Changes

==Note 13==

==Note 13==

The above-mentioned fact about the regular representations of a group is universally known as Cayley's Theorem, typically stated in the following form:

The above-mentioned fact about the regular representations

of a group is universally known as "Cayley's Theorem".  It

is usually stated in the form:  "Every group is isomorphic

the whole idea can be summed up as follows:

  whose meaning you wish to investigate

| Every group is isomorphic to a subgroup of <math>\operatorname{Aut}(X),</math> the group of automorphisms of a suitably chosen set <math>X\!</math>.

  as they play out on all the stages of

  to imagine that symbol playing a role.

This idea of definition by way of context transforming operators

is basically the same as Jeremy Bentham's notion of "paraphrasis",

 

a "method of accounting for fictions by explaining various purported

terms away" (Quine, in Van Heijenoort, 'From Frege to Gödel', p. 216).

Today we'd call these constructions "term models".  This, again, is

the big idea behind Schönfinkel's combinators {S, K, I}, and hence

 

of lambda calculus, and I reckon you all know where that leads.

This idea of contextual definition by way of conduct transforming operators is basically the same as Jeremy Bentham's notion of ''paraphrasis'', a "method of accounting for fictions by explaining various purported terms away" (Quine, in Van Heijenoort, ''From Frege to Gödel'', p.&nbsp;216). Today we'd call these constructions ''term models''.  This, again, is the big idea behind Schönfinkel's combinators <math>\operatorname{S}, \operatorname{K}, \operatorname{I},</math> and hence of lambda calculus, and I reckon you know where that leads.

==Note 14==

==Note 14==