48 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] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 7720 | Two things can only resemble one another in some respect, and that may reintroduce a universal [Lowe] |
| 7712 | On substances, Leibniz emphasises unity, Spinoza independence, Locke relations to qualities [Lowe] |
| 7710 | Perception is a mode of belief-acquisition, and does not involve sensation [Lowe] |
| 7711 | Science requires a causal theory - perception of an object must be an experience caused by the object [Lowe] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 7714 | Personal identity is a problem across time (diachronic) and at an instant (synchronic) [Lowe] |
| 7715 | Mentalese isn't a language, because it isn't conventional, or a means of public communication [Lowe] |
| 7722 | If meaning is mental pictures, explain "the cat (or dog!) is NOT on the mat" [Lowe] |
| 114 | Rhetoric can produce conviction, but not educate people about right and wrong [Plato] |
| 116 | Rhetoric is irrational about its means and its ends [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] |
| 132 | If happiness is the satisfaction of desires, then a life of scratching itches should be happiness [Plato] |
| 4319 | In a fool's mind desire is like a leaky jar, insatiable in its desires, and order and contentment are better [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] |