165 ideas
| 421 | Men who love wisdom must be inquirers into very many things indeed [Heraclitus] |
| 1491 | Everyone has the potential for self-knowledge and sound thinking [Heraclitus] |
| 5196 | Philosophy is a department of logic [Ayer] |
| 5189 | Philosophers should abandon speculation, as philosophy is wholly critical [Ayer] |
| 5863 | Reason is eternal, but men are foolish [Heraclitus] |
| 7919 | Humeans rejected the a priori synthetic, and so rejected even Kantian metaphysics [Ayer, by Macdonald,C] |
| 5195 | Critics say analysis can only show the parts, and not their distinctive configuration [Ayer] |
| 5179 | Philosophy deals with the questions that scientists do not wish to handle [Ayer] |
| 414 | Logos is common to all, but most people live as if they have a private understanding [Heraclitus] |
| 416 | Beautiful harmony comes from things that are in opposition to one another [Heraclitus] |
| 425 | A thing can have opposing tensions but be in harmony, like a lyre [Heraclitus] |
| 5331 | You can't infer that because you have a hidden birth-mark, everybody else does [Ayer] |
| 19463 | Induction assumes some uniformity in nature, or that in some respects the future is like the past [Ayer] |
| 4749 | We cannot analyse the concept of 'truth', because it is simply a mark that a sentence is asserted [Ayer] |
| 9738 | Each line of a truth table is a model [Fitting/Mendelsohn] |
| 9727 | Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn] |
| 9726 | We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn] |
| 9737 | The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn] |
| 13136 | The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn] |
| 13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn] |
| 9734 | Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn] |
| 9736 | A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn] |
| 9735 | A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn] |
| 9741 | Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn] |
| 9740 | If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn] |
| 9739 | If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn] |
| 13137 | Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn] |
| 13140 | Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn] |
| 13139 | Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn] |
| 13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn] |
| 13141 | Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn] |
| 13138 | Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn] |
| 13142 | Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn] |
| 13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn] |
| 13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn] |
| 13146 | B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn] |
| 13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn] |
| 13148 | 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn] |
| 13149 | S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn] |
| 9742 | The system K has no accessibility conditions [Fitting/Mendelsohn] |
| 13114 | □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn] |
| 9743 | The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| 9744 | The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| 9746 | The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn] |
| 9745 | The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9747 | The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9748 | System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9404 | Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn] |
| 13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
| 13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
| 13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
| 13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
| 13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
| 1312 | If everything is and isn't then everything is true, and a midway between true and false makes everything false [Aristotle on Heraclitus] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 5202 | Maths and logic are true universally because they are analytic or tautological [Ayer] |
| 6523 | Positivists regard ontology as either meaningless or stipulated [Ayer, by Robinson,H] |
| 2611 | It is currently held that quantifying over something implies belief in its existence [Ayer] |
| 15658 | The hidden harmony is stronger than the visible [Heraclitus] |
| 13782 | Everything gives way, and nothing stands fast [Heraclitus] |
| 11853 | A mixed drink separates if it is not stirred [Heraclitus] |
| 16520 | We see properties necessary for a kind (in the definition), but not for an individual [Ayer] |
| 427 | It is not possible to step twice into the same river [Heraclitus] |
| 11091 | You can bathe in the same river twice, but not in the same river stage [Quine on Heraclitus] |
| 2064 | If flux is continuous, then lack of change can't be a property, so everything changes in every possible way [Plato on Heraclitus] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 13725 | □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn] |
| 13731 | Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn] |
| 13726 | Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn] |
| 5183 | Only tautologies can be certain; other propositions can only be probable [Ayer] |
| 19461 | Knowing I exist reveals nothing at all about my nature [Ayer] |
| 19459 | To say 'I am not thinking' must be false, but it might have been true, so it isn't self-contradictory [Ayer] |
| 19460 | 'I know I exist' has no counterevidence, so it may be meaningless [Ayer] |
| 6525 | Logical positivists could never give the sense-data equivalent of 'there is a table next door' [Robinson,H on Ayer] |
| 5170 | Material things are constructions from actual and possible occurrences of sense-contents [Ayer] |
| 8824 | No one has defended translational phenomenalism since Ayer in 1940 [Ayer, by Kim] |
| 2614 | Modern phenomenalism holds that objects are logical constructions out of sense-data [Ayer] |
| 5198 | We could verify 'a thing can't be in two places at once' by destroying one of the things [Ierubino on Ayer] |
| 2619 | Whether geometry can be applied to reality is an empirical question outside of geometry [Ayer] |
| 5197 | By changing definitions we could make 'a thing can't be in two places at once' a contradiction [Ayer] |
| 5204 | To say that a proposition is true a priori is to say that it is a tautology [Ayer] |
| 2615 | The concept of sense-data allows us to discuss appearances without worrying about reality [Ayer] |
| 6524 | Positivists prefer sense-data to objects, because the vocabulary covers both illusions and perceptions [Ayer, by Robinson,H] |
| 5193 | Causal and representative theories of perception are wrong as they refer to unobservables [Ayer] |
| 430 | Senses are no use if the soul is corrupt [Heraclitus] |
| 5200 | The main claim of rationalism is that thought is an independent source of knowledge [Ayer] |
| 4729 | Empiricism lacked a decent account of the a priori, until Ayer said it was entirely analytic [O'Grady on Ayer] |
| 5180 | All propositions (especially 'metaphysics') must begin with the senses [Ayer] |
| 5169 | My empiricism logically distinguishes analytic and synthetic propositions, and metaphysical verbiage [Ayer] |
| 5185 | It is further sense-experience which informs us of the mistakes that arise out of sense-experience [Ayer] |
| 1500 | When we sleep, reason closes down as the senses do [Heraclitus, by Sext.Empiricus] |
| 5199 | Empiricism, it is said, cannot account for our knowledge of necessary truths [Ayer] |
| 5163 | Basic propositions refer to a single experience, are incorrigible, and conclusively verifiable [Ayer] |
| 417 | Donkeys prefer chaff to gold [Heraclitus] |
| 426 | Sea water is life-giving for fish, but not for people [Heraclitus] |
| 431 | Health, feeding and rest are only made good by disease, hunger and weariness [Heraclitus] |
| 19464 | We only discard a hypothesis after one failure if it appears likely to keep on failing [Ayer] |
| 5190 | The induction problem is to prove generalisations about the future based on the past [Ayer] |
| 19462 | Induction passes from particular facts to other particulars, or to general laws, non-deductively [Ayer] |
| 5191 | We can't use the uniformity of nature to prove induction, as that would be circular [Ayer] |
| 5177 | Other minds are 'metaphysical' objects, because I can never observe their experiences [Ayer] |
| 5662 | Maybe induction could never prove the existence of something unobservable [Ayer] |
| 5178 | A conscious object is by definition one that behaves in a certain way, so behaviour proves consciousness [Ayer] |
| 5167 | The argument from analogy fails, so the best account of other minds is behaviouristic [Ayer] |
| 2613 | The theory of other minds has no rival [Ayer] |
| 5328 | Originally I combined a mentalistic view of introspection with a behaviouristic view of other minds [Ayer] |
| 5330 | Physicalism undercuts the other mind problem, by equating experience with 'public' brain events [Ayer] |
| 5664 | Consciousness must involve a subject, and only bodies identify subjects [Ayer] |
| 5172 | If the self is meaningful, it must be constructed from sense-experiences [Ayer] |
| 5326 | Qualia must be united by a subject, because they lead to concepts and judgements [Ayer] |
| 5325 | Is something an 'experience' because it relates to other experiences, or because it relates to a subject? [Ayer] |
| 5324 | Bodily identity and memory work together to establish personal identity [Ayer] |
| 5173 | Two experiences belong to one self if their contents belong with one body [Ayer] |
| 5176 | Empiricists can define personal identity as bodily identity, which consists of sense-contents [Ayer] |
| 5668 | People own conscious states because they are causally related to the identifying body [Ayer] |
| 5322 | Self-consciousness is not basic, because experiences are not instrinsically marked with ownership [Ayer] |
| 5661 | We identify experiences by their owners, so we can't define owners by their experiences [Ayer] |
| 5665 | Memory is the best proposal as what unites bundles of experiences [Ayer] |
| 5666 | Not all exerience can be remembered, as this would produce an infinite regress [Ayer] |
| 5327 | Temporal gaps in the consciousness of a spirit could not be bridged by memories [Ayer] |
| 5669 | Personal identity can't just be relations of experiences, because the body is needed to identify them [Ayer] |
| 5171 | The supposed 'gulf' between mind and matter is based on the senseless concept of 'substances' [Ayer] |
| 5329 | Why shouldn't we say brain depends on mind? Better explanation! [Ayer] |
| 5181 | A sentence is factually significant to someone if they know how to verify its proposition [Ayer] |
| 5184 | Factual propositions imply (in conjunction with a few other premises) possible experiences [Ayer] |
| 5186 | Tautologies and empirical hypotheses form the entire class of significant propositions [Ayer] |
| 5164 | A statement is meaningful if observation statements can be deduced from it [Ayer] |
| 5165 | Directly verifiable statements must entail at least one new observation statement [Ayer] |
| 5166 | The principle of verification is not an empirical hypothesis, but a definition [Ayer] |
| 5162 | Sentences only express propositions if they are meaningful; otherwise they are 'statements' [Ayer] |
| 2610 | Talk of propositions is just shorthand for talking about equivalent sentences [Ayer] |
| 6968 | Some people think there are ethical facts, but of a 'queer' sort [Ayer] |
| 6972 | A right attitude is just an attitude one is prepared to stand by [Ayer] |
| 6973 | Moral theories are all meta-ethical, and are neutral as regards actual conduct [Ayer] |
| 6974 | Moral judgements cannot be the logical consequence of a moral philosophy [Ayer] |
| 429 | To God (though not to humans) all things are beautiful and good and just [Heraclitus] |
| 12294 | Good and evil are the same thing [Heraclitus, by Aristotle] |
| 5205 | Moral intuition is worthless if there is no criterion to decide between intuitions [Ayer] |
| 6971 | I would describe intuitions of good as feelings of approval [Ayer] |
| 23725 | Ayer defends the emotivist version of expressivism [Ayer, by Smith,M] |
| 5206 | To say an act is wrong makes no further statement about it, but merely expresses disapproval [Ayer] |
| 6969 | Approval of historical or fictional murders gives us leave to imitate them [Ayer] |
| 6970 | Moral judgements are not expressions, but are elements in a behaviour pattern [Ayer] |
| 5168 | Moral approval and disapproval concerns classes of actions, rather than particular actions [Ayer] |
| 419 | If one does not hope, one will not find the unhoped-for, since nothing leads to it [Heraclitus] |
| 415 | If happiness is bodily pleasure, then oxen are happy when they have vetch to eat [Heraclitus] |
| 5155 | It is hard to fight against emotion, but harder still to fight against pleasure [Heraclitus] |
| 433 | For man character is destiny [Heraclitus] |
| 422 | The people should fight for the law as if for their city-wall [Heraclitus] |
| 614 | Heraclitus said sometimes everything becomes fire [Heraclitus, by Aristotle] |
| 424 | Reason tells us that all things are one [Heraclitus] |
| 5096 | Heraclitus says that at some time everything becomes fire [Heraclitus, by Aristotle] |
| 17539 | The sayings of Heraclitus are still correct, if we replace 'fire' with 'energy' [Heraclitus, by Heisenberg] |
| 3054 | Heraclitus said fire could be transformed to create the other lower elements [Heraclitus, by Diog. Laertius] |
| 15660 | Logos is the source of everything, and my theories separate and explain each nature [Heraclitus] |
| 15251 | The attribution of necessity to causation is either primitive animism, or confusion with logical necessity [Ayer] |
| 12269 | All things are in a state of motion [Heraclitus, by Aristotle] |
| 420 | The cosmos is eternal not created, and is an ever-living and changing fire [Heraclitus] |
| 5208 | A person with non-empirical attributes is unintelligible. [Ayer] |
| 5187 | When we ascribe an attribute to a thing, we covertly assert that it exists [Ayer] |
| 1499 | Heraclitus says intelligence draws on divine reason [Heraclitus, by Sext.Empiricus] |
| 5207 | If theism is non-sensical, then so is atheism. [Ayer] |
| 15659 | Purifying yourself with blood is as crazy as using mud to wash off mud [Heraclitus] |
| 1501 | In their ignorance people pray to statues, which is like talking to a house [Heraclitus] |
| 5209 | The 'truths' expressed by theists are not literally significant [Ayer] |