100 ideas
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| 17240 | Definitions are the first step in philosophy [Hobbes] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 2557 | Analytical philosophy seems to have little interest in how to tell a good analysis from a bad one [Rorty] |
| 2556 | Rational certainty may be victory in argument rather than knowledge of facts [Rorty] |
| 17237 | Definitions of things that are caused must express their manner of generation [Hobbes] |
| 17239 | Definition is resolution of names into successive genera, and finally the difference [Hobbes] |
| 17241 | A defined name should not appear in the definition [Hobbes] |
| 17242 | 'Petitio principii' is reusing the idea to be defined, in disguised words [Hobbes] |
| 4726 | Rorty seems to view truth as simply being able to hold one's view against all comers [Rorty, by O'Grady] |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| 2549 | For James truth is "what it is better for us to believe" rather than a correct picture of reality [Rorty] |
| 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] |
| 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] |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [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] |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [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] |
| 17245 | A part of a part is a part of a whole [Hobbes] |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| 13513 | Models are ways the world might be from a first-order point of view [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] |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [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] |
| 17258 | If we just say one, one, one, one, we don't know where we have got to [Hobbes] |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [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] |
| 17253 | Change is nothing but movement [Hobbes] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 16670 | Accidents are just modes of thinking about bodies [Hobbes] |
| 16621 | Accidents are not parts of bodies (like blood in a cloth); they have accidents as things have a size [Hobbes] |
| 16734 | The complete power of an event is just the aggregate of the qualities that produced it [Hobbes] |
| 17247 | The only generalities or universals are names or signs [Hobbes] |
| 14960 | Bodies are independent of thought, and coincide with part of space [Hobbes] |
| 17250 | If you separate the two places of one thing, you will also separate the thing [Hobbes] |
| 17249 | If you separated two things in the same place, you would also separate the places [Hobbes] |
| 17248 | If a whole body is moved, its parts must move with it [Hobbes] |
| 16790 | A body is always the same, whether the parts are together or dispersed [Hobbes] |
| 17244 | To make a whole, parts needn't be put together, but can be united in the mind [Hobbes] |
| 17233 | Particulars contain universal things [Hobbes] |
| 17246 | Some accidental features are permanent, unless the object perishes [Hobbes] |
| 17251 | The feature which picks out or names a thing is usually called its 'essence' [Hobbes] |
| 17257 | It is the same river if it has the same source, no matter what flows in it [Hobbes] |
| 12853 | Some individuate the ship by unity of matter, and others by unity of form [Hobbes] |
| 17256 | If a new ship were made of the discarded planks, would two ships be numerically the same? [Hobbes] |
| 16794 | As an infant, Socrates was not the same body, but he was the same human being [Hobbes] |
| 17255 | Two bodies differ when (at some time) you can say something of one you can't say of the other [Hobbes] |
| 16582 | We can imagine a point swelling and contracting - but not how this could be done [Hobbes] |
| 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] |
| 2548 | If knowledge is merely justified belief, justification is social [Rorty] |
| 6599 | Knowing has no definable essence, but is a social right, found in the context of conversations [Rorty] |
| 2566 | You can't debate about whether to have higher standards for the application of words [Rorty] |
| 17238 | Science aims to show causes and generation of things [Hobbes] |
| 2553 | The mind is a property, or it is baffling [Rorty] |
| 2550 | Pain lacks intentionality; beliefs lack qualia [Rorty] |
| 2554 | Is intentionality a special sort of function? [Rorty] |
| 17260 | Imagination is just weakened sensation [Hobbes] |
| 19373 | A 'conatus' is an initial motion, experienced by us as desire or aversion [Hobbes, by Arthur,R] |
| 2948 | Sensation is merely internal motion of the sentient being [Hobbes] |
| 17261 | Apart from pleasure and pain, the only emotions are appetite and aversion [Hobbes] |
| 17236 | Words are not for communication, but as marks for remembering what we have learned [Hobbes] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 2565 | Nature has no preferred way of being represented [Rorty] |
| 2560 | Can meanings remain the same when beliefs change? [Rorty] |
| 2562 | A theory of reference seems needed to pick out objects without ghostly inner states [Rorty] |
| 2559 | Davidson's theory of meaning focuses not on terms, but on relations between sentences [Rorty] |
| 2558 | Since Hegel we have tended to see a human as merely animal if it is outside a society [Rorty] |
| 16600 | Prime matter is body considered with mere size and extension, and potential [Hobbes] |
| 17252 | Acting on a body is either creating or destroying a property in it [Hobbes] |
| 17254 | An effect needs a sufficient and necessary cause [Hobbes] |
| 17235 | A cause is the complete sum of the features which necessitate the effect [Hobbes] |
| 17234 | Motion is losing one place and acquiring another [Hobbes] |
| 17259 | 'Force' is the quantity of movement imposed on something [Hobbes] |
| 17243 | Past times can't exist anywhere, apart from in our memories [Hobbes] |