Combining Texts

All the ideas for 'Demonstratives', 'Identity, Essence and Indiscernibility' and 'On the Foundations of Logic and Arithmetic'

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5 ideas

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

17697	The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert]
	Full Idea: The standpoint of pure experience seems to me to be refuted by the objection that the existence, possible or actual, of an arbitrarily large number can never be derived through experience, that is, through experiment.
	From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.130)
	A reaction: Alternatively, empiricism refutes infinite numbers! No modern mathematician will accept that, but you wonder in what sense the proposed entities qualify as 'numbers'.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

17698	Logic already contains some arithmetic, so the two must be developed together [Hilbert]
	Full Idea: In the traditional exposition of the laws of logic certain fundamental arithmetic notions are already used, for example in the notion of set, and to some extent also of number. Thus we turn in a circle, and a partly simultaneous development is required.
	From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.131)
	A reaction: If the Axiom of Infinity is meant, it may be possible to purge the arithmetic from the logic. Then the challenge to derive arithmetic from it becomes rather tougher.

9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay

14381	A statue is essentially the statue, but its lump is not essentially a statue, so statue isn't lump [Yablo, by Rocca]
	Full Idea: Yablo proposes the argument that Statue A is essentially a statue, and Lump 1 is not essentially a statue, so Statue A is not identical with Lump 1.
	From: report of Stephen Yablo (Identity, Essence and Indiscernibility [1987]) by Michael della Rocca - Essentialists and Essentialism I
	A reaction: Della Rocca and Yablo unashamedly elide necessary properties with essential properties, so this argument doesn't bother me too much. It concerns the statue and the clay having different modal properties.

19. Language / C. Assigning Meanings / 10. Two-Dimensional Semantics

14894	Indexicals have a 'character' (the standing meaning), and a 'content' (truth-conditions for one context) [Kaplan, by Macià/Garcia-Carpentiro]
	Full Idea: Kaplan distinguished two different semantic features of indexical expressions: a 'character' that captures the standing meaning of the expression, and a 'content' that consists of their truth-conditional contribution in particular contexts.
	From: report of David Kaplan (Demonstratives [1989]) by Macià/Garcia-Carpentiro - Introduction to 'Two-Dimensional Semantics' 1
	A reaction: This seems so clearly right that there isn't much to dispute. You can't understand the word 'I' or 'now' if you don't understand both its general purpose, and what it is doing in a particular utterance. But will this generalise to other semantics?

14700	'Content' gives the standard modal profile, and 'character' gives rules for a context [Kaplan, by Schroeter]
	Full Idea: Kaplan sees two aspects of meaning, the 'content', reflecting a thing's modal profile, which is modelled by standard possible worlds semantics, and 'character', giving rules for different contexts. Proper names have constant character; indexicals vary.
	From: report of David Kaplan (Demonstratives [1989]) by Laura Schroeter - Two-Dimensional Semantics 1.1.1
	A reaction: This gives rise to 2-D matrices for representing meaning, and the possible worlds are used twice, for evaluating meaning and then for evaluating context of use. I've always been struck by the two-dimensional semantics of passwords.