124 ideas
| 3798 | An overexamined life is as bad as an unexamined one [Dennett] |
| 3801 | Rationality requires the assumption that things are either for better or worse [Dennett] |
| 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] |
| 14308 | We can bring dispositions into existence, as in creating an identifier [Dennett, by Mumford] |
| 7384 | Words are fixed by being attached to similarity clusters, without mention of 'essences' [Dennett] |
| 2526 | Philosophers regularly confuse failures of imagination with insights into necessity [Dennett] |
| 3802 | Why pronounce impossible what you cannot imagine? [Dennett] |
| 7374 | Light wavelengths entering the eye are only indirectly related to object colours [Dennett] |
| 2523 | That every mammal has a mother is a secure reality, but without foundations [Dennett] |
| 3795 | Causal theories require the "right" sort of link (usually unspecified) [Dennett] |
| 7369 | Brains are essentially anticipation machines [Dennett] |
| 4608 | Minds are hard-wired, or trial-and-error, or experimental, or full self-aware [Dennett, by Heil] |
| 7393 | We can't draw a clear line between conscious and unconscious [Dennett] |
| 7367 | Perhaps the brain doesn't 'fill in' gaps in consciousness if no one is looking. [Dennett] |
| 4880 | Sentience comes in grades from robotic to super-human; we only draw a line for moral reasons [Dennett] |
| 2528 | Does consciousness need the concept of consciousness? [Dennett] |
| 2525 | Maybe language is crucial to consciousness [Dennett] |
| 7394 | Conscious events can only be explained in terms of unconscious events [Dennett] |
| 7391 | We can know a lot of what it is like to be a bat, and nothing important is unknown [Dennett] |
| 3158 | Theories of intentionality presuppose rationality, so can't explain it [Dennett] |
| 2527 | Unconscious intentionality is the foundation of the mind [Dennett] |
| 6624 | Dennett denies the existence of qualia [Dennett, by Lowe] |
| 4873 | What is it like to notice an uncomfortable position when you are asleep? [Dennett] |
| 7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
| 7387 | "Qualia" can be replaced by complex dispositional brain states [Dennett] |
| 7376 | We can't assume that dispositions will remain normal when qualia have been inverted [Dennett] |
| 7372 | In peripheral vision we see objects without their details, so blindsight is not that special [Dennett] |
| 7373 | Blindsight subjects glean very paltry information [Dennett] |
| 3797 | I am the sum total of what I directly control [Dennett] |
| 7385 | People accept blurred boundaries in many things, but insist self is All or Nothing [Dennett] |
| 4881 | Being a person must involve having second-order beliefs and desires (about beliefs and desires) [Dennett] |
| 7383 | The psychological self is an abstraction, not a thing in the brain [Dennett] |
| 7386 | Selves are not soul-pearls, but artefacts of social processes [Dennett] |
| 7381 | We tell stories about ourselves, to protect, control and define who we are [Dennett] |
| 7382 | We spin narratives about ourselves, and the audience posits a centre of gravity for them [Dennett] |
| 7370 | The brain is controlled by shifting coalitions, guided by good purposeful habits [Dennett] |
| 7655 | The work done by the 'homunculus in the theatre' must be spread amongst non-conscious agencies [Dennett] |
| 3800 | You can be free even though force would have prevented you doing otherwise [Dennett, by PG] |
| 3803 | Can we conceive of a being with a will freer than our own? [Dennett] |
| 3791 | Awareness of thought is a step beyond awareness of the world [Dennett] |
| 3794 | Foreknowledge permits control [Dennett] |
| 7379 | If an epiphenomenon has no physical effects, it has to be undetectable [Dennett] |
| 7365 | Dualism wallows in mystery, and to accept it is to give up [Dennett] |
| 3159 | Beliefs and desires aren't real; they are prediction techniques [Dennett] |
| 3796 | The active self is a fiction created because we are ignorant of our motivations [Dennett] |
| 3161 | If mind is just an explanation, the explainer must have beliefs [Rey on Dennett] |
| 3986 | The 'intentional stance' is a way of interpreting an entity by assuming it is rational and self-aware [Dennett] |
| 2530 | Could a robot be made conscious just by software? [Dennett] |
| 7371 | All functionalism is 'homuncular', of one grain size or another [Dennett] |
| 4875 | We descend from robots, and our intentionality is composed of billions of crude intentional systems [Dennett] |
| 4879 | There is no more anger in adrenaline than silliness in a bottle of whiskey [Dennett] |
| 7657 | Intelligent agents are composed of nested homunculi, of decreasing intelligence, ending in machines [Dennett] |
| 7366 | It is arbitrary to say which moment of brain processing is conscious [Dennett] |
| 7380 | Visual experience is composed of neural activity, which we find pleasing [Dennett] |
| 4876 | Maybe there is a minimum brain speed for supporting a mind [Dennett] |
| 7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
| 4878 | The materials for a mind only matter because of speed, and a need for transducers and effectors [Dennett] |
| 3987 | Like the 'centre of gravity', desires and beliefs are abstract concepts with no actual existence [Dennett] |
| 3177 | You couldn't drive a car without folk psychology [Dennett] |
| 2524 | A language of thought doesn't explain content [Dennett] |
| 4874 | The predecessor and rival of the language of thought hypothesis is the picture theory of ideas [Dennett] |
| 7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |
| 23803 | States have content if we can predict them well by assuming intentionality [Dennett, by Schulte] |
| 3984 | The nature of content is entirely based on its functional role [Dennett] |
| 4882 | Concepts are things we (unlike dogs) can think about, because we have language [Dennett] |
| 2529 | Maybe there can be non-conscious concepts (e.g. in bees) [Dennett] |
| 21006 | If women share rights with men, they will exhibit similar virtues [Wollstonecraft] |
| 3983 | Learning is evolution in the brain [Dennett] |
| 4872 | Most people see an abortion differently if the foetus lacks a brain [Dennett] |
| 7368 | Originally there were no reasons, purposes or functions; since there were no interests, there were only causes [Dennett] |
| 3985 | Biology is a type of engineering, not a search for laws of nature [Dennett] |
| 4877 | Maybe plants are very slow (and sentient) animals, overlooked because we are faster? [Dennett] |
| 3804 | Darwin's idea was the best idea ever [Dennett] |