78 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] |
4266 | Having beliefs involves recognition, expectation and surprise [Scruton] |
4265 | If an animal has beliefs, that implies not only that it can make mistakes, but that it can learn from them [Scruton] |
4264 | Perception (which involves an assessment) is a higher state than sensation [Scruton] |
4271 | There is consciousness whenever behaviour must be explained in terms of mental activity [Scruton] |
10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
4272 | Our concept of a person is derived from Roman law [Scruton] |
4267 | Conditioning may change behaviour without changing the mind [Scruton] |
4269 | An emotion is a motive which is also a feeling [Scruton] |
4270 | Do we use reason to distinguish people from animals, or use that difference to define reason? [Scruton] |
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] |
4284 | All moral life depends ultimately on piety, which is our recognition of our own dependence [Scruton] |
4273 | Kant's Moral Law is the rules rational beings would accept when trying to live by agreement [Scruton] |
4274 | The modern virtues are courage, prudence, wisdom, temperance, justice, charity and loyalty [Scruton] |
4286 | Only just people will drop their own self-interests when faced with an impartial verdict [Scruton] |
4283 | Sympathy can undermine the moral order just as much as crime does [Scruton] |
21093 | Friendship without community spirit misses out on the main part of virtue [Hume] |
4290 | That which can only be done by a callous person, ought not to be done [Scruton] |
4285 | As soon as we drop self-interest and judge impartially, we find ourselves agreeing about conflicts [Scruton] |
4287 | Utilitarianism merely guides us (by means of sympathy) when the moral law is silent [Scruton] |
4282 | Morality is not a sort of calculation, it is what sets the limits to when calculation is appropriate [Scruton] |
4281 | Utilitarianism says we can't blame Stalin yet, but such a theory is a sick joke [Scruton] |
4280 | Utilitarianism is wrong precisely because it can't distinguish animals from people [Scruton] |
21091 | It would be absurd if even a free constitution did not impose restraints, for the public good [Hume] |
21092 | Nobility either share in the power of the whole, or they compose the power of the whole [Hume] |
4295 | We favour our own animals over foreign ones because we see them as fellow citizens [Scruton] |
4268 | Animals command our sympathy and moral concern initially because of their intentionality [Scruton] |
4291 | Letting your dog kill wild rats, and keeping rats for your dog to kill, are very different [Scruton] |
4263 | Many of the stranger forms of life (e.g. worms) interest us only as a species, not as individuals [Scruton] |
4276 | An animal has individuality if it is nameable, and advanced animals can respond to their name [Scruton] |
4277 | I may avoid stepping on a spider or flower, but fellow-feeling makes me protect a rabbit [Scruton] |
4278 | Lucky animals are eaten by large predators, the less lucky starve, and worst is death by small predators [Scruton] |
4279 | We can easily remove the risk of suffering from an animal's life, but we shouldn't do it [Scruton] |
4289 | Sheep and cattle live comfortable lives, and die an enviably easy death [Scruton] |
4292 | Concern for one animal may harm the species, if the individual is part of a bigger problem [Scruton] |
4294 | Animals are outside the community of rights, but we still have duties towards them [Scruton] |
4296 | Brutal animal sports are banned because they harm the personality of the watcher [Scruton] |
4288 | Many breeds of animals have needs which our own ancestors planted in them [Scruton] |
4293 | Introducing a natural means of controlling animal population may not be very compassionate [Scruton] |