p. 183/6-7 p. 191/5 p. 191/6 p. 191/fn.
p. 192/23-24 p. 193/17-18 p. 193/21-23
p. 232/1-2 p. 232/35-37
are those that cannot be conceived without being tacitly assumed in the act of conception. [The propositions of a deductive system are established as true only by means of inductive verification. Such verification is never complete; it could not amount to demonstration.] noted [There is a class of all possible individuals, called the ‘universe’.]: This assumption is unjustified. [Any proposition is either true or false.]: (and perhaps both) [Not any proposition is both true and false] is changed to read: Any proposition is not both true and false (and perhaps neither). [The principles of identity, excluded middle, and contradiction have been traditionally considered as the only fundamental logical principles. This is a complete mistake. They are neither less, nor more, important than the other principles we have stated.]: But the point is not whether they are more important, but whether they are more fundamental. [The formal principles stated above in terms of implication suffice for the construction of deductive systems] u/l and [Without these two principles it would be impossible to construct a deductive system] also u/l, both sentences connected by a line: Which do you mean? [The development of the primitive propositions stated in Principia Mathematica takes place in virtue of the repeated use of these two principles.] u/l: Nonsense! See pp. 232-3 and 489. [If by ‘the world’ we mean ‘everything that is the case’, then it may be doubted whether the world is a system.]: The expression ‘is the case’ applies only to propositions (we cannot, for example, say ‘a lion is the case’), and ‘everything that is the case’ means ‘all true propositions’. A world of propositions is truly a logician’s world. [A mathematical proposition is independent of what happens to exist.]: Even of the existing mathematician? [Owing to its independence of empirical facts mathematics is a wholly deductive science; hence it employs a method of exact demonstration.]: If mathematical propositions are, as you say, independent of what exists, then they are not concerned with matters of fact—they do not depend
Published on Jun 26, 2013
Part B includes two early essays (Nibbana and Anatta and Sketch for a Proof of Rebirth) as well as notes from a Commonplace Book and Margina...