§4.1: fleshing out the concept ‘a priori’
At first pass, a priori knowledge is knowledge whose justification does not depend on sensory evidence. In the classic sense of the term ‘empirical,’ that is, ‘via the senses,’ the a priori/a posteriori distinction corresponds to the non-empirical/empirical distinction.
This particular usage of the terms may just date back to Kant or Leibniz, but the distinction they mark is as old as philosophy itself: the existence and nature of a priori knowledge is an absolutely central, core issue throughout the history of philosophy. For one thing, as the cases of at least Plato, Descartes, Kant, Frege, and Quine illustrate, some seminal, original philosophical systems and stances have grown out of work on the nature of the a priori. For another thing, a philosopher’s view about the existence and nature of the a priori is inextricably linked to not only various other issues in metaphysics, semantics, and epistemology, but also to their conception of the discipline of philosophy as a whole—including in particular its proper methodology and its scope or range (cf. Peacocoke [2006]).
I began §1.1 above by motivating the claim that ‘one cannot steal one’s own property’ is a strong candidate example of being justified a priori. For another plausible candidate, compare what it would take to be justified in believing the following:
1. Squares have four sides.
2. Neptune has four moons.
For both [1] and [2], understanding the sentence affords a grasp of what would have to be the case for it to express a truth. However, for the case of [1], this understanding also and thereby justifies the belief that what is expressed is true. One need not to take a poll to find out how many people agree, or devise a variety of experiments to test whether one could succeed in constructing a three- or five-sided square, in order to be justified in believing that [1] is true. Although one is justified in believing [1], this justification has nothing to do with that kind of empirical evidence. This might be taken to be a basic, straightforward example of immunity to counterexample, grounded in (some or other variety of) non-empirical justification.
Not so for [2], in which case understanding it does not come remotely close to providing justification for believing that what it expresses is true. Even though I know exactly what [2] means, I have no justification as to whether or not it is true. (Note that it is far from clear that a correlative claim could coherently be made about [1].) Case [2], it seems, could only be justified empirically—akin to cases like ‘There is an apple pie baking nearby’ or ‘This piano needs tuning,’ discussed in §1.1 above.
Further examples of beliefs that are justified a posteriori include my beliefs that it is not currently raining here now, that it rains more frequently in England than in Arizona, and that it is hard to find a direct flight from England to Arizona. Reason, by itself, is not able to afford a grasp of the truth of such statements. (One needs to stick one’s head out the door, or to travel a bit, or to ask meteorologists or travel agents.) Some of the things that some philosophers have argued are justified a priori include elementary truths of logic and mathematics (e.g., ‘No number is both even and odd’), and certain fundamental truths about human beings (e.g., Plato holds that it is knowable a priori that humans have immortal souls; he and others have argued that many moral truths [such as that one ought to keep one’s promises] are also knowable a priori). There are good reasons to doubt that empirical justification could suffice to support these claims; so, it seems, one must either be skeptical that we know them, or else hold that there is a priori justification.
More generally, most philosophers have held that not all of our knowledge can be seen as empirically justified, and so posit the category of a priori knowledge. In particular, from at least Plato on down, the prevalent view is that some of our knowledge is simply immune to counterexample, and that such knowledge could not possibly be justified empirically.
As discussed in §1.2, philosophers who are comfortable with talk of a priori knowledge tend to talk also of rational intuition—that is, the non-empirical faculty of mind involved in a priori justification. Opponents counter that this appeal to rational intuition is merely a label for the problem, not a solution to it, that such appeals to mysterious inexplicable faculties are too obscure to be of any help in rigorous epistemology. The rationalist then counters that no epistemology which denies that there is a priori knowledge is at all adequate to the task of a satisfactory account of our actual human knowledge. Variations on this theme of the obscurity objection to rationalism versus the adequacy objection to empiricism make up a main thread running through the history of Western philosophy.
Some influential variations within this debate are focused on the notion of analytic truth and semantic intuition, and their potential to provide a non-obscure but adequate solution to Plato’s problem. Relatedly, many significant recent episodes have involved the development of understanding-based accounts of a priority, as distinct from acquaintance-based accounts. These themes will be revisited and further developed, especially throughout Part III below.
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Even more so than the cases of ‘necessary’ and ‘analytic,’ there are several different—overlapping but nonetheless prima facie non-equivalent—objects to which the term ‘a priori’ is attributed. To what, precisely, does the term ‘a priori’ appropriately apply? It is not uncommon to find the label ‘a priori’ affixed to, among other things: (i) concept, (ii) inference, (iii) proposition, (iv) truth, (v) knowledge, and (vi) justification. Some useful refinements will emerge from discussing some of the relative merits of these notions.
I will take the notion of an (i) a priori concept first. An important refinement prompted by consideration of this notion is that a priority is distinct from innateness—despite there being some broad and deep connections between these two notions. That is: the claim that one’s knowledge that P is justified a priori does not entail that no experience is required to acquire the concepts needed to grasp P. It is not the claim that all of the concepts involved are innate, or in every sense self-evident, that they can be acquired without causal and communicative interaction with one’s environment and linguistic community. (Indeed, I am suggesting that ‘One cannot steal one’s own property’ is justified a priori, and of course a range of experiences are required in order to acquire the concept of property.) One may need experience to get the concepts, which one can then exploit in cultivating a priori knowledge. What matters for the a priori/a posteriori distinction is whether interaction with, experience of, the specific object of the specific belief is sufficient to justify belief in its truth. Even if I may need to undergo some kinds of experience in order to acquire the concept of number, I do not need acquaintance with every number, to consider each case individually, in order to know that all numbers are either even or odd. In contrast, I do need some kind of contact with the weather in England and the weather in Arizona, by personal experience or the testimony or expertise of others, in order to know that it rains more in England than in Arizona.
Kant (1781) and Frege (1884), among others, are very clear on this point. A priority is not innateness; claims of a priority are compatible with various sorts of important role for experience, when it comes to conditions for acquiring various sorts of concept. What matters is the justification for the specific item of knowledge in question, not its psychological cause. ‘A priori’ is a term of normative epistemology, which applies to relations between concepts; it is not a psychological term, which applies to how in fact this particular person came to have the particular conceptions, or beliefs about those concepts, which they have.
To be sure, the Modern rationalists who were such influential friends of a priority were also quite up to their necks in claims about the innate, God-givenness of much of human knowledge. Plato is another influential example of someone who believes strongly in both rational intuition and innateness. (Famously, Plato taught that all knowledge is recollection—cf., for example, the Meno.) However, the fact that lots of smart people believed in both A and B does not entail that A = B. There are important differences between a priority and innateness, and that is one of the main reasons why I will not speak at all in terms of (i) above, the notion of an a priori concept.
Now as for (ii), the notion of an a priori inference: to be sure, this is an important concept historically and conceptually, tied up as it is with such notions as logical truth, entailment, validity, etc. However, this present work does not directly venture into the philosophy of logic, in any sustained way. First and foremost, inferences pertain to relations between propositions; whereas my primary interest here is in properties of propositions. (Generally, relations between concepts are also and thereby properties of propositions; but questions about relations between propositions arise at another level of inquiry.) In any case, a priori will not be directly applied to inferences below either.
So, what then of (iii) a priori proposition or (iv) a priori truth? ‘A priori truth’ is certainly a common locution in philosophy, and this notion is closely related to the core epistemological distinction that is our present focus—for if a piece of knowledge does not depend on experiential evidence, then it seems that there must be something special and distinctive about the proposition which is the object of knowledge. So, an a priori truth would be something which can be known to be true without sensory evidence.
However, the question of the distinctive status of such truths or propositions seems rather clearly to be, at least to a considerable extent, a semantic question; whereas here we are stalking a distinction that is epistemic (at least: as purely so as is possible). Henceforth, I will avoid the notion of ‘a priori truth’—at worst, it is a potentially misleading label for analytic truth, at best it is a shorthand for one of the more purely epistemic notions to be developed below.
Likewise for (iv), ‘a priori proposition.’ While I am stalking a property of propositions, it is an epistemic property, and not a semantic one. So, the notion of an a priori proposition is not the optimal label for the target. ‘A priority’ does not apply, first and foremost, to semantic notions like ‘meaning’ or ‘proposition,’ but rather to epistemic notions like ‘belief,’ ‘justification,’ ‘warrant,’ ‘knowledge.’
The also common notion of (v) ‘a priori knowledge’ is an improvement, in this respect. It is more clearly not semantic and quite distinct from analytic truth. The idea here is that there are (at least) two different varieties of knowledge—knowledge that depends on experiential evidence, and knowledge that does not. Again, this epistemological distinction is clearly evident in Plato’s work, and throughout much subsequent work in epistemology. Many have held that an adequate epistemology must include both, on the one hand, the (non-empirical) knowledge we can arrive at solely via rational reflection, solely via the faculty of pure reason, and, on the other hand, the (empirical) knowledge that we attain via causal interaction, through sensory channels, with specific individuals and states of affairs in our environment.
Still and all, ‘a priori knowledge’ is at best a convenient shorthand for the more cumbrous but correct ‘belief which is justified a priori.’ For one thing, I wish to ward off any suggestion that ‘a priori knowledge’ essentially involves rational intuition, in any substantive sense, because I certainly want to leave room on the playing field for understanding-based accounts—that is, those who are dismissive of rational intuition (as obscure and unhelpful) but not thereby dismissive of the view that no adequate epistemology can avoid the notion of a priori justification. So I want to be clear and upfront that my use of ‘a priori’ does not essentially connote a distinct and possibly supernatural faculty of mind. For example, at least arguably, semantic intuition might provide the grounds for a priority without appeal to, or need of, any such distinct faculty of mind.
Second, when it comes to one of our ongoing themes of the distinction between framework- (and vehicle-) indifferent metaphysical questions on the one hand and framework-relative semantic and epistemic issues on the other hand, there is a big difference between ‘a priori knowledge’ and ‘a priori justification.’ It rests on the consideration that ‘knowledge’ is a factive term—that is, ‘A knows that P’ entails that P is true. Hence, staking a claim to knowledge involves progressing beyond the framework-relative bounds of epistemology; it makes a claim about the world, in addition to a claim about an agent. So, ‘X is justified a priori’ is a weaker, more purely epistemic claim, as compared with the bolder ‘X is known a priori.’ Just as something could be empirically well-justified but yet not true (e.g., the sun revolves around the earth, all swans are white), it is at least a coherent possibility for something to be justified a priori but not true. As these boundaries are drawn and developed in this present work, a priori justification is the focal epistemological issue.1
The fundamental distinction is the following one between (vi) a priori and a posteriori justification. One core central issue throughout the history of epistemology has concerned exactly how to distinguish between mere belief and genuine knowledge. It is more or less universally conceded that the concepts of truth and justification must be involved in a satisfactory account of this fundamental distinction. That is, for a belief to count as knowledge, at the very least it must be both true (i.e., ‘X knows that P’ can only be true if P is true) and justified (because, in general, we do not count people who are right completely by accident as possessing knowledge). There are lots of involved disputes over exact details, and further conditions.2
So, assuming that knowledge is at least justified true belief (and leaving open the question of what else might be required of an adequate definition of knowledge), it has seemed to Plato and most philosophers since that we need to posit at least two different kinds or types of justification. Henceforth, the term ‘a priori’ will always be understood as applying to (vi) justification.
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The a priori/a posteriori distinction is fundamentally a distinction between two characteristic ways in which beliefs are justified. If the justification is that a belief must involve appeal to sensory evidence, then it is a posteriori. Typically, a posteriori justification rests on a causal story about relations between an agent and the object of knowledge; in contrast, a priori justification has always resisted smooth incorporation into any such straightforward, scientifically tractable model. This is one of the reasons why empiricists and skeptics have always been wary of appeals to a priority.
Why should we believe in a priori knowledge? Next, I will give an overview of some related, classic arguments, to give a sense of the reasons in favor of a priority. They all date back at least to Plato. The arguments are interconnected, and mutually supporting. They are not always distinguished, and may well be seen as three different aspects of the same underlying phenomenon (i.e., Plato’s problem). The core idea is a sort of poverty of experience: all of our actual knowledge cannot possibly be a posteriori inductions from experience, because our actual knowledge outruns, in principled ways, our experiences. Hence, while much or most of our knowledge can be understood as justified by causal connections to the ambient environment (including testimony as a special, mediated case), not all of our knowledge can be seen as so justified. Because our knowledge outstrips our experience in this way, our faculty of reason must be seen as contributing to, supplementing, or structuring what we learn from experience.3
I will refer to three related strands of this line of argument in favor of a priority as: (i) experience is particular but some knowledge is general, (ii) empirical justification can only afford inductive generalizations, and (iii) some knowledge just simply glows with luminous certainty.
The first (i.e., experience is particular but some knowledge is general) strand of the argument is clearly evident in Plato’s dialogues. The world experienced by the senses is a world of Heraclitean flux, constantly changing from moment to moment. Still we, in fact, manage to know a lot of stuff that is indifferent to empirical and psychological contingencies. Therefore, we must have this distinctive and remarkable faculty of mind—that is, rational intuition. Whether we are talking about logic and mathematics, moral truths, or other domains, this strand of the argument has played a key role in the history of epistemology.
This core strand within the poverty-of-experience line of argument is focused on the remarkable differences between the contents which make up our experiences and the contents which compose some of our (presumed) actual knowledge. And it is taken by many (including Plato) to support not only rational intuition but also metaphysical realism about the objects of our a priori knowledge. Many mathematicians, for example, find these considerations compelling, and to warrant not only epistemological but also metaphysical conclusions. Consider, for example, the following sentiments expressed by Russell (1912: 100), from the ranks of mathematicians who defended the indispensability of rational intuition, describing the otherworldly objects of our a priori knowledge:
The world of universals … is unchangeable, rigid, exact, delightful to the mathematician, the logician, the builder of metaphysical systems, and all who love perfection more than life. The world of existence is fleeting, vague, without sharp boundaries, without any clear plan or arrangement.4
The second strand of poverty-of-experience argument for a priority may well just be the distinctive way in which the first strand of the argument gets formulated in response to a certain kind of empiricist agenda. Classic instances include Leibniz’ (1704) response to Locke (1690), Kant’s (1781) response to Hume (1748), and Frege’s (1884) to Mill (1831). You only get inductive generality, not necessity, from experience. Given that we do attain knowledge of (at least some) necessities, it follows that at least some of our knowledge is not merely a matter of what the mind has soaked up or observed via the senses, but must rather be a non-empirical matter—that is, grounded in rational intuition. A posteriori faculties will ground the claim that all events that I have yet encountered have been caused, but not that it is necessary that all events have been caused; or the claim that every murder I have ever encountered is morally unjustified, but not the fully general claim that murder is unjust. Once you stir in the claim that we do in fact have knowledge of these general necessities, this is a seminal influential argument for the rationalist position.
A textbook example for making this point is the well-confirmed but ill-fated inductive generalization that all swans are white. This was taken to be a completely exceptionless law by Europeans, until, surprisingly, black swans were discovered in Australia. They were wrong about swans, and in retrospect the judgment should have been qualified to: all the swans which we have ever observed have been white, but there is nothing contradictory or impossible about a non-white swan. Now, here is the rationalist kicker—this situation could not possibly occur for ‘all squares are four-sided,’ or for ‘2 + 2 = 4.’ Explorers of the nether reaches are not going to discover three- or five-sided squares; or discover a place in which 2 + 2 yields anything but 4. Hence, there is a difference between defeasible inductive generalizations like ‘all swans are white’ and statements which are immune to counterexample; and—the argument continues—only by positing rational intuition (in one form or another) can this evident difference be explained.
As for the last strand of poverty-of-experience line of argument in favor of a priority, ‘luminous certainty’ is a term which occurs in Leibniz (1704) to denote a special phenomenal quality appropriate to certain self-evident unassailable contents. Some knowledge is just bulletproof, solidly and firmly immune to counterexample. Such knowledge just glows with a luminous certainty. To understand some privileged claims is to be sure that they are true. And, so the argument continues, there is nothing within the a posteriori evidence-gathering faculty which could ground or underwrite that. Only a non-empirical source of justification will do.
All three interrelated strands of argument are taken by some (from Plato on down) to support not only rational intuition, but also metaphysical realism about the objects of our a priori knowledge. Many are tempted to continue from metaphysical realism on into an anti-scientistic mysticism (i.e., here we have an obvious and undeniable example of something which lies beyond the bounds of scientific explanation). However, positing rational intuition does not entail any such metaphysical realist or mystical views. These are considerably strong arguments in favor of the positing of a non-empirical source of justification (provided of course that one grants the anti-skeptical premise that we do manage to obtain knowledge of universal, general truths); but per se they are much weaker arguments for any specific metaphysical position. Many of the moderate varieties of both rationalism and empiricism are precisely attempts to concede the force of these epistemological arguments without drawing any unwarranted metaphysical or mystical conclusions.
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To sum up then: ‘A priori’ applies first and foremost to a putative kind of, or source of, justification. Humans have a priori knowledge only if it is not the case that all of our knowledge is justified empirically. Rationalists are philosophers who are enthusiastic about a priori justification, and ‘rational intuition’ is a common but vague term for this non-empirical source of justification. Empiricists are opposed to any substantive form of rational intuition, and the recent naturalist (or radical empiricist) strand within empiricism seems to be opposed to any and all forms of a priority.
As opposed to the metaphysical notion of necessity, or the semantic notion of analytic truth, a priority is an epistemological concept. The bone of contention between proponents and opponents of a priority concerns what is required for an adequate account of human knowledge. (Will a posteriori justification suffice, or not?)
This is a central distinction within the history of philosophy, and much interest has lain in trying to explain these two different kinds of knowledge. What is this psychological and empirical indifference which seems to be a mark of some of our knowledge? What explains the evident fact that some of our knowledge is immune to counterexample?
§4.2: refinements and elaborations
While the notion of a priori justification is more or less as old as philosophical reflection on human knowledge, philosophical accounts of a priority are a much more recent phenomenon. Historically, instances of employing the concept of a priority are common, but attempts to define the notion are rare. Plato gives some suggestive but vague descriptions of the phenomena, and many of his followers were inclined to view a priori knowledge as mystical, non-discursive, not amenable to analysis or reductive definition. In the work of the Modern rationalists (such as Descartes, Spinoza, Leibniz), one finds a priority integrally bound up in the nexus of a certain distinctive kind of Enlightenment-scientistic-theistic world-order (i.e., a priori knowledge is a gift from God, the benevolent omnipotent watchmaker, to allow us a glimpse of the divine geometrical plan). Needless to say, many philosophers today are skeptical about many different aspects of that world-view.
Burge (2000: 13) alleges that Leibniz was the first to attempt to give a rigorous definition of the notion of a priority; and many current discussions of the notion take Kant’s work (on which Leibniz was a principal influence) as its starting point. I will follow in this vein, starting this portion of our investigation from Kant’s Leibnizian definition of the a priori, and investigating a couple of questions which are raised thereby.
Kant’s (1781) most common, official definition is negative: a priori knowledge is knowledge that is not dependent on experience. This immediately gives rise to two related questions: First, what exactly does ‘experience’ mean here? Second, is it possible to give a purely positive definition of a priori knowledge? I will explore both of these in a preliminary way here. They are so central that the discussion of them will continue on into Part IV.
So, what exactly does ‘experience’ mean, when we classify a priori knowledge as independent of experience? Presumably not just ‘current, operative sensory experience,’ as that would count things justified via memory (e.g., ‘it rained yesterday’) and introspection (e.g., ‘I am definitely not repressing my frustrations’) as a priori; and yet there is reason to classify at least some of such things on the a posteriori, empirical side of the divide. (They can be based on causal transactions, and can be deeply fallible, and so lack the distinctive sort of privilege that we have with the paradigm sorts of cases which we want to classify as a priori.) However, we do not want to go too far in the other direction, and characterize experience so broadly as to include any kind of subjective psychological process; for the most extreme Platonic ‘the very light of the mind in her own clearness’ sorts of purely mystical cases (discussed in §1.2) would count as experience in this sense. And if the insights gleaned from a mystical Socratic trance5 do not count as a priori, then nothing does!
Questions regarding whether introspection counts as experience (or, relatedly, whether self-knowledge counts as a priori or empirical) raise vexing complications. Is ‘I am in pain’ a priori or empirical? What about ‘I am currently conscious’? Or how about Descartes’ famous unassailable cogito, ‘I think, therefore I am’? We certainly enjoy a kind of privileged access to our own subjective mental states, but at the same time there is a degree of fallibility, a possibility of error or of self-deception, which marks off at least some such cases as distinct from our paradigmatic a priori cases. We might put it this way: I have privileged access to what my mental states are, but not to whether they are knowledge—as to what their content is, but not as to whether that content is true.6
In any case, what is needed, it seems, for a notion of a priority which is sharp, defensible, interesting, and not out of touch with its broad historical roots, is a sense of ‘experience’ which counts some but not all introspective data, subjective psychological processes, as experiential. This is not an easy thing to define. For example, one fairly compelling way to draw the key a priori/empirical difference would be to do so in terms of the presence, or absence, of a causal link between knower and known. The idea would go something like: A’s knowledge that P is a posteriori iff A’s justification for thinking that P depends upon a causal link between A and P; A’s knowledge that P is a priori iff there is no such causal justificatory link between knower and known.
There certainly is something to this way of drawing the contrast—particularly if we take Plato’s combination of acquaintance-based, rational intuition and metaphysical realism as the typical proponent of a priority (because there are no causal connections between human brains and Platonic universals). It seems to fit well with the paradigm cases of a priori and empirical knowledge. However, on reflection, surely this would put way too much into the a posteriori, empirical basket. For starters, all self-knowledge cases (e.g., I exist, I am conscious, I am hungry) seem to involve causal relations to brain events. Indeed, isn’t every mental event, including a mystical Socratic trance, causally related to brain events? Is everything, then, a posteriori, excepting on a scarcely tenable extreme dualism which denies any causal relations between minds and brains? So, again, what initially seemed to be a straightforward and promising way to distinguish a priori from empirical turns out to be rife with complications.
This challenge as to the exact sense of ‘experience’ which is involved in the notion that a priori knowledge is independent of experience will be further discussed in Part IV (at §7.4). One thing which we can say with a fair degree of security is that it is not clear that any clean, crisp way to define the a priori/a posteriori divide will suffice to capture all historically significant work on the a priori.7
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What, then, of the second question, as to whether or not a priori justification could be defined in a positive way (as opposed to merely as the absence of something, such as empirical experience, or a causal connection between knower and known)? Well, the notion of rational intuition might seem to provide a candidate, the idea being that A’s knowledge that P is a posteriori iff it is justified empirically, and a priori iff it is justified via rational intuition. Fair enough, as far as it goes; the problem here being that it does not go very far at all. As empiricists have long complained, rational intuition thus understood is merely a label for the problem, not a solution to it. The burden of coming up with a satisfactory explanation of a priori justification is merely recast as the burden of coming up with a satisfactory explanation of rational intuition.
The appeal to semantic intuition, or the move from acquaintance-based to understanding-based accounts, is seen by many as a step forward at this point, as it seems to have some promise to flesh in what is required from the above vague appeal to rational intuition, without taking on the obscure epistemological or metaphysical commitments associated with some extreme varieties of rationalism. The task, then, is to flesh in some such strategy, of grounding a priori justification in semantic intuition or understanding, in a satisfactory way. Here the price of this way of addressing the obscurity objection is that the adequacy objection looms larger. The question thus prompted is whether semantic intuition can get beyond mere trifles and trivialities, to do any of the heavy lifting which a solution to Plato’s problem requires. It is a main task of Part III below to show how the notion of the constitutive a priori is a great leap forward, when it comes to these problems.
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As with the cases of ‘necessary’ and especially ‘analytic’ (cf. §3.2) above, one main aim of this chapter is to disavow some of the traditional associations with the term ‘a priori.’ While it is important that the concepts employed herein are recognizably in touch with their historical roots, it is neither desirable nor indeed possible to retain everything that anyone has ever claimed about the a priori, if I am to defend specific and focused theses about the notion. (This present task of pruning some historical associations with ‘a priority’ will overlap somewhat with the task undertaken in the previous section of determining to what to which the term ‘a priori’ first and foremost applies. At a few points below where that is so, this present discussion can be quicker and neater because of that previous work.)
Traditionally, ‘a priori’ has been tightly linked to such notions as (i) innateness, (ii) generality, (iii) infallibility, (iv) privileged access, and (v) unreviseability. These links have come under much scrutiny and pressure, in recent decades. To some extent, these pressures also affect necessity and analyticity; but they are most pertinent here. If immunity to counterexample is assailable anywhere, it is here on the epistemic front (as we are obviously limited, fallible epistemic agents). Furthermore, the idea of self-consciously weaker, less ambitious varieties of a priority has been more explicitly worked out in the literature here (as distinct from the cases of analytic or necessary truth).8
(i) The putative links between a priority and innnateness have already been addressed above in §4.1, in giving reasons against employing the notion of an a priori concept. While lots of influential philosophers (including in particular both Plato and the Modern rationalists) tend to endorse both innateness and a priority, while not distinguishing between these two different sorts of independence from experience, Kant and Frege, among others, are clear about the importance of this distinction. A judgment might be justified a priori, even though there is nothing innate about any of the contents which compose its content.
(ii) As for the relations between a priority and generality, this complicated question has also been broached. Burge (2000) discusses this question, in the course of which he distinguishes two broadly overlapping notions of a priority running through modern epistemology: the first, championed by Leibniz, takes generality to be the key criterion for a priority, and the second, associated with Kant, takes independence from experience to be the crucial mark. These two conceptions would overlap, over a broad range of paradigm cases; but insofar as there could be a priori knowledge of specific phenomena (e.g., Descartes’ cogito), then the two conceptions would not be extensionally equivalent.9
One important present point is exactly one which came up above, in our discussion of the relevant sense of ‘experience’ in the definition of a priority: namely, if we want to count any cases of self-knowledge or of introspection as a priori, then generality is not an exceptionless mark of a priority. (There is more discussion of this point in Part IV.)
(iii) Infallibility was certainly one of the traditional marks of the concept of a priority, and indeed this aspect of immunity to counterexample has been, historically and conceptually, one of the main reasons why the notion is of such enduring philosophical interest. This is of a piece with the ‘luminous certainty’ aspect of a priority. Some knowledge (about mathematics or morality, say) just seems to be completely unassailable.
The view to be developed herein will instance a complex stance on this front. A priori justification, similar to analyticity, will turn out to be framework-relative and hence revisable. However, there is still a sense in which immunity to counterexample is retained. Any case in which what was previously taken to be a priori subsequently gets rejected involves conceptual evolution, and consequently a change of framework. (For example, Democritus’ belief that atoms are indivisible was not contradicted by what we in the twentieth century call ‘the splitting of the atom.’ Rather, the term ‘atom’ has undergone conceptual evolution. Cf. §6.3.)
As distinct from (though consistent with) this framework-relative revisionism about the semantic and epistemic modalities, some recent philosophers have favored a fallibilist stance toward the a priori (cf., e.g., BonJour [1998], Casullo [2003]; and see note 1 above on the putative ‘defeasibility requirement’). Fallibilists about a priority hold that, just as one can be justified a posteriori in believing something that happens to be false (e.g., the sun revolves around the earth), so too one could have a mistaken false belief that is nonetheless (more or less well) justified a priori.
The constitutive a priori view is compatible with this brand of fallibilism; in many respects to be developed, it can be seen as bolstering and extending this approach. Of course, fallibilism too undermines the kind of easy transitioning between a priori justification and a priori knowledge. A fallibilist can only talk confidently of a priori justification (meaning something like a non-empirical means of reliable truth-tracking, of reliably critically evaluating the credibility of certain beliefs). No claim to a priori knowledge could be conclusively justified, for a fallibilist.
This question of fallibilism will recur throughout Parts III and IV, and will be tied off in §7.5. This is an important aspect of our understanding of a priority, in the wake of the challenge of revisability and the externalist challenge. Even further, fallibilism in this sense may well be a non-obvious but inexorable consequence of the move from an acquaintance-based to an understanding-based approach to a priority.
(iv) Questions regarding relations between a priority and privileged access also surfaced above in the course of our discussions of ‘experience,’ and of ‘generality.’ Introspection and self-knowledge do instance a certain kind of immunity to error, and so have found themselves in the mix, when it comes to discussions of a priority. I agree with Burge (2000) (as discussed above) that the canon has not been completely consistent, when it comes to similarities and differences between what we might call introspection and rational intuition. In Part IV (§7.4), I will divide up the two pertinent cases and treat them separately, when it comes to the relations between introspection and a priority.
(v) Finally, then, for the relations between a priority and revisability. The challenge of revisability was one of the great shocks to the modal world-order in the twentieth century; and, looking ahead, incorporating this challenge into a satisfactory theory is a principle aim of this current project. Clearly, there are cases where what was once thought a priori is now thought false. For example, that space is Euclidean, that whales are fish, that there can be no such thing as a sub-atomic particle (since ‘smallest, indivisible’ was originally part of the sense of ‘atom’), etc., were all once considered to be justified a priori (and, arguably, analytically true), but are no longer so-classified; and it is hard to see how to conclusively rule out such a change in status of our beliefs.
On the view to be developed herein, the frameworks composed by our meanings, and which constitute our theoretical attempts to understand, are organic entities which change over time. Since a priority should be understood as framework-relative, what is justifiable a priori will change according to place and time. Nothing is absolutely and unqualifiedly a priori, but rather only a priori relative to certain axioms, postulates, presumptions. A priori should be seen as in large measure a matter of status, not just of content. There will still be a sense in which a priori justification is immune to counterexample; though—given the prevalence of conceptual evolution—that sense is importantly qualified.
§4.3: interim consideration of some candidates
The next order of business is to discuss some exemplary instances from some major prospective categories of a priori knowledge. I will begin with considering some specific putative varietals of the a priori species, and then close this section with some general, interim remarks about relations between a priority and analyticity, as well as necessity. Note though I do little more than flag questions about certain candidates, at this stage. A conclusive discussion of these matters, on a constitutive a priori view, will have to wait until Part IV. I will begin by discussing some of the strongest, least contentious candidates, and move on to more contentious terrain.
It was more or less implicitly assumed, throughout the canon, that all and only necessary truths are knowable a priori and/or analytic; and so the cases with which we begin are strong contenders for all three categories. Paradigm examples of the necessary analytic a priori come from logic and mathematics:
1. 2 + 2 = 4.
2. Squares have four sides.
3. No proposition is simultaneously both true and false.
These seem to bear the traditional rationalists’ hallmarks of universality and generality. They are as strong a candidate as any for the status of being indifferent to anyone’s noticing or grasping them, for not having just become true at any particular point. Bearing in mind the important distinctions between propositions expressed and the sentences that express them, these cases are, it seems, fashioned from the hardest of steel and immune to counterexample in metaphysical, semantic, and epistemic senses.
(Even these are not completely unanimous, as paraconsistent logics reject [3], and certain varieties of constructivism may balk at the claim that there is anything metaphysically necessary about [1] or [2]. Still, the claim that [1]–[3] are necessary, analytic, and a priori is rather orthodox, probably as close as one can get to unanimity in philosophy.)
Many hold that some moral judgments are also necessary analytic a priori:
4. Murder is wrong.
5. One ought to keep one’s promises.
While this view is widespread, and a contributing factor toward many moves in metaphysics, moral philosophy, and theology, it is controversial. Many take the cultural variability of moral judgments to undercut any claim to necessity. The deeper problem here is the intuition of mind-dependence, that is, the notion that moral judgments, perhaps even more so than logical or mathematical ones, are contingent on the sorts of organisms that we are, or the ways in which we are encultured. Thus, while the view that the likes of [4] and [5] are necessary analytic a priori true has had lots and lots of defenders, this view is decidedly more controversial than the view that [1]–[3] are of that status.10
Truths by definition also seem to exhibit the relevant sort of metaphysical, semantic, and epistemic immunity to counterexample. That is, there is reason to put the following in exactly the same category as [2]:
6. Bachelors are unmarried men.
7. Vixens are female foxes.
To be sure, the careful work on conventions done in §§2.1, 2.2., and 3.2 is crucial here. There is nothing necessary about relations between bits of language and their meanings; but, once those conventions are set, it yet might be that what is semantically expressed by certain bits of language in a certain arrangement is necessarily so. Even given that, though, [6] and [7] seem more clearly and obviously analytic than necessary, per se. While there is bound to be large overlap between necessity and analyticity, [2] hooks onto a mind- and language-independent fact of the matter, in a way that [6] and [7] do not seem to. Hence, the inclination to take [6]–[7] to be entirely conventional, and so fundamentally analytic. In turn, the reasons to think that they are analytic are also, and thereby reasons to hold that their justification is, non-empirical.
[§]
We have unearthed some considerable reasons to expect these concepts to fail to be co-extensive, which reasons will be extensively developed in Parts III and IV. For now, here are some important cases which have been offered to show that necessary, analytic, and a priori are not co-extensive. Kant famously argued that there are synthetic a priori truths, such as:
8. Every event has a cause
9. a2 + b2 = c2 (the Pythagorean theorem)
10. Humans are free agents who are subject to moral laws
Given Kant’s assumption that necessity is one of the conditions for a priority,11 these are quite plausibly necessary truths. However, he argues that they are not analytic, not true by definition. According to Kant, it is not a contradiction to judge that they are false (as it would be for the cases of [2], [6], or [7]).
Kant’s ideas here are epochal and seminal. This was one of the most significant shakeups of the world-order, concerning a priority, in the entire history of Western philosophy. As mentioned above at §1.4, to this day, 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?12
Much more recently, Kripke argues that there are necessary a posteriori truths, such as the following:
11. Heat is molecular motion.
12. Gold is the element with atomic number 79.
If science is in the business of discovering the essence of natural phenomena, then it seems that science aims to discover necessities. It is plausible to think that the likes of [11] or [12] are good candidates. For example, anytime molecules get agitated, it has to have the effect of increasing heat; and anytime heat is increased, that can only be because molecules are being agitated. However, despite the plausibility of the claims that [11] or [12] are necessary, there need not be anything a priori or analytic about them. Necessity, as Kripke (1972: 36) puts it, ‘in and of itself has nothing to do with anyone’s knowledge of anything’.
(It will be important to bear in mind below that the Kripke cases are always hypothetical, always of the form: IF science is right that e is the essence of P, then it is necessary but a posteriori that P is e. As a philosopher, not a scientist, Kripke is not in the business of determining the mind-independent nature of physical phenomena, but rather in the business of properly cataloguing the logic and semantics of these, and other, sorts of propositions.13 As we will see, this consideration complicates the question of the proper classification of these Kripkean examples of putative necessary a posteriori truths.)
Kripke also argues that there are contingent a priori statements. I will steer clear of many of his candidate examples (e.g., ‘metre,’ ‘Neptune’), on the grounds that some of them are attendant upon contentious theses in the philosophy of language whose critical evaluation lies beyond the scope of this project.14 However, the Kripkean or Kripke-inspired indexical cases of the contingent a priori (e.g., ‘I am here now’) do play an important role in the maps of the terrain developed in Part IV. Not only do they strongly suggest that analyticity or a priority are not sufficient for necessity; further, they prompt important reflections on the relations between semantic and epistemic immunity to counterexample.
[§]
Now to generalities. First, then, as to the relations between a priority and the analytic/synthetic distinction. While both of these notions have been taken by some to be suspect, anyone who concedes the intelligibility of both notions is bound to concede that there is overlap between a priori knowledge and analytic truth. Basic truths of mathematics and logic provide plausible examples, as do certain relational maxims (‘If X is north of Y, then Y is not north of X’). It is the worth of analytic a priori knowledge, when it comes to substantive problems in metaphysics or epistemology, which is contentious; the claim that (at least) some analytic truths are knowable a priori is, comparatively, fairly secure. (This becomes all the more plausible, less obscure, on the move from acquaintance-based to understanding-based accounts of a priority.)
As for whether all, or only, analytic truths are knowable a priori, that will take some digging and sculpting; how that matter stands on a constitutive a priori approach will be conclusively sorted out in Part IV. Kant famously argued that there are synthetic a priori truths, but many problems with Kant’s arguments have been pressed in the intervening centuries. Ultimately, I will argue that all analytic truths are knowable a priori, but that there are plausible instances of the synthetic a priori (here indexical cases, such as ‘I exist,’ loom large).
Next then for the relations between a priority and the necessary/contingent distinction. Again, it is hardly objectionable that, provided that both necessary truth and a priori knowledge are coherent, then at least some necessary truths are knowable a priori. Again, elementary truths of mathematics and logic provide plausible candidates. However, while not staking any claims about all of Kripke’s putative examples of necessary a posteriori truths and contingent a priori statements, ultimately, I will explain why I think that Kripke is right on both counts.15 This split between metaphysical necessity and any notions of epistemological modality is one of the deep and enduring legacies of the externalist challenge.
§4.4: skepticism about a priority
There is, on the one hand, pressure pushing this current section to be shorter than its closest predecessor §3.3, since some of the reasons for skepticism about necessity and analyticity carry over to a priority as well; so, those considerations are already out on the table, and do not need to be explicated afresh again here. On the other hand, though, in some respects a priority is the most objectionable of the three core modal notions, and so there is also pressure for this section to outstrip its parallel predecessor. Are we not finite and fallible epistemic agents? So, how could there be epistemic immunity to counterexample? Truth in virtue of meaning, maybe, and mind-independent facts, sure, but here we are talking about finite and fallible agents here.
For example, the notion of metaphysical necessity, of something which cannot be otherwise, seems to be perfectly coherent, even though there it may well be impossible to conclusively evaluate any particular candidate for metaphysical necessity. Similarly, most would concede the coherence of analytic truth; though many would question its usefulness or worth when it comes to heavy lifting in philosophy. In contrast, there can seem to be something deeply suspicious about a priority, and that per se. How can there be a source of justification—a way of reliably tracking the truth of mind-independent matters—over and above and apart from the scientifically tractable causal relations between agents and their environments? A priority has seemed to many to be obscure, and perhaps even completely antithetical to a scientific world-view. In short, there seems to be something intrinsically supernatural about a non-empirical means of truth-tracking, and hence, despite its impressive historical pedigree, its very intelligibility is often questioned.
Following Peacocke & Boghossian (2000: 6), I will distinguish and briefly investigate three related sources of skepticism about a priority. Variants of each of them occur in the work of Quine; but the underlying sentiments pretty much thread through the history of the empiricists’ opposition to rational intuition.
The first objection has it that the correct account of the growth of scientific knowledge suffices to refute the idea that an adequate epistemology requires the positing of a priori justification. The idea has it that science has no need of rational intuition, and science is the most effective path to knowledge yet developed. If we don’t need rational intuition to explain scientific progress, and if scientific knowledge is the pinnacle of human knowledge, then it is just old-fashioned mystery-mongering for philosophers to insist on the need for the a priori. Maddy (2000, 2007) and Devitt (2005, 2011) provide recent statements of this line of objection; and both are representative of the prevalent naturalistic idea that the correct account of the growth of human knowledge is a Quine-inspired holistic web of belief.
The second, related objection to the intelligibility of the a priori is the obscurity objection: namely, there can be no satisfactory account of this mysterious, supernatural non-empirical source of justification. It could not possibly be fitted into a seamless scientific world-view, be reduced to the forces which we have good reason to believe govern the rest of the natural realm. In short, there can be no satisfactory explanation for how it is that some things could be non-empirically known.
Finally, the third line of objection is that a priority essentially entails certain instances of knowledge having a property which no instance of human knowledge could possibly have—such as infallibility, unrevisability, immunity to counterexample. Since the characteristic marks of the very idea of a priority are impossible, unsatisfiable, it follows that there can be no a priori knowledge for we finite, fallible agents. (See Kitcher [2000] for a recent example of such an argument.)
To take these three related objections in turn, then. The first is terribly presumptuous, assuming as it does that we have a satisfactory, comprehensive account of the growth of human knowledge in which the a priori plays no role. To the contrary, the idea that not even the actual history of science can be accounted for without appeal to a priori justification has considerable defenders. (Cf., e.g., Pap [1946], Friedman [1992, 2000, 2011], DiSalle [2002], Richardson [2002], and Stump [2003, 2011, 2015], and Part III below for further discussion.) Devitt’s (2011) efforts on this front are valiant, but hardly knock-down—his parting comment that ‘many will remain unconvinced of the possibility of an empirical justification for the [contentious cases of] knowledge’ (2011: 21) is an understatement. Maddy (2000) seems to admit the a priori in the back door after making such a show of chasing it out the front door (I will explain this allegation in §6.3). So, while there is something to this first line of thought, at this point in time it hardly supports categorical skepticism about the a priori.
Insofar as the second line of argument is merely that there is as of yet no satisfactory account of a priority, then that is hard to quibble with. Clearly, many hard questions remain, for proponents of a priority. However, insofar as this is supposed to support the conclusion that there is no a priori, then that is about as compelling as an argument that humans will never cure cancer, or travel to Mars, just because they have not yet managed to do so. True, in the case of the a priori, opponents point out that rationalists have had this problem in their laps for a millennia, and there are grounds for skepticism as to whether they have even made any progress. However, the constitutive a priori orientation developed herein takes a lot of progress to have been made on this question, first by Kant, and subsequently by several others.
As for the third line of argument, this is precisely the main order of business of this entire project. Precisely what do these challenges (reviseability, externalism) show about a priority? Groundwork for answering this objection has been laid throughout Parts I and II, and development of the answer will continue throughout Parts III and IV. The proof will be in the pudding.
[§]
One thing I should note, by way of segue, is that it is instructive to compare the force of these skeptical anti-a priori arguments along the dimension of acquaintance-based versus understanding-based orientations toward a priority. Not only the general ancient obscurity objection, but all of these more specific charges, apply less forcefully to the semantic intuition, understanding-based accounts than they do to the more traditional acquaintance-based approaches. The constitutive a priori view, which will be unpacked next, is, tellingly, a development within this less obscure, less contentious, semantic-understanding-based tradition.
As in the cases of necessity and analyticity, it is awfully hard to ground a firm, clear a priori/a posteriori distinction, even though there clearly are paradigm cases at the poles (e.g., ‘there is an apple pie baking nearby,’ based on current olfactory experience, vs. ‘all squares are four-sided,’ based on a grasp of the concept ‘square’). It may be best to say that there is a range of shades of grey at the a priori-empirical divide. Conceptual evolution is a messy business, as concepts and meanings, like the languages they compose, are organic entities which change over time. However, again, the fact that there are shades of grey hardly entails that nothing is either black or white. The brute data of the poverty of experience remains. We are not about to be black-swanned by three- or five-sided squares, and that is not because we have already experienced all possible squares.
Moving on to Part III, then: now, to take this conceptual apparatus and apply it to the matter of exactly how some major twentieth-century developments in philosophy have affected the landscape of the ancient question of a priority.
NOTES
1. This distinction between the factive term ‘a priori knowledge’ and the more cautious, purely epistemic term ‘a priori justification’ is present in the literature under the guise of whether or not a priority includes or entails an indefeasibility requirement. Is it enough for a belief to be justified non-empirically for it to count as a priori, or is there a further condition along the lines of ‘cannot be defeated by empirical evidence’? Kitcher (1983) and Field (2000) motivate an indefeasibility requirement, while Boghossian (1997), Peacocke (2000), and Casullo (2003) reject one. I am with the latter camp—as I have set things up here, indefeasibility is too much to ask of any purely epistemic notion. (It is no accident that Kitcher, for example, insists on an indefeasibility requirement on the path toward the larger dialectical game of establishing that mathematical knowledge falls short of a priority.) See also the discussion of ‘fallibilisim’ about the a priori in the next section.
2. For example, one famous challenge stems from the Gettier (1963) cases of putative justified true beliefs which nonetheless fail to qualify as knowledge.
3. Herein lies another connection between a priority and innateness: poverty-of-experience arguments are also used to justify claims of innateness (as in the case of Chomsky [1967], for example).
4. Other famous elements of this camp of mathematician-Platonists also includes Descartes, Leibniz, Frege, and Godel (1944, 1947).
5. The allusion here is to Plato’s Symposium, where Socrates reports that his insights came to him while lost in a trance, oblivious to what was going on around him. (Compare the passage from the Phaedo cited in §1.2.)
6. For explorations of distinctions between a priori, epistemic privilege, indubitability, and introspection, cf. the Introduction to Hanson & Hunter (1993).
7. Cf. Baehr (2003) for an argument in favour of the stronger claim that all of the various possible ways of drawing the divide face daunting problems. We will investigate in Part IV some self-knowledge cases in which difference senses of ‘experience’ results in different categorizations.
8. For discussion cf. BonJour (1998), Boghossian & Peacocke (2000), Casullo (2003), Schaffer and Veber (2011).
9. Burge (2000) investigates at length the relations between these points and the controversial roles which intuition plays in Kant’s philosophy of mathematics, and also the ways in which the two notions of a priority are possibly conflated by Frege.
10. There is extensive discussion of a relevant distinction, between natural versus conventional reality, beginning at §5.4.
11. In agreement with much work in the rationalist tradition, Kant takes it as evident that at least some of our knowledge is universal and necessary, and argues that no empirical faculty could justify such claims. He explicitly assumes that anything known a priori is necessarily true.
12. This theme of the ampliative analytic recurs at various junctures, in various guises. Could semantic intuition amplify or add to the store of human knowledge? If not, how could it be of any relevance to Plato’s problem, and if so, how could that be possible?
Indeed, many core, significant notions which pertain to this epistemology/language nexus—from Kant’s (1781) synthetic a priori to Frege’s (1892a) informative identity statements to Kripke’s (1972) necessary a posteriori (and even on to Moore [1903] on the paradox of analysis)—are related to, if not guises of, these questions about the ampliative analytic.
The very idea of the ampliative analytic is also deeply affected by the move from acquaintance-based to understanding-based varieties of a priority—consider all the handwringing over ‘from coherence to worth’ in chapter 3, which gets more worrying to the extent that accounts of a priority get less obscure. Whether, in the final reckoning, my constitutive a priori view is a variety of moderate rationalism or of moderate empiricism hangs in the balance. (Cf. the final pages of chapter 6.)
13. Kripke (1972: 159): ‘Certain statements … if true at all must be necessarily true. One does know a priori, by philosophical analysis, that if such a statement is true then it is necessarily true. … All the cases of the necessary a posteriori advocated in the text have the special character attributed to mathematical statements: philosophical analysis tells us that they cannot be contingently true, so any empirical knowledge of their truth is automatically empirical knowledge that they are necessary.’
14. In particular, careful examination of many of Kripke’s examples would involve serious excavation of the semantics of proper names, descriptive names, natural kind terms, and theoretical terms more generally. I do get rather into natural kind terms in Part III, but otherwise do not make such serious forays into debates regarding the proper semantic treatment of these other sorts of terms herein.
15. To anticipate briefly: a case of knowledge counts as a priori if there is a non-empirical route to actual justification; necessity, or truth in all possible worlds, is light-years from here. These two properties might come apart most dramatically in indexical, cogito cases, or in cases of scientific discoveries of essence.