seems, has nothing to do with that kind of evidence. Some of our beliefs are justified empirically (e.g., ‘There is an apple pie baking nearby,’ based on an olfactory experience; ‘This piano is out of tune,’ based on an auditory experience). Most philosophers hold that not all of our knowledge can be so justified, and so posit the category of a priori justification. In particular, from at least Plato on down, many have held that some of our knowledge is universal, necessary, and simply immune to counterexample, and that such knowledge could not possibly be justified empirically.
Truths of logic (such as [2]), mathematics ([3]), and ethical principles ([4]) are commonly cited candidates for instances of a priori justification:
2. No proposition is at once both true and not true.
3. Two is a factor of every even number.
4. One ought to keep one’s promises.
We will consider these and other candidates at greater length in due course.
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The epistemological notion of a priority is a close relative of the metaphysical notion of necessity and the semantic notion of analyticity. One central thing that these three concepts have in common—and which, to a large extent, accounts for why they are of deep and enduring philosophical interest—is that all are tightly linked, in some way or other, to what we might call immunity to counterexample.3 Further, little attention was paid to such fine distinctions between these three concepts, traditionally, because it was largely presumed that they are co-extensive.4 So, for example, contemporary philosophers may be inclined to read Hume’s (1748: Sect. IV, Part 1) discussion of the category of ‘Relations of Ideas’ as involving a murky, indiscriminate mixture of epistemological, semantic, and metaphysical considerations. (Much the same could be said of Hobbes’ or Locke’s discussions of ‘trifling propositions’5—even more so of Plato’s epochal discussions of the Forms.) For another example, Pap (1958: Ch.1) documents ways in which Leibniz uses interchangeably terms which no longer seem so obviously tightly linked—including ‘necessary,’ ‘universal,’ ‘eternal,’ and ‘certain.’ Whether it be Descartes’ (1641) guiding assumption that ‘conceivable’ entails ‘possible,’ or Kant’s (1781: B15) presumption that necessity is a criterion for a priority, variations abound on the theme that a priori, analytic, and necessary are but different aspects of the same phenomenon.6
In recent decades, there have been some grand shocks to traditional presumptions about the relations between these concepts. One blow comes around 1950 with attacks by Quine (among others, but most famously) on the analytic/synthetic distinction.7 Many have felt that Quine’s arguments against analyticity are decisive, and also raise serious concerns about the concepts of a priority and necessity; others have responded with serious questions both about the cogency of Quine’s argument against analyticity, and about the allegation that these arguments even remotely touch on those other concepts. Another jolt comes around 1970, with Kripke’s arguments, in the wake of some groundbreaking arguments for semantic externalism, that necessity and a priority are not co-extensive concepts—that is, that there are necessities which are not knowable a priori and things knowable a priori that are not necessarily so.8 Kripke poses a challenge not only to certain kinds of rationalism, which hold that one can infer necessity from a priority or vice versa, but also, more generally, to a wide variety of inferences which immediately, or implicitly, slide back or forth among such roughly overlapping but distinct concepts. Kripke’s arguments, too, have provoked a flood of discussion. A third, related shock to the traditional world-order concerns developments in the semantics of indexicality, and in multi-dimensional logics—see especially Kaplan (1989), Stalnaker (2001). This work has further complicated relations between various different senses in which something may (appear to) be immune to counterexample. One goal of this book is to make a contribution toward a clear-headed evaluation of the coherence and significance of a priority, and its relations to necessity and analyticity, in the wake of these developments.
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For starters, I will begin the job of sketching fairly precise working conceptions of the terms ‘necessary’ and ‘analytic.’ The goal is to specify concepts that are refined enough so that specific theses about their interrelations with a priority can be tested, but yet are not out of touch with their broad historical roots. I will start this job in a preliminary way here; this part of the ongoing project will continue through Parts I and II.
Necessity is a concept of metaphysics. To say that something is necessary is to say that it could not fail to be—regardless of time or place, and irrespective of how contingent matters of fact may be altered. Necessary truths are absolutely unalterable, and we have no choice or influence in the matter. Putative examples of necessary truths include:
5. No two solid objects can simultaneously occupy the same spatial location.
6. Increasing an object’s velocity will increase its momentum.
As Kripke (1972) stresses, necessity, per se, has nothing to do with anyone’s knowledge of anything. That something is necessary does not immediately entail any epistemological or semantic conclusions. Necessary truths are a matter of how things stand in mind-independent reality, and are something about which all humans could be mistaken or ignorant.9
As distinct from both ‘a priori’ and ‘necessary,’ ‘analytic’ is a semantic notion. First and foremost, it has to do with meaning, or semantic content. A truth is analytic if and only if it is true by virtue of the meanings of the terms involved; alternatively, the denial of an analytic truth is contradictory. Candidates for analyticity include:
7. Squares have four equal sides.
8. No grandmothers are childless.
To call something analytically true is to say that the meanings of its parts, and the way in which they are combined, suffice to ensure that it is immune to counterexample. So, it is not hard to see why the notion of analyticity has been put to work in both epistemology and metaphysics. (After all, there are close constitutive connections between linguistic meaning and the content of our beliefs, as well as between meaning and the language-independent objects of most of our thought and talk.) On the epistemic front, provided that just grasp of the meanings involved is sufficient for recognizing that an analytic statement is true, it is plausible to think that analyticity may hold the key to a satisfactory theory of the a priori. On the metaphysical front, there have always been philosophers who are wary of the idea that necessity is an objective feature of mind-independent reality. Down this avenue, there is a temptation to think that perhaps the source of our intuitions of necessity resides in language, and in our conventional categories—that is, that what many have mistakenly thought to be metaphysical necessity is more clearly and helpfully characterized as analytic truth.
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To sum up, let me stress the prima facie difference between these concepts. First, to ask whether something is necessary is to ask: Could this possibly be false, should contingent matters go (or had gone) otherwise? Second, to ask whether something is analytic is to ask: Does the meaning of the constituent bits, plus the mode of composition, suffice to ensure that this is true? Lastly, to ask whether something is a priori is to ask: Are we justified non-empirically in believing this to be true?
There will obviously be considerable overlap between these three concepts; but the traditional presumption that they are but different guises of the same underlying phenomenon is no longer very plausible. In Part IV, to help develop my own favored constitutive a priori approach to the question of a priority, I will chart interrelations between these three concepts.
§1.2: some historical background
The following is an outline of the broader history of some relevant philosophical debates. It sketches some core themes running through much of Western philosophy, in a way that will be used to structure much of the succeeding discussion.
Necessity is a metaphysical concept. To say that something is necessary is to say that it could not fail to be—regardless of time or place, and irrespective of how contingent matters of fact may be altered. Necessary truths are absolutely unalterable, and we have no choice or influence in the matter. The concept of necessity is integral to systematic inquiry. Many great leaps forward for human knowledge take the form of discovering that some phenomena—such as fertile soil, lightening, or the plague—are not in fact randomly scattered and unconnected from the rest of nature, but are rather intrinsically related to other phenomena by general principles that are rooted in the very nature of things. In one crucial sense of ‘understanding,’ we understand some phenomenon when we know where it stands in a nexus of causes, laws, and effects such that, given the antecedent conditions and the laws of nature, the phenomenon is necessitated: it could not but happen. Necessary truths, those which capture the features of the world that could not be otherwise, are a very special subset of the set of truths, a set in which philosophers—as well as mathematicians, scientists, and many others, of course—have long been interested.
The epistemological notion of a priority (i.e., justification which does not depend on experiential evidence) is also central to systematic thought about human knowledge. Indeed, this notion of that which can be known to be true just by thinking about it, as opposed to requiring some process of gathering evidence, is sometimes taken to be definitive of the subject matter of the discipline of philosophy. A prevalent (though by no means unanimous or uncontroversial) idea is that discovering or justifying things via thought is to philosophy what discovering or justifying things via the experimental method is to science.
An ancient theme in philosophy concerns the fit that exists between the two concepts of necessity and a priority. In one direction, there is good reason to think that only necessary truths can be known a priori: that is, it is hard to see how one could obtain knowledge of accidental contingencies, of matters of fact that could very well have been otherwise, just by thinking through the content of our concepts. In the other direction, it also seems fairly evident that the only things which can be known a priori must be necessary truths—for if something is contingent, and so varies according to circumstances, how could we know that it is true just by reflecting on the content of our concepts?
In due course we will see that both of these putative connections have been questioned (i.e., there are plenty of reasons to doubt whether all, or only, metaphysical necessities are knowable a priori). However, our immediate concern is with a related but distinct thesis about the connection between necessary and a priori, which has long been a matter of controversy: Plato believed, as many have since, that we have a priori knowledge of necessary truths, that our faculty of reason permits us direct access to certain necessary features of reality. Since many pertinent debates within epistemology and metaphysics date back to Plato’s thought, it will prove worthwhile to explore some of his ideas.
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One key problem that leads Plato to make this claim (i.e., that we have a priori knowledge of necessary truths) is to explain how it is that some of the things that we know seem to be fashioned from the hardest of steel—that is, to be timeless, self-evident, and, quite simply, not conceivably false. I will call this ‘Plato’s problem’:
Plato’s problem: Given that our personal experience is confined to a particular limited perspective, how can we account for our evident knowledge of timeless general certainties?
Take the simplest of examples, ‘2+2=4,’ to illustrate. Such truths exhibit a remarkable indifference to contingent facts and to psychological processes: the facts could change—about how humans count, or how computers calculate, for example—but neither of these sorts of concerns would have any effect on whether two of anything added to two other things equal four things.10 Before anyone ever thought of it, two of anything added to two of anything yielded four; even if most people were mistaken about it, that mistake would not take one of the four away, or add one to it. What makes it true that two of anything added to two of anything yields four does not depend on any particular fact, or on how many people agree with it. What makes it true is, it seems, a general necessary feature of the mind-independent nature of things.
Plato—among many other subsequent thinkers—held that many other kinds of truth, not just mathematics or logic, also have this status of being necessarily true and knowable a priori. (For instance, many have thought that moral truths, such as that one ought to keep one’s promises, or that murder is wrong, are a priori necessities.) The important point for now is the problem raised by our knowledge of these certainties, which are fashioned from the hardest of steel. Some of the things that we know, it seems, are entirely indifferent to particular matters of fact, and are not determined or constrained by the particular perspective from which the knower arrives at them. Rather, they just cannot be false. Plato’s problem is to explain the nature and ground of these hardest-of-steel truths, and of our grasp of them, given the particular and limited nature of our experience. All human experience is finite, particular, contingent; yet some human knowledge is universal and necessary. What must our minds be like, in order that we can come to know such things? What must mind-independent reality be like, in order that such things are knowable about it?
Plato’s seminal answer consists of the metaphysical claim that mind-independent reality must be underlain by an unchanging necessary order, and the epistemological claim that the human mind must have some channel of direct access to this order. His view is that we can attain rational insight into the timeless general features of reality, in virtue of a certain distinctive cognitive faculty, which is capable of a priori knowledge of necessary truths. Here is an excerpt from the dialogue ‘the Phaedo’ in which Plato discusses this faculty, in the course of exploring our ability to grasp such concepts as justice, beauty, and goodness:
[One] attains to the purest knowledge of them who goes to each with the mind alone, not introducing or intruding in the act of … any other sense together with reason, but with the very light of the mind in her own clearness searches into the very truth of each.
[To attain such knowledge one must have] got rid, as far as [one] can, of eyes and ears … these being … distracting elements which when they infect the soul hinder her from acquiring [this kind of transcendent, non-sensory] knowledge.
And thus having got rid of the [limitation to sensory evidence] we shall be pure to hold converse with the pure, and know of ourselves the clear light everywhere, which is no other than the light of truth. (65e–66b)
In the first paragraph here, Plato contrasts this rational faculty of mind, this ‘very light of the mind in her own clearness,’ with the senses (i.e., empirical justification). (It is common among subsequent rationalists to follow Plato in speaking of rational intuition as a kind of mental seeing.) In the second paragraph he asserts that one must ignore the information coming through sensory channels, one must turn off these distractions as much as is possible, in order to really get this rational faculty of mind up and running. In the final paragraph he says that, insofar as one is able to do so, one is then free to mentally tap into the realm of eternal necessary truth.
Let us distinguish these two constituent elements of Plato’s solution to Plato’s problem:
Plato’s metaphysical claim: there are timeless unchanging features of mind-independent reality, underlying the fleeting appearances which we experience, and grounding necessary truths. (This claim is known as ‘metaphysical realism.’)
Plato’s epistemological claim: our minds are endowed with a special faculty, distinct from the senses, by means of which we have cognitive access to necessary truths. (This non-sensory faculty of mind is commonly called ‘rational intuition,’ and commitment to it is called ‘rationalism.’)
Note that both terms ‘metaphysical realism’ and ‘rationalism’ are used rather diversely, and these are but one of many technical senses of each term. To be sure, though, these are, both historically and conceptually, central senses of these terms.
For instance, Descartes (1641) and Russell (1912) are both rationalists, in that they hold that we have a priori access to necessary truths, but this does not imply that they accept all of Plato’s views on the precise nature and workings of rational intuition, or that they themselves do not disagree on pertinent questions. There is lots of room for substantive disagreements among rationalists, as I am using the term. In particular, even though—by definition, in this sense—all rationalists would accept Plato’s distinction between rational intuition and sensory justification, many succeeding, more moderate, rationalists would reject the extravagant claims Plato makes in the second and third paragraphs in the above excerpt. (There is much more extensive discussion of this issue below, first in §1.4 and subsequently throughout Parts II and III.)
[§]
Plato’s realism and rationalism have always had their detractors. Both elements of Plato’s platform have been judged by many to be beyond belief—that is, skepticism surrounds both the metaphysical claim that there are necessary truths lurking out there, beyond the bounds of space and time, and the epistemological claim that we have some faculty for gathering knowledge, in addition to our senses, which taps us into them. What are these queer truths, exactly, that the rationalist claims to be able to see, and what, precisely, is the faculty that provides these obscure visions? Many find the appeal to rational intuition to be hopelessly obscure and unexplanatory, and to just simply not come close to a satisfactory solution to Plato’s problem. Several different philosophical debates, over the ages, have turned on these and related disagreements between Platonists and their opponents.
Empiricism, the doctrine that all knowledge comes from experience, is a longstanding opponent of rationalism. This defining tenet of empiricism stems precisely from skepticism about the appeal to rational intuition. Empiricists’ criticisms, and empiricists’ own distinctive problems, will come up at several junctures in this book. Philosophical naturalism is a variant of empiricism that is, currently, widely associated with Quine’s (1951, 1960, 1969) influence. Naturalism involves privileging the natural sciences as the highest or best sort of knowledge that humans have ever developed, and so holds that other disciplines (including philosophy) ought to remain consistent with the natural sciences, as much as is possible. Naturalism is opposed to the positing of other-worldly Platonic objects, or mysterious occult faculties of mind, on the grounds that science gets on fine without them, and they do not seem to have aided or abetted philosophical progress. (There exists nothing supernatural.) Naturalistic pessimism as to the coherence and worth of a priority will come up at several junctures below.11
Some opponents of Platonism have taken a dismissive stance on Plato’s problem—their response is to deny that we ever attain knowledge of timeless general certainties. One key benefit of this skeptical stance is that one avoids having to face certain epistemological and metaphysical problems; however, the price is that one cannot invoke the notions of necessary truth or a priori knowledge. Most philosophers hold that, despite the difficult problems they bring with them, these notions are indispensable to a satisfactory account of our knowledge of the workings of the world. There are considerable reasons to hold that immunity to counterexample just simply is a brute, undeniable datum.
So, many opponents of Platonism have nonetheless felt the pull of Plato’s problem. There is a strain of anti-Platonism that concedes that we do attain absolute certainty, at least (but not necessarily only) in the case of mathematics and logic; and so, even though Plato’s answers may raise more problems than they solve, still there must be an explanation of these truths, and of our grasp of them. Thus, many attempts have been made to explain how it is that some of the things we know are immune to counterexample, in a way that does not posit obscure faculties of mind intuiting queer abstract objects. Here is where the notion of analyticity gets added into the mix.
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In contrast to both ‘necessary’ and ‘a priori,’ ‘analytic’ is a semantic notion. Just grasp of the meanings involved is sufficient for recognizing that an analytic statement is true. For this reason, many have thought it plausible that analyticity holds the key to Plato’s problem: we have a priori knowledge of necessary truths, so the idea goes, because those truths are analytic. The hope is that analyticity provides an explanation of a priority which is less obscure than rational intuition: that is, all truths knowable a priori are analytic, and that they are analytic explains why they cannot be false.
Hence, within this strand of anti-Platonism, the tight link between a priority and analyticity develops into a semantic, conventionalist solution to Plato’s problem: it is the conventional regularities governing the usage of our words that determines what is necessarily true and knowable a priori. Analyticity holds some promise to explain how it is that some of the things we know exhibit this remarkable indifference to contingent facts and to psychological factors. Many proponents of this line of thought hold that the air of profundity surrounding Plato’s problem is confused obscurantist puffery, that Plato’s problematic metaphysical and epistemological claims—that is, about a mysterious realm of truths and about a mysterious kind of mental access to it—could be avoided by a better semantic theory. In short, many within the empiricist tradition have thought that analyticity could afford a simple, comprehensive solution to certain epistemological and metaphysical questions. All that is worth wanting about Platonic rational intuition can be delivered by the humbler and less problematic faculty of understanding (i.e., mere competent grasp of meaning).
To sum this up, then: Well into the twentieth century, those who take Plato’s problem seriously—that is, those who reject the relevant form of skepticism, and so concede that we do attain knowledge of some certainties—fall, roughly, and with many variations, into two main groups. First, there are the many varieties of rationalism, which explain a priori knowledge by positing a faculty, distinct from the senses, that acquires such knowledge. Second, there are those who seek explanations of our grasp of certainties without appeal to rational intuition (a central paradigm case of which are those who appeal to analyticity to solve Plato’s problem).
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There is one further important stop on this orienting historical overview, as the view I develop and defend in Parts III and IV relies on Kant’s (1781) innovative approach to Plato’s problem. Kant initiates a radical stance concerning the relation between mind and world. At (1787, [Bxvii]), Kant uses the following analogy to explain the hypothesis: astronomers prior to Copernicus had assumed that they are stationary and that the stars revolve around them; Copernicus tried the hypothesis that observers on earth are in motion and the stars are, relatively, at rest, and the result was a great leap forward in our understanding of the universe. In the analogy, the empiricism which Hume had followed to its skeptical end—more specifically, the notions that the mind is a passive recipient of information, and that all knowledge consists of sensory input and inductions therefrom—is compared to pre-Copernican astronomy. Kant’s innovative Copernican hypothesis is the idea that the mind plays an active role in synthesizing and categorizing sensory input—that is, the mind is the director, as opposed to the audience, in conscious experience.
This Copernican Turn is precisely what puts the ‘constitutive’ in the ‘constitutive a priori.’ For Kant here foregrounds what has become known as the ‘constitutive powers of mind’—that is, the active, structuring role which the mind can be seen to play in conscious experience. I will argue that this move, as interpreted and developed by certain figures in mid-twentieth-century philosophy, affords the grounds for the best overall solution to Plato’s problem. (Here I am following Coffa [1991: 263], who reads Carnap and Wittgenstein as extending Kant’s Copernican Turn from its original target of experience and epistemology on into the realm of meaning and semantics.)
Hume is taken by Kant to have demonstrated the impossibility of grounding in experiential input the consistency and regularity of the world, thereby proving that empiricism can afford no satisfactory answer to Plato’s problem. Kant’s hypothesis is that, to some extent, the mind constructs and constitutes this consistency and regularity. Kant provides a theory of a non-empirical source of knowledge: there are active faculties of mind, constitutive powers of mind, which categorize and give form to the matter supplied to mind via the senses, and thereby structure and constitute our knowledge.
The cornerstone of Kant’s philosophical edifice is the synthetic a priori judgment. According to Kant, synthetic a priori judgments are logically possible in that the concept of a synthetic judgment does not entail or contain the concept a posteriori, and neither does a priori entail or contain analytic. Synthetic a priori judgments are possible for agents like us, given the Copernican hypothesis that the mind is an active synthesizer of sensory input. Kant (1781) is dedicated to establishing the legitimacy of these synthetic a priori judgments, on the grounds that this hypothesis does something that none of the alternatives can: namely, account for our actual knowledge. Given the hypothesis that some of our judgments are contributions to, rather than inductions from, experience, there is conceptual space for judgments which are substantial extensions of human knowledge, unlike trivial analytic judgments, but which are not given in, or generalizations from, experience.
According to Kant, as in the case of Copernicus’ Revolution, what we have here is a huge theoretical step forward. As the constitutive powers of mind ground synthetic a priori judgments, synthetic a priori judgments ground the process of inquiry itself. For the first time, we have an explanation of how pure reason—a priori cognition—can increase the volume of human knowledge. Prior to Kant, there is analysis, an a priori activity that cannot really tell us anything we did not already know (according to Kant, anyway, though as we will see in §3.2, Frege [1884] and others will depart from Kant on this point), and there is observation and induction. Hume showed us how little knowledge can be secured by those two faculties, unaided. What Kant believes he has discovered is a type of a priori knowledge, which is universal and necessary, but yet which has real empirical bite, which can constitute significant extensions of human knowledge. For Kant, all significant scientific advances (such as the principle of the conservation of matter) and all mathematical truths (such as ‘a2 + b2 = c2’) are synthetic a priori judgments—that is, they go well beyond experiential input, and they add to our knowledge of the subject concept. All significant advances in inquiry consist in the discovery and elucidation of synthetic a priori judgments, judgments such as ‘Every event has a cause’ and ‘Humans are free agents who are subject to moral law.’ Given the possibility of these universal necessary judgments that constitute genuine extensions of the body of human knowledge, their importance to philosophy or to human knowledge generally cannot be overestimated.
Developing exactly how my own constitutive a priori view departs from the letter of Kant’s theory is one of the main orders of business of Parts II and III below.
§1.3: metaphysics, semantics, epistemology
As has already become evident, our inquiry sprawls across many distinct but interconnected subfields of philosophy. Chief among those are epistemology, semantics, and metaphysics; so some brief orienting remarks on those subfields is in order. For one thing, there is some diversity and fluidity as to how people understand and employ these terms, and so it is important to stipulate precisely how I will use them. Further, this should help to clarify some theses about their interrelations which are subsequently developed. One of my goals in this book is to employ a certain stance on a priority to make a contribution towards a refined conception of the nexus at which these three core subfields within philosophy overlap—particularly with a view to incorporating the many important lessons learned in twentieth-century philosophy.
A point that pertains to the structural order of presentation: Up to here, the narrative order has gone: (i) necessity, then (ii) a priority, then (iii) analyticity. That order is historically accurate—after all, recognition of the importance of semantic questions per se emerges at a relatively late point in philosophical sophistication. However, this order will be henceforth changed, to put semantics in the middle, between metaphysics and epistemology—where it belongs conceptually, as opposed to historically. That is the distinctive geography of the semantic, between mind and world, as meanings are intricately connected both to our beliefs and intentions and to mind- and language-independent objects which most of those beliefs and intentions concern or involve.
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Etymologically, the term ‘metaphysics’ relates to the book that is situated within Aristotle’s corpus after the Physics. The Physics is a study of nature and of natural changes, events, and forces. In the Metaphysics, Aristotle pursues more general and abstract questions. He refers to his pursuit as the study of being qua being—that is, the study of the most general and necessary features something must have in order to count as a being. What sorts of thing exist? Into what categories do they fall? What properties are there in common among existent things, or among these categories?
Over the centuries, ‘metaphysics’ has come to be applied, more generally, to inquiries into the nature of reality that go beyond or behind the methods of science. Whereas scientists aim to characterize some specific range of objects, events, and forces, metaphysicians address such questions such as: What are objects, or events, or forces? The scope of metaphysics is broader than that of the physical sciences—examples of questions that are not scientific but metaphysical include:
1. What is causation?
2. What are moral values?
3. Are numbers mind-independent, or human constructions?
Metaphysics, then, names a rather large sub-field of philosophy, which overlaps with many different strains of inquiry. Whether a certain thing or kind of thing exists, how to distinguish the essential from the accidental properties of something, whether or not distinct things belong in the same general category—these are (at least in part) metaphysical questions. Some core metaphysical debates, through the ages, concern the nature of space and time, exactly what sorts of things minds are, or whether all that exists are concrete particulars. Quite generally, though, metaphysical questions are prone to arise in the course of virtually any inquiry—be it scientific (e.g., Do electrons really exist?), medical (e.g., What exactly is a virus?), legal (e.g., Who exactly count as persons?), and so on.
Semantics is the study of meaning, of the relations between linguistic signs and what they mean or represent. Philosophers have long been interested in semantics because the abilities to represent something specific in thought, and to prompt someone else to consider what one is representing in thought by producing sounds or symbols, are fundamental and distinctive human capacities. So, insofar as we want to know what makes up our cognitive lives, and what makes possible many of the distinctive achievements of our species, some understanding of the semantic properties of thought and language is indispensable.
Semantics is one core component within the sprawling interdisciplinary inquiry into our capacities to represent and communicate using the medium of language (which also involves linguists, psychologists, literary theorists, computer scientists, and so on). Some of the greatest leaps forward in twentieth-century philosophy have come in the field of semantics, and an important legacy of these developments is the explicit appreciation that there is a semantic dimension to any philosophical issue or question.
The word ‘epistemology’ means ‘the study of knowledge.’ The aim of any inquiry—from physics to economics to trying to figure out the best place in the yard to plant tulips—is to acquire knowledge. What, then, is knowledge? What distinguishes knowledge from mere opinion? What is the best method, or methods, of acquiring knowledge? Theoretical work on the concept of knowledge is central to philosophy, because knowledge is presupposed as the target of all manner of debates, endeavors, and projects. Knowledge is valuable, both intrinsically and practically, and so it naturally occurs to us to think about how to acquire it, and how to ensure that one’s beliefs count as knowledge. To do so is to do epistemology.
A core question in epistemology is: What distinguishes knowledge from mere opinion? Can we define sufficient conditions such that, if they obtain between a subject and some object, then the subject attains knowledge of the object? Epistemologists seek to identify and characterize the most reliable paths to knowledge, and to understand what makes these paths reliable. Which beliefs count as justified, and what makes them so?
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Many philosophical questions have metaphysical, semantic, and epistemological aspects—consider, for example, the questions about electrons, viruses, and persons mentioned above. In practice, it can be awfully hard to distinguish these aspects. That is, it is difficult to separate out matters of mind- and language-independent metaphysics from our beliefs about them and from the meanings of the words we use to represent them; or to separate questions about the meanings of words from metaphysical assumptions about what the words refer to and from epistemological issues about beliefs associated with the word; or to try to philosophize about knowledge in abstraction from semantic work on defining the relevant terms and metaphysical work both about what minds are and about what there is to be known. In short, it may seem like a hopeless artificial abstraction, to try to neatly separate out metaphysics from semantics from epistemology.
Nonetheless, since it is the case that many complex philosophical issues have these different metaphysical, semantic, and epistemic dimensions, exacting philosophy is marked by meticulously heeding these distinctions.12 A key point which will loom large in the landscape to be charted herein is that metaphysical questions are questions about mind- and language-independent reality. Strictly speaking, questions of metaphysics are indifferent to human thought and talk, even if, in practice, it can be difficult to pry metaphysical issues so cleanly apart from our beliefs about them and from the meanings of the words which we use to discuss them. (For example, if we are wondering whether or not some phenomenon ought to be classified as a virus, there is a mind-independent metaphysical fact of the matter that we are trying to discern; even though various semantic and epistemological factors irreducibly shape and mold the contours of our investigation.) As will be extensively developed below, this point about mind- and language-independence underlies and grounds some important differences between necessity, on the one hand, and analyticity and a priority, on the other.
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Appeal to a putative, controversial sort of cognition will play a key role at many junctures below. I will call it ‘semantic intuition,’ and it is what is involved in grasping meanings, or understanding concepts. For example, it is via semantic intuition that one knows that all squares are four-sided, and that no grandmother is childless. (Other sorts of cognition are obviously involved in acquiring such concepts as ‘square’ and ‘grandmother’; but it is one’s source of justification for the belief that [say] all squares are four-sided that is of primary interest here, not the question of what it takes to acquire these [or indeed any] concepts. This important distinction between the cause of belief and the justification for a belief is extensively discussed in §4.1.) How is it that we are so sure that tomorrow scientists will not announce the discovery of a three-sided square, or of a grandmother who was not previously a mother? There surely seems to be a kind of immunity to error in this kind of case, in virtue of what these terms mean. As we will see, semantic intuition is also implicated in various kinds of philosophical issues.
One important question about semantic intuition is exactly how it relates to rational intuition, as defined above in our discussion of Plato’s problem. (Is it a kind of rational intuition? Or an alternative to rational intuition?) Further, both Quine (1951) and Kripke (1972) (among several others) have raised serious challenges for otherwise compelling presumptions about semantic intuition. In any case, semantic intuition will eventually play a role in our considered understanding of the notion of a priority, mapped out in Part IV.
§1.4: summary
I begin this section with a quick summary of some core distinctions and stipulations (including the introduction of a couple of terms which have not yet come up), to help to structure what follows.
[1: a priori] A central fissure running throughout the history of philosophy, and which is our primary focus herein, concerns whether an adequate epistemology must countenance a non-empirical (i.e., a priori) source of justification. Those who say YES are motivated (at least principally, among other things) by considerations of adequacy—that is, no epistemology which eschews the a priori can provide an adequate account of human knowledge. Those who say NO are motivated (at least principally, among other considerations) by considerations of obscurity—that is, appeal to a priority is too obscure to be of any (real, concrete, non-metaphorical) help in solving Plato’s (or indeed any) problem.
On some ways of understanding the rationalism/empiricism divide, the above fissure is the core point of contention in that ancient doctrinal divide; but not so on mine. On my orientation, all rationalists, and some but not all empiricists, are proponents of a priority. I will call empiricists who are proponents of a priority ‘moderate empiricists’ (and take Hume [1748], Ayer [1936], and Boghossian [1997] to be exemplars), and empiricists who explicitly avoid any appeal to a priority ‘radical empiricists.’ Maddy (2000, 2007) and Devitt [2005, 2011] provide recent examples; they are typical of the species in taking Quine’s naturalism as providing motivation and inspiration.
It is a matter of some contention whether radical empiricism inevitably collapses into skepticism—for example, BonJour (1998) argues that it does, but that is not how the radical empiricists see it. (There are, of course, several distinct varieties of skepticism, distinctions between which would have to be sifted through in order to really get to the bottom of this.) One could even take the claim that to eschew the a priori is not (yet) to endorse skepticism to be precisely one of the core defining tenets of philosophical naturalism.
[2: rational versus semantic intuition / acquaintance-based versus understanding-based theories of a priority] I use the term ‘intuition’ in a way that is somewhat idiosyncratic, though by no means out of touch with its broad historical roots. ‘Intuition’ names the source of this (putative, alleged) non-empirical justification; and so (as I am using these terms) all proponents of a priority are ipso facto committed to some or other variety of intuition. Hence, all rationalists and some but not all empiricists hold that some such faculty is a necessary ingredient of an adequate epistemology; while radical empiricists completely dismiss intuition (at least in this sense of this diversely used term) as hopelessly obscure.
Hence, ‘intuition’ is a broad and vague notion. One important, preliminary distinction to draw within the category is that between rational intuition and semantic intuition (‘preliminary’ in that each might turn out to have multiple distinct sub-varieties). ‘Rational intuition’ is a (putative, alleged) distinctive non-empirical faculty of mind—often described as a kind of mental seeing—posited as that which is distinctively involved in cases of a priori knowledge. The passage from Plato’s Phaedo cited above provides a paradigm, seminal description of rational intuition (‘very light of the mind in her own clearness’); the classical Modern rationalists (such as Descartes [1641], Leibniz [1704]) provide others, as do some of the great logicians of the twentieth century (Russell [1912], Godel [1944, 1947]). To endorse rational intuition is to more or less adopt what I above call ‘Plato’s epistemological claim,’ in the discussion of Plato’s problem.
I will call such views ‘acquaintance-based’ theories of the a priori, for their positing this distinctive relation between minds and objects of a priori knowledge. And I will call those who posit this sort of rational intuition—or, equivalently, endorse this kind of acquaintance-based approach to a priority—radical rationalists. Bealer (1996, 2000), BonJour (1998), and Chudnoff (2011, 2014) are some recent defenses of varieties of radical rationalism.
Acquaintance-based theories of the a priori can be contrasted with ‘understanding-based’ theories, which tend to talk in terms of semantic intuition, not in terms of rational intuition. The difference is that understanding-based theories are not committed to a distinctive (relatively mysterious) faculty of mind (or to some obscure kind of ‘mental seeing’). Rather, the idea is that all that we need for an adequate account of our universal, necessary knowledge is a thorough account of what it is to possess, grasp, or understand a concept. Semantic intuition is thus taken to be the (humble) faculty of mind involved in understanding concepts, or grasping meanings—to which we are already committed anyway, apart from consideration of Plato’s problem. Many compelling attempts to solve Plato’s problem without taking on Plato’s bold epistemic and metaphysical commitments have had semantic intuition (and the related notion of analytic truth) playing a central role.
In this region of the map, it can be hard to tell the difference between the moderate empiricists and moderate rationalists (i.e., those who identify as rationalist but tend to fashion their account of a priority more along the lines of semantic intuition—as opposed to acquaintance-like, rational intuition; Peacocke [2000, 2004] is a contemporary example of a self-styled moderate rationalist). Perhaps the difference is no more than that the empiricists take semantic intuition to be a categorical alternative to rational intuition, whereas the rationalists take semantic intuition to be more of a specific, relatively benign kind of rational intuition. Or perhaps, when it comes to excavating the nature and workings of semantic intuition, a more substantive divide will emerge, between moderate empiricists and moderate rationalists.
There have been times and places at which people have been tempted to distinguish these moderate empiricist/moderate rationalist camps by posing diagnostic questions about the synthetic a priori.13 However, as we will see in some depth in what follows, the analytic/synthetic distinction is in at least as much need of excavating and bolstering as the a priori/empirical distinction. Another, related, fairly common way to draw this divide among moderates is to ask whether a priori knowledge can be about (mind- and language-independent) reality, or rather whether its scope is confined to mind- and language-dependent matters (cf. Cassam [2000] for investigation). However, both the challenge of revisability and the externalist challenge cloud this way of dividing the rationalists from the moderate empiricists. These matters are extensively discussed in Part III.
[3: the constitutive a priori] The constitutive a priori is situated in this neck of the woods—either a close relative of, or a variety of, the semantic intuition, understanding-based accounts of a priority developed by moderate empiricists and by moderate rationalists. (Cf. the Preface above for a brief overview, and Part III below for extensive detail.) Given its explicitly Kantian flavor, it should come as no surprise that it maps onto the ancient rationalism-empiricism dividing lens in complicated ways.
The main aim of this present work is to investigate and further develop the myriad ways in which the notion of the constitutive a priori (i) provides an insightful, satisfactory way to approach Plato’s problem, and, more generally, (ii) affords an illuminating and insightful way to understand this nexus at which semantics and the philosophy of language overlap with epistemology and metaphysics.
[§]
A central organizing theme of the present work is that there have been two main shocks to the world-order, when it comes to issues surrounding a priority, over the last several decades: that is, the challenge of revisability (cf. especially Quine [1951]) and the externalist challenge (cf. especially Kripke [1972]). (Aforementioned developments in the semantics of indexicality are deeply significant in themselves, and also interrelated with both of those challenges. However, while they are integrally relevant to the entire discussion (cf., e.g., §§2.2, 7.3), they do not play as central a role in the organizational structure of the book.) Here I will give a programmatic overview of the way in which my constitutive a priori approach incorporates these challenges; the details will be fleshed in as the work proceeds.
One epochal consequence of their collective upshot is that they reinforce a firm split between analyticity and a priority on the one hand, and metaphysical necessity on the other hand.14 Analytic truth and a priori knowledge should be understood as framework-relative and revisable—though immunity to counterexample is still preserved, in an important but limited sense. The revisability of analytic truth is entailed by the recognition that languages are organic entities which change over time. For example, on my view, it was once analytically true that whales are fish, and that there can be no such thing as a sub-atomic particle (since ‘indivisible’ was once constitutive of the meaning of ‘atom’). However, given the subsequent changes in the relevant frameworks (and, relatedly, the changes in the meanings of the terms ‘fish’ and ‘atom’), those things are (obviously) no longer analytically true (in any contemporary dialect with which I am familiar).
Given the close, constitutive links between linguistic meaning and mental content, many similar points will also hold of a priority. The root of the close links between analyticity and a priority lies in the fact that the (epistemic) frameworks which are constitutive of our beliefs are themselves (at least partly) constituted by (semantic) meanings. One main sub-theme herein is to defend the coherence and worth of the resultant refined notion of a priority, taking into account this kind conceptual evolution. I will argue that the development of the notion of the constitutive a priori—a pillar in common among recent work inspired by Kant, Carnap, and Wittgenstein—provides the best means to incorporate the challenge of revisability.
The externalist challenge, too, will certainly have drastic effects on our maps of this complex terrain, undermining as it does traditional conceptions of seamless, transparent connections between our concepts and their extensions. However, the range of the externalist challenge is properly limited by judicious sub-categorization within the lexicon—that is, the relevant arguments apply rather differently to ‘Aluminum is a metal’ versus ‘Widows are formerly married women whose spouse has died.’ The notion of semantic deference will turn out to be crucial for understanding the upshot of the externalist arguments: that is, to the extent that a speaker is deferential in their use of a term, the speaker does not have transparent access to the content being entertained or expressed. Further, deference is appropriate to most typical uses of natural kind terms (as well as to many sorts of uses of proper names). As Kripke (1972) shows, externalism about reference and content opens up a gap between metaphysical necessity, on the one hand, and the semantic and epistemic modalities, on the other hand.
However, there is a principled limit to the range of this externalist gap—between what constitutes the sense and what determines the reference, to borrow Frege’s (1892a) familiar terms. (Compare Loar [1991: 120]: ‘Social meanings do not deprive me of semantic autonomy when I insist on it.’) To the extent that the speaker exhibits semantic autonomy, and is not deferential, then the speaker has transparent access to the content being entertained or expressed, and the externalist gap does not open up. Furthermore, there are vast ranges of the lexicon (e.g., ‘and,’ ‘hunter,’ ‘bachelor,’ ‘triangle,’ ‘chair,’ ‘ball,’ ‘spoon,’ etc.) concerning which autonomy is more appropriate than deference, and hence to which the externalist arguments have little applicability.15
Many traditional tenets will be preserved in the resulting overall maps of the terrain sketched in Part IV. There are (framework-relative) analytic truths, and they are one and all knowable a priori. The converse does not hold though—one of the many important morals of our refined understanding of indexicality is that it provides relatively uncontroversial instances of things which are justified a priori but not analytically true (e.g., ‘I am conscious’). Metaphysical necessity will turn out to be a completely different matter than either a priority or analyticity, particularly when it comes to the aforementioned case of deferentially used natural kind terms. (For example, ‘Water is H2O’ might be necessarily true without being either analytic or a priori.) There is nothing framework-relative or revisable about necessary truths; and hence many traditional habits of transitioning between necessity and either of the other two concepts—in either direction—have been undermined.
[§]
Onwards then with developing the case that the constitutive a priori can help us to reach a richer understanding of the relations between these metaphysical, epistemic and semantic varieties of immunity to counterexample, and ultimately of Plato’s problem.
NOTES
1. This notion of ‘a priori’ has been the predominant one at least since Kant (1781). In some earlier usage, the ‘a priori’/‘a posteriori’ contrast depended on whether reasoning went from causes to effects or from effects to causes; and so Descartes’ (1641) ‘a priori’, for example, is not exactly Kant’s or ours—though there is significant overlap. Clearly, though whatever it might have been called at the time, the notion of non-empirical justification was clearly involved in the work of Plato, Descartes, and most other major pre-Kantian philosophers.
According to Burge (2000: 13), Leibniz was the first to define the now standard notion of a priority, which is commonly associated with Kant. Pap’s (1958) thorough analysis of this notion of a priority also begins with Leibniz. For a good overview of historical issues pertaining to a priority, cf. Hanson & Hunter (1993); and for a good recent statement of the centrality of the a priori to a variety of philosophical debates, cf. Peacocke (2006).
2. It has been objected that [1] is a bad example because it is subject to counterexample in cases of co-ownership. I do not think that this putative counterexample succeeds—if you and I co-own something, to whatever degree, I could only possibly steal your part of it, not the part that is already mine. However, this objection does help to show just how difficult it is to come up with an uncontroversial example of a priority.
The notion of the constitutive a priori developed in Parts III and IV will help to explain why this is so—that is, while a priority is coherent and significant, it is framework-relative, all frameworks are more or less constantly under revision, and many distinct frameworks can be simultaneously pertinent to any given question or issue.
3. There is a growing body of literature which distinguishes between such claims as that a priori knowledge, or analytic truth, is (i) universal, (ii) eternal, (iii) indefeasible, etc. (Cf. Casullo [2003] for discussion of the case of a priority, and Russell [2008] for discussion of various distinct senses of analyticity.) We will get into such fine distinctions in Part II.
4. See Kripke (1972: 38–9) for a nice brief statement of the grounds for thinking that all and only necessary truths can be known a priori; this point is also further developed below in §1.2. As for ‘analytic’, there are also considerable grounds for tight connections between it and each of these other two concepts. Indeed, historically and conceptually, much of the interest in analyticity has stemmed from its promise to illuminate the concepts of necessity and a priority.
5. For discussion of Hobbes’ views see Munsat (1971: 19–20); Locke’s discussion occurs at (1690: Bk. IV, sect. 8).
6. Kant’s (1781) famous attempt to distinguish ‘a priori’ from ‘analytic’ is one notable effort to the contrary. However, as we will see, Kant’s efforts at establishing an analytic/synthetic distinction have not withstood scrutiny. Canonical critical discussions include Frege (1884), Quine (1951).
7. In addition to Quine, other seminal work pertaining to what I am calling the challenge of revisability (cf. Part III for extensive discussion) was done by Mates (1950), White (1950), and Goodman (1952).
8. Kripke (1972) is the most thorough and influential source, when it comes to the externalist challenge (cf. Part III for extensive discussion). Other important contributions include Donnellan (1970), Putnam (1975), Burge (1979), and Kaplan (1989).
9. To be sure, this does presuppose a certain degree of realism, which some might find controversial. The relevant degree of realism is nicely articulated by Stalnaker (1984: ix) as follows: ‘The world is the way it is independently of our conceptions of it, and the object of inquiry is to find out the way the world is.’ I will not offer any arguments, to try to convince those who cannot tolerate even that degree of realism; though it is important to note how much more cautious and conservative it is than are many of the notions of ‘metaphysical realism’ floated by philosophers who seek to criticize or reject realism (e.g., Putnam [1992]).
10. Note that we are not talking about the symbols, but about what they signify: We might have spoken a language in which the sentence ‘2 + 2 = 4’ means that seven is even, or that Bob’s your uncle; but that would not be a situation in which two of anything added to two of anything would fail to be equal to four of them. There is further discussion of this important point in §2.1.
11. Experimental philosophy is a recent development within this naturalistic tradition; and there is a growing body of literature dedicated to sorting out whether it has any deep or drastic relevance to the a priori. I will not pursue that question herein. Cf. Weinberg (2014) for an insightful account of how the tools and methods of experimental philosophy can be seen to supplement, rather than undermine or overthrow, traditional a priori tools and methods. As should become clear by Part III (cf., e.g., the discussion of Wittgenstein [1969] in §6.1), this idea that the a priori and the empirical are not discrete containers, but are rather commonly blended together, in complex ways, in the course of inquiry, is also a guiding tenet of the constitutive a priori orientation.
12. For example, one cannot sufficiently justify any metaphysical conclusion using only epistemic or semantic premises. To illustrate, consider what is known as a ‘fallacious appeal to ignorance’—for example, no one can prove that P is false; therefore P. Among the problems with this pattern of reasoning is that its premise is purely an epistemic one (about who knows what), while its conclusion is a metaphysical claim to which such epistemic considerations, while relevant, cannot be considered decisive. Many other such issues pertaining to transgressing borders between these different sub-disciplines will be discussed below. (Cf., e.g., note 14.)
13. Indeed, many proponents (e.g., BonJour [1998]) and opponents (e.g., Aune [2008]) of rationalism alike hold that rationalism is an interesting and significant position only if Kant is right that there are synthetic a priori judgments. Otherwise why fuss about rational intuition, if it is unable to amplify and add to the store of human knowledge?
14. Hence, for example, on the view defended in Parts III and IV, conceivability absolutely and unequivocally does not entail metaphysical possibility. Conceivability is a main source of evidence about possibility, but it is deeply defeasible evidence. Conceivability tells us—first and foremost—about concepts, not about their referents or extensions; and it is the extensions of concepts which are relevant to questions of metaphysical modality.
15. This lack of an externalist gap between what is constitutive of the sense and what determines the reference is, significantly, also evident in the case of the so-called ‘a priori sciences’ of logic and mathematics. More on this in Part III (especially §§6.2 and 6.4–5).