No reply.
2. Instead of an answer to the question, how this intuition of necessity can be alleged by Professor Tait consistently with his other doctrine, the Reviewer quotes, as though it disposed of my question, Professor Tait’s statement that “as the properties of matter might have been such as to render a totally different set of laws axiomatic, these laws [of motion] must be considered as resting on convictions drawn from observation and experiment, and not on intuitive perception.” Whereupon I inquired how Professor Tait knows that “the properties of matter might have been” other {316} than they are. I asked how it happened that his intuition concerning things as they are not, is so certain that, by inference from it, he discredits our intuitions concerning things as they are . . .
No reply: Professor Tait told, à propos of my question, a story of which no one could discover the application; but, otherwise, declined to answer. Nor was any answer given by his disciple.
3. Further, I asked how it happened that Professor Tait accepted as bases for Physics, Newton’s Laws of Motion; which were illustrated but not proved by Newton, and of which no proofs are supplied by Professor Tait, in the Treatise on Natural Philosophy. I went on to examine what conceivable a posteriori warrant there can be if there is no warrant a priori; and I pointed out that neither from terrestrial nor from celestial phenomena can the First Law of Motion be deduced without a petitio principii . . .
No reply: the Reviewer characterized my reasoning as “utterly erroneous” (therein differing entirely from two {317} eminent authorities who read it in proof); but beyond so characterizing it he said nothing.
4. To my assertion that Newton gave no proof of the Laws of Motion, the Reviewer rejoined that “the whole of the Principia was the proof.” On which my comment was that Newton called them “axioms,” and that axioms are not commonly supposed to be proved by deductions from them . . .
The Reviewer quotes from one of Newton’s letters a passage showing that though he called the Laws of Motion “axioms,” he regarded them as principles “made general by induction;” and that therefore he could not have regarded them as a priori.
5. In rejoinder, I pointed out that whatever conception Newton may have had of these “axioms,” he explicitly and distinctly excluded them from the class of “hypotheses.” Hence I inferred that he did not regard the whole of the {318} Principia as the proof, which the Reviewer says it is; since an assumption made at the outset, to be afterwards justified by the results of assuming it, is an “hypothesis” . . .
No reply.
6. Authority aside, I examined on its merits the assertion that the Laws of Motion are, or can be, proved true by the ascertained truth of astronomical predictions; and showed that the process of verification itself assumed those Laws.