2 8o PETER GUTHRIE TAIT 



From this he argued that these physical axioms were & priori and main- 

 tained that Newton's Laws of Motion were also in this sense axiomatic. 

 He wrote (page 316 in Replies to Criticisms): 



" Not a little remarkable, indeed, is the oversight made by Professor Tait, in 

 asserting that 'no d priori reasoning can conduct us demonstratively to a single 

 physical truth,' when he has before him the fact that the system of physical truths 

 constituting Newton's Principia, which he has joined 1 Sir William Thomson in editing, 

 is established by & priori reasoning." 



Unfortunately for Herbert Spencer's argument his quotation from Thomson 

 and Tail's Treatise was incomplete, and the British Quarterly Reviewer 

 shattered the support, which Spencer imagined he had found in the sentence 

 quoted, by simply continuing the quotation. Referring to the passage quoted 

 by Spencer, the Reviewer (in a note to The British Quarterly, January, 

 1874, pp. 215-8) remarked: 



" Had Mr Spencer, however, read the sentence that follows it, we doubt whether 

 we should have heard aught of this quotation. It is : ' Without further remark we shall 

 give Newton's Three Laws; it being remembered that, as the properties of matter 

 might have been such as to render a totally different set of laws axiomatic, these laws 

 must be considered as resting on convictions drawn from observation and experiment, 

 not on intuitive perception.' This not only shows that the term 'axiomatic' is used 

 in the previous sentence in a sense that does not exclude an inductive origin, but it 

 leaves us indebted to Mr Spencer for the discovery of the clearest and most authoritative 

 expression of disapproval of his views respecting the nature of the Laws of Motion." 



This awkward accusation of ignorance of ipsissima verba of the authors he 

 was quoting Spencer did not condescend to answer. Deprived of their 

 support, he turned his battery of words upon the position taken by Thomson 

 and Tait, and proceeded to propound this dilemma : 



Consider, he says, what is implied by framing the thought that " the properties of 

 matter might have been such as to render a totally different set of laws axiomatic"... 

 Does it express an experimentally ascertained truth? If so, I invite Professor Tait 

 to describe the experiments. Is it an intuition? If so, then along with doubt of an 

 intuitive belief concerning things as they are, there goes confidence in an intuitive 

 belief concerning things as they are not. Is it an hypothesis? If so, the implication is 

 that a cognition of which the negation is inconceivable (for an axiom is such) may 

 be discredited by inference from that which is not a cognition at all, but simply a 

 supposition. 



1 This is inaccurate : it was Professor Blackburn who was joined with Thomson in editing 

 the Principia. 



