43 ideas
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 22886 | The modern idea of 'limit' allows infinite quantities to have a finite sum [Bardon] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 22914 | An equally good question would be why there was nothing instead of something [Bardon] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| 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] |