49 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) |
| 15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
| Full Idea: The common feature of every designating term is that designation may change from state to state - thus it can be formalized by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3) | |
| A reaction: Specifying the objects sounds OK, but specifying states sounds rather tough. |
| 15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
| Full Idea: To first order modal logic (with quantification over objects) we can add a second kind of quantification, over intensions. An intensional object, or individual concept, will be modelled by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.3) |
| 15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
| Full Idea: Awareness logic enriched Hintikka's epistemic models with an awareness function, mapping each state to the set of formulas we are aware of at that state. This reflects some bound on the resources we can bring to bear. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) | |
| A reaction: [He cites Fagin and Halpern 1988 for this] |
| 15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
| Full Idea: In justification logics, the logics of knowledge are extended by making reasons explicit. A logic of proof terms was created, with a semantics. In this, mathematical truths are known for explicit reasons, and these provide a measure of complexity. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) |
| 11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
| Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics. | |
| From: Melvin Fitting (Intensional Logic [2007], §1) |
| 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'. |
| 11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
| Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □. | |
| From: Melvin Fitting (Intensional Logic [2007], §3.3) | |
| A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic. |
| 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. |
| 17304 | As causation links across time, grounding links the world across levels [Schaffer,J] |
| Full Idea: Grounding is something like metaphysical causation. Just as causation links the world across time, grounding links the world across levels. Grounding connects the more fundamental to the less fundamental, and thereby backs a certain form of explanation. | |
| From: Jonathan Schaffer (Grounding, Transitivity and Contrastivity [2012], Intro) | |
| A reaction: Obviously you need 'levels' for this, which we should take to be structural levels. |
| 17306 | If ground is transitive and irreflexive, it has a strict partial ordering, giving structure [Schaffer,J] |
| Full Idea: By treating grounding as transitive (and irreflexive), one generates a strict partial ordering that induces metaphysical structure. | |
| From: Jonathan Schaffer (Grounding, Transitivity and Contrastivity [2012], Intro) | |
| A reaction: Schaffer's paper goes on to attach the claim that grounding is transitive, but I didn't find his examples very convincing. |
| 15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
| Full Idea: Definite descriptions pick out different objects in different possible worlds quite naturally. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.4) | |
| A reaction: A definite description can pick out the same object in another possible world, or a very similar one, or an object which has almost nothing in common with the others. |
| 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) |
| 17308 | Explaining 'Adam ate the apple' depends on emphasis, and thus implies a contrast [Schaffer,J] |
| Full Idea: Explaining why ADAM ate the apple is a different matter from explaining why he ATE the apple, and from why he ate THE APPLE. ...In my view the best explanations incorporate ....contrastive information. | |
| From: Jonathan Schaffer (Grounding, Transitivity and Contrastivity [2012], 4.3.1) | |
| A reaction: But why are the contrasts Eve, or throwing it, or a pear? It occurs to me that this is wrong! The contrast is with anything else which could have gone in subject, verb or object position. It is a matter of categories, not of contrasts. |
| 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) |
| 17305 | I take what is fundamental to be the whole spatiotemporal manifold and its fields [Schaffer,J] |
| Full Idea: I myself would prefer to speak of what is fundamental in terms of the whole spatiotemporal manifold and the fields that permeate it, with parts counting as derivative of the whole. | |
| From: Jonathan Schaffer (Grounding, Transitivity and Contrastivity [2012], 4.1.1) | |
| A reaction: Not quite the Parmenidean One, since it has parts, but a nice try at updating the great man. Note the reference to 'fields', suggesting that this view is grounded in the physics rather than metaphysics. How many fields has it got? |
| 17307 | Nowadays causation is usually understood in terms of equations and variable ranges [Schaffer,J] |
| Full Idea: The leading treatments of causation work within 'structural equation models', with events represented via variables each of which is allotted a range of permitted values, which constitute a 'contrast space'. | |
| From: Jonathan Schaffer (Grounding, Transitivity and Contrastivity [2012], 4.3.1) | |
| A reaction: Like Woodward's idea that causation is a graph, this seems to be a matter of plotting or formalising correlations between activities, which is a very Humean approach to causation. |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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. |
| 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) |