Combining Texts

Ideas for 'Parmenides', 'Axiomatic Theories of Truth' and 'Tonk, Plonk and Plink'

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2 ideas

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

16150	One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato]
	Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it.
	From: Plato (Parmenides [c.364 BCE], 144a)
	A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory

16308	Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach]
	Full Idea: While set theory was liberated much earlier from type restrictions, interest in type-free theories of truth only developed more recently.
	From: Volker Halbach (Axiomatic Theories of Truth [2011], 4)
	A reaction: Tarski's theory of truth involves types (or hierarchies).