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Second Meeting: 8th July, 1891.
E. Tregear, President, in the Chair.
New Member.—William Percival Evans, M.A., Ph.D.
Papers. — 1. “Mill on Demonstration and Necessary Truth,” by W. W. Carlile, M.A. (Transactions, p. 644.)
Sir James Hector thanked the author for his most interesting paper. It was a subject difficult to criticize until the paper had been carefully read.
Mr. Maskell agreed with Sir James 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 one 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 shown. 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 one another 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 that, 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 of 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 a “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 was asked how it was possible to possess one of these self-evident truths except by in-heritance, without breaking the chain of cause and effect. Such a statement as that “things which are equal to the same thing are equal to each other “was not a” self-evident” truth; it required reasoning from experience before the mind could place faith in it. The purely mental conception of a line as having “length without breadth” could not be called useless (although it could not be practically represented), because
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arithmetical figures used in trigonometry proved that the boundaries of geometrical figures really had position, but not magnitude of breadth. So that this is almost a necessary truth; and, although abstract truths were little more than hypotheses, still, if they were “working hypotheses,” they were of enormous value. He might instance the value of the Forty-seventh Proposition of the First Book of Euclid: the discoverer of the principle in this problem offered up a hecatomb of oxen to the gods for so great a truth being found; and it had proved of inestimable value to the world in astronomy, navigation, engineering, &c. He could understand the schoolboy's delight if allowed to prove the truth of the Fifth Proposition of the First Book of Euclid by turning the triangle on its back, but he hardly thought such a simplification would be allowed, although many of the propositions might be swept away as being evident at sight, and not made clearer by the attempted proof. As to Mr. Maskell's assertion that the Bosjesman, or any savage, had as much intellectual power as the civilised European, there would be difficulty in measuring the amount of latent power in any individual; but it was certain that the expression of that power was immensely unequal. It would be almost impossible to assert with gravity that the mind of an African who with great difficulty could be taught the use of numbers beyond two or three was equal to any one of the minds of Bacon, Newton, or Herschel, although a potentiality of mind equal to great intellectual effort might lie unrecognised in the brain of the savage.
Mr. Carlile, in reply, expressed his gratification at the appreciative criticism his paper had received. The President had already explained some of the matters to which exception had been taken. He had not meant to suggest that the simplification of the proof of the Fifth Proposition which he suggested in any way detracted from its validity or importance. There were several of the propositions at the beginning of the First Book which were rather obscured than illustrated by the proof furnished of them: the Thirteenth, for instance. If we regard a point in a straight line as an angle of 180°, it was certain that drawing any number of lines through this point could have no tendency to alter the size of this angle; yet this was what was elaborately proved. He thought a desideratum among the definitions was a definition of what was meant by the size of an angle. It proceeded to speak of the size of angles without furnishing any criterion for their measurement. If this were furnished it would necessarily carry with it the proof of the Fourth, Fifth, and Eighth, and a host of other propositions. The size of an angle, and the length of the subtending side in any triangle, were, it seemed to him, two names for the same thing. There was no use of propositions to prove the fact of their concomitant variations.
2. “On the Shifting of Sand-dunes,” by H. C. Field. (Transactions, p. 561.).
Sir James Hector said he thought the subject a most important one. In a new country they should be very careful as to how they interfered with the natural changes of the coast-line. He was of opinion that Mr. Field had done good service in bringing this matter before the Society. They in New Zealand would have to guard against selling lands situated in dangerous positions on the coasts. They should also prevent mischievous people from interfering with mouths of rivers, and thus preventing natural changes. Mr. Field's paper had opened up a subject of extreme practical importance to the colony.
Mr. Beetham thought this a valuable paper. It would encourage those who had the opportunity to note carefully such changes as had been spoken of. There was no doubt great alterations had taken place on our coasts and in our rivers owing to the causes mentioned by Mr. Field.