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Mathematics as Injunctions

G. Spencer Brown in The Laws of Form

In the Notes for Chapter 2 of The Laws of Form, Spencer Brown writes:

It may be helpful at this stage to realize that the primary form of mathematical communication is not description, but injunction. In this respect it is comparable with practical art forms like cookery, in which the taste of a cake, although literally indescribable, can be conveyed to the reader in the form of a set of injunctions called a recipe. Music is a similar art form, the composer does not even attempt to describe the set of sounds he has in mind, much less the set of feelings occasioned through them, but writes down a set of commands which if they are obeyed by the reader, can result in a reproduction, to the reader, of the composer's original experience.

The first sentence of Chapter 2 is an injunction: "Draw a distinction." — thereby beginning a journey into a kind of mathematics, which Bertrand Russell called "a new calculus of great power and simplicity ..."

This is followed by an illuminating observation about Wittgenstein's famous: "whereof one cannot speak, thereof one must be silent".

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