Combining Texts

All the ideas for 'The Sign of Four', 'Through the Looking Glass' and 'Structuralism Reconsidered'

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4 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
8923 Numbers are identified by their main properties and relations, involving the successor function [MacBride]
     Full Idea: The mathematically significant properties and relations of natural numbers arise from the successor function that orders them; the natural numbers are identified simply as the objects that answer to this basic function.
     From: Fraser MacBride (Structuralism Reconsidered [2007], §1)
     A reaction: So Julius Caesar would be a number if he was the successor of Pompey the Great? I would have thought that counting should be mentioned - cardinality as well as ordinality. Presumably Peano's Axioms are being referred to.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
8926 For mathematical objects to be positions, positions themselves must exist first [MacBride]
     Full Idea: The identification of mathematical objects with positions in structures rests upon the prior credibility of the thesis that positions are objects in their own right.
     From: Fraser MacBride (Structuralism Reconsidered [2007], §3)
     A reaction: Sounds devastating, but something has to get the whole thing off the ground. This is why Resnik's word 'patterns' is so appealing. Patterns stare you in the face, and they don't change if all the objects making it up are replaced by others.
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
21982 I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
     Full Idea: "I see nobody on the road," said Alice. - "I only wish I had such eyes," the King remarked. ..."To be able to see Nobody! ...Why, it's as much as I can do to see real people."
     From: Lewis Carroll (C.Dodgson) (Through the Looking Glass [1886], p.189), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7
     A reaction: [Moore quotes this, inevitably, in a chapter on Hegel] This may be a better candidate for the birth of philosophy of language than Frege's Groundwork.
14. Science / C. Induction / 1. Induction
22200 If you eliminate the impossible, the truth will remain, even if it is weird [Conan Doyle]
     Full Idea: When you have eliminated the impossible, whatever remains, however improbable, must be the truth.
     From: Arthur Conan Doyle (The Sign of Four [1890], Ch. 6)
     A reaction: A beautiful statement, by Sherlock Holmes, of Eliminative Induction. It is obviously not true, of course. Many options may still face you after you have eliminated what is actually impossible.