Monday, November 12, 2007

5.5351 There are certain cases where one is led into the temptation to use expressions of the form “a = a” or “p[if…then]p” and such. And indeed this happens when one would like to speak of the prototype: Proposition, Thing, etc. Thus Russell in the “Principles of Mathematics” has rendered the nonsense [Unsinn] “p is a proposition” in symbols with “p[if…then]p” and presented it as a hypothesis in front of certain propositions whose argument places thereby could only be occupied by propositions.

(It is therefore already nonsense to put the hypothesis p[if…then]p in front of a proposition in order to ensure that its arguments are of the right form, because the hypothesis for a non-proposition as argument becomes not false but nonsensical [unsinnig], and because the proposition itself becomes nonsensical [unsinnig] with the incorrect kind of argument, therefore it saves itself from incorrect arguments just as well, or as badly, as the senseless [sinnlose] hypothesis hung on it for this purpose.)

Seems right enough.

Black (p. 297) says that ‘antecedent’ would be a better translation of Hypothese here.

No comments: