260. Is a priori knowledge really possible? Yes; here’s proof. The philosophical debate over the possibility of authentic 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 Descartes posited in the Meditations on First Philosophy that such knowledge is infallible because guaranteed by a non-deceiving God.

261. 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 philosophers (71.1%, according to a fairly recent PhilPapers survey[i]) do indeed believe that a priori knowledge is really possible.

But how can such knowledge be really possible?

262. 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, authentic a priori knowledge is really possible.

263. I will 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.

And the contemporary Kantian neo-rationalism that I defend in Cognition, Content, and the A Priori,[ii] 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.

(I won’t get into that doctrine for the purposes of this set of notes, but will indeed spell it out somewhat it in the next (= 14th) installment of Thinking For A Living; and if you’re really a philosophical masochist, then you can take a look at Cognition, Content and the A Priori, ch. 8.)

264. Opposed to this rationalist story, whether old or new, and whether non-Kantian or Kantian, is an equally prestigious tradition that is 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 will call the constellation of skeptical views just described, intuition-skeptical empiricism.

265. 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 contemporary philosophical scene.[iii]

266. 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 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 in this set of notes, I’m going to spell out a contemporary Kantian conception of apriority, and also prove that at least some a priori knowledge in this sense actually exists.

That in turn will suffice for an initial demonstration of the truth of neo-rationalism.

266. 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. (CPR 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. (CPR 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.

267. In order to do this, I will 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.

268. Now let us 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.

269. 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 <–> 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.

270. Notice that according to this Kantian conception of apriority,

first, it is fully acknowledged that all human knowledge begins in our sense perception of contingent natural objects or facts, and

second, 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.

271. Here, now, are three incontrovertible examples of a priori necessary statements that I and every other rational human animal under normal cognitive conditions believes, or at least can believe, such that their meaning must bear some significant relation to empirical facts, their truth must be learned or confirmed by means of empirical facts, at least in part, and 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.,

272. 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.

(1) There is no such thing as a priori belief that altogether excludes empirical facts, which yields a minimal Empiricism.

(2) But the same time, it does not follow from the minimal Empiricism expressed in (1) 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 (1) and its minimal Empiricism.

That would be clearly and simply be, in Peter Strawson’s lovely phrase, “a non sequitur of numbing grossness.”[iv]

273. Now what about a priori knowledge?

“3+4=7.”

Very few statements, even necessarily true statements, are objectively[v] and authentically 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.

274. And I think I can prove that to you in four short steps.

First, please look at this simple diagram carefully and thoughtfully:

| | | + | | | | = | | | | | | |

Second, I will 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 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.

275. Moreover, although your knowledge that 3+4=7, via the stroke diagram (spoiler alert: here’s where specifically mathematical rational intuition happens[vi]), obviously began in human sensory experience, nevertheless its specific meaning and evidential character were not derived from — 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.

Therefore,

neo-rationalism is true and maximal Empiricism is false.

276. Now wasn’t that fun? In the next set of notes, I’ll sketch a general account of how not only mathematical a priori knowledge, but also the other important kinds of authentic a priori knowledge, are really possible.

NOTES

[i] See D. Bourget and D. Chalmers, “Philosophical Papers Survey 2009,” available online at URL= <http://philpapers.org/surveys/>.

[ii] R. Hanna, Cognition, Content, and the A Priori: A Study in the Philosophy of Mind and Knowledge (aka THE RATIONAL HUMAN CONDITION, Vol. 5) (Oxford: Oxford Univ. Press, 2015), PREVIEW.

[iii] See G. Bealer, “Modal Epistemology and the Rationalist Renaissance,” in T. Gendler and J. Hawthorne (eds.), Conceivability and Possibility (Oxford: Clarendon/Oxford Univ. Press, 2006), pp. 71–125.

[iv] P. Strawson, The Bounds of Sense: An Essay on Kant’s Critique of Pure Reason (London: Methuen, 1959), p. 137. The allusion is ironic, since here Strawson is famously (and mistakenly, as it happens) accusing Kant of committing one of these non sequiturs.

[v] 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.

[vi] See Hanna, Cognition, Content, and the A Priori, chs. 7–8.

***