Combining Texts

Ideas for 'Structures and Structuralism in Phil of Maths', 'What is Philosophy?' and 'Philosophies of Mathematics'

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3 ideas

2. Reason / C. Styles of Reason / 3. Eristic
'Eris' is the divinity of conflict, the opposite of Philia, the god of friendship [Deleuze/Guattari]
     Full Idea: 'Eris' is the Greek divinity of discord, conflict, and strife, the complementary opposite of Philia, the divinity of union and friendship.
     From: G Deleuze / F Guattari (What is Philosophy? [1991], 1.2 n)
     A reaction: Are these actual gods? This interestingly implies that the wonders of dialectic and Socrates' elenchus are simply aspects of friendship, which was elevated by Epicurus to the highest good. The Greeks just wanted wonderful friends and fine speeches.
2. Reason / D. Definition / 7. Contextual Definition
Contextual definitions replace a complete sentence containing the expression [George/Velleman]
     Full Idea: A contextual definition shows how to analyse an expression in situ, by replacing a complete sentence (of a particular form) in which the expression occurs by another in which it does not.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2)
     A reaction: This is a controversial procedure, which (according to Dummett) Frege originally accepted, and later rejected. It might not be the perfect definition that replacing just the expression would give you, but it is a promising step.
2. Reason / D. Definition / 8. Impredicative Definition
Impredicative definitions quantify over the thing being defined [George/Velleman]
     Full Idea: When a definition contains a quantifier whose range includes the very entity being defined, the definition is said to be 'impredicative'.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2)
     A reaction: Presumably they are 'impredicative' because they do not predicate a new quality in the definiens, but make use of the qualities already known.