30 ideas
19335 | Reasonings have a natural ordering in God's understanding, but only a temporal order in ours [Leibniz] |
8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
22278 | Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid] |
8673 | Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend] |
10250 | Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid] |
10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
19367 | Saying we must will whatever we decide to will leads to an infinite regress [Leibniz] |
19351 | Perfections of soul subordinate the body, but imperfections of soul submit to the body [Leibniz] |
19331 | Will is an inclination to pursue something good [Leibniz] |
19346 | Most people facing death would happily re-live a similar life, with just a bit of variety [Leibniz] |
19340 | Metaphysical evil is imperfection; physical evil is suffering; moral evil is sin [Leibniz] |
19366 | You can't assess moral actions without referring to the qualities of character that produce them [Leibniz] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
19326 | God must be intelligible, to select the actual world from the possibilities [Leibniz] |
19327 | The intelligent cause must be unique and all-perfect, to handle all the interconnected possibilities [Leibniz] |
19344 | God prefers men to lions, but might not exterminate lions to save one man [Leibniz] |
19330 | If justice is arbitrary, or fixed but not observed, or not human justice, this undermines God [Leibniz] |
19325 | God is the first reason of things; our experiences are contingent, and contain no necessity [Leibniz] |
19329 | The laws of physics are wonderful evidence of an intelligent and free being [Leibniz] |
19437 | Prayers are useful, because God foresaw them in his great plan [Leibniz] |
19337 | How can an all-good, wise and powerful being allow evil, sin and apparent injustice? [Leibniz] |
19345 | Being confident of God's goodness, we disregard the apparent local evils in the visible world [Leibniz] |