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Single Idea 13829

[filed under theme 5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives ]

Full Idea

Quine said a logical truth is a truth in which only logical constants occur essentially, ...but then a fruitful definition of 'logical constant' is called for.

Gist of Idea

If logical truths essentially depend on logical constants, we had better define the latter

Source

comment on Willard Quine (Carnap and Logical Truth [1954]) by Ian Hacking - What is Logic? §02

Book Ref

'A Philosophical Companion to First-Order Logic', ed/tr. Hughes,R.I.G. [Hackett 1993], p.227


The 9 ideas from 'Carnap and Logical Truth'

If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine]
In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine]
Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine]
Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine]
Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine]
If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine]
Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider]
Examination of convention in the a priori begins to blur the distinction with empirical knowledge [Quine]
Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping [Quine]