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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.
| 15647 | Truth definitions don't produce a good theory, because they go beyond your current language [Halbach] |
| 15650 | Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach] |
| 15648 | Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach] |
| 15649 | In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach] |
| 15652 | We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach] |
| 15651 | Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach] |
| 15655 | Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach] |
| 15654 | If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach] |
| 15656 | Deflationists say truth merely serves to express infinite conjunctions [Halbach] |
| 15657 | To prove the consistency of set theory, we must go beyond set theory [Halbach] |