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Ideas for 'Axiomatic Theories of Truth (2005 ver)', 'What is Knowledge-First Epistemology?' and 'Reply to Professor Marcus'

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3 ideas

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

15652	We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach]
	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.
	From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.1)
	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.

5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic

15651	Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach]
	Full Idea: Quantification over (certain) properties can be mimicked in a language with a truth predicate by quantifying over formulas. Instead of saying that Tom has the property of being a poor philosopher, we can say 'x is a poor philosopher' is true of Tom.
	From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.1)
	A reaction: I love this, and think it is very important. He talks of 'mimicking' properties, but I see it as philosophers mistakenly attributing properties, when actually what they were doing is asserting truths involving certain predicates.

5. Theory of Logic / G. Quantification / 4. Substitutional Quantification

10801	Either reference really matters, or we don't need to replace it with substitutions [Quine]
	Full Idea: When we reconstrue quantification in terms of substituted expressions rather than real values, we waive reference. ...but if reference matters, we cannot afford to waive it as a category; and if it does not, we do not need to.
	From: Willard Quine (Reply to Professor Marcus [1962], p.183)
	A reaction: An odd dilemma to pose. Presumably the substitution account is an attempt to explain how language actually works, without mentioning dubious direct ontological commitment in the quantifiers.