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Single Idea 10200

[from 'Philosophy of Mathematics' by Stewart Shapiro, in 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism ]

Full Idea

We must distinguish between 'realism in ontology' - that mathematical objects exist - and 'realism in truth-value', which is suggested by the model-theoretic framework - that each well-formed meaningful sentence is non-vacuously either true or false.

Gist of Idea

We distinguish realism 'in ontology' (for objects), and 'in truth-value' (for being either true or false)

Source

Stewart Shapiro (Philosophy of Mathematics [1997], Intro)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.4


A Reaction

My inclination is fairly strongly towards realism of the second kind, but not of the first. A view about the notion of a 'truth-maker' might therefore be required. What do the truths refer to? Answer: not objects, but abstractions from objects.