=1433.= General and certain truths are only founded in the habitudes and relations of _abstract ideas_. A sagacious and methodical application of our thoughts, for the finding out of these relations, is the only way to discover all that can be put with truth and certainty concerning them into general propositions. By what steps we are to proceed in these, is to be learned in the schools of mathematicians, who, from very plain and easy beginnings, by gentle degrees, and a continued chain of reasonings, proceed to the discovery and demonstration of truths that appear at first sight beyond human capacity. The art of finding proofs, and the admirable method they have invented for the singling out and laying in order those intermediate ideas that demonstratively show the equality or inequality of unapplicable quantities, is that which has carried them so far and produced such wonderful and unexpected discoveries; but whether something like this, in respect of other ideas, as well as those of magnitude, may not in time be found out, I will not determine. This, I think, I may say, that if other ideas that are the real as well as the nominal essences of their species, were pursued in the way familiar to mathematicians, they would carry our thoughts further, and with greater evidence and clearness than possibly we are apt to imagine.--LOCKE, JOHN. _An Essay concerning Human Understanding, Bk. 4, chap. 12, sect. 7._ =1434.= Those long chains of reasoning, quite simple and easy, which geometers are wont to employ in the accomplishment of their most difficult demonstrations, led me to think that everything which might fall under the cognizance of the human mind might be connected together in a similar manner, and that, provided only that one should take care not to receive anything as true which was not so, and if one were always careful to preserve the order necessary for deducing one truth from another, there would be none so remote at which he might not at last arrive, nor so concealed which he might not discover.--DESCARTES. _Discourse upon Method, part 2; The Philosophy of Descartes [Torrey], (New York, 1892), p. 47._ =1435.= If anyone wished to write in mathematical fashion in metaphysics or ethics, nothing would prevent him from so doing with vigor. Some have professed to do this, and we have a promise of mathematical demonstrations outside of mathematics; but it is very rare that they have been successful. This is, I believe, because they are disgusted with the trouble it is necessary to take for a small number of readers where they would ask as in Persius: _Quis leget haec_, and reply: _Vel duo vel nemo._ --LEIBNITZ.