23 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] |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
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] |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
6237 | Fear of God is not conscience, which is a natural feeling of offence at bad behaviour [Shaftesbury] |
6234 | If an irrational creature with kind feelings was suddenly given reason, its reason would approve of kind feelings [Shaftesbury] |
6233 | A person isn't good if only tying their hands prevents their mischief, so the affections decide a person's morality [Shaftesbury] |
6236 | People more obviously enjoy social pleasures than they do eating and drinking [Shaftesbury] |
6235 | Self-interest is not intrinsically good, but its absence is evil, as public good needs it [Shaftesbury] |
6232 | Every creature has a right and a wrong state which guide its actions, so there must be a natural end [Shaftesbury] |
5642 | For Shaftesbury, we must already have a conscience to be motivated to religious obedience [Shaftesbury, by Scruton] |