109 ideas
| 7910 | Pursue truth with the urgency of someone whose clothes are on fire [Ashvaghosha] |
| 7001 | If you begin philosophy with language, you find yourself trapped in it [Heil] |
| 7037 | Parsimony does not imply the world is simple, but that our theories should try to be [Heil] |
| 7038 | A theory with few fundamental principles might still posit a lot of entities [Heil] |
| 7004 | The view that truth making is entailment is misguided and misleading [Heil] |
| 9535 | 'Contradictory' propositions always differ in truth-value [Lemmon] |
| 9509 | That proposition that both P and Q is their 'conjunction', written P∧Q [Lemmon] |
| 9508 | The sign |- may be read as 'therefore' [Lemmon] |
| 9514 | If A and B are 'interderivable' from one another we may write A -||- B [Lemmon] |
| 9511 | We write the conditional 'if P (antecedent) then Q (consequent)' as P→Q [Lemmon] |
| 9512 | We write the 'negation' of P (not-P) as ¬ [Lemmon] |
| 9510 | That proposition that either P or Q is their 'disjunction', written P∨Q [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] |
| 9516 | A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔ [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] |
| 9534 | Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon] |
| 9517 | The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon] |
| 9518 | A 'theorem' is the conclusion of a provable sequent with zero assumptions [Lemmon] |
| 9533 | A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [Lemmon] |
| 9532 | 'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon] |
| 9531 | 'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology [Lemmon] |
| 9528 | A wff is a 'tautology' if all assignments to variables result in the value T [Lemmon] |
| 9530 | A wff is 'contingent' if produces at least one T and at least one F [Lemmon] |
| 9396 | DN: Given A, we may derive ¬¬A [Lemmon] |
| 9398 | ∧I: Given A and B, we may derive A∧B [Lemmon] |
| 9394 | MPP: Given A and A→B, we may derive B [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] |
| 9395 | MTT: Given ¬B and A→B, we derive ¬A [Lemmon] |
| 9393 | A: we may assume any proposition at any stage [Lemmon] |
| 9400 | ∨I: Given either A or B separately, we may derive A∨B [Lemmon] |
| 9402 | RAA: If assuming A will prove B∧¬B, then derive ¬A [Lemmon] |
| 9397 | CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon] |
| 9522 | 'Modus ponendo tollens' (MPT) says P, ¬(P ∧ Q) |- ¬Q [Lemmon] |
| 9526 | We can change conjunctions into negated conditionals with P→Q -||- ¬(P → ¬Q) [Lemmon] |
| 9527 | The Distributive Laws can rearrange a pair of conjunctions or disjunctions [Lemmon] |
| 9523 | De Morgan's Laws make negated conjunctions/disjunctions into non-negated disjunctions/conjunctions [Lemmon] |
| 9524 | We can change conditionals into disjunctions with P→Q -||- ¬P ∨ Q [Lemmon] |
| 9525 | We can change conditionals into negated conjunctions with P→Q -||- ¬(P ∧ ¬Q) [Lemmon] |
| 9521 | 'Modus tollendo ponens' (MTP) says ¬P, P ∨ Q |- 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] |
| 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] |
| 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] |
| 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] |
| 7035 | God does not create the world, and then add the classes [Heil] |
| 9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
| 7017 | The reductionist programme dispenses with levels of reality [Heil] |
| 7003 | There are levels of organisation, complexity, description and explanation, but not of reality [Heil] |
| 7045 | Realism says some of our concepts 'cut nature at the joints' [Heil] |
| 7065 | Anti-realists who reduce reality to language must explain the existence of language [Heil] |
| 7020 | Concepts don't carve up the world, which has endless overlooked or ignored divisions [Heil] |
| 7007 | I think of properties as simultaneously dispositional and qualitative [Heil] |
| 7015 | A predicate applies truly if it picks out a real property of objects [Heil] |
| 7042 | A theory of universals says similarity is identity of parts; for modes, similarity is primitive [Heil] |
| 7023 | Powers or dispositions are usually seen as caused by lower-level qualities [Heil] |
| 7025 | Are a property's dispositions built in, or contingently added? [Heil] |
| 7034 | Universals explain one-over-many relations, and similar qualities, and similar behaviour [Heil] |
| 7039 | How could you tell if the universals were missing from a world of instances? [Heil] |
| 7009 | Similarity among modes will explain everthing universals were for [Heil] |
| 7041 | Similar objects have similar properties; properties are directly similar [Heil] |
| 7032 | Objects join sets because of properties; the property is not bestowed by set membership [Heil] |
| 7008 | Trope theorists usually see objects as 'bundles' of tropes [Heil] |
| 7018 | Objects are substances, which are objects considered as the bearer of properties [Heil] |
| 7019 | Maybe there is only one substance, space-time or a quantum field [Heil] |
| 7046 | Rather than 'substance' I use 'objects', which have properties [Heil] |
| 7047 | Statues and bronze lumps have discernible differences, so can't be identical [Heil] |
| 7048 | Do we reduce statues to bronze, or eliminate statues, or allow statues and bronze? [Heil] |
| 7028 | If properties were qualities without dispositions, they would be undetectable [Heil] |
| 7029 | Can we distinguish the way a property is from the property? [Heil] |
| 7030 | Properties don't possess ways they are, because that just is the property [Heil] |
| 7051 | Objects only have secondary qualities because they have primary qualities [Heil] |
| 7044 | Secondary qualities are just primary qualities considered in the light of their effect on us [Heil] |
| 7052 | Colours aren't surface properties, because of radiant sources and the colour of the sky [Heil] |
| 7053 | Treating colour as light radiation has the implausible result that tomatoes are not red [Heil] |
| 7066 | If the world is just texts or social constructs, what are texts and social constructs? [Heil] |
| 7021 | If the world is theory-dependent, the theories themselves can't be theory-dependent [Heil] |
| 7026 | Science is sometimes said to classify powers, neglecting qualities [Heil] |
| 7060 | One form of explanation is by decomposition [Heil] |
| 7010 | Dispositionality provides the grounding for intentionality [Heil] |
| 7054 | Intentionality now has internalist (intrinsic to thinkers) and externalist (environment or community) views [Heil] |
| 7011 | Qualia are not extra appendages, but intrinsic ingredients of material states and processes [Heil] |
| 7061 | Philosophers' zombies aim to show consciousness is over and above the physical world [Heil] |
| 7063 | Zombies are based on the idea that consciousness relates contingently to the physical [Heil] |
| 7064 | Functionalists deny zombies, since identity of functional state means identity of mental state [Heil] |
| 7027 | Functionalists say objects can be the same in disposition but differ in quality [Heil] |
| 7062 | Functionalism cannot explain consciousness just by functional organisation [Heil] |
| 7059 | The 'explanatory gap' is used to say consciousness is inexplicable, at least with current concepts [Heil] |
| 7012 | If a car is a higher-level entity, distinct from its parts, how could it ever do anything? [Heil] |
| 7043 | Multiple realisability is actually one predicate applying to a diverse range of properties [Heil] |
| 7058 | Externalism is causal-historical, or social, or biological [Heil] |
| 7057 | Intentionality is based in dispositions, which are intrinsic to agents, suggesting internalism [Heil] |
| 7013 | The Picture Theory claims we can read reality from our ways of speaking about it [Heil] |
| 7002 | If propositions are states of affairs or sets of possible worlds, these lack truth values [Heil] |
| 7016 | The standard view is that causal sequences are backed by laws, and between particular events [Heil] |
| 7036 | The real natural properties are sparse, but there are many complex properties [Heil] |
| 7909 | The Eightfold Path concerns morality, wisdom, and tranquillity [Ashvaghosha] |
| 7908 | At the end of a saint, he is not located in space, but just ceases to be disturbed [Ashvaghosha] |