58 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] |
9572 | Realists about sets say there exists a null set in the real world, with no members [Chihara] |
9550 | We only know relational facts about the empty set, but nothing intrinsic [Chihara] |
9562 | In simple type theory there is a hierarchy of null sets [Chihara] |
9573 | The null set is a structural position which has no other position in membership relation [Chihara] |
9551 | What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara] |
9549 | The set theorist cannot tell us what 'membership' is [Chihara] |
9571 | ZFU refers to the physical world, when it talks of 'urelements' [Chihara] |
9563 | A pack of wolves doesn't cease when one member dies [Chihara] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara] |
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] |
9553 | Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara] |
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] |
10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
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] |
9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara] |
9566 | No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
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] |
9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |