207 ideas
18450 | Philosophy has its own mode of death, by separating soul from body [Porphyry] |
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] |
9535 | 'Contradictory' propositions always differ in truth-value [Lemmon] |
9509 | That proposition that both P and Q is their 'conjunction', written P∧Q [Lemmon] |
9511 | We write the conditional 'if P (antecedent) then Q (consequent)' as P→Q [Lemmon] |
9510 | That proposition that either P or Q is their 'disjunction', written P∨Q [Lemmon] |
9512 | We write the 'negation' of P (not-P) as ¬ [Lemmon] |
9513 | We write 'P if and only if Q' as P↔Q; it is also P iff Q, or (P→Q)∧(Q→P) [Lemmon] |
9514 | If A and B are 'interderivable' from one another we may write A -||- B [Lemmon] |
9508 | The sign |- may be read as 'therefore' [Lemmon] |
9516 | A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔ [Lemmon] |
9517 | The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon] |
9530 | A wff is 'contingent' if produces at least one T and at least one F [Lemmon] |
9532 | 'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon] |
9533 | A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [Lemmon] |
9528 | A wff is a 'tautology' if all assignments to variables result in the value T [Lemmon] |
9518 | A 'theorem' is the conclusion of a provable sequent with zero assumptions [Lemmon] |
9534 | Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon] |
9519 | A 'substitution-instance' is a wff formed by consistent replacing variables with wffs [Lemmon] |
9529 | A wff is 'inconsistent' if all assignments to variables result in the value F [Lemmon] |
9531 | 'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology [Lemmon] |
9396 | DN: Given A, we may derive ¬¬A [Lemmon] |
9393 | A: we may assume any proposition at any stage [Lemmon] |
9399 | ∧E: Given A∧B, we may derive either A or B separately [Lemmon] |
9401 | ∨E: Derive C from A∨B, if C can be derived both from A and from B [Lemmon] |
9398 | ∧I: Given A and B, we may derive A∧B [Lemmon] |
9397 | CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon] |
9394 | MPP: Given A and A→B, we may derive B [Lemmon] |
9402 | RAA: If assuming A will prove B∧¬B, then derive ¬A [Lemmon] |
9395 | MTT: Given ¬B and A→B, we derive ¬A [Lemmon] |
9400 | ∨I: Given either A or B separately, we may derive A∨B [Lemmon] |
9521 | 'Modus tollendo ponens' (MTP) says ¬P, P ∨ Q |- Q [Lemmon] |
9522 | 'Modus ponendo tollens' (MPT) says P, ¬(P ∧ Q) |- ¬Q [Lemmon] |
9525 | We can change conditionals into negated conjunctions with P→Q -||- ¬(P ∧ ¬Q) [Lemmon] |
9524 | We can change conditionals into disjunctions with P→Q -||- ¬P ∨ Q [Lemmon] |
9523 | De Morgan's Laws make negated conjunctions/disjunctions into non-negated disjunctions/conjunctions [Lemmon] |
9527 | The Distributive Laws can rearrange a pair of conjunctions or disjunctions [Lemmon] |
9526 | We can change conjunctions into negated conditionals with P→Q -||- ¬(P → ¬Q) [Lemmon] |
9537 | Truth-tables are good for showing invalidity [Lemmon] |
9538 | A truth-table test is entirely mechanical, but this won't work for more complex logic [Lemmon] |
9536 | If any of the nine rules of propositional logic are applied to tautologies, the result is a tautology [Lemmon] |
9539 | Propositional logic is complete, since all of its tautologous sequents are derivable [Lemmon] |
13909 | Write '(∀x)(...)' to mean 'take any x: then...', and '(∃x)(...)' to mean 'there is an x such that....' [Lemmon] |
13902 | 'Gm' says m has property G, and 'Pmn' says m has relation P to n [Lemmon] |
13911 | The 'symbols' are bracket, connective, term, variable, predicate letter, reverse-E [Lemmon] |
13910 | Our notation uses 'predicate-letters' (for 'properties'), 'variables', 'proper names', 'connectives' and 'quantifiers' [Lemmon] |
13904 | Universal Elimination (UE) lets us infer that an object has F, from all things having F [Lemmon] |
13906 | With finite named objects, we can generalise with &-Intro, but otherwise we need ∀-Intro [Lemmon] |
13908 | UE all-to-one; UI one-to-all; EI arbitrary-to-one; EE proof-to-one [Lemmon] |
13901 | Predicate logic uses propositional connectives and variables, plus new introduction and elimination rules [Lemmon] |
13903 | Universal elimination if you start with the universal, introduction if you want to end with it [Lemmon] |
13905 | If there is a finite domain and all objects have names, complex conjunctions can replace universal quantifiers [Lemmon] |
13900 | 'Some Frenchmen are generous' is rendered by (∃x)(Fx→Gx), and not with the conditional → [Lemmon] |
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] |
9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
18392 | Classes have cardinalities, so their members must all be treated as units [Armstrong] |
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] |
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] |
18451 | The presence of the incorporeal is only known by certain kinds of disposition [Porphyry] |
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] |
17678 | Universals are just the repeatable features of a world [Armstrong] |
15034 | Are genera and species real or conceptual? bodies or incorporeal? in sensibles or separate from them? [Porphyry] |
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] |
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] |
18459 | Diversity arises from the power of unity [Porphyry] |
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] |
18452 | Memory is not conserved images, but reproduction of previous thought [Porphyry] |
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] |
18453 | Intelligence is aware of itself, so the intelligence is both the thinker and the thought [Porphyry] |
18462 | The soul is everywhere and nowhere in the body, and must be its cause [Porphyry] |
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] |
18463 | Successful introspection reveals the substrate along with the object of thought [Porphyry] |
18458 | The soul is bound to matter by the force of its own disposition [Porphyry] |
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] |
18464 | Justice is each person fulfilling his function [Porphyry] |
18448 | We should avoid the pleasures of love, or at least, should not enact our dreams [Porphyry] |
18444 | Civil virtues make us behave benevolently, and thereby unite citizens [Porphyry] |
18445 | Civil virtues control the passions, and make us conform to our nature [Porphyry] |
18446 | Purificatory virtues detach the soul completely from the passions [Porphyry] |
18447 | There are practical, purificatory, contemplative, and exemplary virtues [Porphyry] |
18456 | Unified real existence is neither great nor small, though greatness and smallness participate in it [Porphyry] |
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] |
18454 | Time is the circular movement of the soul [Porphyry] |
18455 | Some think time is seen at rest, as well as in movement [Porphyry] |
18401 | The pure present moment is too brief to be experienced [Armstrong] |
18460 | God is nowhere, and hence everywhere [Porphyry] |
18461 | Everything existing proceeds from divinity, and is within divinity [Porphyry] |
18449 | Nature binds or detaches body to soul, but soul itself joins and detaches soul from body [Porphyry] |
18457 | Individual souls are all connected, though distinct, and without dividing universal Soul [Porphyry] |