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Ayn Rand's Introduction to Objectivist Epistemology includes an essay by Leonard Peikoff entitled "The Analytic-Synthetic Dichotomy." The section "Necessity and Contingency" concludes with the following paragraph:
Truth is the identification of a fact with reality. Whether the fact in question is metaphysical or man-made, the fact determines the truth: if the fact exists, there is no alternative in regard to what is true. For instance, the fact that the U.S. has 50 states was not metaphysically necessary -- but as long as this is men's choice, the proposition that "The U.S. has 50 states" is necessarily true. A true proposition must describe the facts as they are. In this sense, a "necessary truth" is a redundancy, and a "contingent truth" a self-contradiction. (Introduction to Objectivist Epistemology, 2nd ed., eds. Binswanger and Peikoff, NAL Books, 1990, p. 111, emphasis in original.)
I have no objection to part of what is being said in this passage, in fact I heartily agree with it, namely, that facts determine truths. The non-man-made fact of the moon's having craters makes-true the proposition expressed by 'The moon has craters.' And similarly for the man-made fact regarding the 50 states cited by Peikoff. So I cheerfully agree that "if the fact exists, there is no alternative in regard to what is true." We can put the point as follows given that there is a fact F and a proposition p that records F:
a. It is impossible that F exist and p not be true. This is logically equivalent to
a*. It is necessary that if F exists, then p is true. But from (a*) one cannot validly infer
b. If F exists, then p is necessarily true.
To think otherwise is to commit the modal fallacy of confusing the necessitas consequentiae with the necessitas consequentiis, the necessity of the consequence with the necessity of the consequent. But Peikoff commits this very fallacy in the above passage and in the surrounding text. He says that 'necessary truth' is a redundancy because he holds that all truths are necessary. In the immediately preceding paragraph we read, "Some facts are not necessary, but all truths are." (111, emphasis in original) Now what is his reason for maintaining that all truths are necessary? It is given by (a) and (a*) above. But we cannot validly move from these true equivalent propositions to all truths are necessary.
And surely it is false to say that all truths are necessary. 'I am blogging now' is true and is made true by the (man-made) fact of my blogging now. But it is contingently true. I might have decided to go for a bike ride at this time. Had I so decided, then 'I am riding my bike now,' which is actually false would have been true, and 'I am blogging now' which is actually true would have been false. So it ought to be self-evident that 'I am blogging now' and 'I am riding my bike now' (or rather the propositions they are used to express) are both of them contingent. It is contingently true that I am blogging now and contingently false that I am riding my bike now. Therefore, it is false to say as Peikoff does that all truths are necessary truths. Some truths are necessary and some are contingent.
Peikoff tells us that "Truths about metaphysical and about man-made facts are . . . qua truths, both equally necessary." (111, emphasis in original.) Now this is plainly false as I have just shown. But what is interesting is the fallacy, the mistake in reasoning, that Peikoff is committing. The mistake is the move from
c. Necessarily, every truth is true. (Necessarily, for every p, if p is true, then p is true)
d. Every truth is necessarily true. (For every p, if if p is true, then p is necessarily true.)
(c) is indisputably true. (d), however, is false since some propositions are contingently true. so the inference is invalid. The necessity that attaches to the consequence does not attach to the consequent.
Peikoff states that "Some facts are not necessary, but all truths are." This is incoherent. If some facts are not necessary, then the propositions that record these facts are not necessary either. It is not necessary that I be blogging now even though I am blogging now. The proposition expressed by 'I am blogging now,' though true, is contingently true. Surely there is no necessity that I be blogging now! As Peikoff corrctly states, "man has free will." (110) Since I am freely blogging now, and could have done otherwise, the fact of my blogging now is contingently existent, whence it follows that the proposition recording this fact is contingenty true.