Representations, Wittgenstein, and all the rest

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SUMMARY

This discussion revolves around the philosophical implications of self-identity as articulated by Ludwig Wittgenstein, particularly in relation to mathematical representations. Participants debate whether expressions like "1 = 1" should be interpreted as identity or equivalence, referencing Wittgenstein's distinction between nonsense and senselessness. The conversation also touches on the application of group representations in mathematics, specifically the general linear group and automorphism groups, while highlighting the importance of clarity in philosophical discourse.

PREREQUISITES
  • Understanding of Wittgenstein's philosophy, particularly concepts from "Tractatus Logico-Philosophicus" and "On Certainty"
  • Familiarity with mathematical representations and group theory, including general linear groups and automorphism groups
  • Knowledge of equivalence relations in mathematics
  • Basic understanding of topology, particularly concepts like genus and homeomorphism
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  • Explore Wittgenstein's concept of language games and their implications for identity and representation
  • Research the properties of group homomorphisms and their applications in mathematics
  • Study the differences between injective and non-injective representations in group theory
  • Investigate the relationship between topology and algebra, focusing on concepts like genus and homeomorphism
USEFUL FOR

Philosophers, mathematicians, and students of logic interested in the intersections of language, identity, and mathematical representation.

  • #31
The using of 'different than' alienates me ##-## one thing can be more different or less different from another thing than a third thing is, but one thing can't properly be said to be 'different than' another thing ##-## e.g. an elephant is more different from an amoeba than it is from a mouse, and an elephant is much bigger than either an amoeba or a mouse ##\dots##
 
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  • #32
A practical example: if a vending machine accepts US nickels, dimes, and quarters, whether I deposit 2 quarters or 5 dimes does not affect whether I get the candy bar ##-## if it's a 50-cent candy bar (as in the '70s) then I get the candy bar either way.

In the '80s in Chicago I knew a grocer who had formally studied engineering ##-## sometimes people would show up who wanted to spend their 'change jar' coin money ##-## he would tell them to sort it by which kind of coin, and then he would put the coins on the scale and accept them at value according to their weight ##-## he said that he knew that the per-coin weight varied a little but he didn't care if $35 worth of dimes was off by a dime or two one way or the other, he wasn't going to count them one-by-one, and he didn't want turn away a customer ##\dots##

A US nickel 'weighs' (under standard conditions) very close to 5 grams (5.000 g according to US Mint specs). I've used $2 worth of them to calibrate a scale.
 
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