35 ideas
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
16078 | Clay is intrinsically and atomically the same as statue (and that lacks 'modal properties') [Rudder Baker] |
16077 | The clay is not a statue - it borrows that property from the statue it constitutes [Rudder Baker] |
16080 | Is it possible for two things that are identical to become two separate things? [Rudder Baker] |
16076 | Constitution is not identity, as consideration of essential predicates shows [Rudder Baker] |
16081 | The constitution view gives a unified account of the relation of persons/bodies, statues/bronze etc [Rudder Baker] |
16082 | Statues essentially have relational properties lacked by lumps [Rudder Baker] |
3772 | The will, in the beginning, is entirely produced by desire [Mill] |
3769 | With early training, any absurdity or evil may be given the power of conscience [Mill] |
3767 | Motive shows the worth of the agent, but not of the action [Mill] |
3771 | Virtues only have value because they achieve some further end [Mill] |
3768 | Orthodox morality is the only one which feels obligatory [Mill] |
7202 | The English believe in the task of annihilating evil for the victory of good [Nietzsche on Mill] |
5935 | Mill's qualities of pleasure is an admission that there are other good states of mind than pleasure [Ross on Mill] |
3764 | Actions are right if they promote pleasure, wrong if they promote pain [Mill] |
3776 | Utilitarianism only works if everybody has a totally equal right to happiness [Mill] |
3765 | Only pleasure and freedom from pain are desirable as ends [Mill] |
3763 | Ultimate goods such as pleasure can never be proved to be good [Mill] |
3766 | Better to be Socrates dissatisfied than a fool satisfied [Mill] |
3770 | General happiness is only desirable because individuals desire their own happiness [Mill] |
6697 | Moral rules protecting human welfare are more vital than local maxims [Mill] |
3774 | Rights are a matter of justice, not of benevolence [Mill] |
3773 | No individual has the right to receive our benevolence [Mill] |
3775 | A right is a valid claim to society's protection [Mill] |