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Single Idea 15652

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

Full Idea

The reduction of 2nd-order theories (of properties or sets) to axiomatic theories of truth may be conceived as a form of reductive nominalism, replacing existence assumptions (for comprehension axioms) by ontologically innocent truth assumptions.

Gist of Idea

We can use truth instead of ontologically loaded second-order comprehension assumptions about properties

Source

Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.1)

Book Ref

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.3

A Reaction

I like this very much, as weeding properties out of logic (without weeding them out of the world). So-called properties in logic are too abundant, so there is a misfit with their role in science.

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]