34 ideas
| 12124 | Metaphysics is the best knowledge, because it is the simplest [Bacon] |
| 12123 | Natural history supports physical knowledge, which supports metaphysical knowledge [Bacon] |
| 12119 | Physics studies transitory matter; metaphysics what is abstracted and necessary [Bacon] |
| 12120 | Physics is of material and efficient causes, metaphysics of formal and final causes [Bacon] |
| 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] |
| 10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
| 10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
| 10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
| 10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
| 10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
| 10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
| 10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
| 10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
| 10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
| 10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
| 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] |
| 10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
| 1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
| 10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
| 12121 | We don't assume there is no land, because we can only see sea [Bacon] |
| 12117 | Science moves up and down between inventions of causes, and experiments [Bacon] |
| 12127 | Many different theories will fit the observed facts [Bacon] |
| 12126 | People love (unfortunately) extreme generality, rather than particular knowledge [Bacon] |
| 12125 | Teleological accounts are fine in metaphysics, but they stop us from searching for the causes [Bacon] |
| 12118 | Essences are part of first philosophy, but as part of nature, not part of logic [Bacon] |