51 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] |
9912 | There are no such things as numbers [Benacerraf] |
9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
9151 | Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K] |
13891 | To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C] |
17904 | A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf] |
17906 | To explain numbers you must also explain cardinality, the counting of things [Benacerraf] |
9898 | We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf] |
17903 | Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf] |
9897 | The application of a system of numbers is counting and measurement [Benacerraf] |
9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf] |
9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
8697 | Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend] |
8304 | No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe] |
9906 | If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf] |
9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf] |
9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
9909 | The number 3 defines the role of being third in a progression [Benacerraf] |
9911 | Number words no more have referents than do the parts of a ruler [Benacerraf] |
8925 | Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf] |
9938 | How can numbers be objects if order is their only property? [Benacerraf, by Putnam] |
9910 | Number-as-objects works wholesale, but fails utterly object by object [Benacerraf] |
9903 | Number words are not predicates, as they function very differently from adjectives [Benacerraf] |
9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
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] |
23053 | The great interest of the human race is cordial unity and unlimited mutual aid [Owen] |
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] |