52 ideas
| 7454 | Gassendi is the first great empiricist philosopher [Hacking] |
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| 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] |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| 21122 | Liberal Nationalism says welfare states and democracy needed a shared sense of nationality [Shorten] |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| 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] |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| 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] |
| 7447 | Probability was fully explained between 1654 and 1812 [Hacking] |
| 7448 | Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence) [Hacking] |
| 7449 | Epistemological probability based either on logical implications or coherent judgments [Hacking] |
| 7450 | In the medieval view, only deduction counted as true evidence [Hacking] |
| 7451 | Formerly evidence came from people; the new idea was that things provided evidence [Hacking] |
| 7452 | An experiment is a test, or an adventure, or a diagnosis, or a dissection [Hacking, by PG] |
| 7459 | Follow maths for necessary truths, and jurisprudence for contingent truths [Hacking] |
| 21136 | Utilitarians conflate acts and omissions; causing to drown and failing to save are the same [Shorten] |
| 21135 | There are eight different ways in which groups of people can be oppressed [Shorten, by PG] |
| 21118 | Constitutional Patriotism unites around political values (rather than national identity) [Shorten] |
| 21129 | Democracy is a method of selection, or it involves participation, or it concerns public discussion [Shorten] |
| 21130 | Some say democracy is intrinsically valuable, others that it delivers good outcomes [Shorten] |
| 21126 | Representative should be either obedient, or sensible, or typical [Shorten] |
| 21128 | There is 'mirror representation' when the institution statistically reflects the population [Shorten] |
| 21127 | In a changed situation a Mandated Representative can't keep promises and fight for constituents [Shorten] |
| 21117 | Liberal citizens have a moral requirement to respect freedom and equality [Shorten] |
| 21134 | Maybe the rational autonomous liberal individual is merely the result of domination [Shorten] |
| 21113 | Liberal equality concerns rights, and liberal freedom concerns choice of ends [Shorten] |
| 21121 | Liberal Nationalism encourages the promotion of nationalistic values [Shorten] |
| 21115 | Liberalism should not make assumptions such as the value of choosing your own life plan [Shorten] |
| 21114 | Liberals treat individuals as mutual strangers, rather than as social beings [Shorten] |
| 21123 | Liberal Nationalism is more communitarian, and Constitutional Patriotism more cosmopolitan [Shorten] |
| 21124 | Religious toleration has been institutionalised by the separation of church and state [Shorten] |