Read Part I, Part II, Part III, Part Interlude, Part IV, Part V, Part VI. Part Last.

In going through Feser’s book, many in the comments profess to be confused about what truth means, and about the difference from there being one overall (or foundational) Truth, and many individual truths. I believe one of us even took up Pilate’s speech and asked, without irony, “*Quid est veritas*?” (To even ask the question presupposes its existence.)

Several other readers also claimed to be empiricists, which are those who believe in truth but say that all truths are discovered solely by observation. Empiricism is false: all truths cannot be discovered by observation. Quite simply, even its defining statement is self-contradictory. I asked yesterday how do we know, since we have not observed them, that there are an infinity of numbers. Answer came there none. This small example proves empiricism false.

But since those who wish to hold to empiricism (for fear of what abandoning it implies?) will not be satisfied by so telegraphic a proof, here is a longer one, given by the (non-theist) philosopher David Stove. I find it exceptionally lovely. We’ve seen this before, but today we’re seeing it again.

Stove shows each of us must come equipped with knowledge which cannot be learned. Stuff that is only known to be true only through introspection, via what we call intuition or faith, or what yesterday we called revelation; philosophers usually settle on the technical term *a priori* (or on phrases more technical still).

This is just one (of many) proofs given by David Stove in his *The Rationality of Induction*^{1} He made this argument in the support of revealed knowledge in his larger work showing induction is reasonable^{2}. A man named Bolzano is named in the proof: all you need know about that gentleman is that he disputed the idea that we all of us come with built-in knowledge.

Reading this passage, as with reading any proof, requires some sophistication. This cannot be avoided. The formula numbers are as they appeared in Stove’s book. The unseen formula “(149)” is here equivalent to “(166)” below.

First, as to our knowledge of validity. Bolzano says that the validity of

barbara, or rather, that thebarbaraschema 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, allF, allG, either ‘xisFand allFareGis false’, or ‘xisG‘ 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

knowthat 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

(167) O

_{1}.But even if our logic learner

hasfound by experience that O_{1}he will be no further advanced. To learn (167), he needs to know, not only that O_{1}, 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

(170) O

_{2}.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

notenough.

As a sketch: to even know that an observation confirms some statement is to use the knowledge that “observations confirms this statement”, and the knowledge of that could not have been discovered observationally, or empirically. We must already know (at least) this before we begin. Just as we must know the axioms before we begin mathematics. Axioms by definition are truths which cannot be proved.

Read Part I, Part II, Part III, Part Interlude, Part IV, Part V, Part VI. Part Last.

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^{1}p. 162-163. This book, especially the second half, is a treasure that all statisticians, probabilists, and logicians should read.

^{2}Yes, some people think it isn’t. Bolazno was not one of these: he thought all (as in all) knowledge was known empirically.