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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.
Gist of Idea
Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true'
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.2
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.
| 3300 | Aristotle's logic is based on the subject/predicate distinction, which leads him to substances and properties [Aristotle, by Benardete,JA] |
| 3319 | Frege gives a functional account of predication so that we can dispense with predicates [Frege, by Benardete,JA] |
| 6076 | For Frege, predicates are names of functions that map objects onto the True and False [Frege, by McGinn] |
| 18894 | Predicates form a hierarchy, from the most general, down to names at the bottom [Sommers] |
| 10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
| 15651 | Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach] |