61 ideas
| 1887 | You cannot divide anything into many parts, because after the first division you are no longer dividing the original [Sext.Empiricus] |
| Full Idea: You cannot divide anything (such as the decad) into many parts, because as soon as you separate the first part, you are no longer dividing the original. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], II.215) |
| 1885 | Proof moves from agreed premises to a non-evident inference [Sext.Empiricus] |
| Full Idea: Dogmatists define proof as "an argument which, by means of agreed premises, reveals by way of deduction a nonevident inference". | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], II.135) |
| 13252 | Some truths have true negations [Beall/Restall] |
| Full Idea: Dialetheism is the view that some truths have true negations. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 7.4) | |
| A reaction: The important thing to remember is that they are truths. Thus 'Are you feeling happy?' might be answered 'Yes and no'. |
| 13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
| Full Idea: The truthmaker thesis is that an object is a truthmaker for a sentence if and only if its existence entails the sentence. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.3) | |
| A reaction: The use of the word 'object' here is even odder than usual, and invites many questions. And the 'only if' seems peculiar, since all sorts of things can make a sentence true. 'There is someone in the house' for example. |
| 13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
| Full Idea: The inference of 'distribution' (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically. It is straightforward to construct a 'stage' at which the LHS is true but the RHS is not. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 6.1.2) | |
| A reaction: This seems to parallel the iterative notion in set theory, that you must construct your hierarchy. All part of the general 'constructivist' approach to things. Is some kind of mad platonism the only alternative? |
| 13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
| Full Idea: Relevant logic endorses excluded middle, ..but says instances of the law may fail. Bv¬B is true in every situation that settles the matter of B. It is necessary that there is some such situation. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: See next idea for the unusual view of necessity on which this rests. It seems easier to assert something about all situations than just about 'some' situation. |
| 13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
| Full Idea: The argument from P to A is 'relevantly' valid if and only if, for every situation in which each premise in P is true, so is A. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: I like the idea that proper inference should have an element of relevance to it. A falsehood may allow all sorts of things, without actually implying them. 'Situations' sound promising here. |
| 13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
| Full Idea: We have not abandoned classical logic in our acceptance of relevant logic. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.4) | |
| A reaction: It appears that classical logic is straightforwardly accepted, but there is a difference of opinion over when it is applicable. |
| 13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
| Full Idea: Relevant consequence says the conclusion of a relevantly invalid argument is not 'carried in' the premises - it does not follow from the premises. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.3.3) | |
| A reaction: I find this appealing. It need not invalidate classical logic. It is just a tougher criterion which is introduced when you want to do 'proper' reasoning, instead of just playing games with formal systems. |
| 13254 | A doesn't imply A - that would be circular [Beall/Restall] |
| Full Idea: We could reject the inference from A to itself (on grounds of circularity). | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: [Martin-Meyer System] 'It's raining today'. 'Are you implying that it is raining today?' 'No, I'm SAYING it's raining today'. Logicians don't seem to understand the word 'implication'. Logic should capture how we reason. Nice proposal. |
| 13255 | Relevant logic may reject transitivity [Beall/Restall] |
| Full Idea: Some relevant logics reject transitivity, but we defend the classical view. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: [they cite Neil Tennant for this view] To reject transitivity (A?B ? B?C ? A?C) certainly seems a long way from classical logic. But in everyday inference Tennant's idea seems good. The first premise may be irrelevant to the final conclusion. |
| 13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
| Full Idea: A logic is 'free' to the degree it refrains from existential import of its singular and general terms. Classical logic must have non-empty domain, and each name must denote in the domain. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 7.1) | |
| A reaction: My intuition is that logic should have no ontology at all, so I like the sound of 'free' logic. We can't say 'Pegasus does not exist', and then reason about Pegasus just like any other horse. |
| 13235 | Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall] |
| Full Idea: Nowadays we think of the consequence relation itself as the primary subject of logic, and view logical truths as degenerate instances of this relation. Logical truths follow from any set of assumptions, or from no assumptions at all. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: This seems exactly right; the alternative is the study of necessities, but that may not involve logic. |
| 13238 | Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall] |
| Full Idea: According to the Peripatetics (Aristotelians), only syllogistic laws stated in variables belong to logic, and not their applications to concrete terms. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.5) | |
| A reaction: [from Lukasiewicz] Seems wrong. I take it there are logical relations between concrete things, and the variables are merely used to describe these relations. Variables lack the internal powers to drive logical necessities. Variables lack essence! |
| 13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |
| Full Idea: Through much of the 20th century the conception of logic was inherited from Frege and Russell, as knowledge of a body of logical truths, as arithmetic or geometry was a knowledge of truths. This is odd, and a historical anomaly. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: Interesting. I have always taken this idea to be false. I presume logic has minimal subject matter and truths, and preferably none at all. |
| 13232 | Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall] |
| Full Idea: Logic does not study formal languages for their own sake, which is formal grammar. Logic evaluates arguments, and primarily considers formal languages as interpreted. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.1) | |
| A reaction: Hodges seems to think logic just studies formal languages. The current idea strikes me as a much more sensible view. |
| 13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
| Full Idea: The model theory of classical predicate logic is mathematics if anything is. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 4.2.1) | |
| A reaction: This is an interesting contrast to the claim of logicism, that mathematics reduces to logic. This idea explains why students of logic are surprised to find themselves involved in mathematics. |
| 13253 | There are several different consequence relations [Beall/Restall] |
| Full Idea: We are pluralists about logical consequence because we take there to be a number of different consequence relations, each reflecting different precisifications of the pre-theoretic notion of deductive logical consequence. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: I don't see how you avoid the slippery slope that leads to daft logical rules like Prior's 'tonk' (from which you can infer anything you like). I say that nature imposes logical conquence on us - but don't ask me to prove it. |
| 13240 | A sentence follows from others if they always model it [Beall/Restall] |
| Full Idea: The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 3.2) | |
| A reaction: This why the symbol |= is often referred to as 'models'. |
| 12196 | A valid hypothetical syllogism is 'that which does not begin with a truth and end with a falsehood' [Sext.Empiricus] |
| Full Idea: Philo (of Megara) says that a valid hypothetical syllogism is 'that which does not begin with a truth and end with a falsehood,' as for instance the syllogism 'If it is day, I converse,' when in fact it is day and I am conversing. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], II.110) | |
| A reaction: Russell endorses this, and Rumfitt quotes it as the classic case of denying that there is any modal aspect (such as 'logical necessity') involved in logical consequence. He labels it 'material or Philonian consequence'. |
| 13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
| Full Idea: If mathematical truth reduces to logical truth then it is important what counts as logically true, …but if logicism is not a going concern, then the body of purely logical truths will be less interesting. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: Logicism would only be one motivation for pursuing logical truths. Maybe my new 'Necessitism' will derive the Peano Axioms from broad necessary truths, rather than from logic. |
| 13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
| Full Idea: The Paradox of the Preface is an apology, that you are committed to each proposition in the book, but admit that collectively they probably contain a mistake. There is a contradiction, of affirming and denying the conjunction of propositions. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.4) | |
| A reaction: This seems similar to the Lottery Paradox - its inverse perhaps. Affirm all and then deny one, or deny all and then affirm one? |
| 1902 | Since Socrates either died when he was alive (a contradiction) or died when he was dead (meaningless), he didn't die [Sext.Empiricus] |
| Full Idea: If Socrates died, he died either when he lived or when he died; so he was either dead when he was alive, or he was twice dead when he was dead. So he didn't die. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.111) | |
| A reaction: One of my favourites. Of all the mysteries facing us, the one that boggles me most is how anything can happen in the 'present' moment, if the present is just the overlap point between past and future. |
| 13244 | Relevant necessity is always true for some situation (not all situations) [Beall/Restall] |
| Full Idea: In relevant logic, the necessary truths are not those which are true in every situation; rather, they are those for which it is necessary that there is a situation making them true. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: This seems to rest on the truthmaker view of such things, which I find quite attractive (despite Merricks's assault). Always ask what is making some truth necessary. This leads you to essences. |
| 1889 | If an argument has an absurd conclusion, we should not assent to the absurdity, but avoid the absurd argument [Sext.Empiricus] |
| Full Idea: If an argument leads to confessedly absurd conclusions, we should not assent to the absurdity just because of the argument, but avoid the argument because of the absurdity. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], II.252) | |
| A reaction: cf. G.E.Moore. Denying that you have a hand seems to be an absurdity, but I'm not sure if I can give a criterion for absurdity in such a case. One person's modus ponens is another person's modus tollens. |
| 1871 | Whether honey is essentially sweet may be doubted, as it is a matter of judgement rather than appearance [Sext.Empiricus] |
| Full Idea: Honey appears to sceptics to be sweet, but whether it is also sweet in its essence is for us a matter of doubt, since this is not an appearance but a judgement. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], I.20) |
| 1883 | How can the intellect know if sensation is reliable if it doesn't directly see external objects? [Sext.Empiricus] |
| Full Idea: Just as you can't know if a portrait of Socrates is good without seeing the man, so when the intellect gazes on sensations but not the external objects it cannot know whether they are similar. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], II.75) |
| 1890 | We distinguish ambiguities by seeing what is useful [Sext.Empiricus] |
| Full Idea: It is the experience of what is useful in each affair that brings about the distinguishing of ambiguities. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], II.258) |
| 1870 | The basis of scepticism is the claim that every proposition has an equal opposing proposition [Sext.Empiricus] |
| Full Idea: The main basic principle of the sceptic system is that of opposing to every proposition an equal proposition. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], I.12) |
| 1882 | The necks of doves appear different in colour depending on the angle of viewing [Sext.Empiricus] |
| Full Idea: The necks of doves appear different in hue according to the differences in the angle of inclination. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], I.120) |
| 1881 | The same oar seems bent in water and straight when out of it [Sext.Empiricus] |
| Full Idea: The same oar seems bent when in the water but straight when out of the water. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], I.119) |
| 1872 | The same tower appears round from a distance, but square close at hand [Sext.Empiricus] |
| Full Idea: The same tower appears round from a distance, but square close at hand. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], I.32) |
| 1873 | If we press the side of an eyeball, objects appear a different shape [Sext.Empiricus] |
| Full Idea: When we press the eyeball at one side the forms, figures and sizes of the objects appear oblong and narrow. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], I.47) |
| 1874 | How can we judge between our impressions and those of other animals, when we ourselves are involved? [Sext.Empiricus] |
| Full Idea: We cannot judge between our own impressions and those of other animals, because we ourselves are involved in the dispute. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], I.59) |
| 1878 | Water that seems lukewarm can seem very hot on inflamed skin [Sext.Empiricus] |
| Full Idea: The same water which seems very hot when poured on inflamed spots seems lukewarm to us. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], I.101) |
| 1880 | Some actions seem shameful when sober but not when drunk [Sext.Empiricus] |
| Full Idea: Actions which seem shameful to us when sober do not seem shameful when drunk. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], I.109) |
| 1877 | If we had no hearing or sight, we would assume no sound or sight exists, so there may be unsensed qualities [Sext.Empiricus] |
| Full Idea: A man with touch, taste and smell, but no hearing or sight, will assume nothing audible or visible exists, so maybe an apple has qualities which we have no senses to perceive. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], I.96) |
| 1879 | Sickness is perfectly natural to the sick, so their natural perceptions should carry some weight [Sext.Empiricus] |
| Full Idea: Health is natural for the healthy but unnatural for the sick, and sickness is unnatural for the healthy but natural for the sick, so we must give credence to the natural perceptions of the sick. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], I.103) |
| 1876 | If we enjoy different things, presumably we receive different impressions [Sext.Empiricus] |
| Full Idea: The enjoyment of different things is an indication that we get varying impressions from the underlying objects. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], I.80) |
| 1911 | Even if all known nations agree on a practice, there may be unknown nations which disagree [Sext.Empiricus] |
| Full Idea: Even among practices on which all known cultures are agreed, disagreement about them may possibly exist amongst some of the nations which are unknown to us. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.234) |
| 1910 | With us it is shameful for men to wear earrings, but among Syrians it is considered noble [Sext.Empiricus] |
| Full Idea: It is a shameful thing with us for men to wear earrings, but among some of the barbarians, such as the Syrians, it is a token of nobility. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.203) |
| 1886 | If you don't view every particular, you may miss the one which disproves your universal induction [Sext.Empiricus] |
| Full Idea: Induction cannot establish the universal by means of the particular, since limited particulars may omit crucial examples which disprove the universal, and infinite particulars are impossible to know. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], II.204) |
| 13239 | Judgement is always predicating a property of a subject [Beall/Restall] |
| Full Idea: All judgement, for Kant, is essentially the predication of some property to some subject. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.5) | |
| A reaction: Presumably the denial of a predicate could be a judgement, or the affirmation of ambiguous predicates? |
| 1884 | If we utter three steps of a logical argument, they never exist together [Sext.Empiricus] |
| Full Idea: If we say "If day exists, lights exists", and then "day exists", and then "light exists", then parts of the judgement never exist together, and so the whole judgement will have no real existence. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], II.109) |
| 13248 | We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall] |
| Full Idea: Situation semantics is a variation of the truth-conditional approach, taking the salient unit of analysis not to be the possible world, or some complete consistent index, but rather the more modest 'situation'. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.4) | |
| A reaction: When I read Davidson (and implicitly Frege) this is what I always assumed was meant. The idea that worlds are meant has crept in to give truth conditions for modal statements. Hence situation semantics must cover modality. |
| 13233 | Propositions commit to content, and not to any way of spelling it out [Beall/Restall] |
| Full Idea: Our talk of propositions expresses commitment to the general notion of content, without a commitment to any particular way of spelling this out. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.1) | |
| A reaction: As a fan of propositions I like this. It leaves open the question of whether the content belongs to the mind or the language. Animals entertain propositions, say I. |
| 22187 | Genetic behaviours that have enhanced human success include aggression, rape and xenophobia [Wilson,EO, by Okasha] |
| Full Idea: Wilson claimed that many human behaviours, including aggression, rape, and xenophobia, had a genetic basis, and were adaptations favoured by natural selection because they enhanced the reproductive success of our ancestors. | |
| From: report of Edmund O. Wilson (Sociobiology [1975]) by Samir Okasha - Philosophy of Science: Very Short Intro (2nd ed) 7 | |
| A reaction: This led to the Sociobiology Wars, when E.O. Wilson was attacked by Richard Lewontin and Stephen Jay Gould. |
| 1894 | Some say that causes are physical, some say not [Sext.Empiricus] |
| Full Idea: Some affirm cause to be corporeal, some incorporeal. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.14) |
| 1897 | Knowing an effect results from a cause means knowing that the cause belongs with the effect, which is circular [Sext.Empiricus] |
| Full Idea: To know an effect belongs to a cause, we must also know that that cause belongs to that effect, and this is circular. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.21) |
| 1898 | Cause can't exist before effect, or exist at the same time, so it doesn't exist [Sext.Empiricus] |
| Full Idea: If cause neither subsists before its effect, nor subsists along with it, nor does the effect precede the cause, it would seem that it has no substantial existence at all. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.27) |
| 1896 | If there were no causes then everything would have been randomly produced by everything [Sext.Empiricus] |
| Full Idea: If causes were non-existent everything would have been produced by everything, and at random. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.18) |
| 1895 | Causes are either equal to the effect, or they link equally with other causes, or they contribute slightly [Sext.Empiricus] |
| Full Idea: The majority say causes are immediate (when they are directly proportional to effects), or associate (making an equal contribution to effects), or cooperant (making a slight contribution). | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.15) |
| 1900 | If time and place are infinitely divided, it becomes impossible for movement ever to begin [Sext.Empiricus] |
| Full Idea: If bodies, and the places and times when they are said to move, are divided into infinity, motion will not occur, it being impossible to find anything which will initiate the first movement. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.76) |
| 1899 | Does the original self-mover push itself from behind, or pull itself from in front? [Sext.Empiricus] |
| Full Idea: Self-movement must move in some particular direction, but if it pushes it will be behind itself, and if it pulls it will be in front of itself. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.68) | |
| A reaction: This is the same as Aquinas's First Way of proving God's existence. |
| 1901 | If all atoms, times and places are the same, everything should move with equal velocity [Sext.Empiricus] |
| Full Idea: If objects are reducible to atoms, and each thing passes in an atomic time with its own first atom into an atomic point of space, then all moving things are of equal velocity. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.77) |
| 1903 | If motion and rest are abolished, so is time [Sext.Empiricus] |
| Full Idea: Since time does not seem to subsist without motion or even rest, if motion is abolished, and likewise rest, time is abolished. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.141) |
| 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] |
| Full Idea: There can't be a time when there was no time, so time is not limited; but unlimited time means past and present are non-existent (so time is limited to the present), or they exist (which means they are present). Time does not exist. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.142) |
| 1905 | How can time be divisible if we can't compare one length of time with another? [Sext.Empiricus] |
| Full Idea: Time is clearly divisible (into past, present and future), but it can't be, because a divisible thing is measured by some part of itself (divisions of length), but the two parts must coincide to make the measurement (e.g. present must coincide with past). | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.143) |
| 1891 | How can we agree on the concept of God, unless we agree on his substance or form or place? [Sext.Empiricus] |
| Full Idea: How shall we be able to reach a conception of God when we have no agreement about his substance or his form or his place of abode? | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.3) |
| 1892 | The existence of God can't be self-evident or everyone would have agreed on it, so it needs demonstration [Sext.Empiricus] |
| Full Idea: The existence of God is not pre-evident, for if it was the dogmatists would have agreed about it, whereas their disagreements show it is non-evident, and in need of demonstration. | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.6) |
| 1893 | If God foresaw evil he would presumably prevent it, and if he only foresees some things, why those things? [Sext.Empiricus] |
| Full Idea: If God had forethought for all, there would be no evil in the world, yet they say the world is full of evil. And if he forethinks some things, why those and not others? | |
| From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], III.9) |