Combining Texts

All the ideas for 'Science and Method', 'Reply to Hellman' and 'Abstract Objects:intro to Axiomatic Metaphysics'

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4 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry

10245	One geometry cannot be more true than another [Poincaré]
	Full Idea: One geometry cannot be more true than another; it can only be more convenient.
	From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics
	A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate.

9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta

10414	Abstract objects are constituted by encoded collections of properties [Zalta, by Swoyer]
	Full Idea: In Zalta's view abstract objects are correlated with collections of properties. ..They encode, as well as exemplify, properties; indeed, an abstract object (such as a Euclidean triangle) is constituted by the properties it encodes.
	From: report of Edward N. Zalta (Abstract Objects:intro to Axiomatic Metaphysics [1983]) by Chris Swoyer - Properties 6.3
	A reaction: If we are going to explain abstract objects with properties, then properties had better not be abstract objects. Zalta has a promising idea if we start from a nominalist and naturalistic view of properties (built from physical powers). 'Encode'?

9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta

10415	Properties make round squares and round triangles distinct, unlike exemplification [Zalta, by Swoyer]
	Full Idea: On Zalta's view, properties with the same encoding extensions are identical, but may be distinct with the same exemplification extension. So the properties of being a round square and a round triangle are distinct, but with the same exemplification.
	From: report of Edward N. Zalta (Abstract Objects:intro to Axiomatic Metaphysics [1983]) by Chris Swoyer - Properties
	A reaction: (For Zalta's view, see Idea 10414) I'm not sure about 'encoding' (cf. Hodes's use of the word), but the idea that an abstract object is just a bunch of possible properties (assuming properties have prior availability) seems promising.

12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence

9379	A sentence is obvious if it is true, and any speaker of the language will instantly agree to it [Quine]
	Full Idea: A sentence is obvious if (a) it is true and (b) any speaker of the language is prepared, for any reason or none, to assent to it without hesitation, unless put off by being asked so obvious a question.
	From: Willard Quine (Reply to Hellman [1975], p.206), quoted by Paul Boghossian - Analyticity Reconsidered §III
	A reaction: This comes from someone who is keen to deny a priori knowledge, but what are we to make of the expostulations "It's obvious, you idiot!", and "Now I see it, it's obvious!", and "It seemed obvious, but I was wrong!"?