44 ideas
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| 22886 | The modern idea of 'limit' allows infinite quantities to have a finite sum [Bardon] |
| 22914 | An equally good question would be why there was nothing instead of something [Bardon] |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| 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] |