103 ideas
19648 | Since Kant we think we can only access 'correlations' between thinking and being [Meillassoux] |
19674 | The Copernican Revolution decentres the Earth, but also decentres thinking from reality [Meillassoux] |
19657 | In Kant the thing-in-itself is unknowable, but for us it has become unthinkable [Meillassoux] |
19675 | Since Kant, philosophers have claimed to understand science better than scientists do [Meillassoux] |
19649 | Since Kant, objectivity is defined not by the object, but by the statement's potential universality [Meillassoux] |
19666 | If we insist on Sufficient Reason the world will always be a mystery to us [Meillassoux] |
19656 | Non-contradiction is unjustified, so it only reveals a fact about thinking, not about reality? [Meillassoux] |
9535 | 'Contradictory' propositions always differ in truth-value [Lemmon] |
9512 | We write the 'negation' of P (not-P) as ¬ [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] |
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] |
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] |
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] |
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] |
9534 | Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon] |
9394 | MPP: Given A and A→B, we may derive B [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] |
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] |
19664 | Paraconsistent logics are to prevent computers crashing when data conflicts [Meillassoux] |
19665 | Paraconsistent logic is about statements, not about contradictions in reality [Meillassoux] |
19663 | We can allow contradictions in thought, but not inconsistency [Meillassoux] |
9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
19677 | What is mathematically conceivable is absolutely possible [Meillassoux] |
19659 | The absolute is the impossibility of there being a necessary existent [Meillassoux] |
19662 | It is necessarily contingent that there is one thing rather than another - so something must exist [Meillassoux] |
19654 | We must give up the modern criterion of existence, which is a correlation between thought and being [Meillassoux] |
6504 | For physicalists, the only relations are spatial, temporal and causal [Robinson,H] |
6520 | If reality just has relational properties, what are its substantial ontological features? [Robinson,H] |
19660 | Possible non-being which must be realised is 'precariousness'; absolute contingency might never not-be [Meillassoux] |
19671 | The idea of chance relies on unalterable physical laws [Meillassoux] |
6485 | When a red object is viewed, the air in between does not become red [Robinson,H] |
6521 | Representative realists believe that laws of phenomena will apply to the physical world [Robinson,H] |
6509 | Representative realists believe some properties of sense-data are shared by the objects themselves [Robinson,H] |
6522 | Phenomenalism can be theistic (Berkeley), or sceptical (Hume), or analytic (20th century) [Robinson,H] |
19651 | Unlike speculative idealism, transcendental idealism assumes the mind is embodied [Meillassoux] |
6502 | Can we reduce perception to acquisition of information, which is reduced to causation or disposition? [Robinson,H] |
6513 | Would someone who recovered their sight recognise felt shapes just by looking? [Robinson,H] |
6512 | Secondary qualities have one sensory mode, but primary qualities can have more [Robinson,H] |
6497 | We say objects possess no intrinsic secondary qualities because physicists don't need them [Robinson,H] |
19647 | The aspects of objects that can be mathematical allow it to have objective properties [Meillassoux] |
6494 | If objects are not coloured, and neither are sense-contents, we are left saying that nothing is coloured [Robinson,H] |
6499 | Shape can be experienced in different ways, but colour and sound only one way [Robinson,H] |
6500 | If secondary qualities match senses, would new senses create new qualities? [Robinson,H] |
6484 | Most moderate empiricists adopt Locke's representative theory of perception [Robinson,H] |
6508 | Sense-data leads to either representative realism or phenomenalism or idealism [Robinson,H] |
6480 | Sense-data do not have any intrinsic intentionality [Robinson,H] |
6482 | For idealists and phenomenalists sense-data are in objects; representative realists say they resemble objects [Robinson,H] |
6505 | Sense-data are rejected because they are a veil between us and reality, leading to scepticism [Robinson,H] |
6506 | 'Sense redly' sounds peculiar, but 'senses redly-squarely tablely' sounds far worse [Robinson,H] |
6507 | Adverbialism sees the contents of sense-experience as modes, not objects [Robinson,H] |
6511 | If there are only 'modes' of sensing, then an object can no more be red or square than it can be proud or lazy. [Robinson,H] |
19652 | How can we mathematically describe a world that lacks humans? [Meillassoux] |
19668 | Hume's question is whether experimental science will still be valid tomorrow [Meillassoux] |
6515 | An explanation presupposes something that is improbable unless it is explained [Robinson,H] |
6517 | If all possibilities are equal, order seems (a priori) to need an explanation - or does it? [Robinson,H] |
6481 | If intentional states are intrinsically about other things, what are their own properties? [Robinson,H] |
19650 | The transcendental subject is not an entity, but a set of conditions making science possible [Meillassoux] |
6503 | Physicalism cannot allow internal intentional objects, as brain states can't be 'about' anything [Robinson,H] |
6519 | Locke's solidity is not matter, because that is impenetrability and hardness combined [Robinson,H] |
19667 | If the laws of nature are contingent, shouldn't we already have noticed it? [Meillassoux] |
19670 | Why are contingent laws of nature stable? [Meillassoux] |
19653 | The ontological proof of a necessary God ensures a reality external to the mind [Meillassoux] |
19658 | Now that the absolute is unthinkable, even atheism is just another religious belief (though nihilist) [Meillassoux] |