Meaning, Understanding, and A Priori Knowledge

Abstract

According to the most popular account of the a priori, which we might call Analytic Account of the A Priori, we can explain the a priori in terms of the notion of analyticity. According to the least popular account of the a priori, the explanation of the a priori proceeds by appealing to the faculties used in the acquisition of a priori knowledge (or justification), such as the faculty of rational intuition – call this Rationalist Account of the A Priori. The main aim of this paper is to challenge the analytic account of the a priori to motivate a return to rationalism. To achieve this aim, I discuss and challenge two very different analytic accounts of the a priori: a concept-based account that relies on meaning-justification links, and an understanding-based account that does not rely on such links. I argue that the former is both extensionally inadequate and explanatorily deficient, and the latter can be made to work but only by employing such a rich notion of understanding that renders it a form of rationalism in disguise. I conclude by motivating a rationalist faculty-based account of the a priori.

1 Introduction

The way we come to know, say, that either it is raining or it is not raining is intuitively different from the way we come to know that it is raining. Whereas it seems that we can know that either it is raining or it is not raining independently of experience, we cannot come to know that it is raining without some experience of the world. The distinction between a priori and a posteriori knowledge is supposed to capture this intuitive difference between two ways of coming to know. Roughly, a priori knowledge can be understood as knowledge acquired in a way that is suitably independent of the thinker’s experience. But even if we assume that there is a priori knowledge, and that the notion of the a priori is in good standing, a pressing question remains about its possibility. What is peculiar about the possibility of the a priori is the putative fact that a thinker can come to know truths about the world in a way that is suitably independent of her experience, that is, without looking at the world. But how is it possible to come to know truths about the world without looking at it? This, in a nutshell, is the problem of the a priori.

According to the most popular account of the a priori, which we might call Analytic Account of the A Priori, we can explain the a priori in terms of the notion of analyticity.¹ According to the least popular account of the a priori, we can explain the a priori by appealing to the faculties used its acquisition, such as the faculty of rational intuition – call this Rationalist Account of the A Priori. The main aim of this paper is to challenge the analytic account of the a priori in order to motivate a return to rationalism. To achieve this aim, I discuss and challenge two very different analytic accounts of the a priori: a concept-based account that relies on meaning-justification links, and an understanding-based account that does not rely on such links.

Here is the plan. I start in section 2 with some background. In section 3, I introduce what I take to be the most developed analytic account of the a priori, a concept-based account which relies on meaning-justifications links. In section 3.1, I argue that this account of the a priori is both extensionally inadequate and explanatorily deficient. In section 4, I discuss a very different kind of analytic account of the a priori, an understanding-based account which does not rely on meaning-justification links but on understanding alone. I argue that this account can be made to work, but only by employing such a rich notion of understanding that renders it a form of rationalism in disguise.

I do not intend to offer a knockdown argument against any of the two versions of the analytic account of the a priori, but rather raise enough challenges to motivate looking elsewhere to explain the possibility of the a priori. In particular, I aim to motivate an account of the a priori that distances itself from semantic considerations and the notion of analyticity to explain the phenomenon at hand, one that is closer in spirit to the traditional rationalist account of the a priori. I do that in section 5. Before proceeding, however, let me start by setting up the background of the debate.

2 Some Background

According to the traditional rationalist account of the a priori, the prevailing view about the a priori throughout most of the history of philosophy, a priori knowledge is possible because we have a special faculty of rational intuition which, somehow, enables us to discover truths about the world without looking at it. This account of the a priori has been widely rejected as most philosophers nowadays regard the existence of such a faculty with much suspicion.² The task is then to explain the possibility of the a priori without appealing to the existence of special faculties. This task was undertaken by proponents of the analytic account of the a priori.

The central tenet of this analytic account is that a priori knowledge, though genuine, concerns truths in some sense less substantial or world-involving, or at least cognitively less demanding, than those acquired through our a posteriori sources of knowledge. According to one version of the analytic account, a priori knowledge does not provide us with substantial knowledge about the world, but only with knowledge about our meanings or concepts. In Humean terms, a priori knowledge was seen as mere knowledge of ‘relations of ideas’ as opposed to substantial knowledge of ‘matters of fact.’ What is knowable a priori was regarded as trivial or tautological, or at least, as less substantial or cognitively less demanding, and so not in need of the postulation of special faculties to explain its possibility.

The analytic account of the a priori was close to orthodoxy during the first half of the twentieth century, championed within the logical positivist movement, and it is most standardly formulated as the claim that a priori knowledge is mere knowledge of analytic truths.³

The notion of analyticity is nowadays read both epistemically and metaphysically. According to the metaphysical notion of analyticity, a statement S is analytic if and only if S is true in virtue of its meaning alone; according to the epistemological notion of analyticity a statement S is analytic if and only if mere grasp of S’s meaning suffices for us to be justified in believing S’s truth.⁴

The metaphysical notion of analyticity was at the heart of the logical positivist account of the a priori. The idea was that metaphysical analytic truths were devoid of factual content, and that they were true no matter how the world turned out to be. If a priori knowledge is knowledge of metaphysical analytic truths, then there is no mystery of the a priori. If analytic truths are not about the world, there is nothing mysterious in the possibility of coming to know them without looking at the world, that is, a priori. Problem solved.

Following Quine’s (1951, 1954) influential work, and more recently Boghossian (1997) and Williamson (2007), many nowadays question the intelligibility of the metaphysical notion of analyticity behind this account of the a priori, and it is now widely rejected.⁵

I need not be drawn into that debate here, however, for even if the metaphysical notion of analyticity were in order, it would not be sufficient to explain the a priori. No doubt that if what we come to know a priori were made true by meanings alone we would remove the mystery of the a priori: nothing mysterious about acquiring knowledge about the world without looking at it if the knowledge thus acquired is not about the extra-linguistic world but about meanings or concepts. However, even if a priori knowledge were mere knowledge of metaphysical analytic truths, we would still need an explanation of what justifies us in believing in such truths, or how we come to know truths made true by meanings alone.

This, I think, was rather clear to the logical empiricists, and they move from one notion of analyticity to the other with ease. Here’s A. J. Ayer (1936)⁶:

I think that we can preserve the logical import of Kant’s distinction between analytic and synthetic propositions, while avoiding the confusions which mar his actual account of it, if we say that a proposition is analytic when its validity depends solely on the definitions of the symbols it contains, and synthetic when its validity is determined by the facts of experience. Thus, the proposition ‘There are ants which have established a system of slavery’ is a synthetic proposition. For we cannot tell whether it is true or false merely by considering the definitions of the symbols which constitute it. We have to resort to actual observation of the behaviour of ants. (p. 73)

Carnap (1947) says something similar. He characterizes “the concept of analyticity, i.e., truth based upon meaning” (p. 222) and claims that,

[…] it is sufficient to understand the statement [i.e., the meaning of an analytic statement] in order to establish its truth; knowledge of (extra-linguistic) facts is not involved. (Ibid.)

With the rejection of the metaphysical notion of analyticity, many abandoned the empiricist project of explaining the a priori through knowledge of meanings, or semantic understanding. Boghossian’s (1997) claimed that by distinguishing metaphysical analyticity from epistemic analyticity we could agree with Quine regarding the incoherence of the metaphysical notion of analyticity, but not with Quine’s conclusion regarding the untenability of the analytic account of the a priori.⁷ To explain the a priori, Boghossian argued, all we need is epistemic analyticity, and we can dispense with the dubious notion of metaphysical analyticity. This idea has found many supporters, and the idea that semantic understanding is all we need to explain the a priori is, once more, widely held.

There was, however, very good reason for embracing both notions of analyticity. If meanings made sentences true, then it is plausible to claim that understanding sentences’ meanings is enough for epistemic justification. Take the sentence “Apples are nutritious.” Understanding the meaning of this sentence does seem to somehow justify our belief that the sentence means that apples are nutritious. Understanding relates us, in some way, to facts about meanings. Semantic understanding does seem to be a source of justification about what things mean. Semantic understanding, however, does not seem to relate us to facts about the truth-makers of sentences, and so it is not clear how it can be the source by which we came to know that a sentence is true (unless the sentence is meta-semantic). If we reject the property of truth in virtue of meaning alone, it is not at all clear how understanding sentences’ meanings could yield epistemic justification and knowledge.

This point is clearly made by Margolis and Laurence (2001), when they say, in reply to Boghossian (1997), that,

We agree that the case against metaphysical analyticity is compelling. But the problem for Boghossian is that these considerations extend to epistemic analyticity as well. After all, if p really is an independent fact that makes S true, then just knowing that S means that p could not suffice for the needed justification; one would also need to be justified in believing that p (p. 294)

Despite this clear worry, the idea that semantic understanding is the source of the a priori is, once again, close to orthodoxy. Among some of the defenders of this orthodoxy are Boghossian (1997, 2003a, b, 2011), Peacocke (1993, 2004), Hale and Wright (2000), Jenkins (2008, 2012), and Balcerak Jackson and Balcerak Jackson (2012). My aim is to criticise this orthodoxy, thus motivating looking elsewhere to explain the a priori. In particular, I will examine two very different analytic accounts of the a priori: (i) a concept-based account, in section 3, and (ii) an understanding-based account, in section 4.

It might be worth clarifying from the outset that I do not aim to dispute that semantic understanding is a source of epistemic justification. It seems clear that semantic understanding plays a necessary role in our justification to believe in the content of both analytic and synthetic sentences. Moreover, it seems correct to say that semantic understanding is an a priori source of epistemic justification (and knowledge).⁸ My quarrel is purely with the claim that semantic understanding can provide more than mere knowledge of what sentences mean, which is the thesis entailed by the analytic account of the a priori. Let us now see in more detail how this account is supposed to work.

3 Understanding with Meaning-Constitution

What characterizes the most popular analytic account of the a priori, which is a concept-based account, is the claim that the conditions on understanding the meaning of a certain word (or grasping a certain concept) somehow explain what justifies a thinker in holding a certain sentence containing that word true (or in believing a certain proposition containing that concept). Here is what motivates this view. Take the sentence “All bachelors are unmarried”. If a thinker took this sentence to be false it seems that we would have good reason to believe that she did not understand one of its constituent terms, most likely the word ‘bachelor’. In the same vein, someone who thinks that bachelors are a type of Indian food clearly does not understand the meaning of the word “bachelor”. This in turn is taken to suggest that there is a minimum requirement for understanding. This suggestion is taken very seriously by proponents of the analytic account of the a priori, who claim that a thinker who understands the meaning of the word ‘bachelor’ cannot fail to accept, say, that all bachelors are unmarried. The idea is that it is constitutive of a thinker’s understanding of the word ‘bachelor’ or it is constitutive of the thinker’s grasp of the concept bachelor to believe that all bachelors are unmarried. It follows that necessarily, anyone who understands the meaning of the word ‘bachelor’ is disposed to accept that all bachelors are unmarried.⁹

A similar line of thought is applied to logical terms. For example, it is claimed that to understand the meaning of ‘if..., then…’ (or to grasp the concept conditional), a thinker has to be disposed to infer according to a certain set of inferences that constitute the meaning of ‘if..., then...’ (or that provide the conditions under which the thinker possesses the concept conditional). Many take modus ponens to give the possession conditions for the concept conditional. The idea is that it is constitutive of the thinker’s understanding of ‘if..., then...’ (or grasp of the concept conditional) to be disposed to infer according to modus ponens.

Here is the principle that underlies this account:

(Meaning constitution - MC) Necessarily, whoever grasps a concept C is disposed to hold a certain believe or to employ those rules of inference that are built into the possession conditions for C.

But how do we get from (MC) to a priori justification (and knowledge), which is the thing we want to explain? Different proposals differ in their details about how to link meaning-constitution or concept-possession with epistemic justification. But the basic idea is that if a thinker could not have thoughts involving a certain concept without being disposed to hold certain beliefs or to use certain rules of inference, then the thinker is thereby (prima-facie) justified, just in virtue of possessing those concepts, to hold those beliefs or to employ those rules of inference that are built into the possession conditions for a given concept.

This idea is explicitly endorsed by Boghossian (2003b):

Suppose that it’s true that my taking p and ‘if p, then q’ as a warrant for believing q is constitutive of my being able to have if thoughts in the first place. Then doesn’t it follow that I could not have been epistemically blameworthy in taking p and ‘if p, then q’ as reason for believing q even in the absence of any reason for taking those premises to be a reason for believing that conclusion? If inferring from those premises to that conclusion is required, if I am to have the ingredient propositions, then it looks as though so inferring cannot be held against me, even if the inference is, as I shall put it, blind — unsupported by any positive warrant. (pp. 25-26)

Here is the epistemic principles behind this idea¹⁰:

(BLIND) If a thinker is not epistemically blameworthy in holding a certain belief or in using a certain rule of inference, then the thinker is (prima-facie) justified in holding that belief or in using that rule of inference.

Assuming that a thinker is not epistemically blameworthy in holding those beliefs or in employing those rules of inference that give the possession conditions for a concept, together with (MC) and (BLIND) we get the principle that links concept possession with justification:

(Meaning-justification link – MJL): Necessarily, whoever grasps concept a C is justified in employing those rules of inference or in holding those beliefs that are built into the possession conditions for C.¹¹

Since understanding a word is a matter of linguistic competence, and grasping a concept a matter of conceptual competence, linguistic or conceptual competence is taken to be all that is required to explain the a priori.

This account of the a priori is what Boghossian (2003b) calls the Constitutive Model. Similar accounts have been proposed by others.¹² I will focus on Boghossian’s account as it is the most explicit and developed analytic account of the a priori available.¹³

Williamson (2007) is well-known for his critique of MJL. He criticises MJL by rejecting MC.¹⁴ His main claim is that there are no possession conditions for a concept, and he appeals to several examples to support this claim. One of those examples is the one of the logician Vann McGee (1985) who rejects modus ponens, which is taken to give the possession condition for the conditional, but who clearly fully understands the meaning of ‘if…then…’. Some have been unconvinced by Williamson’s counter-examples to MJL.¹⁵ I will offer a very different kind of argument against this account of the a priori. I argue that even if we assume the truth of MJL, this account still fails to explain the a priori. In other words, my strategy will be to concede the most I can to Boghossian and argue that even if we do so, we are still unable to explain the a priori. This, I hope, should motivate a different approach to explain the a priori.

Now, as Boghossian (2003a, b) notes, even if MC is true, there are several counter-examples to MJL, cases in which a thinker is not justified in having a certain belief or in employing a certain rule of inference just because of its putative role in constituting meanings. Here are two famous examples of concepts with possession conditions that are epistemically dubious: Prior’s tonk and Dummett’s boche¹⁶:

$$ {\displaystyle \begin{array}{l}\left(\mathrm{TONK}\right)\kern8.40em \left(\mathrm{BOCHE}\right)\\ {}\frac{\mathrm{A}}{\mathrm{A}\ \mathrm{tonk}\ \mathrm{B}}\kern0.5em \frac{\mathrm{A}\ \mathrm{tonk}\ \mathrm{B}}{\mathrm{B}}\kern0.5em \frac{\mathrm{x}\ \mathrm{is}\ \mathrm{German}}{\mathrm{x}\ \mathrm{is}\ \mathrm{boche}}\kern0.5em \frac{\mathrm{x}\ \mathrm{is}\ \mathrm{boche}}{\mathrm{x}\ \mathrm{is}\ \mathrm{cruel}}\end{array}} $$

It is clear that just by grasping the purported concept tonk a thinker is not justified to infer any B from any A – nor is anyone justified to believe that all Germans are cruel. A thinker who employed such rules of inference would be epistemically blameworthy. We thus need to restrict MJL to rule out such counter-examples. As Boghossian (2003b) argues, two strategies are available to the proponent of MJL: (i) she can either provide a way of ruling out such concepts as genuine concepts, or (ii) she can provide a way of restricting MJL to concepts with possession conditions that a thinker is justified in holding.

The first type of strategy has been adopted by those who claim that concepts with possession conditions that are not truth-preserving are spurious.¹⁷ The problem is that even if this strategy works to rule out cases like tonk, it is not clear that it works to rule out boche-like concepts. Whereas it is plausible to claim that tonk is not a concept – e.g., we could argue that it cannot play a role in one’s thoughts – it is not clear why we cannot have boche-like concepts.¹⁸ After all, it seems that we are able to express complete thoughts with boche-like concepts. In fact, there are such concepts, concepts that have been used to express derogatory thoughts, like the concept geek.¹⁹ It is plausible to claim that those thinkers who have been using such concepts are able to express complete thoughts. In any case, as Boghossian argues, there are other counter-examples that would not be ruled out by restricting MJL in this way:

$$ {\displaystyle \begin{array}{l}\left(\mathrm{FLURG}\right)\kern12.50em \left(\mathrm{AQUA}\right)\\ {}\begin{array}{cccc}\frac{\begin{array}{l}\mathrm{X}\ \mathrm{is}\ \mathrm{an}\ \mathrm{elliptical}\ \\ {}\kern1.5em \mathrm{equation}\end{array}}{\mathrm{x}\ \mathrm{is}\ \mathrm{flurg}}& \frac{\mathrm{x}\ \mathrm{is}\ \mathrm{flurg}}{\begin{array}{l}\kern1.5em \mathrm{x}\ \mathrm{can}\ \mathrm{be}\ \\ {}\mathrm{correlated}\ \mathrm{with}\ \mathrm{a}\ \\ {}\mathrm{modular}\ \mathrm{form}\end{array}}& \frac{\mathrm{x}\ \mathrm{is}\ \mathrm{water}}{\mathrm{x}\ \mathrm{is}\ \mathrm{aqua}}& \frac{\mathrm{x}\ \mathrm{is}\ \mathrm{aqua}}{\mathrm{x}\ \mathrm{is}\ {\mathrm{H}}_2\mathrm{O}}\end{array}\end{array}} $$

Although the possession conditions for both flurg and aqua are truth-preserving it seems clear that no one would be epistemically justified in reasoning with those rules just because of their putative roles in constituting meanings. For example, no one would be a priori justified in believing that water is H₂O just by introducing aqua into our language via those inference rules.

If this is correct, then further restrictions are required to safeguard MJL from this type of counterexample.²⁰ Safeguarding MJL by ruling out such concepts as genuine concepts seems wrong. If this strategy seems implausible in the case of boche-like concepts with constitutive rules that are not truth-preserving, it seems even more so for concepts with truth-preserving constitutive rules such as aqua and flurg.²¹ This is not to say that such concepts are acceptable, for they are clearly defective. However, a way of dealing with this kind of counterexample without imposing too strong demands on what counts as a genuine concept would be comparatively preferable. And that is what Boghossian (2003a, b) offers.

Boghossian claims that concepts such as aqua and flurg are defective because they exclude the possibility that the epistemic commitments introduced by their constitutive-rules might be wrong. In order for those concepts to be epistemically acceptable they should not prejudge factual claims. If possible, a thinker should be able to question whether there is anything that satisfies the commitments introduced by their constitutive rules. The idea is that instead of accepting the unconditional rules of inference for aqua, the thinker should only accept that if there is a property with such-and-such a role, then that property is aqua. This allows a thinker to possess the concept aqua and question whether anything is aqua.

Following Ramsey-Carnap-Lewis account of theoretical terms, Boghossian suggests a way of demarcating defective from non-defective concepts. Representing aqua theory as T(aqua), Boghossian divides it into two components, the Ramsey sentence (S) and the Carnap sentence (M):

$$ {\displaystyle \begin{array}{l}\left(\mathrm{S}\right)\exists \mathrm{F}\ \mathrm{T}\left(\mathrm{F}\right)\\ {}\left(\mathrm{M}\right)\exists \mathrm{F}\ \mathrm{T}\left(\mathrm{F}\right)\to \mathrm{T}\left(\mathrm{aqua}\right)\end{array}} $$

T(aqua) is logically equivalent to the conjunction of both components. The idea is that to possess the concept aqua requires one to accept (M) but need not accept (S). Thus, one can have the concept aqua but dispute whether water is H₂O.²²

The main thread of the idea being suggested here is that some concepts are such that we are not justified in reasoning according to their possession conditions just by grasping them. Those are the concepts that introduce certain commitments whose blind acceptance would be unjustified. Such concepts are defective. By conditionalizing on the existence of an appropriate semantic value that would make their constitutive rules truth-preserving, such concepts become non-defective, and such that we would no longer be epistemically blameworthy in accepting their possession conditions.

Boghossian (2003a, b) further claims that not all concepts are such that we can doubt or question their possession conditions. Arguably, certain logical concepts, such as the concept conditional, are such that we cannot coherently conditionalize on the existence of an appropriate semantic value that would make their constitutive rules truth-preserving because they would be presupposed in any such conditionalization. Thus, we would not be violating BLIND by reasoning according to the possession conditions for logical concepts. We are justified in holding the possession condition for our logical concepts just by grasping them.²³

So, on this account, we have two types of concepts: unconditionalizable concepts and conditionalizable concepts. Unconditionalizable concepts are non-defective. Conditionalizable concepts are defective but become non-defective when conditionalized.

Here is the new version of MJL that follows from these considerations:

MJL*: Necessarily, whoever grasps a non-defective concept C is justified in employing those rules of inference or in holding those beliefs that are built into the possession conditions for C.

Does this model provide a good answer for how semantic understanding suffices for epistemic justification, which is what we need in order to explain the a priori with the analytic? I shall now argue that it does not.

3.1 What Is Epistemically Analytic?

Boghossian uses Ramsey-Carnap-Lewis account of theoretical terms to distinguish defective from non-defective concepts. A defective concept is a concept whose possession conditions are such that we are epistemically blameworthy in holding just by grasping them. Such defectiveness can, nonetheless, be corrected by conditionalizing over the possession conditions for such concepts. So, a thinker who correctly grasps a concept like boche must be willing to affirm its conditional version – the Carnap sentence of T(boche) – but not its defective unconditionalized version – that is, T(boche).²⁴ Such a thinker becomes epistemically responsible, one who performs her epistemic duties by her willingness to question whether there is anything that falls under such a concept. If she cannot coherently question the possession conditions for a certain concept, then she has no epistemic duty to do so, and she can accept them just by grasping the concept at stake. Here is Boghossian (2003b):

You don’t ever want the possession conditions for a concept to foreclose on the possible falsity of some particular set of claims about the world, if you can possibly avoid it. You want the possessor of the concept to be able coherently to ask whether there is anything that falls under it, and you want people to disagree whether there is. If in a certain range of cases, however, it is logically impossible to hold the governing theory at arm’s length then, in those cases, obviously, it can hardly be a requirement that one do so. But in those cases where it is possible, it ought to be done. (pp. 31-32)

Now, let us recapitulate the dialectic so far. The aim of the analytic account of the a priori is to explain how semantic understanding suffices for epistemic justification. We were offered MJL to explain that. MJL, however, faces several counterexamples and had to be restricted. Those restrictions show that sometimes semantic understanding does not suffice for epistemic justification because a thinker is epistemically blameworthy in holding the possession conditions for a concept. By restricting MJL, we got MJL* according to which we are entitled to hold the possession conditions for a non-defective concept just by grasping it. Concepts whose possession conditions are coherently questionable are defective. But by conditionalizing over their possession conditions they become non-defective. Logical concepts are, purportedly, the only concepts whose possession conditions are not coherently questionable. Thus, on this account, only two types of sentences can be (epistemically) analytic, and (directly) a priori knowable: (i) conditional sentences (i.e. sentences that express Carnap sentences), and (ii) sentences that express basic logical truths.

The problem is that it is implausible to claim that only truths that express Carnap sentences and logical truths are knowable a priori in a non-inferential way – and are, thus, epistemically analytic. Among the truths that have been traditionally regarded as knowable a priori are, for example, the most fundamental truths of epistemology, metaphysics, and ethics. For example, take the truth that it is wrong to torture people for pleasure. Such a truth seems knowable directly a priori and is neither a logical truth nor is it expressed by a Carnap sentence. A paradigmatically analytic truth such as “no object can be both red and green all over at the same time” is, also, arguably, neither reducible to a logical truth nor is it expressed by a Carnap sentence. An account of the a priori that leaves without explanation how such truths are a priori knowable is extensionally inadequate, and thus clearly deficient.

To this one might say that moral truths like the one given are not basic but rather inferred from more basic moral truths. But what could such more basic moral truths be? Is it a moral truth written into the possession condition for the concepts wrong or torture? If so, as competent speakers we should be disposed to accept the truths that are written into the possession conditions for wrong and torture just by grasping such concepts, and it is not at all clear what such truths could be. Also, to use Peacocke’s (1992) useful expression, the claim that it is wrong to torture people for pleasure is primitively compelling, as it is not compelling in virtue of one finding something else compelling. Such a truth does seem directly knowable a priori, but one whose epistemic status this account lacks the resources to explain.

Now consider the epistemic principle BLIND. This is an a priori principle, something that if knowable, is knowable a priori. If BLIND is a priori, then it is either inferred from more basic epistemic principles or is directly knowable a priori. If it is inferred, it must be inferred from the possession conditions for concepts such as blameworthy, but it is not clear what the possession conditions for such a concept could be. BLIND does seem to be directly knowable a priori. But if BLIND is directly knowable a priori, then it must itself be written into the possession conditions for blameworthy, and there is no non-question-begging reason to think that it is. Moreover, BLIND is neither a logical truth nor does it express a Carnap sentence, and so not something that, on this account, could be directly knowable a priori. Thus, it seems that on this account we are incapable of explaining how we come to know a principle such as BLIND.

At this juncture, someone might claim that even if Boghossian’s account fails to explain all cases of basic a priori knowledge, it at least succeeds in explaining our knowledge of basic logical truths. However, we also have good reason to think that it too fails to do that.²⁵

All this account says is that we can hold the possession conditions for logical concepts because they are so basic that we cannot coherently doubt them. But this leaves MJL* close to vacuity. After all, what is doing the explanatory work are not considerations about what the possession conditions for a concept are, but principle BLIND. More precisely, it is claimed that one cannot coherently doubt the correctness of certain logical inferences or the truth of certain statements given the central role they play in one’s thinking. This in turn is taken to show that one is not blameworthy in blindly employ them. If one is not blameworthy in employing a certain rule of inference, then, according to BLIND, one is justified in using it. The explanatorily work is, thus, done solely by BLIND, and not by MC.

Now notice the dialectic of the debate. The aim was to explain how semantic understanding suffices for epistemic justification. We were given MJL to do that. But then we were confronted with several counterexamples that forced us to make some restrictions to MJL. This gave us MJL*, according to which we can follow some basic rules of inferences (or accept certain logical truths) that are written into the possession conditions for our logical concepts because we cannot coherently doubt such rules. But then we are left with no explanation of how semantic understanding suffices for epistemic justification. Even if it is true that there are some rules of inference (or some truths) that are so basic to our thought that we cannot coherently doubt them, this is no explanation of how we know such rules, only an explanation (if at all) of which rules are basic.

The idea that we cannot coherently doubt certain logical truths or rules of inference given the central role they play in one’s thinking is just the old idea that basic logical truths and inferences are so basic that we cannot do without them, an idea that does little to explain how we know them. This, as I understand it, can be taken as a version of the criticism of vacuity that Quine (1954) raised against the positivist analytic account of the a priori:

(...) now it seems to imply nothing that is not already implied by the fact that elementary logic is obvious or can be resolved into obvious steps. (p. 112)

I thus submit that we have good reason to think that this account of the a priori does not cover all cases of the a priori, and fails to adequately explain those that it does cover.

4 Understanding without Meaning-Constitution

Let us now turn to a very different way of defending the analytic account of the a priori, one that does not rely on a principle such as MJL. This is the account proposed by Balcerak Jackson and Balcerak Jackson (2012). They aim to show how we can generate knowledge “purely on the basis of understanding” (p. 185, my emphasis) without appealing to any meaning-justification links. If this proposal were successful, we could agree with Williamson (2007) that no belief is constitutive of meaning, reject MJL, and uphold the analytic account of the a priori. They claim that “[t]o the extent that our discussion makes it possible that one can ground knowledge in understanding, it contributes to Boghossian’s project of developing and defending an epistemological conception of analyticity” (p.186). My aim is to briefly consider this proposal to provide further support to the claim that we should look somewhere other than semantic considerations, and the notion of analyticity, to explain the a priori.

Now, how could we generate a priori knowledge purely on the basis of semantic understanding if no beliefs are required for understanding? If, for example, my understanding of the meaning of ‘bachelor’ does not require me to believe that all bachelors are unmarried, how are we to explain how we know that all bachelors are unmarried just by understanding the meaning of “all bachelors are unmarried” or by grasping the thought that all bachelors are unmarried?

Balcerak Jackson and Balcerak Jackson (2012) appeal to an analogy between chess and mathematical competence, and understanding, to make their case. They argue that just as a chess player can be perfectly competent in the use of her abilities without holding any particular chess-beliefs, one can be perfectly competent in understanding the meaning of a word without holding any particular beliefs.²⁶ They claim that, “[t]hese analogies suggest a picture of understanding as being (or involving) a set of cognitive capacities, just as chess and mathematical competence are.” (p. 196) But what type of capacities are these? According to them, these capacities are capacities such as the capacity to identify the actual and possible extension of a concept, the reflective capacity to think about a concept, and so on. Here is how they illustrate their proposal:

Consider again the ability to classify cases that come with understanding of the concept expressed by “knowledge” and other concepts. One might systematically apply this ability to various actual and hypothetical subjects and begin to notice patterns. For example, one might notice that among all the subjects one has considered, all of them who known that p have also had a true belief that p. This provides some justification for the hypothesis that knowledge requires true belief, and one can strengthen this justification by considering further cases of different sorts, seeking out the cases that seem most likely to provide counterexamples if there are any, trying to rule out alternative hypotheses, and so on. (p. 197)

They are right to claim that we need to understand or grasp the concept knowledge to be able to reflect on whether actual or hypothetical subjects have knowledge. However, grasp of concepts (or understanding concepts) only plays an enabling role in the justification of our belief that knowledge requires true belief. No doubt that understanding of the concept knowledge enables us to reflect upon the claim that knowledge requires true belief, and it also enables us to exercise one’s imaginative and reflective abilities by considering actual and hypothetical subjects. Understanding of concepts, however, grounds all propositional knowledge, be it a priori or empirical. For example, we could not come to know that grass is green without understanding of the concepts grass and green and their modes of combination. Understanding of the concepts grass and green (and their modes of combination) enables us to entertain the thought that grass is green, but it is our perceptual abilities that, somehow, justify us in believing that grass is green. Likewise, understanding of the concept knowledge enables us to entertain the thought that knowledge requires belief, but it is our imaginative and reflective abilities that, somehow, confer justification upon our belief that knowledge requires true belief. Understanding of concepts, and concept possession, is required in any (propositional) cognitive enterprise, but the claim behind the analytic account of the a priori is one of sufficiency, not of necessity.

To illustrate the point being made here, consider a case in which we were trying to find out whether the colour blue is our friends’ favourite colour. First, we need to understand the concept expressed by ‘blue’, and other concepts. One might systematically apply this ability to all our actual friends, and even consider hypothetical friends and begin to notice patters. For example, we can come to realise that all our actual friends enjoy looking at the sky when it is blue, that they all have more blue pieces of clothing than of any other colour, and so on. We can even wonder if a possible friend would behave in a similar way. This seems to provide some justification for the hypothesis that blue is our friends’ favourite colour, and one can strengthen this justification by considering further cases of different sorts, like friends we have lost touch with, look for counterexamples, and so on.

To be justified in believing that blue is our friends’ favourite colour we need to understand the concepts expressed by ‘blue’, ‘friends’, and ‘favourite’ (and their modes of combination). However, it is clear that we cannot come to know what our friend’s favourite colour is a priori. If it is clear that mere understanding of concepts is not sufficient for knowledge in this case, it should also be clear in the knowledge example above that mere understanding of the concept knowledge is not sufficient to come to know that knowledge requires true belief as I followed the same argumentative pattern as Balcerak Jackson & Balcerak Jackson did when elaborating on that example. No doubt that conceptual understanding enables us to exercise a set of cognitive capacities. However, even if those capacities are grounded in conceptual understanding in the sense that we could not exercise them without understanding of concepts, such knowledge is not acquired purely on the basis of conceptual understanding, but rather on the basis of those other capacities.

To this one might reply that I am missing the point given the way Balcerak Jackson & Balcerak Jackson conceive of the capacity of understanding. After all, they have a very rich notion of understanding, one that includes many distinct cognitive abilities, abilities such as imagination, reflection, and even “[...] the ability to make a certain logical inference, and perhaps also the ability to engage in various kinds of inductive and abductive reasoning” (p.196). However, the ability to reflect upon a thought seems very different from the ability to imagine counter-examples, or the ability to make logical inferences, or the ability to understand a concept, and there is no clear non-question-begging reason to label all these distinct abilities under ‘understanding.’

However, if we include in our conception of understanding all the a priori faculties, faculties such as reflection, imagination, reasoning, grasp of concepts and so on, as Balcerak Jackson & Balcerak Jackson do, then it seems clear that we can generate a priori knowledge purely on the basis of understanding thus conceived. It should, nonetheless, be clear that what we get is no longer an analytic account of the a priori but a form of rationalism in disguise. What grounds the a priori, on this account and the rationalist account, are special faculties exercised in the acquisition of a priori knowledge – regardless of whether one calls them ‘understanding’ or ‘rational intuition.’ Labelling all the purportedly a priori faculties under ‘understanding’ does not alter the fact that understanding of concepts only plays an enabling role in the acquisition of a priori knowledge, and that imagination, reflection, and reasoning play the more fundamental, justificatory role.

I thus submit that Balcerak Jackson & Balcerak Jackson proposal appeals to such a rich notion of understanding, one that includes so many distinct cognitive abilities (viz. imagination, reflection, reasoning, and so on), that renders their account more akin to a form of rationalism than a form of analytic account of the a priori. I do, nonetheless, think that a form of rationalist along these lines, one that looks at the cognitive abilities involved in the acquisition of a priori knowledge is a much more promising way of explaining the a priori.

5 Concluding Remarks

I have explored two very different analytic accounts of the a priori: (i) a more traditional concept-based account, and (ii) a less traditional understanding-based account. In section 3 I argued that the concept-based analytic account of the a priori is both extensionally inadequate and explanatorily deficient. In section 4 I argued that the understanding-based account can be made to work, but only by employing a very rich notion of understanding making it a form of rationalism in disguise. I am aware that these considerations do not offer conclusive reasons to reject the analytic account of the a priori, but they do seem to me to motivate a different type of explanation of the a priori, one that distances itself from semantic considerations regarding the properties of what is knowable a priori, and that focus instead on the faculties used to come to know a priori truths.

The understanding-based analytic account of the a priori is closer in letter (even if not in spirit) to the sort of account I am suggesting here. The aim of the understanding-based account of the a priori is to explain the a priori solely on the basis of conceptual understanding. However, given the insufficient resources of conceptual understanding to do the required work, a richer notion of understanding is used, one that includes such distinct faculties as imagination, reflection, grasp of concepts, reasoning, and so on. We have no non-question-begging reason to include all these faculties under the label of ‘understanding’, but we do have good reason to examine the role they play in the acquisition of a priori knowledge.

I am aware that a faculty-based account of the a priori also faces difficult challenges. My aim here, however, was rather more modest: challenge the analytic account of the a priori, and motivate a rationalist faculty-based account, one that is closer in spirit to the traditional rationalist account of the a priori. It seems to me that a better way of explaining the a priori is to veer away from semantic considerations and focus instead on the cognitive faculties used by the thinkers in the acquisition of such knowledge.