108 ideas
1887 | You cannot divide anything into many parts, because after the first division you are no longer dividing the original [Sext.Empiricus] |
22764 | Ordinary speech is not exact about what is true; we say we are digging a well before the well exists [Sext.Empiricus] |
22752 | Reasoning is impossible without a preconception [Sext.Empiricus] |
22285 | Impredicative definitions are circular, but fine for picking out, rather than creating something [Potter] |
1885 | Proof moves from agreed premises to a non-evident inference [Sext.Empiricus] |
22301 | The Identity Theory says a proposition is true if it coincides with what makes it true [Potter] |
6021 | It is only when we say a proposition that we speak truly or falsely [Sext.Empiricus] |
22324 | It has been unfortunate that externalism about truth is equated with correspondence [Potter] |
10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
13044 | Infinity: There is at least one limit level [Potter] |
10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
22279 | Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter] |
12196 | A valid hypothetical syllogism is 'that which does not begin with a truth and end with a falsehood' [Sext.Empiricus] |
22291 | Deductivism can't explain how the world supports unconditional conclusions [Potter] |
6020 | 'Man is a rational mortal animal' is equivalent to 'if something is a man, that thing is a rational mortal animal' [Sext.Empiricus] |
10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
22295 | Modern logical truths are true under all interpretations of the non-logical words [Potter] |
1902 | Since Socrates either died when he was alive (a contradiction) or died when he was dead (meaningless), he didn't die [Sext.Empiricus] |
10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
22310 | The formalist defence against Gödel is to reject his metalinguistic concept of truth [Potter] |
22298 | Why is fictional arithmetic applicable to the real world? [Potter] |
16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
22287 | If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete [Potter] |
16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
22284 | 'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers [Potter] |
13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
22744 | Parts are not parts if their whole is nothing more than the parts [Sext.Empiricus] |
22762 | Some properties are inseparable from a thing, such as the length, breadth and depth of a body [Sext.Empiricus] |
10709 | Priority is a modality, arising from collections and members [Potter] |
22281 | A material conditional cannot capture counterfactual reasoning [Potter] |
1889 | If an argument has an absurd conclusion, we should not assent to the absurdity, but avoid the absurd argument [Sext.Empiricus] |
1871 | Whether honey is essentially sweet may be doubted, as it is a matter of judgement rather than appearance [Sext.Empiricus] |
1883 | How can the intellect know if sensation is reliable if it doesn't directly see external objects? [Sext.Empiricus] |
22748 | Some say motion is perceived by sense, but others say it is by intellect [Sext.Empiricus] |
1890 | We distinguish ambiguities by seeing what is useful [Sext.Empiricus] |
22759 | Fools, infants and madmen may speak truly, but do not know [Sext.Empiricus] |
20795 | Some things are their own criterion, such as straightness, a set of scales, or light [Sext.Empiricus] |
22760 | Madmen are reliable reporters of what appears to them [Sext.Empiricus] |
22327 | Knowledge from a drunken schoolteacher is from a reliable and unreliable process [Potter] |
1870 | The basis of scepticism is the claim that every proposition has an equal opposing proposition [Sext.Empiricus] |
1882 | The necks of doves appear different in colour depending on the angle of viewing [Sext.Empiricus] |
1881 | The same oar seems bent in water and straight when out of it [Sext.Empiricus] |
1872 | The same tower appears round from a distance, but square close at hand [Sext.Empiricus] |
1873 | If we press the side of an eyeball, objects appear a different shape [Sext.Empiricus] |
20794 | How can sceptics show there is no criterion? Weak without, contradiction with [Sext.Empiricus] |
1874 | How can we judge between our impressions and those of other animals, when we ourselves are involved? [Sext.Empiricus] |
1878 | Water that seems lukewarm can seem very hot on inflamed skin [Sext.Empiricus] |
1880 | Some actions seem shameful when sober but not when drunk [Sext.Empiricus] |
1877 | If we had no hearing or sight, we would assume no sound or sight exists, so there may be unsensed qualities [Sext.Empiricus] |
1879 | Sickness is perfectly natural to the sick, so their natural perceptions should carry some weight [Sext.Empiricus] |
1876 | If we enjoy different things, presumably we receive different impressions [Sext.Empiricus] |
1910 | With us it is shameful for men to wear earrings, but among Syrians it is considered noble [Sext.Empiricus] |
1911 | Even if all known nations agree on a practice, there may be unknown nations which disagree [Sext.Empiricus] |
6026 | How can you investigate without some preconception of your object? [Sext.Empiricus] |
1886 | If you don't view every particular, you may miss the one which disproves your universal induction [Sext.Empiricus] |
22746 | If we try to conceive of a line with no breadth, it ceases to exist, and so has no length [Sext.Empiricus] |
22741 | The incorporeal is not in the nature of body, and so could not emerge from it [Sext.Empiricus] |
22273 | Traditionally there are twelve categories of judgement, in groups of three [Potter] |
1884 | If we utter three steps of a logical argument, they never exist together [Sext.Empiricus] |
22763 | We can only dream of a winged man if we have experienced men and some winged thing [Sext.Empiricus] |
22290 | The phrase 'the concept "horse"' can't refer to a concept, because it is saturated [Potter] |
22283 | Compositionality should rely on the parsing tree, which may contain more than sentence components [Potter] |
22282 | 'Direct compositonality' says the components wholly explain a sentence meaning [Potter] |
22296 | Compositionality is more welcome in logic than in linguistics (which is more contextual) [Potter] |
22754 | Saying the good is useful or choiceworth or happiness-creating is not the good, but a feature of it [Sext.Empiricus] |
22755 | Like a warming fire, what is good by nature should be good for everyone [Sext.Empiricus] |
22756 | If a desire is itself desirable, then we shouldn't desire it, as achieving it destroys it [Sext.Empiricus] |
6032 | Right actions, once done, are those with a reasonable justification [Sext.Empiricus] |
1517 | The tektraktys (1+2+3+4=10) is the 'fount of ever-flowing nature' [Sext.Empiricus] |
1894 | Some say that causes are physical, some say not [Sext.Empiricus] |
1897 | Knowing an effect results from a cause means knowing that the cause belongs with the effect, which is circular [Sext.Empiricus] |
1898 | Cause can't exist before effect, or exist at the same time, so it doesn't exist [Sext.Empiricus] |
1896 | If there were no causes then everything would have been randomly produced by everything [Sext.Empiricus] |
1895 | Causes are either equal to the effect, or they link equally with other causes, or they contribute slightly [Sext.Empiricus] |
1900 | If time and place are infinitely divided, it becomes impossible for movement ever to begin [Sext.Empiricus] |
1901 | If all atoms, times and places are the same, everything should move with equal velocity [Sext.Empiricus] |
22747 | A man walking backwards on a forwards-moving ship is moving in a fixed place [Sext.Empiricus] |
1899 | Does the original self-mover push itself from behind, or pull itself from in front? [Sext.Empiricus] |
1903 | If motion and rest are abolished, so is time [Sext.Empiricus] |
1904 | Time must be unlimited, but past and present can't be non-existent, and can't be now, so time does not exist [Sext.Empiricus] |
22749 | Time doesn't end with the Universe, because tensed statements about destruction remain true [Sext.Empiricus] |
22750 | Time is divisible, into past, present and future [Sext.Empiricus] |
1905 | How can time be divisible if we can't compare one length of time with another? [Sext.Empiricus] |
22742 | Socrates either dies when he exists (before his death) or when he doesn't (after his death) [Sext.Empiricus] |
22751 | If the present is just the limit of the past or the future, it can't exist because they don't exist [Sext.Empiricus] |
22730 | All men agree that God is blessed, imperishable, happy and good [Sext.Empiricus] |
1891 | How can we agree on the concept of God, unless we agree on his substance or form or place? [Sext.Empiricus] |
22739 | God must suffer to understand suffering [Sext.Empiricus] |
22738 | The Divine must lack the virtues of continence and fortitude, because they are not needed [Sext.Empiricus] |
22734 | God is defended by agreement, order, absurdity of denying God, and refutations [Sext.Empiricus] |
22736 | God's sensations imply change, and hence perishing, which is absurd, so there is no such God [Sext.Empiricus] |
22740 | God without virtue is absurd, but God's virtues will be better than God [Sext.Empiricus] |
1892 | The existence of God can't be self-evident or everyone would have agreed on it, so it needs demonstration [Sext.Empiricus] |
22735 | The original substance lacked motion or shape, and was given these by a cause [Sext.Empiricus] |
22732 | The perfections of God were extrapolations from mankind [Sext.Empiricus] |
22728 | Gods were invented as watchers of people's secret actions [Sext.Empiricus] |
22737 | An incorporeal God could do nothing, and a bodily god would perish, so there is no God [Sext.Empiricus] |
22731 | It is mad to think that what is useful to us, like lakes and rivers, are gods [Sext.Empiricus] |
1893 | If God foresaw evil he would presumably prevent it, and if he only foresees some things, why those things? [Sext.Empiricus] |