30 ideas
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
5515 | Imaginary cases are good for revealing our beliefs, rather than the truth [Parfit] |
10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
10283 | A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W] |
10284 | There are three different standard presentations of semantics [Hodges,W] |
10285 | I |= φ means that the formula φ is true in the interpretation I [Hodges,W] |
10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |
10288 | Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W] |
10289 | Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W] |
10287 | If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W] |
10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
5516 | Reduction can be by identity, or constitution, or elimination [Parfit, by PG] |
3539 | Personal identity is just causally related mental states [Parfit, by Maslin] |
5514 | Psychologists are interested in identity as a type of person, but philosophers study numerical identity [Parfit] |
1393 | One of my future selves will not necessarily be me [Parfit] |
5521 | If my brain-halves are transplanted into two bodies, I have continuity, and don't need identity [Parfit] |
5522 | Over a period of time what matters is not that 'I' persist, but that I have psychological continuity [Parfit] |
1392 | If we split like amoeba, we would be two people, neither of them being us [Parfit] |
5519 | It is fine to save two dying twins by merging parts of their bodies into one, and identity is irrelevant [Parfit] |
5520 | If two humans are merged surgically, the new identity is a purely verbal problem [Parfit] |
1391 | Concern for our own lives isn't the source of belief in identity, it is the result of it [Parfit] |
5518 | It doesn't matter whether I exist with half my components replaced (any more than an audio system) [Parfit] |
9762 | We should focus less on subjects of experience, and more on the experiences themselves [Parfit] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |