Today, a technical interregnum, a necessary pause for proof of that claim that each of us must come equipped with knowledge that cannot be learned. Stuff that is only known to be true only through introspection, via what we call intuition or, sometimes, faith; philosophers usually settle on the technical term a priori (or on phrases more technical still).
Here is one (of many) proofs given by David Stove in his The Rationality of Induction1 He made this argument in the support of a priori knowledge in his larger work showing induction is reasonable2. All you need know about Bolzano (named below), is that he disputed the idea that we all of us come with built-in knowledge. The formula numbers are as they appeared in the book.
Reading this passage, as with reading any proof, requires some sophistication. This cannot be avoided. But if you are comfortable with the idea of built-in knowledge, then you can skip this and start after the quote. Careful readers will recognize that Stove’s simple argument is also a proof that empiricism—the belief that all knowledge comes from observation—is false.
First, as to our knowledge of validity. Bolzano says that the validity of barbara, or rather, that the barbara schema always preserves truth, is a hypothesis reasonably believed by us, just because of the extensive experience we have had of never finding a counter-example to it. That is, our grounds for believing (149), or rather, for believing
(166) For all x, all F, all G, either ‘x is F and all F are G is false’, or ‘x is G‘ is true,
consist just of observations we have made, such as
(151) Abe is black and Abe is a person now in this room and all persons now in this room are black.
That is putting it starkly; still it is, in essence, what Bolzano believes. We learn deductive logic by inductive inference.
But now, this is tacitly to concede, to certain propositions of non-deductive logic, precisely the intuitive status which Bolzano expressly denies to any proposition of deductive logic. Our putative logic learner is supposed to be devoid of all intuitive logical knowledge. Yet Bolzano is evidently crediting him with knowing, straight off, at least this much: that
(167): (151) confirms (149).
Of course, he need not be supposed to know that he knows (167); still, he is evidently being supposed to know it. But to know (167) is to have some logical knowledge, even is only non-deductive logical knowledge.
And Bolzano must suppose that (167) is known by our logic learner intuitively. Otherwise he would have to have learnt it, as he is supposed to be learning (166), by experience. And how would he accomplish this?
It must at any rate be from some observation-statements. I do not know what kind of observation-statements Bolzano would regard as confirming (167): let us just call these observation-statements
But even if our logic learner has found by experience that O1 he will be no further advanced. To learn (167), he needs to know, not only that O1, but that
(169): (168) confirms (167).
But this is a proposition of logic too. If he does not know (169) intuitively, as by hypothesis he does not, then he will have to learn it, too, from experience. No doubt from some observations
But that is not enough. He will also need to know that
(171): (170) confirms (169);
and so on.
Obviously, he is never going to make it. Experience is not enough.
Especially careful readers—especially those convinced by this proof, as I am—will recognize that in order to interpret this proof, to assimilate it and follow it, requires precisely the kind of built-in knowledge of which the proof speaks. We must have a priori knowledge.
We are finally ready to tackle the notion that some propositions are “just true.” Propositions of this sort are usually the kinds of truths spoken of above, but there are also moral or ethical truths, too (of these, another day). The claim that there exist “universal truths”—propositions which say are just plain true—is consistent with claim that all truth is conditional, because whatever a priori knowledge we have is conditional on our intuition, or is taken “on faith.” To speak of these truths (in a technical sense) we must first affix the condition, “Given my faith or intuition, this proposition is just true.”
This seems to open the way to relativism because, as direct experience tells us, different people will claim a certain proposition true or false just because their intuitions or faith direct them oppositely. Many times, of course, these differences are mistakes in reasoning, or there are other pieces of evidence that are assumed (as in French speaking chickens) that the speaker is not aware of or does not acknowledge. Skip these cases and focus on just those claims where nothing is assumed except intuition or faith.
The claim is that we must have some shared beliefs about what is true, and it is these beliefs which we speak of when we say “there are truths.” One is that “Other minds exist.” Or, more properly, “Given our intuitions or faith, other minds exist.” The only possible escape from believing this shared truth is solipsism, which is “Given my intuition, only I exist.” Deep, or metaphysical solipsists stop here. But other solipsists (there are varieties of the breed) might allow that “Given my intuition, it is true I exist; but I believe it is logically possible that others might exist.”
But to acknowledge “logical possibility” is to acknowledge at least the truth that logical propositions are true. So that if those other minds exist, they must have this knowledge, too because that is what a mind is. And then if one really is a metaphysical solipsist (good luck finding one) it is still true that “all” share beliefs about what is true—it just the case that “all” is one person. (How many solipsists will jump in and tell me, “Briggs, you don’t exist! Stop claiming you do!”)
In practice, of course, we all really do admit that truth (given our intuitions) that others minds exist. This, then, if just one of many truths that exist. The logical knowledge spoken of by Stove are others. Our task is now clear: since truths, via shared faith or intuition exist, we must identify what they are; we must also identify falsehoods, and that which is only probable. More on this later.
1p. 162-163. This book, especially the second half, is a treasure that all statisticians, probabilists, and logicians should read.
2Yes, some people think it isn’t. Bolazno was not one of these: he thought all (as in all) knowledge was known empirically.