39 ideas
| 125 | Is a gifted philosopher unmanly if he avoids the strife of the communal world? [Plato] |
| 1654 | In "Gorgias" Socrates is confident that his 'elenchus' will decide moral truth [Vlastos on Plato] |
| 4321 | We should test one another, by asking and answering questions [Plato] |
| 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] |
| 10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
| 10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
| 10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
| 10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [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] |
| 22200 | If you eliminate the impossible, the truth will remain, even if it is weird [Conan Doyle] |
| 116 | Rhetoric is irrational about its means and its ends [Plato] |
| 114 | Rhetoric can produce conviction, but not educate people about right and wrong [Plato] |
| 135 | All activity aims at the good [Plato] |
| 122 | Moral rules are made by the weak members of humanity [Plato] |
| 139 | A good person is bound to act well, and this brings happiness [Plato] |
| 128 | Is it natural to simply indulge our selfish desires? [Plato] |
| 4322 | In slaking our thirst the goodness of the action and the pleasure are clearly separate [Plato] |
| 136 | Good should be the aim of pleasant activity, not the other way round [Plato] |
| 134 | Good and bad people seem to experience equal amounts of pleasure and pain [Plato] |
| 4319 | In a fool's mind desire is like a leaky jar, insatiable in its desires, and order and contentment are better [Plato] |
| 132 | If happiness is the satisfaction of desires, then a life of scratching itches should be happiness [Plato] |
| 130 | Is the happiest state one of sensual, self-indulgent freedom? [Plato] |
| 120 | Should we avoid evil because it will bring us bad consequences? [Plato] |
| 118 | I would rather be a victim of crime than a criminal [Plato] |
| 140 | Self-indulgent desire makes friendship impossible, because it makes a person incapable of co-operation [Plato] |
| 131 | If absence of desire is happiness, then nothing is happier than a stone or a corpse [Plato] |
| 119 | A criminal is worse off if he avoids punishment [Plato] |
| 129 | Do most people praise self-discipline and justice because they are too timid to gain their own pleasure? [Plato] |
| 4320 | The popular view is that health is first, good looks second, and honest wealth third [Plato] |
| 137 | As with other things, a good state is organised and orderly [Plato] |
| 141 | A good citizen won't be passive, but will redirect the needs of the state [Plato] |
| 123 | Do most people like equality because they are second-rate? [Plato] |
| 124 | Does nature imply that it is right for better people to have greater benefits? [Plato] |