Number Theory


Refutation of Linear Algebra as not Bivalent © Copyright 2018 by Colin James III All Rights Reserved.

Authors: Colin James III

Linear implication, resource interpretation to avoid the frame problem, and the linear transformation property are not tautologous. In particular, Tony Hoare's 1985 vending machine example as stated below is not tautologous: "Suppose a candy bar by candy, and a dollar by $1. To state a dollar will buy one candy bar, write the implication $1 ⇒ candy. But in ordinary (classical or intuitionistic) logic, from A and A ⇒ B one can conclude A ∧ B. So, ordinary logic leads us to believe that we can buy the candy bar and keep our dollar!"

Comments: 2 Pages. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

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[v1] 2018-05-21 22:55:01

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