Outlines of a formalist philosophy of mathematics (Studies in logic and the foundations of mathematics) by Haskell B Curry (PDF)

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Reviews from Amazon users which were colected at the time this book was published on the website:

⭐There is much more to this book than the other reviewer has revealed. That reviewer simply ignores or has skimmed over most of Curry’s arguments. Far from being biased, this book attempts simply to background as many unnecessary assumptions as possible. In fact Curry makes many positive statements about both intuitionism and Platonism. Keep in mind that any book can be made to look biased if you cherry-pick quotes out of context.

⭐Formalism is here openly adopted not because there are any good reasons for it but because it suits certain philosophical prejudices. Consider the rejection of intuitionism: “the resulting criterion of truth is vague at best, and depends on metaphysical assumptions from which mathematics, if it is to have the pre-philosophical character above mentioned, must be free” (p. 5). “It should be emphasized that the reason for this [rejection] is not that these assumptions are invalid. There is, in fact, much to be said for these assumptions.” (pp. 6-7). But Curry doesn’t like them so they are rejected simply for that reason and that reason alone. Instead, “The definition I advocate is briefly this: Mathematics is the science of formal systems” (p. 56). Intuitionism is faulted for not accounting for the “acceptability of classical analysis” which is an “empirical fact” (p. 61). But the obvious “empirical fact” that there has been much mathematics where there have been no formal systems is not mentioned.

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