Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: gether; for on them does npt depend the doctrine I mean to establish, SECT- III. The subject continued. Intuitive truths distinguishable into classes. the notions attending the perception of certain truth, we formerly mentioned this as one, - That in regard to such truth, we suppose we should entertain the same sentiments and belief if we were
perfectly acquainted with all nature . Lest it should be thought that we mean to extend this notion too far, it seems proper to introduce here the following remarks. 1. The axioms and demonstrated conclusions of geometry are certainly true, and certainly agreeable to the nature of things. Thus we judge of them at present; and thus we necessarily believe, that we should judge of them, even if we were endued with omniscience and infallibility. It is a natural dictate of human understanding, that the contrary of these truths must for ever remain absurd and impossible, and that omnipotence itself cannot change their na- Jure; though it might so deprave our judgment as to make us disbelieve, or not perceive them -j-. See part 1. chap. 1. t Some authors are of opinion, that all mathematical truth is resolvable into identical propositions. The following remark to this purpose is taken from a Dissertation on Evidence, printed at Berlin in the year 1764.
Omnes mathematicorum propositiones sunt i-
denticw, et repraesentantur hac formula, ff=M Sunt veritates iden-
tic, sub varia forma expressse, imo ipsum, quod dicitur, contra-
dictionis principium, vtrio modo enunciatum et involutum; siqui- “ dem omnes hujus generis propositiones revera in eo contineantur.
Secundum nostram autcm intelligendi facultatem ca est propositi- 2. That my body exists, and is endued with a thinking, active, and permanent principle, which…
