Peirce's synthetic reading resulted in an original view of the relationship between logic and mathematics, very different from the logicist
What is strikingly absent in a volume on one of the founders of modern logic is a more comprehensive treatment of Frege's formal systems (that in the book Begriffsschrift [Bs] and that in the book Grundgesetze der Arithmetik [GgA]) and his logicist
treatment of arithmetic.
Frege's reflections on language took place in the context of his logicist
project in the philosophy of mathematics and can only, with significant retrospective license, be read as intended to constitute the articulation of a systematic theory of meaning which underlies the rest of philosophical inquiry.
For Leibniz arithmetic was a purely rational activity involving proofs but his logicist
program failed because of the irreducibility of asymmetrical relational propositions to monadic ones.
Leibniz for Grosholz is not a logicist
but rather a pragmatic user of multiple modes of representation, helping to demonstrate "why the philosophical project of fmding the sole correct representation of mathematics is misguided" (p.
Aristotle had seen dynamis as mere potential, an answer to Megarian logicist
polemics against the possibility of change.
39) Caputo then adds that (the Avicennian) essentialism reaches its high levels with Duns Scotus who is the "foremost logicist
and essentialist philosopher of the High Middle Ages.
So, even though the grue puzzle was effective against its stated logicist
targets, it is not thereby an enduring difficulty regarding experience's ability to impart epistemic justification via inductive evidence.