45 ideas
| 2510 | Traditionally philosophy is an a priori enquiry into general truths about reality [Katz] |
| 2516 | Most of philosophy begins where science leaves off [Katz] |
| 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] |
| 22886 | The modern idea of 'limit' allows infinite quantities to have a finite sum [Bardon] |
| 14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
| 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] |
| 1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
| 2521 | 'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction [Katz] |
| 22914 | An equally good question would be why there was nothing instead of something [Bardon] |
| 2513 | We don't have a clear enough sense of meaning to pronounce some sentences meaningless or just analytic [Katz] |
| 2522 | Experience cannot teach us why maths and logic are necessary [Katz] |
| 2517 | Structuralists see meaning behaviouristically, and Chomsky says nothing about it [Katz] |
| 2519 | It is generally accepted that sense is defined as the determiner of reference [Katz] |
| 2520 | Sense determines meaning and synonymy, not referential properties like denotation and truth [Katz] |
| 2518 | Sentences are abstract types (like musical scores), not individual tokens [Katz] |
| 22902 | Why does an effect require a prior event if the prior event isn't a cause? [Bardon] |
| 22905 | Becoming disordered is much easier for a system than becoming ordered [Bardon] |
| 22913 | The universe expands, so space-time is enlarging [Bardon] |
| 22889 | We should treat time as adverbial, so we don't experience time, we experience things temporally [Bardon, by Bardon] |
| 22900 | How can we question the passage of time, if the question takes time to ask? [Bardon] |
| 22898 | What is time's passage relative to, and how fast does it pass? [Bardon] |
| 22897 | The A-series says a past event is becoming more past, but how can it do that? [Bardon] |
| 22901 | The B-series needs a revised view of causes, laws and explanations [Bardon] |
| 22896 | The B-series is realist about time, but idealist about its passage [Bardon] |
| 22903 | The B-series adds directionality when it accepts 'earlier' and 'later' [Bardon] |
| 22910 | To define time's arrow by causation, we need a timeless definition of causation [Bardon] |
| 22909 | We judge memories to be of the past because the events cause the memories [Bardon] |
| 22904 | The psychological arrow of time is the direction from our memories to our anticipations [Bardon] |
| 22906 | The direction of entropy is probabilistic, not necessary, so cannot be identical to time's arrow [Bardon] |
| 22907 | It is arbitrary to reverse time in a more orderly universe, but not in a sub-system of it [Bardon] |
| 22883 | It seems hard to understand change without understanding time first [Bardon] |
| 22890 | We experience static states (while walking round a house) and observe change (ship leaving dock) [Bardon] |
| 22884 | The motion of a thing should be a fact in the present moment [Bardon] |
| 22892 | Experiences of motion may be overlapping, thus stretching out the experience [Bardon] |
| 22911 | At least eternal time gives time travellers a possible destination [Bardon] |
| 22912 | Time travel is not a paradox if we include it in the eternal continuum of events [Bardon] |
| 22882 | We use calendars for the order of events, and clocks for their passing [Bardon] |