40 ideas
| 9065 | S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P) [Keefe/Smith] |
| Full Idea: S5 collapses iterated modalities (so ◊□P → □P, and ◊◊P → ◊P). | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §5) | |
| A reaction: It is obvious why this might be controversial, and there seems to be a general preference for S4. There may be confusions of epistemic and ontic (and even semantic?) possibilities within a single string of modalities. |
| 458 | Nothing could come out of nothing, and existence could never completely cease [Empedocles] |
| Full Idea: From what in no wise exists, it is impossible for anything to come into being; for Being to perish completely is incapable of fulfilment and unthinkable. | |
| From: Empedocles (fragments/reports [c.453 BCE], B012), quoted by Anon (Lyc) - On Melissus 975b1-4 |
| 5112 | Empedocles says things are at rest, unless love unites them, or hatred splits them [Empedocles, by Aristotle] |
| Full Idea: Empedocles claims that things are alternately changing and at rest - that they are changing whenever love is creating a unity out of plurality, or hatred is creating plurality out of unity, and they are at rest in the times in between. | |
| From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Physics 250b26 | |
| A reaction: I suppose one must say that this an example of Ruskin's 'pathetic fallacy' - reading human emotions into the cosmos. Being constructive little creatures, we think goodness leads to construction. I'm afraid Empedocles is just wrong. |
| 9064 | Objects such as a cloud or Mount Everest seem to have fuzzy boundaries in nature [Keefe/Smith] |
| Full Idea: A common intuition is that a vague object has indeterminate or fuzzy spatio-temporal boundaries, such as a cloud. Mount Everest can only have arbitrary boundaries placed around it, so in nature it must have fuzzy boundaries. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §5) | |
| A reaction: We would have to respond by questioning whether Everest counts precisely as an 'object'. At the microscopic or subatomic level it seems that virtually everything has fuzzy boundaries. Maybe boundaries don't really exist. |
| 9044 | If someone is borderline tall, no further information is likely to resolve the question [Keefe/Smith] |
| Full Idea: If Tek is borderline tall, the unclarity does not seem to be epistemic, because no amount of further information about his exact height (or the heights of others) could help us decide whether he is tall. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: One should add also that information about social conventions or conventions about the usage of the word 'tall' will not help either. It seems fairly obvious that God would not know whether Tek is tall, so the epistemic view is certainly counterintuitive. |
| 9048 | The simplest approach, that vagueness is just ignorance, retains classical logic and semantics [Keefe/Smith] |
| Full Idea: The simplest approach to vagueness is to retain classical logic and semantics. Borderline cases are either true or false, but we don't know which, and, despite appearances, vague predicates have well-defined extensions. Vagueness is ignorance. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: It seems to me that you must have a rather unhealthy attachment to the logicians' view of the world to take this line. It is the passion of the stamp collector, to want everything in sets, with neatly labelled properties, and inference lines marked out. |
| 9055 | The epistemic view of vagueness must explain why we don't know the predicate boundary [Keefe/Smith] |
| Full Idea: A key question for the epistemic view of vagueness is: why are we ignorant of the facts about where the boundaries of vague predicates lie? | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §2) | |
| A reaction: Presumably there is a range of answers, from laziness, to inability to afford the instruments, to limitations on human perception. At the limit, with physical objects, how do we tell whether it is us or the object which is afflicted with vagueness? |
| 9049 | Supervaluationism keeps true-or-false where precision can be produced, but not otherwise [Keefe/Smith] |
| Full Idea: The supervaluationist view of vagueness is that 'tall' comes out true or false on all the ways in which we can make 'tall' precise. There is a gap for borderline cases, but 'tall or not-tall' is still true wherever you draw a boundary. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: [Kit Fine is the spokesperson for this; it preserves classical logic, but not semantics] This doesn't seem to solve the problem of vagueness, but it does (sort of) save the principle of excluded middle. |
| 9056 | Vague statements lack truth value if attempts to make them precise fail [Keefe/Smith] |
| Full Idea: The supervaluationist view of vagueness proposes that a sentence is true iff it is true on all precisifications, false iff false on all precisifications, and neither true nor false otherwise. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3) | |
| A reaction: This seems to be just a footnote to the Russell/Unger view, that logic works if the proposition is precise, but otherwise it is either just the mess of ordinary life, or the predicate doesn't apply at all. |
| 9058 | Some of the principles of classical logic still fail with supervaluationism [Keefe/Smith] |
| Full Idea: Supervaluationist logic (now with a 'definite' operator D) fails to preserve certain classical principles about consequence and rules of inference. For example, reduction ad absurdum, contraposition, the deduction theorem and argument by cases. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3) | |
| A reaction: The aim of supervaluationism was to try to preserve some classical logic, especially the law of excluded middle, in the face of problems of vagueness. More drastic views, like treating vagueness as irrelevant to logic, or the epistemic view, do better. |
| 9059 | The semantics of supervaluation (e.g. disjunction and quantification) is not classical [Keefe/Smith] |
| Full Idea: The semantics of supervaluational views is not classical. A disjunction can be true without either of its disjuncts being true, and an existential quantification can be true without any of its substitution instances being true. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3) | |
| A reaction: There is a vaguely plausible story here (either red or orange, but not definitely one nor tother; there exists an x, but which x it is is undecidable), but I think I will vote for this all being very very wrong. |
| 9060 | Supervaluation misunderstands vagueness, treating it as a failure to make things precise [Keefe/Smith] |
| Full Idea: Why should we think vague language is explained away by how things would be if it were made precise? Supervaluationism misrepresents vague expressions, as vague only because we have not bothered to make them precise. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3) | |
| A reaction: The theory still leaves a gap where vagueness is ineradicable, so the charge doesn't seem quite fair. Logicians always yearn for precision, but common speech enjoys wallowing in a sea of easy-going vagueness, which works fine. |
| 9050 | A third truth-value at borderlines might be 'indeterminate', or a value somewhere between 0 and 1 [Keefe/Smith] |
| Full Idea: One approach to predications in borderline cases is to say that they have a third truth value - 'neutral', 'indeterminate' or 'indefinite', leading to a three-valued logic. Or a degree theory, such as fuzzy logic, with infinite values between 0 and 1. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: This looks more like a strategy for computer programmers than for metaphysicians, as it doesn't seem to solve the difficulty of things to which no one can quite assign any value at all. Sometimes you can't be sure if an entity is vague. |
| 9061 | People can't be placed in a precise order according to how 'nice' they are [Keefe/Smith] |
| Full Idea: There is no complete ordering of people by niceness, and two people could be both fairly nice, nice to intermediate degrees, while there is no fact of the matter about who is the nicer. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §4) | |
| A reaction: This is a difficulty if you are trying to decide vague predicates by awarding them degrees of truth. Attempts to place a precise value on 'nice' seem to miss the point, even more than utilitarian attempts to score happiness. |
| 9062 | If truth-values for vagueness range from 0 to 1, there must be someone who is 'completely tall' [Keefe/Smith] |
| Full Idea: Many-valued theories still seem to have a sharp boundary between sentences taking truth-value 1 and those taking value less than 1. So there is a last man in our sorites series who counts as 'completely tall'. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §4) | |
| A reaction: Lovely. Completely nice, totally red, perfectly childlike, an utter mountain, one hundred per cent amused. The enterprise seems to have the same implausibility found in Bayesian approaches to assessing evidence. |
| 9063 | How do we decide if my coat is red to degree 0.322 or 0.321? [Keefe/Smith] |
| Full Idea: What could determine which is the correct function, settling that my coat is red to degree 0.322 rather than 0.321? | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §4) | |
| A reaction: It is not just the uncertainty of placing the coat on the scale. The two ends of the scale have all the indeterminacy of being red rather than orange (or, indeed, pink). You are struggling to find a spot on the ruler, when the ruler is placed vaguely. |
| 13209 | There is no coming-to-be of anything, but only mixing and separating [Empedocles, by Aristotle] |
| Full Idea: Empedocles says there is no coming-to-be of anything, but only a mingling and a divorce of what has been mingled. | |
| From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314b08 | |
| A reaction: Aristotle comments that this prevents Empedocleans from distinguishing between superficial alteration and fundamental change of identity. Presumably, though, that wouldn't bother them. |
| 9045 | Vague predicates involve uncertain properties, uncertain objects, and paradoxes of gradual change [Keefe/Smith] |
| Full Idea: Three interrelated features of vague predicates such as 'tall', 'red', 'heap', 'child' are that they have borderline cases (application is uncertain), they lack well-defined extensions (objects are uncertain), and they're susceptible to sorites paradoxes. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: The issue will partly depend on what you think an object is: choose from bundles of properties, total denial, essential substance, or featureless substance with properties. The fungal infection of vagueness could creep in at any point, even the words. |
| 9047 | Many vague predicates are multi-dimensional; 'big' involves height and volume; heaps include arrangement [Keefe/Smith] |
| Full Idea: Many vague predicates are multi-dimensional. 'Big' of people depends on both height and volume; 'nice' does not even have clear dimensions; whether something is a 'heap' depends both the number of grains and their arrangement. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: Anyone who was hoping for a nice tidy theory for this problem should abandon hope at this point. Huge numbers of philosophical problems can be simplified by asking 'what exactly do you mean here?' (e.g. tall or bulky?). |
| 9053 | If there is a precise borderline area, that is not a case of vagueness [Keefe/Smith] |
| Full Idea: If a predicate G has a sharply-bounded set of cases falling in between the positive and negative, this shows that merely having borderline cases is not sufficient for vagueness. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: Thus you might have 'pass', 'fail' and 'take the test again'. But there seem to be two cases in the border area: will decide later, and decision seems impossible. And the sharp boundaries may be quite arbitrary. |
| 457 | Substance is not created or destroyed in mortals, but there is only mixing and exchange [Empedocles] |
| Full Idea: There is no creation of substance in any one of mortal existence, nor any end in execrable death, but only mixing and exchange of what has been mixed. | |
| From: Empedocles (fragments/reports [c.453 BCE], B008), quoted by Plutarch - 74: Reply to Colotes 1111f | |
| A reaction: also Aristotle 314b08 |
| 462 | One vision is produced by both eyes [Empedocles] |
| Full Idea: One vision is produced by both eyes | |
| From: Empedocles (fragments/reports [c.453 BCE], B088), quoted by Strabo - works 8.364.3 |
| 22765 | Wisdom and thought are shared by all things [Empedocles] |
| Full Idea: Wisdom and power of thought, know thou, are shared in by all things. | |
| From: Empedocles (fragments/reports [c.453 BCE]), quoted by Sextus Empiricus - Against the Logicians (two books) II.286 | |
| A reaction: Sextus quotes this, saying that it is 'still more paradoxical', and that it explicitly includes plants. This may mean that Empedocles was not including inanimate matter. |
| 1524 | For Empedocles thinking is almost identical to perception [Empedocles, by Theophrastus] |
| Full Idea: Empedocles assumes that thinking is either identical to or very similar to sense-perception. | |
| From: report of Empedocles (fragments/reports [c.453 BCE], A86) by Theophrastus - On the Senses 9 | |
| A reaction: Not to be sniffed at. We can, of course, control our thinking (though we can't control the controller) and we contemplate abstractions, but that might be seen as a sort of perception. Vision is not as visual as we think. |
| 552 | Empedocles said good and evil were the basic principles [Empedocles, by Aristotle] |
| Full Idea: Empedocles was the first to give evil and good as principles. | |
| From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Metaphysics 985a | |
| A reaction: Once you start to think that good and evil will only matter if they have causal powers, it is an easy step to the idea of a benevolent god, and a satanic anti-god. Otherwise the 'principles' could be ignored. |
| 589 | 'Nature' is just a word invented by people [Empedocles] |
| Full Idea: Nature is but a word of human framing. | |
| From: Empedocles (fragments/reports [c.453 BCE], B008), quoted by Aristotle - Metaphysics 1015a |
| 21823 | The principle of 'Friendship' in Empedocles is the One, and is bodiless [Empedocles, by Plotinus] |
| Full Idea: In Empedocles we have a dividing principle, 'Strife', set against 'Friendship' - which is the One and is to him bodiless, while the elements represent matter. | |
| From: report of Empedocles (fragments/reports [c.453 BCE]) by Plotinus - The Enneads 5.1.09 | |
| A reaction: The first time I've seen the principle of Love in Empedocles identified with the One of Parmenides. Plotinus is a trustworthy reporter, I think, because he was well read, and had access to lost texts. |
| 2680 | Empedocles said that there are four material elements, and two further creative elements [Empedocles, by Aristotle] |
| Full Idea: Empedocles holds that the corporeal elements are four, but that all the elements, including those which create motion, are six in number. | |
| From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314a16 |
| 6002 | Empedocles says bone is water, fire and earth in ratio 2:4:2 [Empedocles, by Inwood] |
| Full Idea: Empedocles used numerical ratios to explain different kinds of matter; for example, bone is two parts water, four parts fire, two parts earth; and blood is an equal blend of all four elements. | |
| From: report of Empedocles (fragments/reports [c.453 BCE]) by Brad Inwood - Empedocles | |
| A reaction: Why isn't the ration 1:2:1? This presumably shows the influence of Pythagoras (who had also been based in Italy, like Empedocles), as well as that of the earlier naturalistic philosophers. It was a very good theory, though wrong. |
| 13207 | Fire, Water, Air and Earth are elements, being simple as well as homoeomerous [Empedocles, by Aristotle] |
| Full Idea: Empedocles says that Fire, Water, Air and Earth are four elements, and are thus 'simple' rather than flesh, bone and bodies which, like these, are 'homoeomeries'. | |
| From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314a26 | |
| A reaction: The translation is not quite clear. I take it that flesh and bone may look simple, because they are homoeomerous, but they are not really - but what is his evidence for that? Compare Idea 13208. |
| 459 | All change is unity through love or division through hate [Empedocles] |
| Full Idea: These elements never cease their continuous exchange, sometimes uniting under the influence of Love, so that all become One, at other times again moving apart through the hostile force of Hate. | |
| From: Empedocles (fragments/reports [c.453 BCE], B017), quoted by Simplicius - On Aristotle's 'Physics' 158.1- |
| 13218 | The elements combine in coming-to-be, but how do the elements themselves come-to-be? [Aristotle on Empedocles] |
| Full Idea: Empedocles says it is evident that all the other bodies down to the 'elements' have their coming-to-be and their passing-away: but it is not clear how the 'elements' themselves, severally in their aggregated masses, come-to-be and pass-away. | |
| From: comment on Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 325b20 | |
| A reaction: Presumably the elements are like axioms - and are just given. How do electrons and quarks come-to-be? |
| 13225 | Love and Strife only explain movement if their effects are distinctive [Aristotle on Empedocles] |
| Full Idea: It is not an adequate explanation to say that 'Love and Strife set things moving', unless the very nature of Love is a movement of this kind and the very nature of Strife a movement of that kind. | |
| From: comment on Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 333b23 | |
| A reaction: I take this to be of interest for showing Aristotle's quest for explanations, and his unwillingness to be fobbed off with anything superficial. I take a task of philosophy to be to push explanations further than others wish to go. |
| 460 | If the one Being ever diminishes it would no longer exist, and what could ever increase it? [Empedocles] |
| Full Idea: Besides these elements, nothing else comes into being, nor does anything cease. For if they had been perishing continuously, they would Be no more; and what could increase the Whole? And whence could it have come? | |
| From: Empedocles (fragments/reports [c.453 BCE], B017), quoted by Simplicius - On Aristotle's 'Physics' 158.1- |
| 651 | Eurytus showed that numbers underlie things by making pictures of creatures out of pebbles [Eurytus, by Aristotle] |
| Full Idea: Eurytus assigned numbers to things by taking some pebbles and using them to create likeness of the shapes of living things, such as a man or a horse. | |
| From: report of Eurytus (fragments/reports [c.400 BCE]) by Aristotle - Metaphysics 1092b | |
| A reaction: Pythagorean. Digitising reality. |
| 5090 | Maybe bodies are designed by accident, and the creatures that don't work are destroyed [Empedocles, by Aristotle] |
| Full Idea: Is it just an accident that teeth and other parts of the body seem to have some purpose, and creatures survive because they happen to be put together in a useful way? Everything else has been destroyed, as Empedocles says of his 'cow with human head'. | |
| From: report of Empedocles (fragments/reports [c.453 BCE], 61) by Aristotle - Physics 198b29 | |
| A reaction: Good grief! Has no one ever noticed that Empedocles proposed the theory of evolution? It isn't quite natural selection, because we aren't told what does the 'destroying', but it is a little flash of genius that was quietly forgotten. |
| 466 | God is pure mind permeating the universe [Empedocles] |
| Full Idea: God is mind, holy and ineffable, and only mind, which darts through the whole cosmos with its swift thought. | |
| From: Empedocles (fragments/reports [c.453 BCE], B134), quoted by Ammonius - On 'De Interpretatione' 4.5.249.6 |
| 461 | God is a pure, solitary, and eternal sphere [Empedocles] |
| Full Idea: God is equal in all directions to himself and altogether eternal, a rounded Sphere enjoying a circular solitude. | |
| From: Empedocles (fragments/reports [c.453 BCE], B028), quoted by John Stobaeus - Anthology 1.15.2 |
| 1719 | In Empedocles' theory God is ignorant because, unlike humans, he doesn't know one of the elements (strife) [Aristotle on Empedocles] |
| Full Idea: It is a consequence of Empedocles' view that God is the most unintelligent thing, for he alone is ignorant of one of the elements, namely strife, whereas mortal creatures are familiar with them all. | |
| From: comment on Empedocles (fragments/reports [c.453 BCE]) by Aristotle - De Anima 410b08 |
| 1522 | It is wretched not to want to think clearly about the gods [Empedocles] |
| Full Idea: Wretched is he who cares not for clear thinking about the gods. | |
| From: Empedocles (fragments/reports [c.453 BCE], B132), quoted by Clement - Miscellanies 5.140.5.1 |