73 ideas
| 18390 | All metaphysical discussion should be guided by a quest for truthmakers [Armstrong] |
| 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] |
| 18467 | Truth-making can't be entailment, because truthmakers are portions of reality [Armstrong] |
| 18468 | Armstrong says truthmakers necessitate their truth, where 'necessitate' is a primitive relation [Armstrong, by MacBride] |
| 18377 | Negative truths have as truthmakers all states of affairs relevant to the truth [Armstrong] |
| 18382 | The nature of arctic animals is truthmaker for the absence of penguins there [Armstrong] |
| 18394 | In mathematics, truthmakers are possible instantiations of structures [Armstrong] |
| 18386 | What is the truthmaker for 'it is possible that there could have been nothing'? [Armstrong] |
| 18384 | One truthmaker will do for a contingent truth and for its contradictory [Armstrong] |
| 18387 | The truthmakers for possible unicorns are the elements in their combination [Armstrong] |
| 18381 | Necessitating general truthmakers must also specify their limits [Armstrong] |
| 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] |
| 18396 | The set theory brackets { } assert that the member is a unit [Armstrong] |
| 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] |
| 18393 | For 'there is a class with no members' we don't need the null set as truthmaker [Armstrong] |
| 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] |
| 18392 | Classes have cardinalities, so their members must all be treated as units [Armstrong] |
| 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] |
| 18385 | Logical atomism builds on the simple properties, but are they the only possible properties? [Armstrong] |
| 18391 | 'Naturalism' says only the world of space-time exists [Armstrong] |
| 18374 | Truthmaking needs states of affairs, to unite particulars with tropes or universals. [Armstrong] |
| 18372 | We need properties, as minimal truthmakers for the truths about objects [Armstrong] |
| 18379 | The determinates of a determinable must be incompatible with each other [Armstrong] |
| 18378 | Length is a 'determinable' property, and one mile is one its 'determinates' [Armstrong] |
| 18373 | If tropes are non-transferable, then they necessarily belong to their particular substance [Armstrong] |
| 18400 | Properties are not powers - they just have powers [Armstrong] |
| 18397 | Powers must result in some non-powers, or there would only be potential without result [Armstrong] |
| 18399 | How does the power of gravity know the distance it acts over? [Armstrong] |
| 18371 | The class of similar things is much too big a truthmaker for the feature of a particular [Armstrong] |
| 8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
| 6019 | If someone squashed a horse to make a dog, something new would now exist [Mnesarchus] |
| 18389 | When entities contain entities, or overlap with them, there is 'partial' identity [Armstrong] |
| 18388 | Possible worlds don't fix necessities; intrinsic necessities imply the extension in worlds [Armstrong] |
| 18375 | General truths are a type of negative truth, saying there are no more ravens than black ones [Armstrong] |
| 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] |
| 18368 | For all being, there is a potential proposition which expresses its existence and nature [Armstrong] |
| 18370 | A realm of abstract propositions is causally inert, so has no explanatory value [Armstrong] |
| 18380 | Negative causations supervene on positive causations plus their laws? [Armstrong] |
| 18401 | The pure present moment is too brief to be experienced [Armstrong] |