seeking the path
p. 495/14-15 p. 495/21-27
implies that logic is closely related to the sciences because Miss Stebbing’s discussion is not irrelevant. [They found it necessary to formulate explicitly the logical principles involved, and in so doing they had to use logical principles. This procedure appears to be circular; in one sense it is circular, but the circularity is not necessarily vicious. There is, however, reason to suppose that Whitehead and Russell aimed at affecting an analysis that did not involve any kind of circularity. This would mean that the primitive propositions of the system exhibited in Principia Mathematica are to be regarded as properly primitive, rather than as undemonstrated propositions.]: The circularity shows that the propositions are, in fact, primitive. [There is a fundamental difference between inference by logical principles from asserted matters of fact, and inference by logical principles from purely logical propositions. The latter cannot be asserted in the same sense as a proposition concerning a matter of fact can be asserted. Thus we may say that we do not assert the truth of mathematics; we assert the validity of the logical structure exhibited by the system of mathematical propositions.]: If logical inference is either inductive or deductive, the second is not logical inference. [… It is for this reason that mathematics cannot be regarded as a system of true propositions; it is a structure.]: Then why, on pp. 230-233, do you say it is a science and deductive? The Principle of Deduction (p. 192) is “what is implied by a true proposition is true”. Since mathematics does not contain true propositions, this Principle does not apply to it. [The problem of the logical justification of induction is not one that need concern the scientist.]: Why not? It should give him sleepless nights. [As Mr. Keynes says: ‘Hume’s statement of the case against induction has never been improved upon; and the successive attempts of philosophers, led by Kant, to discover a transcendental solution have prevented them from meeting the hostile arguments on their own ground and from finding a solution along lines which might, conceivably, have satisfied Hume himself.’]: This seems to suppose that there ought to be a solution.
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...