28 ideas
| 8074 | There is a five shilling fine for each point of divergence from the thinking of Aristotle [Oxford Univ 1350] |
| 6947 | Metaphysics does not rest on facts, but on what we are inclined to believe [Peirce] |
| 6937 | Reason aims to discover the unknown by thinking about the known [Peirce] |
| 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] |
| 21492 | Realism is basic to the scientific method [Peirce] |
| 6949 | If someone doubted reality, they would not actually feel dissatisfaction [Peirce] |
| 6940 | The feeling of belief shows a habit which will determine our actions [Peirce] |
| 6941 | We are entirely satisfied with a firm belief, even if it is false [Peirce] |
| 6942 | We want true beliefs, but obviously we think our beliefs are true [Peirce] |
| 6943 | A mere question does not stimulate a struggle for belief; there must be a real doubt [Peirce] |
| 6598 | We need our beliefs to be determined by some external inhuman permanency [Peirce] |
| 6944 | Demonstration does not rest on first principles of reason or sensation, but on freedom from actual doubt [Peirce] |
| 6948 | Doubts should be satisfied by some external permanency upon which thinking has no effect [Peirce] |
| 6945 | Once doubt ceases, there is no point in continuing to argue [Peirce] |
| 6939 | What is true of one piece of copper is true of another (unlike brass) [Peirce] |
| 6938 | Natural selection might well fill an animal's mind with pleasing thoughts rather than true ones [Peirce] |
| 6946 | If death is annihilation, belief in heaven is a cheap pleasure with no disappointment [Peirce] |