67 ideas
| 23853 | Truth is not a object we love - it is the radiant manifestation of reality [Weil] |
| 8083 | Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin] |
| 7727 | Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner] |
| 10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
| 11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
| 11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read] |
| 11011 | Same say there are positive, negative and neuter free logics [Read] |
| 11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
| 8686 | Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend] |
| 10986 | Not all validity is captured in first-order logic [Read] |
| 10972 | The non-emptiness of the domain is characteristic of classical logic [Read] |
| 11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
| 10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
| 10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read] |
| 10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square [Read] |
| 10973 | A theory is logically closed, which means infinite premisses [Read] |
| 11007 | Quantifiers are second-order predicates [Read] |
| 10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
| 22277 | Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter] |
| 10971 | A logical truth is the conclusion of a valid inference with no premisses [Read] |
| 10988 | Any first-order theory of sets is inadequate [Read] |
| 10975 | Compactness does not deny that an inference can have infinitely many premisses [Read] |
| 10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
| 10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read] |
| 10976 | Compactness makes consequence manageable, but restricts expressive power [Read] |
| 11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
| 11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
| 10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
| 10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
| 10997 | Von Neumann numbers are helpful, but don't correctly describe numbers [Read] |
| 23855 | Creation produced a network or web of determinations [Weil] |
| 11016 | Would a language without vagueness be usable at all? [Read] |
| 11019 | Supervaluations say there is a cut-off somewhere, but at no particular place [Read] |
| 11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read] |
| 11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations [Read] |
| 10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
| 11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
| 10989 | The standard view of conditionals is that they are truth-functional [Read] |
| 10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
| 11017 | Some people even claim that conditionals do not express propositions [Read] |
| 10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
| 10982 | How can modal Platonists know the truth of a modal proposition? [Read] |
| 10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read] |
| 10981 | A possible world is a determination of the truth-values of all propositions of a domain [Read] |
| 11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read] |
| 10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
| 11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
| 10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
| 23848 | The aesthete's treatment of beauty as amusement is sacreligious; beauty should nourish [Weil] |
| 23854 | Beauty is the proof of what is good [Weil] |
| 23837 | Respect is our only obligation, which can only be expressed through deeds, not words [Weil] |
| 23844 | The most important human need is to have multiple roots [Weil] |
| 23838 | The need for order stands above all others, and is understood via the other needs [Weil] |
| 23836 | Obligations only bind individuals, not collectives [Weil] |
| 23840 | A citizen should be able to understand the whole of society [Weil] |
| 23843 | Even the poorest should feel collective ownership, and participation in grand display [Weil] |
| 23846 | Culture is an instrument for creating an ongoing succession of teachers [Weil] |
| 23839 | A lifelong head of society should only be a symbol, not a ruler [Weil] |
| 23842 | Party politics in a democracy can't avoid an anti-democratic party [Weil] |
| 23847 | Socialism tends to make a proletariat of the whole population [Weil] |
| 23845 | The capitalists neglect the people and the nation, and even their own interests [Weil] |
| 23841 | By making money the sole human measure, inequality has become universal [Weil] |
| 23835 | People have duties, and only have rights because of the obligations of others to them [Weil] |
| 23852 | To punish people we must ourselves be innocent - but that undermines the desire to punish [Weil] |
| 23850 | The soldier-civilian distinction should be abolished; every citizen is committed to a war [Weil] |
| 23851 | Education is essentially motivation [Weil] |
| 23849 | Religion should quietly suffuse all human life with its light [Weil] |