75 ideas
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] |
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] |
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] |
10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
10975 | Compactness does not deny that an inference can have infinitely many premisses [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] |
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] |
10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
10989 | The standard view of conditionals is that they are truth-functional [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] |
1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
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] |
20489 | Human beings can never really flourish in a long-term state of nature [Wolff,J] |
20483 | Collective rationality is individuals doing their best, assuming others all do the same [Wolff,J] |
20532 | Should love be the first virtue of a society, as it is of the family? [Wolff,J] |
20490 | For utilitarians, consent to the state is irrelevant, if it produces more happiness [Wolff,J] |
20493 | Social contract theory has the attracton of including everyone, and being voluntary [Wolff,J] |
20494 | Maybe voting in elections is a grant of legitimacy to the winners [Wolff,J] |
20500 | We can see the 'general will' as what is in the general interest [Wolff,J] |
20497 | How can dictators advance the interests of the people, if they don't consult them about interests? [Wolff,J] |
20506 | 'Separation of powers' allows legislative, executive and judicial functions to monitor one another [Wolff,J] |
20530 | Political choice can be by utility, or maximin, or maximax [Wolff,J] |
20487 | A realistic and less utopian anarchism looks increasingly like liberal democracy [Wolff,J] |
20488 | It is hard for anarchists to deny that we need experts [Wolff,J] |
20529 | Utilitarianism probably implies a free market plus welfare [Wolff,J] |
20510 | A system of democracy which includes both freedom and equality is almost impossible [Wolff,J] |
20511 | Democracy expresses equal respect (which explains why criminals forfeit the vote) [Wolff,J] |
20502 | Democracy has been seen as consistent with many types of inequality [Wolff,J] |
20496 | A true democracy could not tolerate slavery, exploitation or colonialism [Wolff,J] |
20498 | We should decide whether voting is for self-interests, or for the common good [Wolff,J] |
20499 | Condorcet proved that sensible voting leads to an emphatically right answer [Wolff,J] |
20509 | Occasional defeat is acceptable, but a minority that is continually defeated is a problem [Wolff,J] |
20524 | Market prices indicate shortages and gluts, and where the profits are to be made [Wolff,J] |
20518 | Liberty principles can't justify laws against duelling, incest between siblings and euthanasia [Wolff,J] |
20531 | Either Difference allows unequal liberty, or Liberty makes implementing Difference impossible [Wolff,J] |
20526 | Utilitarians argue for equal distribution because of diminishing utility of repetition [Wolff,J] |
20528 | Difference Principle: all inequalities should be in favour of the disadvantaged [Wolff,J] |
20503 | Political equality is not much use without social equality [Wolff,J] |
20512 | Standard rights: life, free speech, assembly, movement, vote, stand (plus shelter, food, health?) [Wolff,J] |
20513 | If natural rights are axiomatic, there is then no way we can defend them [Wolff,J] |
20514 | If rights are natural, rather than inferred, how do we know which rights we have? [Wolff,J] |
20522 | Utilitarians might say property ownership encourages the best use of the land [Wolff,J] |
20534 | Rights and justice are only the last resorts of a society, something to fall back on [Wolff,J] |
20492 | Following some laws is not a moral matter; trivial traffic rules, for example [Wolff,J] |