Re: All Liar, No Paradox

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

ALNP.  Note 2

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| 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.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
inquiry e-lab: http://stderr.org/pipermail/inquiry/
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o