124 ideas
| 9535 | 'Contradictory' propositions always differ in truth-value [Lemmon] |
| 9512 | We write the 'negation' of P (not-P) as ¬ [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] |
| 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] |
| 9509 | That proposition that both P and Q is their 'conjunction', 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] |
| 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] |
| 9516 | A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔ [Lemmon] |
| 9518 | A 'theorem' is the conclusion of a provable sequent with zero assumptions [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] |
| 9517 | The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon] |
| 9529 | A wff is 'inconsistent' if all assignments to variables result in the value F [Lemmon] |
| 9519 | A 'substitution-instance' is a wff formed by consistent replacing variables with wffs [Lemmon] |
| 9531 | 'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology [Lemmon] |
| 9534 | Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon] |
| 9397 | CP: Given a proof of B from A as assumption, we may derive A→B [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] |
| 9402 | RAA: If assuming A will prove B∧¬B, then derive ¬A [Lemmon] |
| 9395 | MTT: Given ¬B and A→B, we derive ¬A [Lemmon] |
| 9396 | DN: Given A, we may derive ¬¬A [Lemmon] |
| 9394 | MPP: Given A and A→B, we may derive B [Lemmon] |
| 9400 | ∨I: Given either A or B separately, we may derive A∨B [Lemmon] |
| 9522 | 'Modus ponendo tollens' (MPT) says P, ¬(P ∧ Q) |- ¬Q [Lemmon] |
| 9521 | 'Modus tollendo ponens' (MTP) 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] |
| 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] |
| 3137 | Varieties of singular terms are used to designate token particulars [Rey] |
| 3143 | Physics requires the existence of properties, and also the abstract objects of arithmetic [Rey] |
| 13076 | Scholastics treat relations as two separate predicates of the relata [Cover/O'Leary-Hawthorne] |
| 13102 | If you individuate things by their origin, you still have to individuate the origins themselves [Cover/O'Leary-Hawthorne] |
| 13103 | Numerical difference is a symmetrical notion, unlike proper individuation [Cover/O'Leary-Hawthorne] |
| 13104 | Haecceity as property, or as colourless thisness, or as singleton set [Cover/O'Leary-Hawthorne] |
| 13100 | Maybe 'substance' is more of a mass-noun than a count-noun [Cover/O'Leary-Hawthorne] |
| 13068 | We can ask for the nature of substance, about type of substance, and about individual substances [Cover/O'Leary-Hawthorne] |
| 13069 | The general assumption is that substances cannot possibly be non-substances [Cover/O'Leary-Hawthorne] |
| 13072 | Modern essences are sets of essential predicate-functions [Cover/O'Leary-Hawthorne] |
| 17080 | Modern essentialists express essence as functions from worlds to extensions for predicates [Cover/O'Leary-Hawthorne] |
| 13101 | Necessity-of-origin won't distinguish ex nihilo creations, or things sharing an origin [Cover/O'Leary-Hawthorne] |
| 3145 | The Indiscernibility of Identicals is a truism; but the Identity of Indiscernibles depends on possible identical worlds [Rey] |
| 13081 | Even extreme modal realists might allow transworld identity for abstract objects [Cover/O'Leary-Hawthorne] |
| 3172 | Empiricism says experience is both origin and justification of all knowledge [Rey] |
| 3166 | Animal learning is separate from their behaviour [Rey] |
| 13071 | We can go beyond mere causal explanations if we believe in an 'order of being' [Cover/O'Leary-Hawthorne] |
| 3232 | Abduction could have true data and a false conclusion, and may include data not originally mentioned [Rey] |
| 3128 | It's not at all clear that explanation needs to stop anywhere [Rey] |
| 3136 | The three theories are reduction, dualism, eliminativism [Rey] |
| 3141 | Is consciousness 40Hz oscillations in layers 5 and 6 of the visual cortex? [Rey] |
| 3148 | Dualist privacy is seen as too deep for even telepathy to reach [Rey] |
| 3164 | Intentional explanations are always circular [Rey] |
| 3138 | Arithmetic and unconscious attitudes have no qualia [Rey] |
| 3142 | Why qualia, and why this particular quale? [Rey] |
| 3224 | If qualia have no function, their attachment to thoughts is accidental [Rey] |
| 3227 | Are qualia a type of propositional attitude? [Rey] |
| 3226 | Are qualia irrelevant to explaining the mind? [Rey] |
| 3229 | If colour fits a cone mapping hue, brightness and saturation, rotating the cone could give spectrum inversion [Rey] |
| 3223 | Self-consciousness may just be nested intentionality [Rey] |
| 3162 | Experiments prove that people are often unaware of their motives [Rey] |
| 3163 | Brain damage makes the unreliability of introspection obvious [Rey] |
| 3196 | Free will isn't evidence against a theory of thought if there is no evidence for free will [Rey] |
| 3195 | If reason could be explained in computational terms, there would be no need for the concept of 'free will' [Rey] |
| 3165 | Behaviourism is eliminative, or reductionist, or methodological [Rey] |
| 3180 | Maybe behaviourists should define mental states as a group [Rey] |
| 3167 | Animals don't just respond to stimuli, they experiment [Rey] |
| 3173 | How are stimuli and responses 'similar'? [Rey] |
| 3179 | Behaviour is too contingent and irrelevant to be the mind [Rey] |
| 3186 | If a normal person lacked a brain, would you say they had no mind? [Rey] |
| 3127 | Dualism and physicalism explain nothing, and don't suggest any research [Rey] |
| 3188 | Homuncular functionalism (e.g. Freud) could be based on simpler mechanical processes [Rey] |
| 3216 | Is the room functionally the same as a Chinese speaker? [Rey] |
| 3220 | Searle is guilty of the fallacy of division - attributing a property of the whole to a part [Rey] |
| 3206 | One computer program could either play chess or fight a war [Rey] |
| 3140 | If you explain water as H2O, you have reduced water, but not eliminated it [Rey] |
| 3134 | Human behaviour can show law-like regularity, which eliminativism can't explain [Rey] |
| 3199 | Connectionism assigns numbers to nodes and branches, and plots the outcomes [Rey] |
| 3201 | Connectionism explains well speed of perception and 'graceful degradation' [Rey] |
| 3202 | Connectionism explains irrationality (such as the Gamblers' Fallacy) quite well [Rey] |
| 3200 | Pattern recognition is puzzling for computation, but makes sense for connectionism [Rey] |
| 3150 | Can identity explain reason, free will, non-extension, intentionality, subjectivity, experience? [Rey] |
| 3129 | Physicalism offers something called "complexity" instead of mental substance [Rey] |
| 3139 | Some attitudes are information (belief), others motivate (hatred) [Rey] |
| 3174 | Good grammar can't come simply from stimuli [Rey] |
| 3171 | Children speak 90% good grammar [Rey] |
| 3170 | We train children in truth, not in grammar [Rey] |
| 3213 | Animals may also use a language of thought [Rey] |
| 3215 | Images can't replace computation, as they need it [Rey] |
| 3194 | CRTT is good on deduction, but not so hot on induction, abduction and practical reason [Rey] |
| 3147 | Problem-solving clearly involves manipulating images [Rey] |
| 3175 | Animals map things over time as well as over space [Rey] |
| 3207 | Simple externalism is that the meaning just is the object [Rey] |
| 3176 | Anything bears a family resemblance to a game, but obviously not anything counts as one [Rey] |
| 3181 | A one hour gap in time might be indirectly verified, but then almost anything could be [Rey] |
| 3204 | The meaning of "and" may be its use, but not of "animal" [Rey] |
| 3205 | Semantic holism means new evidence for a belief changes the belief, and we can't agree on concepts [Rey] |
| 3209 | Causal theories of reference (by 'dubbing') don't eliminate meanings in the heads of dubbers [Rey] |
| 3210 | If meaning and reference are based on causation, then virtually everything has meaning [Rey] |
| 3149 | Referential Opacity says truth is lost when you substitute one referring term ('mother') for another ('Jocasta') [Rey] |
| 3169 | A simple chaining device can't build sentences containing 'either..or', or 'if..then' [Rey] |
| 3221 | Our desires become important when we have desires about desires [Rey] |