Re: Peter Cameron • Infinity and Foundation
We always encounter a multitude of problems whenever we try to rationalize mathematics by reducing it to logic, where logic itself is reduced to a purely deductive style. A number of thinkers have proposed it is time — well past time — to stop counting so heavily on that idea and to join a Declaration of Independence for Mathematics.
Davis and Hersh come to mind here, as well a Tymozco (sp?). In his later book, Hersh specifically mentions Dewey (that would be chapter XX of the greater logic) as a member of “the fold”.
There are inklings of this declaration in Leibniz and Boole, outlined more clearly by Peirce’s analysis of the relation between logic and mathematics, succinctly summed up in what I trace here —
☞ Definition and Determination : 4 ✍
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