Thursday, November 08, 2007

5.501 An expression in brackets whose terms are propositions I indicate – if the order of terms in the brackets is indifferent – by a sign of the form “(ξ)” [but with a line over it]. “ξ” is a variable whose values are the terms of the expression in brackets, and the line over the variables indicates that it represents all its values in the brackets.

(Thus if ξ has the three values P, Q, R, then (ξ) [with a line over it] = (P, Q, R).)

The values of the variables are to be determined.

The determination is the description of the propositions that the variable represents.

How the description of the terms of the expression in brackets is done is not essential.

We can distinguish three kinds of description: 1. Direct enumeration. In this case we can put in place of the variable simply its constant values. 2. Giving a function fx, whose values for all values of x are the propositions to be described. 3. Giving a formal law, according to which those propositions are constructed. In this case the terms of the expression in brackets are all the terms of a formal series.

OK. More definitions, pretty much. Friedlander (p. 77) argues that Ogden’s ‘determination’ is preferable to P&McG’s ‘stipulation’, which sounds too arbitrary. Black (p. 276) suggests ‘prescribed’ and ‘prescription.’