Combining Texts

All the ideas for 'Syntactic Structure', 'The Same F' and 'On the Nature of Mathematical Reasoning'

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4 ideas

2. Reason / F. Fallacies / 8. Category Mistake / c. Category mistake as semantic

18009	Chomsky established the view that category mistakes are well-formed but meaningless [Chomsky, by Magidor]
	Full Idea: The view of Chomsky in 1957 that category mistakes are syntactically well-formed but meaningless is a very standard one.
	From: report of Noam Chomsky (Syntactic Structure [1957]) by Ofra Magidor - Category Mistakes 1.3
	A reaction: I'm going off the idea that they are meaningless, largely because I am beginning to sympathise with the view that any composition of meaningful components is meaningful (even if blatantly false).

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite

15923	Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Poincaré, by Lavine]
	Full Idea: Poincaré rejected the actual infinite. He viewed mathematics that is apparently concerned with the actual infinite as actually concerning the finite linguistic definitions the putatively describe actually infinite objects.
	From: report of Henri Poincaré (On the Nature of Mathematical Reasoning [1894]) by Shaughan Lavine - Understanding the Infinite

9. Objects / F. Identity among Objects / 3. Relative Identity

12155	Statements of 'relative identity' are really statements of resemblance [Perry]
	Full Idea: Statements of 'relative' identity are not identity statements at all, but what I would prefer to call 'statements of resemblance' or 'common property staztements'.
	From: John Perry (The Same F [1970], n12)
	A reaction: This seems like a neat way to sweep the problem from our sight. There remains a nervous metaphysical problem, though, because something seems to be identical when we spot a resemblance. Even two shades of red have something identical in them.

19. Language / C. Assigning Meanings / 1. Syntax

18007	Syntax is independent of semantics; sentences can be well formed but meaningless [Chomsky, by Magidor]
	Full Idea: In 1957 Chomsky argues that syntax is an independent field from semantics. …To support this claim he argues that the now-famous category mistake 'Colourless green ideas sleep furiously' is grammatical but meaningless.
	From: report of Noam Chomsky (Syntactic Structure [1957]) by Ofra Magidor - Category Mistakes 1.3
	A reaction: I'm tempted by the thought that this famous sentence actually is meaningful, although the meaning is fragmentary, and any proposition which can be assembled from it appears to be blatantly false.