Knowledge without proof

For nearly four hundred years, the central question of philosophy has been epistemological: Is it possible to know, and if so, how? Descartes struck the first blow, and almost the last, in his attempt to doubt his way to certainty. Though his effort satisfied himself, later thinkers ran into a small problem; like a man measuring a ruler against its own mirror image, Descartes’ rigorous deductions proved that human reason is trustworthy, as long as one trusts reason enough to rely upon it for the proof.

A brief burst of optimism in the possibility that knowledge could be stamped upon a blank mind by the external world withered under the realization that all knowledge of the external world must be mediated through the senses, the reliability of which is just as doubtable as that of reason, and just as incapable of verification. How can we evaluate the trustworthiness of our sense perceptions, other than by comparison against the perceptions of our senses?

And so four centuries of philosophy may be distilled into various permutations and developments of the first half of Descartes’ famous (and misquoted) maxim. “I think,” with emphasis to be placed upon the utter, singular insularity of the pronoun and the uncertainty of the verb. I, and I alone, think, and am not sure. If reason must be doubted, what can be trusted except the single fact that I am a thing, thinking about itself? If the senses are untrustworthy, what can I really know of any other things outside the thing that is me?

Various schools have dealt differently with the dilemma. Solipsism is perhaps the most honest response, accepting the situation at least theoretically. Existentialism offers the most emotionally satisfying solution, proposing by sheer will or luck to rebuild something from the wreckage of meaning – “something” being as specific as one can get. Pragmatism is cheerfully American in its practically impractical determination to ignore all such stuffy questions and concentrate on what works. (Leaving rather vague the question of how we are to judge what works, or what “working” would actually entail.) And postmodernism, at least in its philosophical dimensions, offers the oddest answer in its focus on closely studying and vigorously defending the correct understanding of whatever it is that it insists we cannot know.

All this from one simple assumption, that one cannot know what cannot be proven (in this case, the general reliability of reason and of the senses) — a proposition that provides perhaps the only common theme among all the disparate philosophies from the Enlightenment onward, even among those, like Kant, who appear to accept the possibility of innate knowledge. It is ironic that such an influential premise would be so obviously false as an absolute proposition, so questionable as a mere assumption, and so definitely contradicted by every evidence of human experience.

This epistemological assumption is found even in the definition of knowledge commonly used by those from more conservative philosophical climes, where the existence of such a thing as knowledge is still believed to be possible. Knowledge, so defined, consists of “justified true belief.” In other words: knowledge is belief which actually corresponds with reality and for which we have, as Plato writes, “an account of the reason why [we believe]” (Meno 98).

As a matter of pure logic, the proposition that it is impossible to know what cannot be proven is fatally flawed, for it cannot meet its own criteria; there is no way to prove that what cannot be proven is unknowable, and so the standard falls by its own hand. It might without contradiction actually be true, but the truer it is the less could its truth be known.

So we appear to be at an impasse. Logically, either truth can be known without proof or truth cannot be known without proof. It is impossible to prove the truth of either proposition (a fact which itself fits more comfortably with the former than with the latter opinion). Since neither can be proven, those who accept the latter view must do so on grounds of prejudice (in its most literal meaning) rather than knowledge. Yet prejudice is a powerful thing, and the former proposition in no way benefits by pointing out the lack of support for the latter, so the question is worth further consideration. If we cannot determine the truth of either possibility by direct examination, perhaps more light may be thrown on the issue by working in the other direction.

Let us assume, for the moment, that it is true that nothing can be known except what is provable. Proof comes through logic and reason, working from premise to conclusion. If all men are mortal and Socrates is a man, then I can prove that Socrates is mortal; but only if I do in fact know that all men are mortal and Socrates is a man. So proof must begin with knowledge, and knowledge is a necessary condition for proof. Thus it follows that either knowledge preexists proof, or else there is no proof and therefore no knowledge.

It is now possible to restate the dilemma advanced earlier: Either truth can be known without proof, or knowledge is impossible, and reason also (since reason depends upon knowledge of basic laws of thought).

It is important to note, again, that neither of these proposition can be proven, though both are logically possible and one must necessarily be true and the other false. (Unless in fact reason itself is untrustworthy, a point to which we will return shortly.) It is ironic that the foundational question of philosophy cannot, in one sense, be settled philosophically.

It is possible, however, to sketch the two camps. On the one hand, we have a reality which is quite literally unthinkable; a reality the very existence of which cannot be asserted without recourse to truth claims which cannot be meaningful if they are true; a reality in which even our own existence is unknowable (since unprovable). Our every instinct, our every thought, even the very arguments which may be advanced in support of such a reality, testify that in fact we do not and can not actually believe in it. To say that it exists is to deny it. Even to suggest it might exist on the basis of the evidence is to appeal to knowledge the existence of which is denied by our conclusion.

Now, such a theoretical reality does have one argumentative strength: it is irrefutable. Its fundamentally irrational nature strikes just as hard against attempts to demonstrate its impossibility (for it if is actual, then the reason I use to disprove its existence cannot be trusted) as against attempts to demonstration its actuality. But let us be clear about what it is: an unthinkable world, indefensible on its own terms, and without a shred of actual or possible evidence to speak in its defense.

The traditional argument against the existence of such a reality is to point out that it is prima facie indefensible. As Aristotle argues, he who denies the law of non-contradiction, tacitly affirms it by that very denial. Putting the point more broadly, the more convinced one is that knowledge is impossible, the more thoroughly one denies one’s own first principle. But perhaps this argument puts too much weight upon human cognition, and in so doing begs the question. Merely entertaining the possibility of a world utterly without knowledge and reason puts us so far beyond the threshold of human thought that no attempted refutation can survive.

So, I will repeat the concession that no chain of logic can drag away the possibility that all knowledge must be proven, and that therefore no knowledge is possible. If we give up the argument at this point, however, we have already conceded the central question. For, if not all knowledge must be proven, then logic is not the only source of truth.

Thus far I have spent little time defending the view that some knowledge is possible without proof, and no time at all clarifying what sorts of knowledge might be known without proof. Taking the latter first, I would suggest that the laws of reason, the basic reliability of the senses, and the existence of the self, at least, are known without proof. With slightly less certainty, I would also propose that the existence of other persons, the existence of God, and a rudimentary moral code are also known without proof; but my purpose here is not to provide an exhaustive list of innate knowledge (an uncertain task at best). So long as one item of knowledge is known without proof, the categorical proposition that nothing is known without proof is disproved.

The difficulty of defending such a position, of course, lies in the fact that the existence of knowledge that cannot be proven cannot be proven. In this case, the proof of the pudding is in the eating; and only in the eating. The skeptic may seize upon this fact as evidence against the possibility of innate knowledge, but it is worth remembering that proof is impossible for either side of the argument, a fact which is only problematic if we assume the premise that all knowledge must be proven. Absent that irrational prejudice, the actual cognitive experience of any normal human should be amply sufficient to convince him of the existence of innate knowledge.

In each case, we find ourselves treating the laws of reason, the basic reliability of the senses, and the existence of the self, at least, as being self-evidentially true, and most so when we are least aware of their operation. We do not experience them as matters of habit, instinct, or convenience, but rather as truths upon which only a sustained and focused operation of the will can cast the least doubt, and that only momentarily. It is worth noting that even so committed a theoretical skeptic as David Hume admitted that “it seems certain, that though a man, in a flush of humour, after intense reflection on the many contradictions and imperfections of human reason, may entirely renounce all belief and opinion, it is impossible for him to persevere in this total scepticism, or make it appear in his conduct for a few hours.” We know, and we know that we know; though the knowledge is of a sort which cannot, by its nature, be proven.

In closing, a quick comment should be made upon the matter of definitions raised above. Having objected to the definition of knowledge as “justified true belief,” the matter cannot be remedied by simply dispensing with the idea of justification to leave knowledge defined simply as “true belief.” Clearly, not all true beliefs can rightly be called knowledge. (It is almost certain that a few of the innumerable conspiracy theories now current are actually true, but that does not automatically bequeath the title of “knowledge” upon the proponents of those lucky few, despite the fact that their beliefs are in fact accidentally true.) Perhaps the solution is a subdivision of knowledge, somewhat along the lines of the medieval distinction between intellectus and ratio.