Combining Texts

All the ideas for 'works (all lost)', 'The Architecture of Mathematics' and 'There are no ordinary things'

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3 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

10190	From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki]
	Full Idea: From the axiomatic point of view, mathematics appears as a storehouse of abstract forms - the mathematical structures.
	From: Nicholas Bourbaki (The Architecture of Mathematics [1950], 221-32), quoted by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.79
	A reaction: This seems to be the culmination of the structuralist view that developed from Dedekind and Hilbert, and was further developed by philosophers in the 1990s.

7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic

9052	Vague predicates lack application; there are no borderline cases; vague F is not F [Unger, by Keefe/Smith]
	Full Idea: In a slogan, Unger's thesis is that all vague predicates lack application ('nihilism', says Williamson). Classical logic can be retained in its entirety. There are no borderline cases: for vague F, everything is not F; nothing is either F or borderline F.
	From: report of Peter Unger (There are no ordinary things [1979]) by R Keefe / P Smith - Intro: Theories of Vagueness §1
	A reaction: Vague F could be translated as 'I'm quite tempted to apply F', in which case Unger is right. This would go with Russell's view. Logic and reason need precise concepts. The only strategy with vagueness is to reason hypothetically.

9. Objects / A. Existence of Objects / 5. Simples

16070	There are no objects with proper parts; there are only mereological simples [Unger, by Wasserman]
	Full Idea: Eliminativism is often associated with Unger, who defends 'mereological nihilism', that there are no composite objects (objects with proper parts); there are only mereological simples (with no proper parts). The nihilist denies statues and ships.
	From: report of Peter Unger (There are no ordinary things [1979]) by Ryan Wasserman - Material Constitution 4
	A reaction: The puzzle here is that he has a very clear notion of identity for the simples, but somehow bars combinations from having identity. So identity is simplicity? 'Complex identity' doesn't sound like an oxymoron. We're stuck if there are no simples.