112 ideas
13773 | For the truth you need Prodicus's fifty-drachma course, not his one-drachma course [Socrates] |
343 | The unexamined life is not worth living for men [Socrates] |
7421 | A philosopher is one who cares about what other people care about [Socrates, by Foucault] |
1649 | Socrates opened philosophy to all, but Plato confined moral enquiry to a tiny elite [Vlastos on Socrates] |
16241 | The metaphysics of nature should focus on physics [Maudlin] |
16257 | Kant survives in seeing metaphysics as analysing our conceptual system, which is a priori [Maudlin] |
16276 | Wide metaphysical possibility may reduce metaphysics to analysis of fantasies [Maudlin] |
5842 | Philosophical discussion involves dividing subject-matter into categories [Socrates, by Xenophon] |
648 | Socrates began the quest for something universal with his definitions, but he didn't make them separate [Socrates, by Aristotle] |
16244 | If the universe is profligate, the Razor leads us astray [Maudlin] |
16255 | The Razor rightly prefers one cause of multiple events to coincidences of causes [Maudlin] |
164 | It is legitimate to play the devil's advocate [Socrates] |
1647 | In Socratic dialogue you must say what you believe, so unasserted premises are not debated [Vlastos on Socrates] |
115 | Socrates was pleased if his mistakes were proved wrong [Socrates] |
22099 | The method of Socrates shows the student is discovering the truth within himself [Socrates, by Carlisle] |
5844 | Socrates always proceeded in argument by general agreement at each stage [Socrates, by Xenophon] |
11389 | Socrates sought essences, which are the basis of formal logic [Socrates, by Aristotle] |
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
639 | Socrates developed definitions as the basis of syllogisms, and also inductive arguments [Socrates, by Aristotle] |
10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
18087 | If x changes by less and less, it must approach a limit [Dedekind] |
13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
16243 | The Humean view is wrong; laws and direction of time are primitive, and atoms are decided by physics [Maudlin] |
16271 | Lewis says it supervenes on the Mosaic, but actually thinks the Mosaic is all there is [Maudlin] |
16273 | If the Humean Mosaic is ontological bedrock, there can be no explanation of its structure [Maudlin] |
16275 | The 'spinning disc' is just impossible, because there cannot be 'homogeneous matter' [Maudlin] |
16258 | To get an ontology from ontological commitment, just add that some theory is actually true [Maudlin] |
16259 | Naïve translation from natural to formal language can hide or multiply the ontology [Maudlin] |
16253 | A property is fundamental if two objects can differ in only that respect [Maudlin] |
16263 | Fundamental physics seems to suggest there are no such things as properties [Maudlin] |
16260 | Existence of universals may just be decided by acceptance, or not, of second-order logic [Maudlin] |
1652 | Socrates did not consider universals or definitions as having separate existence, but Plato made Forms of them [Socrates, by Aristotle] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
16277 | Logically impossible is metaphysically impossible, but logically possible is not metaphysically possible [Maudlin] |
16249 | A counterfactual antecedent commands the redescription of a selected moment [Maudlin] |
16254 | Induction leaps into the unknown, but usually lands safely [Maudlin] |
16245 | Laws should help explain the things they govern, or that manifest them [Maudlin] |
1650 | For Socrates our soul, though hard to define, is our self [Vlastos on Socrates] |
23252 | Socrates first proposed that we are run by mind or reason [Socrates, by Frede,M] |
9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
199 | The common belief is that people can know the best without acting on it [Socrates] |
195 | No one willingly commits an evil or base act [Socrates] |
1653 | Socrates did not accept the tripartite soul (which permits akrasia) [Vlastos on Socrates] |
5843 | People do what they think they should do, and only ever do what they think they should do [Socrates, by Xenophon] |
5253 | Socrates was shocked by the idea of akrasia, but observation shows that it happens [Aristotle on Socrates] |
5839 | For Socrates, wisdom and prudence were the same thing [Socrates, by Xenophon] |
5867 | For Socrates, virtues are forms of knowledge, so knowing justice produces justice [Socrates, by Aristotle] |
5069 | Socrates was the first to base ethics upon reason, and use reason to explain it [Taylor,R on Socrates] |
5836 | All human virtues are increased by study and practice [Socrates, by Xenophon] |
5840 | The wise perform good actions, and people fail to be good without wisdom [Socrates, by Xenophon] |
185 | Socrates despised good looks [Socrates, by Plato] |
5070 | Socrates conservatively assumed that Athenian conventions were natural and true [Taylor,R on Socrates] |
5838 | A well-made dung basket is fine, and a badly-made gold shield is base, because of function [Socrates, by Xenophon] |
344 | If death is like a night of dreamless sleep, such nights are very pleasant [Socrates] |
339 | Men fear death as a great evil when it may be a great blessing [Socrates] |
5837 | Things are both good and fine by the same standard [Socrates, by Xenophon] |
3017 | The only good is knowledge, and the only evil is ignorance [Socrates, by Diog. Laertius] |
1646 | Socrates was the first to put 'eudaimonia' at the centre of ethics [Socrates, by Vlastos] |
2 | We should not even harm someone who harms us [Socrates] |
1663 | By 'areté' Socrates means just what we mean by moral virtue [Vlastos on Socrates] |
345 | A good man cannot be harmed, either in life or in death [Socrates] |
4323 | Socrates is torn between intellectual virtue, which is united and teachable, and natural virtue, which isn't [PG on Socrates] |
8003 | Socrates agrees that virtue is teachable, but then denies that there are teachers [Socrates, by MacIntyre] |
126 | We should ask what sort of people we want to be [Socrates] |
4111 | Socrates believed that basically there is only one virtue, the power of right judgement [Socrates, by Williams,B] |
7808 | Socrates made the civic values of justice and friendship paramount [Socrates, by Grayling] |
346 | One ought not to return a wrong or injury to any person, whatever the provocation [Socrates] |
23907 | Courage is scientific knowledge [Socrates, by Aristotle] |
341 | Wealth is good if it is accompanied by virtue [Socrates] |
7585 | Socrates emphasises that the knower is an existing individual, with existence his main task [Socrates, by Kierkegaard] |
5841 | Obedience to the law gives the best life, and success in war [Socrates, by Xenophon] |
347 | Will I stand up against the law, simply because I have been unjustly judged? [Socrates] |
1661 | Socrates was the first to grasp that a cruelty is not justified by another cruelty [Vlastos on Socrates] |
5846 | A lover using force is a villain, but a seducer is much worse, because he corrupts character [Socrates, by Xenophon] |
16248 | Evaluating counterfactuals involves context and interests [Maudlin] |
16250 | We don't pick a similar world from many - we construct one possibility from the description [Maudlin] |
16268 | The counterfactual is ruined if some other cause steps in when the antecedent fails [Maudlin] |
16267 | If we know the cause of an event, we seem to assent to the counterfactual [Maudlin] |
16269 | If the effect hadn't occurred the cause wouldn't have happened, so counterfactuals are two-way [Maudlin] |
16247 | Laws are primitive, so two indiscernible worlds could have the same laws [Maudlin] |
16272 | Fundamental laws say how nature will, or might, evolve from some initial state [Maudlin] |
16242 | Laws of nature are ontological bedrock, and beyond analysis [Maudlin] |
16251 | 'Humans with prime house numbers are mortal' is not a law, because not a natural kind [Maudlin] |
16270 | If laws are just regularities, then there have to be laws [Maudlin] |
16264 | I believe the passing of time is a fundamental fact about the world [Maudlin] |
16265 | If time passes, presumably it passes at one second per second [Maudlin] |
16266 | There is one ordered B series, but an infinitude of A series, depending on when the present is [Maudlin] |
1657 | Socrates holds that right reason entails virtue, and this must also apply to the gods [Vlastos on Socrates] |
1662 | A new concept of God as unswerving goodness emerges from Socrates' commitment to virtue [Vlastos on Socrates] |
338 | Socrates is accused of denying the gods, saying sun is stone and moon is earth [Socrates, by Plato] |