194 ideas
| 18390 | All metaphysical discussion should be guided by a quest for truthmakers [Armstrong] |
| 17663 | If you know what it is, investigation is pointless. If you don't, investigation is impossible [Armstrong] |
| 4036 | What matters is not how many entities we postulate, but how many kinds of entities [Armstrong, by Mellor/Oliver] |
| 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] |
| 15547 | Negative existentials have 'totality facts' as truthmakers [Armstrong, by Lewis] |
| 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] |
| 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] |
| 18386 | What is the truthmaker for 'it is possible that there could have been nothing'? [Armstrong] |
| 18381 | Necessitating general truthmakers must also specify their limits [Armstrong] |
| 4742 | Correspondence may be one-many or many one, as when either p or q make 'p or q' true [Armstrong] |
| 15544 | If what is actual might have been impossible, we need S4 modal logic [Armstrong, by Lewis] |
| 18396 | The set theory brackets { } assert that the member is a unit [Armstrong] |
| 18393 | For 'there is a class with no members' we don't need the null set as truthmaker [Armstrong] |
| 10073 | There cannot be a set theory which is complete [Smith,P] |
| 21122 | Liberal Nationalism says welfare states and democracy needed a shared sense of nationality [Shorten] |
| 10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
| 10075 | A 'partial function' maps only some elements to another set [Smith,P] |
| 10074 | A 'total function' maps every element to one element in another set [Smith,P] |
| 10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
| 10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
| 10605 | Two functions are the same if they have the same extension [Smith,P] |
| 10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
| 10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
| 10602 | A 'natural deduction system' has no axioms but many rules [Smith,P] |
| 10613 | No nice theory can define truth for its own language [Smith,P] |
| 10078 | An 'injective' ('one-to-one') function creates a distinct output element from each original [Smith,P] |
| 10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
| 10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
| 10070 | If everything that a theory proves is true, then it is 'sound' [Smith,P] |
| 10086 | Soundness is true axioms and a truth-preserving proof system [Smith,P] |
| 10596 | A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P] |
| 10598 | A theory is 'negation complete' if it proves all sentences or their negation [Smith,P] |
| 10597 | 'Complete' applies both to whole logics, and to theories within them [Smith,P] |
| 10069 | A theory is 'negation complete' if one of its sentences or its negation can always be proved [Smith,P] |
| 10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
| 10080 | 'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P] |
| 10087 | A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P] |
| 10088 | Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P] |
| 10081 | A set is 'enumerable' is all of its elements can result from a natural number function [Smith,P] |
| 10083 | A set is 'effectively enumerable' if a computer could eventually list every member [Smith,P] |
| 10084 | A finite set of finitely specifiable objects is always effectively enumerable (e.g. primes) [Smith,P] |
| 10085 | The set of ordered pairs of natural numbers <i,j> is effectively enumerable [Smith,P] |
| 10601 | The thorems of a nice arithmetic can be enumerated, but not the truths (so they're diffferent) [Smith,P] |
| 10600 | Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P] |
| 10599 | For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P] |
| 10610 | The reals contain the naturals, but the theory of reals doesn't contain the theory of naturals [Smith,P] |
| 18392 | Classes have cardinalities, so their members must all be treated as units [Armstrong] |
| 10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
| 10608 | The number of Fs is the 'successor' of the Gs if there is a single F that isn't G [Smith,P] |
| 10618 | All numbers are related to zero by the ancestral of the successor relation [Smith,P] |
| 10849 | Baby arithmetic covers addition and multiplication, but no general facts about numbers [Smith,P] |
| 10850 | Baby Arithmetic is complete, but not very expressive [Smith,P] |
| 10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
| 10852 | Robinson Arithmetic (Q) is not negation complete [Smith,P] |
| 10068 | Natural numbers have zero, unique successors, unending, no circling back, and no strays [Smith,P] |
| 10603 | The logic of arithmetic must quantify over properties of numbers to handle induction [Smith,P] |
| 10848 | Multiplication only generates incompleteness if combined with addition and successor [Smith,P] |
| 10604 | Incompleteness results in arithmetic from combining addition and successor with multiplication [Smith,P] |
| 18385 | Logical atomism builds on the simple properties, but are they the only possible properties? [Armstrong] |
| 8507 | Some think of reality as made of things; I prefer facts or states of affairs [Armstrong] |
| 18391 | 'Naturalism' says only the world of space-time exists [Armstrong] |
| 9497 | Without modality, Armstrong falls back on fictionalism to support counterfactual laws [Bird on Armstrong] |
| 17688 | Negative facts are supervenient on positive facts, suggesting they are positive facts [Armstrong] |
| 18374 | Truthmaking needs states of affairs, to unite particulars with tropes or universals. [Armstrong] |
| 17691 | Nothing is genuinely related to itself [Armstrong] |
| 10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
| 7024 | Properties are universals, which are always instantiated [Armstrong, by Heil] |
| 17679 | All instances of some property are strictly identical [Armstrong] |
| 15550 | Properties are contingently existing beings with multiple locations in space and time [Armstrong, by Lewis] |
| 15754 | Without properties we would be unable to express the laws of nature [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] |
| 9478 | Even if all properties are categorical, they may be denoted by dispositional predicates [Armstrong, by Bird] |
| 12677 | Armstrong holds that all basic properties are categorical [Armstrong, by Ellis] |
| 4034 | Whether we apply 'cold' or 'hot' to an object is quite separate from its change of temperature [Armstrong] |
| 8535 | To the claim that every predicate has a property, start by eliminating failure of application of predicate [Armstrong] |
| 8537 | Tropes fall into classes, because exact similarity is symmetrical and transitive [Armstrong] |
| 4444 | One moderate nominalist view says that properties and relations exist, but they are particulars [Armstrong] |
| 18373 | If tropes are non-transferable, then they necessarily belong to their particular substance [Armstrong] |
| 8538 | Trope theory needs extra commitments, to symmetry and non-transitivity, unless resemblance is exact [Armstrong] |
| 4445 | If properties and relations are particulars, there is still the problem of how to classify and group them [Armstrong] |
| 18400 | Properties are not powers - they just have powers [Armstrong] |
| 14330 | To be realists about dispositions, we can only discuss them through their categorical basis [Armstrong] |
| 17666 | Actualism means that ontology cannot contain what is merely physically possible [Armstrong] |
| 17667 | Dispositions exist, but their truth-makers are actual or categorical properties [Armstrong] |
| 17687 | If everything is powers there is a vicious regress, as powers are defined by more 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] |
| 8506 | Particulars and properties are distinguishable, but too close to speak of a relation [Armstrong] |
| 4448 | Should we decide which universals exist a priori (through words), or a posteriori (through science)? [Armstrong] |
| 17678 | Universals are just the repeatable features of a world [Armstrong] |
| 4032 | The problem of universals is how many particulars can all be of the same 'type' [Armstrong] |
| 17669 | Realist regularity theories of laws need universals, to pick out the same phenomena [Armstrong] |
| 8539 | Universals are required to give a satisfactory account of the laws of nature [Armstrong] |
| 10729 | Universals explain resemblance and causal power [Armstrong, by Oliver] |
| 17677 | Past, present and future must be equally real if universals are instantiated [Armstrong] |
| 15442 | Universals are abstractions from their particular instances [Armstrong, by Lewis] |
| 17686 | Universals are abstractions from states of affairs [Armstrong] |
| 4446 | It is claimed that some universals are not exemplified by any particular, so must exist separately [Armstrong] |
| 4442 | Most thinkers now reject self-predication (whiteness is NOT white) so there is no Third Man problem [Armstrong] |
| 8505 | Refusal to explain why different tokens are of the same type is to be an ostrich [Armstrong] |
| 8529 | Deniers of properties and relations rely on either predicates or on classes [Armstrong] |
| 4440 | 'Resemblance Nominalism' finds that in practice the construction of resemblance classes is hard [Armstrong] |
| 8532 | Resemblances must be in certain 'respects', and they seem awfully like properties [Armstrong] |
| 4439 | 'Resemblance Nominalism' says properties are resemblances between classes of particulars [Armstrong] |
| 4031 | It doesn't follow that because there is a predicate there must therefore exist a property [Armstrong] |
| 8530 | Change of temperature in objects is quite independent of the predicates 'hot' and 'cold' [Armstrong] |
| 8536 | We want to know what constituents of objects are grounds for the application of predicates [Armstrong] |
| 4431 | 'Predicate Nominalism' says that a 'universal' property is just a predicate applied to lots of things [Armstrong] |
| 4433 | Concept and predicate nominalism miss out some predicates, and may be viciously regressive [Armstrong] |
| 4432 | 'Concept Nominalism' says a 'universal' property is just a mental concept applied to lots of things [Armstrong] |
| 8531 | In most sets there is no property common to all the members [Armstrong] |
| 4436 | 'Class Nominalism' may explain properties if we stick to 'natural' sets, and ignore random ones [Armstrong] |
| 4434 | 'Class Nominalism' says that properties or kinds are merely membership of a set (e.g. of white things) [Armstrong] |
| 4435 | 'Class Nominalism' cannot explain co-extensive properties, or sets with random members [Armstrong] |
| 18371 | The class of similar things is much too big a truthmaker for the feature of a particular [Armstrong] |
| 4437 | 'Mereological Nominalism' sees whiteness as a huge white object consisting of all the white things [Armstrong] |
| 4438 | 'Mereological Nominalism' may work for whiteness, but it doesn't seem to work for squareness [Armstrong] |
| 17668 | It is likely that particulars can be individuated by unique conjunctions of properties [Armstrong] |
| 15753 | Essences might support Resemblance Nominalism, but they are too coarse and ill-defined [Armstrong] |
| 18389 | When entities contain entities, or overlap with them, there is 'partial' identity [Armstrong] |
| 10024 | The type-token distinction is the universal-particular distinction [Armstrong, by Hodes] |
| 10728 | A thing's self-identity can't be a universal, since we can know it a priori [Armstrong, by Oliver] |
| 17680 | The identity of a thing with itself can be ruled out as a pseudo-property [Armstrong] |
| 15542 | All possibilities are recombinations of properties in the actual world [Armstrong, by Lewis] |
| 17693 | The necessary/contingent distinction may need to recognise possibilities as real [Armstrong] |
| 4743 | The truth-maker for a truth must necessitate that truth [Armstrong] |
| 11003 | The best version of reductionist actualism around is Armstrong's combinatorial account [Armstrong, by Read] |
| 18388 | Possible worlds don't fix necessities; intrinsic necessities imply the extension in worlds [Armstrong] |
| 6498 | Armstrong suggests secondary qualities are blurred primary qualities [Armstrong, by Robinson,H] |
| 7440 | Secondary qualities are microscopic primary qualities of physical things [Armstrong] |
| 3900 | Maybe experience is not essential to perception, but only to the causing of beliefs [Armstrong, by Scruton] |
| 4253 | Externalism says knowledge involves a natural relation between the belief state and what makes it true [Armstrong] |
| 17685 | Induction aims at 'all Fs', but abduction aims at hidden or theoretical entities [Armstrong] |
| 17683 | Science suggests that the predicate 'grue' is not a genuine single universal [Armstrong] |
| 17675 | Unlike 'green', the 'grue' predicate involves a time and a change [Armstrong] |
| 17674 | The raven paradox has three disjuncts, confirmed by confirming any one of them [Armstrong] |
| 17672 | A good reason for something (the smoke) is not an explanation of it (the fire) [Armstrong] |
| 17684 | To explain observations by a regular law is to explain the observations by the observations [Armstrong] |
| 17676 | Best explanations explain the most by means of the least [Armstrong] |
| 7437 | Consciousness and experience of qualities are not the same [Armstrong] |
| 18375 | General truths are a type of negative truth, saying there are no more ravens than black ones [Armstrong] |
| 5690 | A mental state without belief refutes self-intimation; a belief with no state refutes infallibility [Armstrong, by Shoemaker] |
| 7434 | Behaviourism is false, but mind is definable as the cause of behaviour [Armstrong] |
| 7436 | The manifestations of a disposition need never actually exist [Armstrong] |
| 5493 | If pains are defined causally, and research shows that the causal role is physical, then pains are physical [Armstrong, by Lycan] |
| 4600 | Armstrong and Lewis see functionalism as an identity of the function and its realiser [Armstrong, by Heil] |
| 7429 | Causal Functionalism says mental states are apt for producing behaviour [Armstrong] |
| 7438 | A causal theory of mentality would be improved by a teleological element [Armstrong] |
| 7431 | The identity of mental states with physical properties is contingent, because the laws of nature are contingent [Armstrong] |
| 7432 | One mental role might be filled by a variety of physical types [Armstrong] |
| 17664 | Each subject has an appropriate level of abstraction [Armstrong] |
| 8533 | Predicates need ontological correlates to ensure that they apply [Armstrong] |
| 4035 | There must be some explanation of why certain predicates are applicable to certain objects [Armstrong] |
| 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] |
| 21136 | Utilitarians conflate acts and omissions; causing to drown and failing to save are the same [Shorten] |
| 21135 | There are eight different ways in which groups of people can be oppressed [Shorten, by PG] |
| 21118 | Constitutional Patriotism unites around political values (rather than national identity) [Shorten] |
| 21129 | Democracy is a method of selection, or it involves participation, or it concerns public discussion [Shorten] |
| 21130 | Some say democracy is intrinsically valuable, others that it delivers good outcomes [Shorten] |
| 21126 | Representative should be either obedient, or sensible, or typical [Shorten] |
| 21128 | There is 'mirror representation' when the institution statistically reflects the population [Shorten] |
| 21127 | In a changed situation a Mandated Representative can't keep promises and fight for constituents [Shorten] |
| 21117 | Liberal citizens have a moral requirement to respect freedom and equality [Shorten] |
| 21134 | Maybe the rational autonomous liberal individual is merely the result of domination [Shorten] |
| 21113 | Liberal equality concerns rights, and liberal freedom concerns choice of ends [Shorten] |
| 21121 | Liberal Nationalism encourages the promotion of nationalistic values [Shorten] |
| 21115 | Liberalism should not make assumptions such as the value of choosing your own life plan [Shorten] |
| 21114 | Liberals treat individuals as mutual strangers, rather than as social beings [Shorten] |
| 21123 | Liberal Nationalism is more communitarian, and Constitutional Patriotism more cosmopolitan [Shorten] |
| 21124 | Religious toleration has been institutionalised by the separation of church and state [Shorten] |
| 17692 | We can't deduce the phenomena from the One [Armstrong] |
| 17689 | Absences might be effects, but surely not causes? [Armstrong] |
| 18380 | Negative causations supervene on positive causations plus their laws? [Armstrong] |
| 4798 | In recent writings, Armstrong makes a direct identification of necessitation with causation [Armstrong, by Psillos] |
| 17682 | A universe couldn't consist of mere laws [Armstrong] |
| 17662 | Science depends on laws of nature to study unobserved times and spaces [Armstrong] |
| 17690 | Oaken conditional laws, Iron universal laws, and Steel necessary laws [Armstrong, by PG] |
| 17670 | Newton's First Law refers to bodies not acted upon by a force, but there may be no such body [Armstrong] |
| 8582 | Regularities are lawful if a second-order universal unites two first-order universals [Armstrong, by Lewis] |
| 17671 | A naive regularity view says if it never occurs then it is impossible [Armstrong] |
| 8541 | Regularities theories are poor on causal connections, counterfactuals and probability [Armstrong] |
| 8540 | The introduction of sparse properties avoids the regularity theory's problem with 'grue' [Armstrong] |
| 17681 | The laws of nature link properties with properties [Armstrong] |
| 16246 | Rather than take necessitation between universals as primitive, just make laws primitive [Maudlin on Armstrong] |
| 9480 | Armstrong has an unclear notion of contingent necessitation, which can't necessitate anything [Bird on Armstrong] |
| 5492 | How can essences generate the right powers to vary with distance between objects? [Armstrong] |
| 18401 | The pure present moment is too brief to be experienced [Armstrong] |