106 ideas
18559 | Philosophy is empty if it does not in some way depend on matters of fact [Machery] |
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] |
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] |
9517 | The 'scope' of a connective is the connective, the linked formulae, and the brackets [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] |
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] |
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] |
9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
18564 | Do categories store causal knowledge, or typical properties, or knowledge of individuals? [Machery] |
18604 | Are quick and slow categorisation the same process, or quite different? [Machery] |
18573 | For each category of objects (such as 'dog') an individual seems to have several concepts [Machery] |
18602 | A thing is classified if its features are likely to be generated by that category's causal laws [Machery] |
18565 | There may be ad hoc categories, such as the things to pack in your suitcase for a trip [Machery] |
18570 | There may be several ways to individuate things like concepts [Machery] |
18615 | Horizontal arguments say eliminate a term if it fails to pick out a natural kind [Machery] |
18616 | If a term doesn't pick out a kind, keeping it may block improvements in classification [Machery] |
18614 | Vertical arguments say eliminate a term if it picks out different natural kinds in different theories [Machery] |
18609 | Psychologists use 'induction' as generalising a property from one category to another [Machery] |
18610 | 'Ampliative' induction infers that all members of a category have a feature found in some of them [Machery] |
18562 | Connectionists cannot distinguish concept-memories from their background, or the processes [Machery] |
18561 | We can identify a set of cognitive capacities which are 'higher order' [Machery] |
18574 | Concepts for categorisation and for induction may be quite different [Machery] |
18588 | Concept theories aim at their knowledge, processes, format, acquisition, and location [Machery] |
18611 | We should abandon 'concept', and just use 'prototype', 'exemplar' and 'theory' [Machery] |
18567 | In the philosophy of psychology, concepts are usually introduced as constituents of thoughts [Machery] |
18569 | In philosophy theories of concepts explain how our propositional attitudes have content [Machery] |
18563 | By 'concept' psychologists mean various sorts of representation or structure [Machery] |
18557 | Psychologists treat concepts as long-term knowledge bodies which lead to judgements [Machery] |
18560 | Psychologist treat concepts as categories [Machery] |
18558 | Concept theorists examine their knowledge, format, processes, acquisition and location [Machery] |
18592 | The concepts OBJECT or AGENT may be innate [Machery] |
18566 | Concepts should contain working memory, not long-term, because they control behaviour [Machery] |
18584 | One hybrid theory combines a core definition with a prototype for identification [Machery] |
18585 | Heterogeneous concepts might have conflicting judgements, where hybrid theories will not [Machery] |
18578 | Concepts as definitions was rejected, and concepts as prototypes, exemplars or theories proposed [Machery] |
18575 | The concepts for a class typically include prototypes, and exemplars, and theories [Machery] |
18583 | Many categories don't seem to have a definition [Machery] |
18590 | Classical theory implies variety in processing times, but this does not generally occur [Machery] |
18591 | Classical theory can't explain facts like typical examples being categorised quicker [Machery] |
18594 | Knowing typical properties of things is especially useful in induction [Machery] |
18593 | The term 'prototype' is used for both typical category members, and the representation [Machery] |
18606 | The prototype view predicts that typical members are easier to categorise [Machery] |
18595 | Prototype theories are based on computation of similarities with the prototype [Machery] |
18596 | Prototype theorists don't tell us how we select the appropriate prototype [Machery] |
18603 | Maybe concepts are not the typical properties, but the ideal properties [Machery] |
18605 | It is more efficient to remember the prototype, than repeatedly create it from exemplars [Machery] |
18597 | Concepts as exemplars are based on the knowledge of properties of each particular [Machery] |
18598 | Exemplar theories need to explain how the relevant properties are selected from a multitude of them [Machery] |
18599 | In practice, known examples take priority over the rest of the set of exemplars [Machery] |
18587 | The theory account is sometimes labelled as 'knowledge' or 'explanation' in approach [Machery] |
18600 | Theory Theory says category concepts are knowledge stores explaining membership [Machery] |
18601 | Theory Theory says concepts are explanatory knowledge, and concepts form domains [Machery] |
18607 | Theory theorists rely on best explanation, rather than on similarities [Machery] |
18608 | If categorisation is not by similarity, it seems to rely on what properties things might have [Machery] |
18577 | The word 'grandmother' may be two concepts, with a prototype and a definition [Machery] |
18589 | For behaviourists concepts are dispositions to link category members to names [Machery] |
7752 | Only the utterer's primary intention is relevant to the meaning [Grice] |
7751 | Meaning needs an intention to induce a belief, and a recognition that this is the speaker's intention [Grice] |
7753 | We judge linguistic intentions rather as we judge non-linguistic intentions, so they are alike [Grice] |
18612 | Americans are more inclined to refer causally than the Chinese are [Machery] |
18613 | Artifacts can be natural kinds, when they are the object of historical enquiry [Machery] |