76 ideas
| 8721 | An 'impredicative' definition seems circular, because it uses the term being defined [Friend] |
| 8680 | Classical definitions attempt to refer, but intuitionist/constructivist definitions actually create objects [Friend] |
| 3678 | Reductio ad absurdum proves an idea by showing that its denial produces contradiction [Friend] |
| 8705 | Anti-realists see truth as our servant, and epistemically contrained [Friend] |
| 14415 | A ground must be about its truth, and not just necessitate it [Merricks] |
| 14408 | Truthmaker needs truths to be 'about' something, and that is often unclear [Merricks] |
| 14395 | If a ball changes from red to white, Truthmaker says some thing must make the change true [Merricks] |
| 14398 | Truthmaker says if an entity is removed, some nonexistence truthmaker must replace it [Merricks] |
| 14403 | If Truthmaker says each truth is made by the existence of something, the theory had de re modality at is core [Merricks] |
| 14397 | Truthmaker demands not just a predication, but an existing state of affairs with essential ingredients [Merricks] |
| 14396 | If 'truth supervenes on being', worlds with the same entities, properties and relations have the same truths [Merricks] |
| 14400 | If truth supervenes on being, that won't explain why truth depends on being [Merricks] |
| 14394 | It is implausible that claims about non-existence are about existing things [Merricks] |
| 14390 | Truthmaker isn't the correspondence theory, because it offers no analysis of truth [Merricks] |
| 14412 | Speculations about non-existent things are not about existent things, so Truthmaker is false [Merricks] |
| 14414 | I am a truthmaker for 'that a human exists', but is it about me? [Merricks] |
| 14418 | Being true is not a relation, it is a primitive monadic property [Merricks] |
| 14391 | If the correspondence theory is right, then necessary truths must correspond to something [Merricks] |
| 14419 | Deflationism just says there is no property of being truth [Merricks] |
| 8713 | In classical/realist logic the connectives are defined by truth-tables [Friend] |
| 8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
| 8694 | Free logic was developed for fictional or non-existent objects [Friend] |
| 8665 | A 'proper subset' of A contains only members of A, but not all of them [Friend] |
| 8672 | A 'powerset' is all the subsets of a set [Friend] |
| 8677 | Set theory makes a minimum ontological claim, that the empty set exists [Friend] |
| 8666 | Infinite sets correspond one-to-one with a subset [Friend] |
| 8682 | Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend] |
| 8709 | The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend] |
| 8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
| 8675 | Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend] |
| 8674 | The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend] |
| 8667 | The 'integers' are the positive and negative natural numbers, plus zero [Friend] |
| 8668 | The 'rational' numbers are those representable as fractions [Friend] |
| 8670 | A number is 'irrational' if it cannot be represented as a fraction [Friend] |
| 8661 | The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend] |
| 8664 | Cardinal numbers answer 'how many?', with the order being irrelevant [Friend] |
| 8671 | The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend] |
| 8663 | Raising omega to successive powers of omega reveal an infinity of infinities [Friend] |
| 8662 | The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend] |
| 8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
| 8676 | Is mathematics based on sets, types, categories, models or topology? [Friend] |
| 8678 | Most mathematical theories can be translated into the language of set theory [Friend] |
| 8701 | The number 8 in isolation from the other numbers is of no interest [Friend] |
| 8702 | In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend] |
| 8699 | Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend] |
| 8696 | Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend] |
| 8695 | Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend] |
| 8700 | 'In re' structuralism says that the process of abstraction is pattern-spotting [Friend] |
| 8681 | The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend] |
| 8712 | Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend] |
| 8716 | Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend] |
| 8706 | Constructivism rejects too much mathematics [Friend] |
| 8707 | Intuitionists typically retain bivalence but reject the law of excluded middle [Friend] |
| 14393 | The totality state is the most plausible truthmaker for negative existential truths [Merricks] |
| 14413 | Some properties seem to be primitive, but others can be analysed [Merricks] |
| 14416 | An object can have a disposition when the revelant conditional is false [Merricks] |
| 8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
| 14392 | Fregeans say 'hobbits do not exist' is just 'being a hobbit' is not exemplified [Merricks] |
| 14410 | You believe you existed last year, but your segment doesn't, so they have different beliefs [Merricks] |
| 14417 | Counterfactuals aren't about actuality, so they lack truthmakers or a supervenience base [Merricks] |
| 14402 | If 'Fido is possibly black' depends on Fido's counterparts, then it has no actual truthmaker [Merricks] |
| 8685 | Studying biology presumes the laws of chemistry, and it could never contradict them [Friend] |
| 8688 | Concepts can be presented extensionally (as objects) or intensionally (as a characterization) [Friend] |
| 14406 | Presentists say that things have existed and will exist, not that they are instantaneous [Merricks] |
| 14407 | Presentist should deny there is a present time, and just say that things 'exist' [Merricks] |
| 14411 | Maybe only presentism allows change, by now having a property, and then lacking it [Merricks] |
| 14405 | How can a presentist explain an object's having existed? [Merricks] |
| 21244 | Conceiving a greater being than God leads to absurdity [Anselm] |
| 21241 | Even the fool can hold 'a being than which none greater exists' in his understanding [Anselm] |
| 21242 | If that than which a greater cannot be thought actually exists, that is greater than the mere idea [Anselm] |
| 1421 | A perfection must be independent and unlimited, and the necessary existence of Anselm's second proof gives this [Malcolm on Anselm] |
| 21245 | The word 'God' can be denied, but understanding shows God must exist [Anselm] |
| 21246 | Guanilo says a supremely fertile island must exist, just because we can conceive it [Anselm] |
| 21247 | Nonexistence is impossible for the greatest thinkable thing, which has no beginning or end [Anselm] |
| 21243 | An existing thing is even greater if its non-existence is inconceivable [Anselm] |
| 1420 | Anselm's first proof fails because existence isn't a real predicate, so it can't be a perfection [Malcolm on Anselm] |