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Single Idea 10829

[filed under theme 5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic ]

Full Idea

One may be of the opinion that no sentence ought to be considered as a truth of logic if, no matter how it is interpreted, it asserts that there are sets of certain sorts.

Gist of Idea

A sentence can't be a truth of logic if it asserts the existence of certain sets

Source

George Boolos (On Second-Order Logic [1975], p.44)

Book Ref

Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.516

A Reaction

My intuition is that in no way should any proper logic assert the existence of anything at all. Presumably interpretations can assert the existence of numbers or sets, but we should be able to identify something which is 'pure' logic. Natural deduction?

The 22 ideas with the same theme [overview of what must exist to enable logic]:

19256 Our research always hopes that reality embodies the logic we are employing [Peirce]
23196 Logic is a fiction, which invents the view that one thought causes another [Nietzsche]
21222 Logicians presuppose a world, and ignore logic/world connections, so their logic is impure [Husserl, by Velarde-Mayol]
21223 Phenomenology grounds logic in subjective experience [Husserl, by Velarde-Mayol]
12444 Logic is concerned with the real world just as truly as zoology [Russell]
14464 Logic can be known a priori, without study of the actual world [Russell]
10057 Logic can only assert hypothetical existence [Russell]
22329 Logic is highly general truths abstracted from reality [Russell, by Glock]
21707 Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B]
14167 The only classes are things, predicates and relations [Russell]
18162 The propositions of logic are analytic tautologies [Wittgenstein]
12219 Whether a modal claim is true depends on how the object is described [Quine, by Fine,K]
22437 Logical languages are rooted in ordinary language, and that connection must be kept [Quine]
18962 Unfashionably, I think logic has an empirical foundation [Putnam]
11970 Logicians like their entities to exhibit a maximum degree of purity [Kaplan]
12766 Logical space is abstracted from the actual world [Stalnaker]
12341 Logic is a mathematical account of a universe of relations [Badiou]
10829 A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
10454 In first-order we can't just assert existence, and it is very hard to deny something's existence [Bach]
10253 Either logic determines objects, or objects determine logic, or they are separate [Shapiro]
14943 Maybe mathematical logic rests on information-processing [Ladyman/Ross]
15652 We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach]