PUNISHING A SENIOR WRANGLER. 147 



" axioms^'' says of them that due familiarity with physical phenomena 

 gives the power of seeing " at once " " their necessary truth." These 

 last words, which express his conception of an axiom, express also the 

 usual conception. An axiom is defined as a " self-evident truth," or a 

 truth that is seen at once ; and the definition otherwise worded is — a 

 " truth so evident at first sight that no process of reasoning or demon- 

 stration can make it plainer." Now, I contend that Prof. Tait, by thus 

 committing himself to a definition of physical axioms identical with that 

 which is given of mathematical axioms, tacitly admits that they have 

 the same a priori character ; and I further contend that no such nature 

 as that which he describes physical axioms to have, can be acquired by 

 experiment or observation during the life of an individual. Axioms, if 

 defined as truths of which the necessity!^ at once seen, are thereby de- 

 fined as truths of which the negation is inconceivable ; and the familiar 

 contrast between them and the truths established by individual expe- 

 riences is, that these last never become such that their negations are 

 inconceivable, however multitudinous the experiences may be. Thou- 

 sands of times has the sportsman heard the report that follows the flash 

 from his gun, but still he can imagine the flash as occurring silently ; 

 and countless daily experiments on the burning of coal leave him able 

 to conceive coal as remaining in the fire without ignition. So that the 

 " convictions drawn from observation and experiment " during a single 

 life can never acquire that character which Prof. Tait admits physical 

 axioms to have : in other words, physical axioms cannot be derived 

 from personal observation and experiment. Thus, otherwise applying 

 the reviewer's words, I " doubt whether we should have heard aught 

 of this quotation" to which he calls my attention, had he studied the 

 matter more closely ; and he " leaves us indebted to " him " for the 

 discovery of" a passage which serves to make clearer the untenability 

 of the doctrine he so dogmatically afiirms. 



I turn now to what the reviewer says concernifig the special argu- 

 ments I used to show that the first law of motion cannot be proved 

 experimentally. After a bare enunciation of my positions, he says : 



" On the utterly erroneous character of these statements we do not care to 

 dwell, we wish simply to call our reader's attention to the conclusion arrived at. 

 Is that a disproof of the possibility of an inductive proof? We thought that 

 every tolerably educated man was aware that the proof of a scientific law con- 

 sisted in showing that, ty assuming its truth, we could explain the observed 

 phenomena." 



Probably the reviewer expects his readers to conclude that he 

 could easily dispose of the statements referred to if he tried. Among 

 scientific men, however, this cavalier passing over of my arguments 

 will perhaps be ascribed to another cause. I will give him my reason 

 for saying this. Those arguments, read in proof by one of the most 

 eminent physicists, and by a specially-honored mathematician, liad 

 their entire concurrence ; and I have since had from another mathe- 



