Do we agree with W. Tait's thesis that finitistic reasoning = PRA?
https://www.jstor.org/stable/2026089?seq=1
>and the finitist has no concept of a function. He can only see each particular instance as valid. Indeed, if it were otherwise, the function that assigns to the Godel number of each closed term of type N the value of that term and assigns 0 to each number that is not the Godel number of such a term would be finitist. Since this function is not primitive recursive, our thesis would be contradicted.
As a finitist, it seems to me perfectly possible to speak of functions as methods for taking an object of type A and producing an object of type B. Why would this not be finitist?
https://www.jstor.org/stable/2026089?seq=1
>and the finitist has no concept of a function. He can only see each particular instance as valid. Indeed, if it were otherwise, the function that assigns to the Godel number of each closed term of type N the value of that term and assigns 0 to each number that is not the Godel number of such a term would be finitist. Since this function is not primitive recursive, our thesis would be contradicted.
As a finitist, it seems to me perfectly possible to speak of functions as methods for taking an object of type A and producing an object of type B. Why would this not be finitist?
