Re: All Liar, No Paradox
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ALNP. Note 2
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| Algebraic Calculation
|
| For algebras, two rules
| are commonly accepted
| as implicit in the
| use of the sign =.
|
| Rules of Substitution and Replacement
|
| Rule 1. Substitution
|
| If e = f, and if h is an expression constructed
| by substituting f for any appearance of e in g,
| then g = h.
|
| Rule 2. Replacement
|
| If e = f, and if every token of a given independent
| variable expression v in e = f is replaced by an
| expression w, it not being necessary for v, w
| to be equivalent or for w to be independent
| or variable, and if as a result of this
| procedure e becomes j and f becomes k,
| then j = k.
|
| George Spencer Brown, 'Laws of Form',
| George Allen & Unwin, London, UK, 1969,
| combining texts at pp. 26-27 and p. 140.
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