99 ideas
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| 162 | Can we understand an individual soul without knowing the soul in general? [Plato] |
| 160 | The highest ability in man is the ability to discuss unity and plurality in the nature of things [Plato] |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| 166 | A speaker should be able to divide a subject, right down to the limits of divisibility [Plato] |
| 6887 | Linguistic philosophy approaches problems by attending to actual linguistic usage [Mautner] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 6881 | Analytic philosophy studies the unimportant, and sharpens tools instead of using them [Mautner] |
| 5439 | The 'hermeneutic circle' says parts and wholes are interdependent, and so cannot be interpreted [Mautner] |
| 9959 | 'Real' definitions give the essential properties of things under a concept [Mautner] |
| 9961 | 'Contextual definitions' replace whole statements, not just expressions [Mautner] |
| 9958 | Recursive definition defines each instance from a previous instance [Mautner] |
| 9960 | A stipulative definition lays down that an expression is to have a certain meaning [Mautner] |
| 9957 | Ostensive definitions point to an object which an expression denotes [Mautner] |
| 6219 | The fallacy of composition is the assumption that what is true of the parts is true of the whole [Mautner] |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| 6888 | Fuzzy logic is based on the notion that there can be membership of a set to some degree [Mautner] |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| 6877 | Entailment is logical requirement; it may be not(p and not-q), but that has problems [Mautner] |
| 6880 | Strict implication says false propositions imply everything, and everything implies true propositions [Mautner] |
| 6879 | 'Material implication' is defined as 'not(p and not-q)', but seems to imply a connection between p and q [Mautner] |
| 6878 | A person who 'infers' draws the conclusion, but a person who 'implies' leaves it to the audience [Mautner] |
| 6889 | Vagueness seems to be inconsistent with the view that every proposition is true or false [Mautner] |
| 6890 | Quantifiers turn an open sentence into one to which a truth-value can be assigned [Mautner] |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 7953 | Reasoning needs to cut nature accurately at the joints [Plato] |
| 16121 | I revere anyone who can discern a single thing that encompasses many things [Plato] |
| 153 | It takes a person to understand, by using universals, and by using reason to create a unity out of sense-impressions [Plato] |
| 154 | We would have an overpowering love of knowledge if we had a pure idea of it - as with the other Forms [Plato] |
| 6886 | Counterfactuals are not true, they are merely valid [Mautner] |
| 6885 | Counterfactuals are true if in every world close to actual where p is the case, q is also the case [Mautner] |
| 6884 | Counterfactuals say 'If it had been, or were, p, then it would be q' [Mautner] |
| 6883 | Maybe counterfactuals are only true if they contain valid inference from premisses [Mautner] |
| 6882 | Counterfactuals presuppose a belief (or a fact) that the condition is false [Mautner] |
| 5449 | Essentialism is often identified with belief in 'de re' necessary truths [Mautner] |
| 6898 | Fallibilism is the view that all knowledge-claims are provisional [Mautner] |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| 6452 | 'Sense-data' arrived in 1910, but it denotes ideas in Locke, Berkeley and Hume [Mautner] |
| 151 | True knowledge is of the reality behind sense experience [Plato] |
| 165 | If the apparent facts strongly conflict with probability, it is in everyone's interests to suppress the facts [Plato] |
| 4783 | Observing lots of green x can confirm 'all x are green' or 'all x are grue', where 'grue' is arbitrary [Mautner, by PG] |
| 4782 | 'All x are y' is equivalent to 'all non-y are non-x', so observing paper is white confirms 'ravens are black' [Mautner, by PG] |
| 9296 | The soul is self-motion [Plato] |
| 23997 | Plato saw emotions and appetites as wild horses, in need of taming [Plato, by Goldie] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 6899 | The references of indexicals ('there', 'now', 'I') depend on the circumstances of utterance [Mautner] |
| 159 | Only a good philosopher can be a good speaker [Plato] |
| 5946 | 'Phaedrus' pioneers the notion of philosophical rhetoric [Lawson-Tancred on Plato] |
| 158 | An excellent speech seems to imply a knowledge of the truth in the mind of the speaker [Plato] |
| 6896 | Double effect is the distinction between what is foreseen and what is intended [Mautner] |
| 6897 | Double effect acts need goodness, unintended evil, good not caused by evil, and outweighing [Mautner] |
| 155 | Beauty is the clearest and most lovely of the Forms [Plato] |
| 143 | The two ruling human principles are the natural desire for pleasure, and an acquired love of virtue [Plato] |
| 5452 | 'Essentialism' is opposed to existentialism, and claims there is a human nature [Mautner] |
| 157 | Most pleasure is release from pain, and is therefore not worthwhile [Plato] |
| 144 | Reason impels us towards excellence, which teaches us self-control [Plato] |
| 156 | Bad people are never really friends with one another [Plato] |
| 148 | If the prime origin is destroyed, it will not come into being again out of anything [Plato] |
| 152 | The mind of God is fully satisfied and happy with a vision of reality and truth [Plato] |
| 150 | We cannot conceive of God, so we have to think of Him as an immortal version of ourselves [Plato] |
| 149 | There isn't a single reason for positing the existence of immortal beings [Plato] |
| 146 | Soul is always in motion, so it must be self-moving and immortal [Plato] |