Combining Texts

Ideas for 'Mahaprajnaparamitashastra', 'What do powers do when they are not manifested?' and 'Philosophy of Logic'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

---

5 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

18954	Before the late 19th century logic was trivialised by not dealing with relations [Putnam]
	Full Idea: It was essentially the failure to develop a logic of relations that trivialised the logic studied before the end of the nineteenth century.
	From: Hilary Putnam (Philosophy of Logic [1971], Ch.3)
	A reaction: De Morgan, Peirce and Frege were, I believe, the people who put this right.

5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic

18956	Asserting first-order validity implicitly involves second-order reference to classes [Putnam]
	Full Idea: The natural understanding of first-order logic is that in writing down first-order schemata we are implicitly asserting their validity, that is, making second-order assertions. ...Thus even quantification theory involves reference to classes.
	From: Hilary Putnam (Philosophy of Logic [1971], Ch.3)
	A reaction: If, as a nominalist, you totally rejected classes, presumably you would get by in first-order logic somehow. To say 'there are no classes so there is no logical validity' sounds bonkers.

5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic

18962	Unfashionably, I think logic has an empirical foundation [Putnam]
	Full Idea: Today, the tendency among philosophers is to assume that in no sense does logic itself have an empirical foundation. I believe this tendency is wrong.
	From: Hilary Putnam (Philosophy of Logic [1971], Ch.9)
	A reaction: I agree, not on the basis of indispensability to science, but on the basis of psychological processes that lead from experience to logic. Russell and Quine are Putnam's allies here, and Frege is his opponent. Putnam developed a quantum logic.

5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic

18961	We can identify functions with certain sets - or identify sets with certain functions [Putnam]
	Full Idea: Instead of identifying functions with certain sets, I might have identified sets with certain functions.
	From: Hilary Putnam (Philosophy of Logic [1971], Ch.9)

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth

18955	Having a valid form doesn't ensure truth, as it may be meaningless [Putnam]
	Full Idea: I don't think all substitution-instances of a valid schema are 'true'; some are clearly meaningless, such as 'If all boojums are snarks and all snarks are egglehumphs, then all boojums are egglehumphs'.
	From: Hilary Putnam (Philosophy of Logic [1971], Ch.3)
	A reaction: This seems like a very good challenge to Quine's claim that it is only form which produces a logical truth. Keep deductive and semantic consequence separate, with two different types of 'logical truth'.