(Hanna, 2015)
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Is A Priori Knowledge Really Possible? Yes; Here’s Proof
The philosophical debate over the real possibility of a priori knowledge—that is, non-stipulative, non-trivial knowledge of the way the world necessarily is, obtained sufficiently independently of any and all sense-experiential episodes and/or contingent natural facts—is no less important today than it was when Plato posited in the Meno that we are able to have such knowledge owing to a pre-natal close encounter that our disembodied souls had with the Forms, and when René Descartes posited in the Meditations on First Philosophy that such knowledge is infallible because guaranteed by a non-deceiving God. Of course, neither the platonic story nor the Cartesian story about our purported a priori abilities has many adherents today. Nevertheless, a large majority of contemporary professional academic philosophers do indeed believe that a priori knowledge exists: 72.8%, according to a 2020 PhilPapers survey (Bourget and Chalmers, 2023), which in fact marks a slight increase in the collective reponse to the same question as reported in a survey done 10 years earlier (Bourget and Chalmers, 2014). And if a priori knowledge exists, then it’s really possible.
The classical story, shared by Plato and Descartes, goes something like this: Rational human animals have special non-empirical cognitive capacities—perhaps minimally analogous to sense-perceptual capacities—that connect them, rational human cognizers, directly to certain abstract and necessary features of the world. These capacities yield what are called “rational intuitions,” and by consulting these rational intuitions, rational human cognizers are able to receive reliable information about the way the world necessarily is. These rational intuitions, in turn, act as sufficient justifiers of rational human cognizers’ beliefs about certain kinds of propositions, namely, necessary truths, and because of these intuitional sufficient justifiers, a priori knowledge is really possible.
I’ll call the thesis that a priori knowledge of necessary truth is really possible, via the human cognitive capacity for rational intuitions, rationalism. The old rationalism, in addition, says (i) that rational intuitions always deliver absolutely infallible information about the abstract truth-making objects of necessary propositions, and (ii) that the abstract truth-making objects of rational human intuitional a priori knowledge are non-spatiotemporal, causally irrelevant, and causally inert entities (for example, Plato’s Forms, or Descartes’s “true and immutable natures”). The new rationalism, or neo-rationalism, by an important contrast, says (i*) that rational intuitions do at least sometimes, although not always, deliver reliable, but not absolutely infallible, information about the abstract truth-making objects of necessary propositions (Chapman et al., 2013). And the contemporary Kantian neo-rationalism that I defend in Cognition, Content, and the A Priori, by another important contrast, also says (ii*) that the truth-making objects of rational human intuitional a priori knowledge are indeed abstract, but neither non-spatiotemporal nor causally irrelevant, precisely because they are abstract in the non-platonic, Kantian sense only (Hanna, 2015: chs. 6-8).
Opposed to this rationalist story, whether old or new, and whether non-Kantian or Kantian, is an equally prestigious tradition that’s skeptical about our purported capacity to achieve a priori knowledge of necessary truth via rational-intuitional means.
Such intuition-skeptical attacks on rationalism come in many forms. Some attacks attempt to show that rationalists can tell no satisfactory story about the connection between the mind and the world such that rational intuitions could reliably deliver a priori knowledge of necessary features of the world. Other attacks attempt to show that rational intuitions are so inherently fallible that they can never satisfactorily justify purportedly a priori knowledge. Further attacks attempt to show that we can gain all the knowledge we think we have (both a posteriori and purportedly a priori) via purely sense-experiential means, and that parsimony requires that we not posit other (perhaps metaphysically and epistemically dubious) epistemic capacities. And still other attacks claim that, contrary to widely-held methodological and meta-philosophical beliefs, philosophers do not really rely on rational intuitions as evidence either for philosophical theories or for any other significant claims. I’ll call the constellation of skeptical views just described, intuition-skeptical empiricism.
Whatever the plausibility of intuition-skeptical empiricist attacks on rationalism, at the same time many contemporary philosophers are reluctant to accept intuition-skeptical empiricist conclusions. Indeed, since the late 1980s there has been a renewed and steadily growing interest in rationalism and the a priori; and gradually, what George Bealer has very aptly and rightly dubbed a rationalist renaissance has emerged onto the 21st century philosophical scene (Bealer, 2006). At the same time, however, even despite this rationalist renaissance, the all-important neo-rationalist notion of rational intuition has not been either adequately defended or fully developed, especially as regards solving the two core problems about rational intuition: first, how rational intuitions can sufficiently justify beliefs (the justification problem), and second, how to explain the real possibility of rational intuitions (the explanation problem). So here is where contemporary philosophers now find themselves, after all these dialectical skirmishes: intuition-skeptical empiricism is arguably false; but intuition-skeptical attacks on rationalism are, as yet, not directly answered, or at least not decisively answered. Given this fact, many contemporary philosophers will, as it were, talk out of both sides of their mouths, by (on the one side) declaring themselves neo-rationalists, while (on the other side) also ruefully admitting, at least implicitly in their work, that they have no direct or decisive responses to the most important intuition-skeptical empiricist attacks on rationalism, and correspondingly, no direct or decisive solutions to one or both of the two core problems about rational intuition—the justification problem, and the explanation problem.
In what follows, following on from (Chapman et al., 2013; and Hanna, 2015), I’m going to spell out a broadly Kantian conception of apriority, and then prove that at least some a priori knowledge in this sense actually exists. That in turn will suffice for an initial demonstration of both the real possibility of a priori knowledge and also the truth of neo-rationalism.
What is apriority? In the first Critique, Kant says that
Although all our cognition commences with experience, yet it does not on that account all arise from experience.… It is therefore a question requiring closer investigation , and one not to be dismissed at first glance, whether there is any such cognition independent of all experience and even of all impressions of the senses. One calls such cognitions a priori, and distinguishes them from empirical ones, which have their sources a posteriori, namely in experience. (Kant, 1781/1787/1997: p. 136, B1-2)
Nevertheless, that text must also be juxtaposed with this one:
[W]e will understand by a priori cognitions not those that occur independently of this or that experience, but rather those that occur absolutely independently of all experience. Opposed to these are empirical cognitions, or those that are possible only a posteriori, i.e., through experience…. Experience teaches us, to be sure, that something is constituted thus and so, but not that it could not be otherwise. First, then, if a proposition is thought along with its necessity, then it is an a priori judgment; …. Second: Experience never gives its judgments true or strict but only assumed and comparative universality (through induction), so properly it must be said: as far as we have perceived, there is no exception to this or that rule. Thus if a judgment is thought in strict universality, i.e., in such a way that no exception is allowed to be possible, then it is not derived from experience, but is rather valid absolutely a priori…. Necessity and strict universality are therefore secure indicators (Kennzeichen) of an a priori cognition, and also belong together inseparably. But since in their use it is sometimes easier to show the empirical limitation in judgments than contingency in them, or is often more plausible to show the unrestricted universality that we ascribe to a judgment than its necessity, it is advisable to employ separately these two criteria, each of which is infallible. (Kant, 1781/1787/1997: p. 137, B2-4)
I think that these two Kantian texts collectively express a deep twofold insight that explains how it can be true both that (1) “all our cognition commences with experience” and also that (2) there exist “a priori cognitions [which are] not those that occur independently of this or that experience, but rather those that occur absolutely independently of all experience.” Above all, we need to have a clear and precise account of what “absolute experience-independence” means, and, correspondingly, what “experience-dependence” means.
In order to do this, I’ll need to rehearse some terminological definitions. By empirical facts I mean inner or outer sensory experiences and/or contingent natural objects or facts. And I am understanding the relation of necessary determination to be equivalent to strong supervenience in the following way:
X necessarily determines Y if and only if the Y-facts strongly supervene on the X-facts.
In turn,
Y-facts strongly supervene on X-facts if and only if X-facts necessitate Y-facts and there cannot be a change in anything’s Y-facts without a corresponding change in its X-facts.
In other words, in the relation of necessary determination, both the existence of the Y-facts and also the specific character of the Y-facts are metaphysically controlled by the existence and specific character of the X-facts. The necessary determination relation can also be strengthened to a constitutive dependence relation insofar as not only the existence and specific character of the Y-facts but also the essences or natures of the Y-facts are metaphysically controlled by the existence and specific character of the X-facts:
Y-facts constitutively depend on X-facts if and only if X-facts necessitate Y-facts and there cannot be a change in anything’s Y-facts without a corresponding change in its X-facts, and the essence or nature of anything’s Y-facts presuppose the essence or nature of its X-facts.
Then we can also say that the Y-facts are “grounded by” the X-facts.
Now let’s take it as a given that necessarily, all human cognition begins in sense perception of contingent natural objects or facts. Then Kant’s deep insight is this: apriority, or experience-independence, is the underdetermination of the meaning, truth, and/or justification of a belief by any and all actual or possible empirical facts. Otherwise put, apriority is the necessary and constitutive underdetermination of the meaning, truth, and/or justification of a belief by any and all empirical facts. Or still otherwise put, precisely to the extent that a belief is a priori, then its meaning, truth, and/or justification is neither strongly supervenient on nor grounded by any and all empirical facts.So, to formulate this conception of apriority as a handy set of necessary equivalences that you can make into a meme and post on your Instagram site:
apriority –> experience-independence –> the necessary and constitutive underdetermination of the meaning, truth, and/or justification of a belief S by any and all empirical facts –> the meaning, truth, and/or justification of a belief is neither strongly supervenient on nor grounded by any and all empirical facts.
Correspondingly, then, aposteriority is the necessary and constitutive determination of the meaning, truth, and/or justification of a belief by any or all actual or possible empirical facts. Otherwise put, aposteriority is the necessary and constitutive determination of the meaning, truth, and/or justification of a belief by any or all empirical facts. Or still otherwise put, precisely to the extent that a belief a posteriori, then its meaning, truth, and/or justification is either strongly supervenient on or grounded by any or all empirical facts. So, to formulate this conception of aposteriority as another handy, Instagram-ready set of necessary equivalences:
aposteriority –> experience-dependence ßà the necessary and constitutive determination of the meaning, truth, and/or justification of a belief by any or all empirical facts –> the meaning, truth, and/or justification of a belief is either strongly supervenient on or grounded by any or all empirical facts.
There are two features of this broadly Kantian conception of apriority that every historian of modern philosophy and every contemporary epistemologist should learn by heart—or at the very least, write out in longhand, carefully fold up, and keep under their pillows. First, according to this broadly Kantian conception of apriority, it’s fully acknowledged that all human knowledge begins in our sense perception of contingent natural objects or facts. Second, according to this broadly Kantian conception of apriority, it is perfectly possible for a belief to be such that (i) that belief’s meaning must bear some significant relation to empirical facts, (ii) that belief’s truth or falsity must be learned or confirmed by means of empirical facts, at least in part, and (iii) that belief’s justification must be supported by sense-experiential evidence about empirical facts and established by experimental methods, at least in part, and also for that belief to a necessary and priori.
Here, now, are three incontrovertible examples of a priori necessary statements that you, I, and every other rational human animal under normal cognitive conditions believes, or at least can believe, whenever it’s brought to their attention, such that these statements’ meaning must bear some significant relation to empirical facts, such that their truth must be learned or confirmed by means of empirical facts, at least in part, and such that their belief-justification must be supported by sense-experiential evidence about empirical facts and established by experimental methods, at least in part:
It is not always true that it is the case that Socrates is mortal and also not the case that Socrates is mortal.
If Socrates is a bachelor, then Socrates is an unmarried male.
3 martinis + 4 martinis = 7 martinis, i.e.,
In this connection—leaving aside the seven thirst-quenching martinis represented by those seven little martini-pictures, that is—Kant’s two deep insights are these. (i) There is no such thing as a priori belief that altogether excludes empirical facts, which yields a minimal Empiricism. (ii) But the same time, it does not follow from the minimal Empiricism expressed in (i) that any version of maximal Empiricism—say, classical Lockean-Humean Empiricism, or Quine’s radical Empiricism—is true. Maximal Empiricism says that the meaning, truth, and/or justification of all beliefs are necessarily or constitutively determined by, strongly supervenient on, grounded by, or, even more radically, reducible to empirical facts. But this does not follow from (i) and its minimal Empiricism. That would be clearly and simply be, in Peter Strawson’s lovely phrase, “a non sequitur of numbing grossness” (Strawson, 1959: p. 137). Nevertheless, even despite its numbing grossness, it’s a non sequitur that’s in fact committed by a great many philosophers, who’ve been blinded by classical and/or contemporary Empiricism.
Now what about a priori knowledge? Well, consider this statement: “3+4=7.” Very few statements, even necessarily true statements, are objectively[i] knowable in such a way that one’s believing that statement is (i) completely convincing, intrinsically compelling, or self-evident, (ii) evidentially delivered to belief by a properly-functioning cognitive mechanism, aka cognitively virtuous, and also (iii) essentially reliable, that is, such that it includes a non-accidental or necessary tie to the necessary-truth-makers of belief. But this is one of those statements. And I think I can prove that to you in four short steps.
First, please look at this simple stroke diagram carefully and thoughtfully:
| | | + | | | | = | | | | | | |
Second, I’ll define some terminology. By clarity, I mean that the meaning of your belief is directly present to your consciousness. By distinctness, I mean that the meaning of your belief is consciously discriminable by you from the different meanings of different beliefs. And by indubitability, I mean that it is epistemically impossible for you to sincerely believe the denial of a belief, once you’ve adequately understood that belief. The main point I am making here is that the clarity, distinctness, and indubitability of a belief all add up to its being self-evident, by which I mean that it is completely convincing to you or intrinsically compelling for you .
Third, now having looked at the simple stroke diagram once already, and also having understood what I mean by “clarity,” “distinctness,” “indubitability,” and “self-evident,” please look carefully and thoughtfully again at the simple stroke diagram, and at the same time read the symbol sequence “3+4=7,” while assertorically saying to yourself, “Three plus four equals seven.”
Fourth, by virtue of doing all that, therefore—to use Descartes’s famous terminology—it is clearly, distinctly, indubitably, and self-evidently objectively known by you that necessarily, 3+4=7.
Moreover, although your knowledge that 3+4=7, via the simple stroke diagram, obviously began in human sensory experience, nevertheless its specific meaning and evidential character were not derived from it. That is, they were neither necessarily nor constitutively determined by, or otherwise put, they were necessarily and constitutively underdetermined by any and all empirical facts. So you also know it a priori.
Now, here’s a different proof that a priori knowledge is really possible. Dear Reader, please read this sentence:
(*) You, the reader of this very sentence, are consciously reading this very sentence from left to right here and now.
Now, please read sentence (*) again, this time (even) more slowly and carefully. Obviously, insofar as you read it, it’s true. Moreover, your belief in its truth is sufficiently justified by the intrinsically compelling evidence yielded by the phenomenology—i.e., the subjectively experienced intentional performance, intentional content, and specific qualitative characters—of your conscious act or process of reading it. The sentence cannot read itself, because it’s not conscious; and nobody else but you consciously read that very sentence in the same way, at the same time, and in the same place, that you did. On the contrary to both of those, because the sentence is in English you consciously read it from left to right, and you also consciously read it right here and now, just as the sentence says. Even if nothing else in the world had existed but that sentence and your consciously reading it from left to right here and now; even if you had consciously read that sentence in a dream; or even if an evil scientist had somehow produced in you a hallucination of your consciously reading that sentence: it would still be true, and your belief in its truth would still be sufficiently justified by the intrinsically compelling evidence yielded by the phenomenology of your conscious act or process of reading it. There are no epistemic gaps between you, the reader of sentence (*), and your consciously reading that very sentence. So you have skepticism-proof, a priori knowledge of sentence (*). Or in Descartes’s technical terminology, you have clear, distinct, and certain intuitive knowledge of it (Descartes, 1984-1985b, 1984-1985c, 1984-1985d, 1984-1985e).
Moreover, given the fact that you have skepticism-proof a priori knowledge of sentence (*), Dear Reader, at least twelve other truths also follow self-evidently from it:
1. Therefore, you exist.
2. Therefore, you are conscious.
3. Since you can tell the difference between your left and your right, between now and elsewhen, and also between here and elsewhere, therefore you are an egocentrically-centered, conscious subject locally embedded in orientable spacetime.
4. Therefore, you are also embodied.
5. Therefore, your embodied consciousness exists as locally embedded in orientable spacetime.
6. Therefore, your embodied conscious act or process of reading sentence (*) also exists.
7. Therefore, you also possess a capacity for consciously reading legible sentences like sentence (*) .
8. Therefore, legible sentences also exist, both as types and as tokens of those types instantiated in actual spacetime.
9. Therefore, legible texts exist, both as types and as tokens of those types instantiated in actual spacetime.
10. Therefore, the manifestly real external spacetime world that contains both types and tokens of legible texts exists.
11. Therefore not only you, an egocentrically-centered, embodied conscious subject locally embedded in orientable spacetime, possessing the capacity for reading, exist, but also the manifestly real external spacetime world that contains both types and tokens of legible texts, exists.
12. Because I, R.H., consciously wrote sentence (*), but you, Dear Reader, who are not R.H., consciously read sentence (*), therefore at least two conscious subjects, who are communicating intersubjectively by means of writing and reading, exist in the manifestly real spacetime world that contains both types and tokens of legible texts.
Sentence (*) is what I’ve called a caveat lector sentence (Hanna, 2024). Because of its explicitly self-referential and self-orienting spatiotemporal properties, I’ll call it more specifically a self-locating caveat lector sentence. In what immediately follows, I’m going to argue that self-locating caveat lector sentences are more epistemically fundamental than the classical Cartesian Cogito, that the philosophy of reading, and not the philosophy of thinking and existence, is truly first philosophy in the Cartesian sense, and that therefore our knowledge of self-locating caveat lector sentences like sentence (*) is a priori knowledge.
What is the Cogito? Descartes formulates it in three slightly different ways:
Observing that this truth “I am thinking, therefore I exist” was so firm and sure that all the most extravagant suppositions of the skeptics were incapable of shaking it, I decided that I could accept it without scruple as the first principle of the philosophy I was seeking. (Descartes, 1984-1985c: p. 127, AT VI: 32)
But I have convinced myself that there is absolutely nothing in the world, no sky, no earth, no minds, no bodies. Does it now follow that I too do not exist? No: if I convinced myself of something then I certainly existed. But there is a deceiver of supreme power and cunning who who is deliverately and constantly deceiving me; and let him deceive me as much as he can, he will never bring it about that I am nothing as long as I am something. So after considering everything very thoroughly, I must finally conclude that this proposition, I am, I exist, is necessarily true whenever it is put forward by me or conceived in my mind. (Descartes, 1984-1985d: pp. 16-17, AT VIII: 25)
For it is a contradiction to suppose that what thinks does not, at the very same time when it is thinking, exist. Accordingly, this piece of knowledge—I am thinking, therefore I exist—is the first and most certain of all to occur to anyone who philosophizes in an orderly way. (Descartes, 1984-1985e: p. 195, AT VIIIA: 7)
No matter which formulation we consider, however, it’s essential to notice that the Cogito itself is nothing more and nothing less than a certain legible text that’s embedded within a larger legible text—indeed, also a published text—in philosophy, whether the Discourse on the Method, the Meditations on First Philosophy, or the Principles of Philosophy. To be sure, Descartes’s three formulations of the Cogito are all about thinking and existence, but even so, he’s very explicit that the Cogito itself is just “this truth ‘I am thinking, therefore I exist’,” “this proposition, I am, I exist,” and “this piece of knowledge—I am thinking, therefore I exist” ([boldfacings] added).
Now, in order for Descartes to have written the Cogito, he must already have been able to read the Cogito—otherwise, he wouldn’t have known what he was writing. Therefore, Descartes must have already possessed the capacity for reading, including the capacity for reading self-locating caveat lector sentences like sentence (*). But reading the Cogito does not epistemically or logically guarantee either the existence of the body of the thinking subject or the existence of the external world beyond the body of the thinking subject, or the existence of many thinking subjects—aka “other minds”—and not only one solipsistic thinking subject, without various other premises and subsidiary reasoning, including an appeal to the existence of a non-deceiving God, all of which are—famously and/or notoriously—epistemically questionable in various ways (see, e.g., Markie, 1992; Beyssade, 1992; Loeb, 1992). By a diametric contrast, however, reading self-locating caveat lector sentences does indeed epistemically or logically guarantee not only that you, an egocentrically-centered, embodied conscious subject locally embedded in orientable spacetime, possessing the capacity for reading, exist, but also that the manifestly real external spacetime world that contains both types and tokens of legible texts, exists, and also that at least two intersubjectively communicating conscious subjects exist in that manifestly real spacetime world—as per entailments 11. and 12. of sentence (*). As a consequence, self-locating caveat lector sentences are more epistemically fundamental than the Cogito, the philosophy of reading (see, e.g., Hanna, 2024), and not the philosophy of thinking and existence, is truly first philosophy in the Cartesian sense, and therefore your knowledge of self-locating caveat lector sentences like (*) is a priori knowledge.
In view of what I’ve argued, therefore, a priori knowledge is really possible, neo-rationalism is true, and maximal Empiricism is false. And for a detailed explanation of precisely how a priori knowledge is really possible, an explanation involving (i) a weak form of transcendental idealism, (ii) ontological structuralism, and (iii) an epistemic appeal to the pattern matching powers of our innate capacity for imagination, see (Hanna, 2015: chs. 6-8).
NOTE
[i] By something’s being objectively believable, or its being objectively knowable, I mean simply that it can be believed or known by any rational human animal under normal cognitive conditions, and therefore that it isn’t merely idiosyncratic.
REFERENCES
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(Hanna, 2024). Hanna, R. “Caveat Lector: From Wittgenstein to The Philosophy of Reading.” Journal for the Philosophy of Language, Mind and the Arts 5: forthcoming. Available online in preview HERE.
(Kant, 1781/1787/1997). Kant. I. Critique of Pure Reason. Trans. P. Guyer and A. Wood. Cambridge: Cambridge Univ. Press. (1781 or A edition: Ak 4: 1-251; 1787 or B edition: Ak 3)
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