antecedent. It is "the implied," the necessary condition of their truth. They are "the implier." It is clear then that by this definition, applied through this statement of implications, the conclusion of every syllogism is logically prior to its premisses.
Now let us turn to passages (d) (p. 46) and (e) (p. 205). Passage (d) will give us all we want. Passage (e) merely confirms it.
It amounts to this. Mathematics are logically prior to Mechanics and Physics. [I shall represent Mathematics, in this argument, by Ma; Mechanics and Physics by Me.] That is to say, Ma does not imply the truth of Me, but Me does imply the truth of Ma. So (1) Me might be false (much of it[1]) without Ma being false; but (2) if Ma were false, then Me would be false.
Here the general definition of Logical Priority is the same as that fulfilled by Consequent in relation to Antecedent and Conclusion in relation to Premisses, considered in accordance with the traditional rules of Formal Logic.
- ↑ This reservation can make no difference. The two requirements which follow from the logical priority of Ma to Me must obviously follow in respect of the same elements of Me, viz., those to which Ma is prior. And these elements of Me are determined by one of the requirements as results of an "explicit deduction" from Ma—results so strict that the falsity of the mathematical premisses Ma will involve their falsity. Thus you cannot account for the required possible falsity of Me while Ma is true, by supposing that some part of Me depends on a false premiss introduced into the chain at a point lower down than Ma.
