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Tag Archives: mathematical logic

Yet another excerpt from The Book of Real and Imaginary Drugs. I achieved a new high in self promotion.

The Double Negator

If you are a geometer, you draw pictures. But what do you do if you are a logician? I guess you can still draw pictures, like proof trees and so on, but these wouldn’t be pictures of the objects you work on. Intuitively, this is obvious. We say “I can draw a triangle.” not “I can draw a triangle picture. ” On the other hand one cannot draw a tautology.

So we have a natural question here: In logic, what is the verb that corresponds to draw? I think it is easy to answer this question once we look at some standard terminology in mathematical logic: sentence, term, syntax, parsing, . . . As the reader has hopefully guessed, the verb I am talking about is write.

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A review of a book of mine called A Modest Collection of Impossibilities. It was written by Michio Sato and published in The Journal of Mathematics Education and Pedagogy.

A Modest Collection of Impossibilities

Karl Hede’s A Modest Collection of Impossibilities is a book written in the style of Euclid’s Elements, obviously inspired by Spinoza’s Ethica Ordinae Geometrico Demonstrata. Mathematical rigor is the main characteristic of the book, which gives it a rigid structure whose building blocks are formal definitions, theorems and proofs. But this doesn’t give A Modest Collection of Impossibilities the dull mood of a mathematics book at all. On the contrary, the witty style of Hede, combined with his highly original ideas, offers us an exiting reading experience.

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