Combining Texts

All the ideas for 'Leibniz', 'works' and 'Syntactic Structure'

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5 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 / k. Infinitesimals
18086 Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher]
     Full Idea: Weierstrass effectively eliminated the infinitesimalist language of his predecessors.
     From: report of Karl Weierstrass (works [1855]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.6
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
18092 Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock]
     Full Idea: After Weierstrass had stressed the importance of limits, one now needed to be able to prove the existence of such limits.
     From: report of Karl Weierstrass (works [1855]) by David Bostock - Philosophy of Mathematics 4.4
     A reaction: The solution to this is found in work on series (going back to Cauchy), and on Dedekind's cuts.
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
7566 The Identity of Indiscernibles is really the same as the verification principle [Jolley]
     Full Idea: Various writers have noted that the Identity of Indiscernibles is really tantamount to the verification principle.
     From: Nicholas Jolley (Leibniz [2005], Ch.3)
     A reaction: Both principles are false, because they are the classic confusion of epistemology and ontology. The fact that you cannot 'discern' a difference between two things doesn't mean that there is no difference. Things beyond verification can still be discussed.
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.