23O JOURNAL OF SCIENCE. 



in the world of fact. The difficulty however, was not peculiar to the 

 mathematical reasoning. They had seen that even what were called 

 identical propositions rested on assumptions. Geometry only became of 

 real interest and value when it was ascertained that propositions which 

 were literally and necessarily true of the lines and circles that we 

 supposed ourselves to construct were approximately true of the lines 

 and circles of nature. 



Sir James Hector thanked the author for his most interesting 

 paper ; it was a subject difficult to criticise until the paper had been 

 carefully read. 



Mr. Maskell agreed with Sir J. Hector that the best thanks of the 

 Society were due to Mr. Carlile for his excellent paper which invested 

 a dry and difficult subject with much more interest than probably any- 

 body expected. For himself he found several very suggestive points in 

 the paper, not so much as to the particular question treated as on 

 general grounds. In the first place it reminded him of what seemed to 

 be the general fault of all English writers on philosophy and logic, that 

 they never seemed to refer to any but English, Scotch, or a few German 

 authors. Now if they would study French, Spanish, or Italian works 

 also they might enlarge their views and possibly gain insight into quite 

 new and correctly suggestive trains of thought. Then again Mr. 

 Carlile, he thought, had attached far too much importance to the 

 notions of Professor Huxley, a man who to the speaker's mind, was 

 as bad a specimen of blatant assumption and of illogical absurdity 

 (except of course when dealing with actual facts of natural history) as 

 the modern era has to show. There was one point, only incidentally 

 referred to in the paper, which would perhaps require correction. Mr. 

 Carlile parenthetically remarked that the axiom that two things which 

 are equal to a third are equal to each other would be incomprehensible 

 to a Bushman or a Damaraman. Taken as referring to any particular 

 or existing savage, this would be probably true : taken as a general 

 statement, with the inference that any necessary difference exists 

 between the brain and intellect of a savage and the brain and intellect 

 of a cultivated Englishman it would certainly not be correct, in spite of 

 the prevailing theory of the present day which usually affirms it, if not 

 in terms, at least by implication. 



The President said : Greatly as he admired the work of Professor 

 Huxley in the domain of natural science, he shared with others the 

 regret that the learned Professor should ever step outside the limits of 

 his own domain and enter the fields of politics and theology, where his 

 logic was by no means unassailable. He (the president) had been struck 

 with astonishment when reading Huxley many years ago to find that 

 he had stated that all dream images were vague and undefined. This 

 is contrary to the facts of experience with most observers. Undefined 

 images might occupy the mind of one who was discussing a subject like 

 " Man " from a racial point of view, but in the case of " triangle " there 

 was no mental conception possible of a triangle generally ; it was 

 absolutely necessary to conceive the idea of a triangle as either 

 equilateral, scalene, isosceles, &c. As to necessary truths, it was almost 

 certainly held that the axioms of Euclid were necessary truths, but he 

 had read a clever psychological article in a recent Magazine in which it 



