53 ideas
| 21360 | Unobservant thinkers tend to dogmatise using insufficient facts [Aristotle] |
| Full Idea: Those whom devotion to abstract discussions has rendered unobservant of the facts are too ready to dogmatise on the basis of a few observations. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 316a09) | |
| A reaction: I totally approve of the idea that a good philosopher should be 'observant'. Prestige in modern analytic philosophy comes from logical ability. There should be some rival criterion for attentiveness to facts, with equal prestige. |
| 9847 | A contextual definition permits the elimination of the expression by a substitution [Dummett] |
| Full Idea: The standard sense of a 'contextual definition' permits the eliminating of the defined expression, by transforming any sentence containing it into an equivalent one not containing it. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.11) | |
| A reaction: So the whole definition might be eliminated by a single word, which is not equivalent to the target word, which is embedded in the original expression. Clearly contextual definitions have some problems |
| 9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
| Full Idea: For sentential or first-order logic, the logical truths are represented by valid formulas; in higher-order logics, by sentences formulated in purely logical terms. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 3) |
| 9896 | A prime number is one which is measured by a unit alone [Dummett] |
| Full Idea: A prime number is one which is measured by a unit alone. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 11) | |
| A reaction: We might say that the only way of 'reaching' or 'constructing' a prime is by incrementing by one till you reach it. That seems a pretty good definition. 64, for example, can be reached by a large number of different routes. |
| 18255 | Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett] |
| Full Idea: It is essential to a quantitative domain of any kind that there should be an operation of adding its elements; that this is more fundamental thaat that they should be linearly ordered by magnitude is apparent from cyclic domains like that of angles. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit') |
| 9895 | A number is a multitude composed of units [Dummett] |
| Full Idea: A number is a multitude composed of units. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 2) | |
| A reaction: This is outdated by the assumption that 0 and 1 are also numbers, but if we say one is really just the 'unit' which is preliminary to numbers, and 0 is as bogus a number as i is, we might stick with the original Greek distinction. |
| 9852 | We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett] |
| Full Idea: A child understands 'there are just as many nuts as apples' as easily by pairing them off as by counting them. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: I find it very intriguing that you could know that two sets have the same number, without knowing any numbers. Is it like knowing two foreigners spoke the same words, without understanding them? Or is 'equinumerous' conceptually prior to 'number'? |
| 13212 | Infinity is only potential, never actual [Aristotle] |
| Full Idea: Nothing is actually infinite. A thing is infinite only potentially. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 318a21) | |
| A reaction: Aristotle is the famous spokesman for this view, though it reappeared somewhat in early twentieth century discussions (e.g. Hilbert). I sympathise with this unfashionable view. Multiple infinites are good fun, but no one knows what they really are. |
| 9829 | The identity of a number may be fixed by something outside structure - by counting [Dummett] |
| Full Idea: The identity of a mathematical object may sometimes be fixed by its relation to what lies outside the structure to which it belongs. It is more fundamental to '3' that if certain objects are counted, there are three of them. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5) | |
| A reaction: This strikes me as Dummett being pushed (by his dislike of the purely abstract picture given by structuralism) back to a rather empiricist and physical view of numbers, though he would totally deny that. |
| 9828 | Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett] |
| Full Idea: The number 0 is not differentiated from 1 by its position in a progression, otherwise there would be no difference between starting with 0 and starting with 1. That is enough to show that numbers are not identifiable just as positions in structures. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5) | |
| A reaction: This sounds conclusive, but doesn't feel right. If numbers are a structure, then where you 'start' seems unimportant. Where do you 'start' in St Paul's Cathedral? Starting sounds like a constructivist concept for number theory. |
| 9876 | Set theory isn't part of logic, and why reduce to something more complex? [Dummett] |
| Full Idea: The two frequent modern objects to logicism are that set theory is not part of logic, or that it is of no interest to 'reduce' a mathematical theory to another, more complex, one. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: Dummett says these are irrelevant (see context). The first one seems a good objection. The second one less so, because whether something is 'complex' is a quite different issue from whether it is ontologically more fundamental. |
| 13221 | Existence is either potential or actual [Aristotle] |
| Full Idea: Some things are-potentially while others are-actually. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 327b24) | |
| A reaction: I've read a lot of Aristotle, but am still not quite clear what this distinction means. I like the distinction between a thing's actual being and its 'modal profile', but the latter may extend well beyond what Aristotle means by potential being. |
| 16100 | True change is in a thing's logos or its matter, not in its qualities [Aristotle] |
| Full Idea: In that which underlies a change there is a factor corresponding to the definition [logon] and there is a material factor. When a change is in these constitutive factors there is coming to be or passing away, but in a thing's qualities it is alteration. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 317a24) | |
| A reaction: This seems to be a key summary of Aristotle's account of change, in the context of his hylomorphism (form-plus-matter). The logos is the account of the thing, which seems to be the definition, which seems to give the form (principle or structure). |
| 16101 | A change in qualities is mere alteration, not true change [Aristotle] |
| Full Idea: When a change occurs in the qualities [pathesi] and is accidental [sumbebekos], there is alteration (rather than true change). | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 317a27) | |
| A reaction: [tr. partly Gill] Aristotle doesn't seem to have a notion of 'properties' in quite our sense. 'Pathe' seems to mean experienced qualities, rather than genuine causal powers. Gill says 'pathe' are always accidental. |
| 12133 | If the substratum persists, it is 'alteration'; if it doesn't, it is 'coming-to-be' or 'passing-away' [Aristotle] |
| Full Idea: Since we must distinguish the substratum and the property whose nature is to be predicated of the substratum,..there is alteration when the substratum persists...but when nothing perceptible persists as a substratum, this is coming-to-be and passing-away. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 319b08-16) | |
| A reaction: As usual, Aristotle clarifies the basis of the problem, by distinguishing two different types of change. Notice the empirical character of his approach, resting on whether or not the substratum is 'perceptible'. |
| 13213 | All comings-to-be are passings-away, and vice versa [Aristotle] |
| Full Idea: Every coming-to-be is a passing away of something else and every passing-away some other thing's coming-to-be. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 319a07) | |
| A reaction: This seems to be the closest that Aristotle gets to sympathy with the Heraclitus view that all is flux. When a sparrow dies and disappears, I am not at all clear what comes to be, except some ex-sparrow material. |
| 9884 | The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett] |
| Full Idea: The distinction between concrete and abstract objects, or Frege's corresponding distinction between actual and non-actual objects, is not a sharp dichotomy, but resembles a scale upon which objects occupy a range of positions. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: This might seem right if you live (as Dummett chooses to) in the fog of language, but it surely can't be right if you think about reality. Is the Equator supposed to be near the middle of his scale? Either there is an equator, or there isn't. |
| 9869 | Realism is just the application of two-valued semantics to sentences [Dummett] |
| Full Idea: Fully fledged realism depends on - indeed, may be identified with - an undiluted application to sentences of the relevant kind of straightforwards two-valued semantics. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: This is the sort of account you get from a whole-heartedly linguistic philosopher. Personally I would say that Dummett has got it precisely the wrong way round: I adopt a two-valued semantics because my metaphysics is realist. |
| 9880 | Nominalism assumes unmediated mental contact with objects [Dummett] |
| Full Idea: The nominalist superstition is based ultimately on the myth of the unmediated presentation of genuine concrete objects to the mind. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: Personally I am inclined to favour nominalism and a representative theory of perception, which acknowledges some 'mediation', but of a non-linguistic form. Any good theory here had better include animals, which seem to form concepts. |
| 9885 | The existence of abstract objects is a pseudo-problem [Dummett] |
| Full Idea: The existence of abstract objects is a pseudo-problem. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: This remark follows after Idea 9884, which says the abstract/concrete distinction is a sliding scale. Personally I take the distinction to be fairly sharp, and it is therefore probably the single most important problem in the whole of human thought. |
| 9858 | Abstract objects nowadays are those which are objective but not actual [Dummett] |
| Full Idea: Objects which are objective but not actual are precisely what are now called abstract objects. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: Why can there not be subjective abstract objects? 'My favourites are x, y and z'. 'I'll decide later what my favourites are'. 'I only buy my favourites - nothing else'. |
| 9859 | It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett] |
| Full Idea: If someone argued that assuming the existence of the Equator explains nothing, and it has no causal powers, so everything would be the same if it didn't exist, so we needn't accept its existence, we should gape at the crudity of the misunderstanding. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: Not me. I would gape if someone argued that latitude 55° 14' (and an infinity of other lines) exists for the same reasons (whatever they may be) that the Equator exists. A mode of description can't create an object. |
| 9860 | 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett] |
| Full Idea: 'We've crossed the Equator' is judged true if we are nearer the other Pole, so it not for philosophers to deny that the Earth has an equator, and we see that the Equator is not a concept or relation or function, so it must be classified as an object. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: A lovely example of linguistic philosophy in action (and so much the worse for that, I would say). A useful label here, I suggest (unoriginally, I think), is that we should label such an item a 'semantic object', rather than a real object in our ontology. |
| 9872 | Abstract objects need the context principle, since they can't be encountered directly [Dummett] |
| Full Idea: To recognise that there is no objection in principle to abstract objects requires acknowledgement that some form of the context principle is correct, since abstract objects can neither be encountered nor presented. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16) | |
| A reaction: I take this to be an immensely important idea. I consider myself to be a philosopher of thought rather than a philosopher of language (Dummett's distinction, he being one of the latter). Thought connects to the world, but does it connect to abstracta? |
| 12134 | Matter is the substratum, which supports both coming-to-be and alteration [Aristotle] |
| Full Idea: Matter, in the proper sense of the term, is to be identified with the substratum which is receptive of coming-to-be and passing-away; but the substratum of the remaining kinds of change is also matter, because these substrata receive contraries. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 320a03) | |
| A reaction: This must be compared with his complex discussion of the role of matter in his Metaphysics, where he has introduced 'form' as the essence of things. I don't think the two texts are inconsistent, but it's tricky... See Idea 12133 on types of change. |
| 16572 | Does the pure 'this' come to be, or the 'this-such', or 'so-great', or 'somewhere'? [Aristotle] |
| Full Idea: The question might be raised whether substance (i.e. the 'this') comes-to-be at all. Is it not rather the 'such', the 'so-great', or the 'somewhere', which comes-to-be? | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 317b21) | |
| A reaction: This is interesting because it pulls the 'tode ti', the 'this-such', apart, showing that he does have a concept of a pure 'this', which seems to constitute the basis of being ('ousia'). We can say 'this thing', or 'one of these things'. |
| 16573 | Philosophers have worried about coming-to-be from nothing pre-existing [Aristotle] |
| Full Idea: In addition, coming-to-be may proceed out of nothing pre-existing - a thesis which, more than any other, preoccupied and alarmed the earliest philosophers. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 317b29) | |
| A reaction: This is the origin of the worry about 'ex nihilo' coming-to-be. Christians tended to say that only God could create in this way. |
| 13214 | The substratum changing to a contrary is the material cause of coming-to-be [Aristotle] |
| Full Idea: The substratum [hupokeimenon?] is the material cause of the continuous occurrence of coming-to-be, because it is such as to change from contrary to contrary. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 319a19) | |
| A reaction: Presumably Aristotle will also be seeking the 'formal' cause as well as the 'material' cause (not to mention the 'efficient' and 'final' causes). |
| 13215 | If a perceptible substratum persists, it is 'alteration'; coming-to-be is a complete change [Aristotle] |
| Full Idea: There is 'alteration' when the substratum is perceptible and persists, but changes in its own properties. ...But when nothing perceptible persists in its identity as a substratum, and the thing changes as a whole, it is coming-to-be of a substance. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 319b11-17) | |
| A reaction: [compressed] Note that a substratum can be perceptible - it isn't just some hidden mystical I-know-not-what (as Locke calls it). This whole text is a wonderful source on the subject of physical change. Note too the reliance on what is perceptible. |
| 9848 | Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett] |
| Full Idea: Husserl says the only ground for assuming the replaceability of one content by another is their identity; we are therefore not entitled to define their identity as consisting in their replaceability. | |
| From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by Michael Dummett - Frege philosophy of mathematics Ch.12 | |
| A reaction: This is a direct challenge to Frege. Tricky to arbitrate, as it is an issue of conceptual priority. My intuition is with Husserl, but maybe the two are just benignly inerdefinable. |
| 9842 | Frege introduced criteria for identity, but thought defining identity was circular [Dummett] |
| Full Idea: In his middle period Frege rated identity indefinable, on the ground that every definition must take the form of an identity-statement. Frege introduced the notion of criterion of identity, which has been widely used by analytical philosophers. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.10) | |
| A reaction: The objection that attempts to define identity would be circular sounds quite plausible. It sounds right to seek a criterion for type-identity (in shared properties or predicates), but token-identity looks too fundamental to give clear criteria. |
| 16717 | Which of the contrary features of a body are basic to it? [Aristotle] |
| Full Idea: What sorts of contrarities, and how many of them, are to be accounted 'originative sources' of body? | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 329b04) | |
| A reaction: Pasnau says these pages of Aristotle are the source of the doctrine of primary and secondary qualities. Essentially, hot, cold, wet and dry are his four primary qualities. |
| 17722 | The concept 'red' is tied to what actually individuates red things [Peacocke] |
| Full Idea: The possession conditions for the concept 'red' of the colour red are tied to those very conditions which individuate the colour red. | |
| From: Christopher Peacocke (Explaining the A Priori [2000], p.267), quoted by Carrie Jenkins - Grounding Concepts 2.5 | |
| A reaction: Jenkins reports that he therefore argues that we can learn something about the word 'red' from thinking about the concept 'red', which is his new theory of the a priori. I find 'possession conditions' and 'individuation' to be very woolly concepts. |
| 9849 | Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett] |
| Full Idea: One powerful argument for a thesis that one notion is conceptually prior to another is the possibility of defining the first without reference to the second. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: You'd better check whether you can't also define the second without reference to the first before you rank their priority. And maybe 'conceptual priority' is conceptually prior to 'definition' (i.e. definition needs a knowledge of priority). Help! |
| 9850 | An argument for conceptual priority is greater simplicity in explanation [Dummett] |
| Full Idea: An argument for conceptual priority is greater simplicity in explanation. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: One might still have to decide priority between two equally simple (or complex) concepts. I begin to wonder whether 'priority' has any other than an instrumental meaning (according to which direction you wish to travel - is London before Edinburgh?). |
| 9873 | Abstract terms are acceptable as long as we know how they function linguistically [Dummett] |
| Full Idea: To recognise abstract terms as perfectly proper items of a vocabulary depends upon allowing that all that is necessary for the lawful introduction of a range of expressions into the language is a coherent account of how they are to function in sentences. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16) | |
| A reaction: Why can't the 'coherent account' of the sentences include the fact that there must be something there for the terms to refer to? How else are we to eliminate nonsense words which obey good syntactical rules? Cf. Idea 9872. |
| 9993 | There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait] |
| Full Idea: Dummett uses the term 'logical abstraction' for the construction of the abstract objects as equivalence classes, but it is not clear why we should call this construction 'logical'. | |
| From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by William W. Tait - Frege versus Cantor and Dedekind n 14 | |
| A reaction: This is a good objection, and Tait offers a much better notion of 'logical abstraction' (as involving preconditions for successful inference), in Idea 9981. |
| 9857 | We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett] |
| Full Idea: We arrive at the concept of suicide by considering both occurrences in the sentence 'Cato killed Cato' of the proper name 'Cato' as simultaneously replaceable by another name, say 'Brutus', and so apprehending the pattern common to both sentences. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.14) | |
| A reaction: This is intended to illustrate Frege's 'logical abstraction' technique, as opposed to wicked psychological abstraction. The concept of suicide is the pattern 'x killed x'. This is a crucial example if we are to understand abstraction... |
| 9833 | To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett] |
| Full Idea: To get units by abstraction, units arrived at by abstraction from forks must the identical to that abstracted from spoons, with no trace of individuality. But if spoons can no longer be differentiated from forks, they can't differ from one another either. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8) | |
| A reaction: [compressed] Dummett makes the point better than Frege did. Can we 'think of a fork insofar as it is countable, ignoring its other features'? What are we left thinking of? Frege says it must still be the whole fork. 'Nice fork, apart from the colour'. |
| 9836 | Fregean semantics assumes a domain articulated into individual objects [Dummett] |
| Full Idea: A Fregean semantics assumes a domain already determinately articulated into individual objects. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8) | |
| A reaction: A more interesting criticism than most of Dummett's other challenges to the Frege/Davidson view. I am beginning to doubt whether the semantics and the ontology can ever be divorced from the psychology, of thought, interests, focus etc. |
| 13216 | Matter is the limit of points and lines, and must always have quality and form [Aristotle] |
| Full Idea: The matter is that of which points and lines are limits, and it is something that can never exist without quality and without form. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 320b16) | |
| A reaction: There seems to be a contradiction here somewhere. Matter has to be substantial enough to have a form, and yet seems to be the collective 'limit' of the points and lines. I wonder what 'limit' is translating? Sounds a bit too modern. |
| 17994 | The primary matter is the substratum for the contraries like hot and cold [Aristotle] |
| Full Idea: We must reckon as an 'orginal source' and as 'primary' the matter which underlies, though it is inseparable from the contrary qualities: for 'the hot' is not matter for 'the cold' nor 'cold' for 'hot', but the substratum is matter for them both. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 329a30) | |
| A reaction: A much discussed passage. |
| 13224 | There couldn't be just one element, which was both water and air at the same time [Aristotle] |
| Full Idea: No one supposes a single 'element' to persist, as the basis of all, in such a way that it is Water as well as Air (or any other element) at the same time. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 332a09) | |
| A reaction: Of course, we now think that oxygen is a key part of both water and of air, but Aristotle's basic argument still seems right. How could multiplicity be explained by a simply unity? The One is cool, but explains nothing. |
| 16594 | The Four Elements must change into one another, or else alteration is impossible [Aristotle] |
| Full Idea: These bodies (Fire, Water and the like) change into one another (and are not immutable as Empedocles and other thinkers assert, since 'alteration' would then have been impossible). | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 329b1) | |
| A reaction: This is why Aristotle proposes that matter [hule] underlies the four elements. Gill argues that by matter Aristotle means the elements. |
| 13223 | Fire is hot and dry; Air is hot and moist; Water is cold and moist; Earth is cold and dry [Aristotle] |
| Full Idea: The four couples of elementary qualities attach themselves to the apparently 'simple' bodies (Fire, Air, Earth, Water). Fire is hot and dry, whereas Air is hot and moist (being a sort of aqueous vapour); Water is cold and moist, and Earth is cold and dry. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 330b02) | |
| A reaction: This is the traditional framework accepted throughout the middle ages, and which had a huge influence on medicine. It all looks rather implausible now. Aristotle was a genius, but not critical enough about evidence. |
| 13220 | Bodies are endlessly divisible [Aristotle] |
| Full Idea: Bodies are divisible through and through. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 326b27) | |
| A reaction: This is Aristotle's flat rejection of atomism, arrived at after several sustained discussions, in this text and elsewhere. I don't think we are in a position to say that Aristotle is wrong. |
| 13210 | Wood is potentially divided through and through, so what is there in the wood besides the division? [Aristotle] |
| Full Idea: If having divided a piece of wood I put it together, it is equal to what it was and is one. This is so whatever the point at which I cut the wood. The wood is therefore divided potentially through and through. So what is in the wood besides the division? | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 316b11) | |
| A reaction: Part of a very nice discussion of the implications of the thought experiment of cutting something 'through and through'. It seems to me that the arguments are still relevant, in the age of quarks, electrons and strings. |
| 13211 | If a body is endlessly divided, is it reduced to nothing - then reassembled from nothing? [Aristotle] |
| Full Idea: Dividing a body at all points might actually occur, so the body will be both actually indivisible and potentially divided. Then nothing will remain and the body passes into what is incorporeal. So it might be reassembled out of points, or out of nothing. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 316b24) | |
| A reaction: [a bit compressed] This sounds like an argument in favour of atomism, but Aristotle was opposed to that view. He is aware of the contradictions that seem to emerge with infinite division. Graham Priest is interesting on the topic. |
| 18257 | Why should the limit of measurement be points, not intervals? [Dummett] |
| Full Idea: By what right do we assume that the limit of measurement is a point, and not an interval? | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit') |
| 13228 | There is no time without movement [Aristotle] |
| Full Idea: There can be no time without movement. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 337a24) | |
| A reaction: See Shoemaker's nice thought experiment as a challenge to this. Intuition seems to cry out that if movement stopped for a moment, that would not stop time, even though there was no way to measure its passing. |
| 16595 | If each thing can cease to be, why hasn't absolutely everything ceased to be long ago? [Aristotle] |
| Full Idea: If some one of the things 'which are' is constantly disappearing, why has not the whole of 'what is' been used up long ago and vanished away - assuming of course that the material of all the several comings-to-be was infinite? | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 318a17) | |
| A reaction: This thought is the basis of Aquinas's Third Way for proving the existence of God (as the force which prevents the vicissitudes of nature from sliding into oblivion). |
| 13227 | Being is better than not-being [Aristotle] |
| Full Idea: Being is better than not-being. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 336b29) | |
| A reaction: [see also Metaphysics 1017a07 ff, says the note] This peculiar assumption is at the heart of the ontological argument. Is the existence of the plague bacterium, or of Satan, or of mass-murderers, superior? |
| 13226 | An Order controls all things [Aristotle] |
| Full Idea: There is an Order controlling all things. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 336b13) | |
| A reaction: Presumably the translator provides the capital letter. How do we get from 'there is an order in all things' to 'there is an order which controls all things'? |