25 ideas
| 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] |
| 18085 | Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy] |
| 18084 | When successive variable values approach a fixed value, that is its 'limit' [Cauchy] |
| 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] |
| 12790 | Generalisations must be invariant to explain anything [Leuridan] |
| 12789 | Biological functions are explained by disposition, or by causal role [Leuridan] |
| 14388 | Mechanisms must produce macro-level regularities, but that needs micro-level regularities [Leuridan] |
| 12787 | Mechanisms can't explain on their own, as their models rest on pragmatic regularities [Leuridan] |
| 14384 | We can show that regularities and pragmatic laws are more basic than mechanisms [Leuridan] |
| 14386 | Mechanisms are ontologically dependent on regularities [Leuridan] |
| 14389 | There is nothing wrong with an infinite regress of mechanisms and regularities [Leuridan] |
| 14387 | Rather than dispositions, functions may be the element that brought a thing into existence [Leuridan] |
| 14382 | Pragmatic laws allow prediction and explanation, to the extent that reality is stable [Leuridan] |
| 14385 | Strict regularities are rarely discovered in life sciences [Leuridan] |
| 14383 | A 'law of nature' is just a regularity, not some entity that causes the regularity [Leuridan] |