70 ideas
| 1695 | Without extensive examination firm statements are hard, but studying the difficulties is profitable [Aristotle] |
| Full Idea: It is hard to make firm statements on these questions without having examined them many times, but to have gone through the various difficulties is not unprofitable. | |
| From: Aristotle (Categories [c.331 BCE], 08b23) | |
| A reaction: Suggesting that philosophy is more like drawing the map than completing the journey. |
| 1697 | The contrary of good is bad, but the contrary of bad is either good or another evil [Aristotle] |
| Full Idea: What is contrary to a good thing is necessarily bad, as we see with health and sickness. But the contrary of bad is sometimes good, sometimes not, as we see with excess, opposed by both deficiency and moderation. | |
| From: Aristotle (Categories [c.331 BCE], 13b36) |
| 1698 | Both sides of contraries need not exist (as health without sickness, white without black) [Aristotle] |
| Full Idea: With contraries it is not necessary if one exists for the other to exist too, for if everyone were well health would exist but not sickness, and if everything were white whiteness would exist but not black. | |
| From: Aristotle (Categories [c.331 BCE], 14a06) |
| 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 |
| 11034 | The differentiae of genera which are different are themselves different in kind [Aristotle] |
| Full Idea: The differentiae of genera which are different and not subordinate one to the other are themselves different in kind. | |
| From: Aristotle (Categories [c.331 BCE], 01b16) | |
| A reaction: This seems to be indicating a category mistake, as he warns us not to attribute the wrong kind of differentiae to something we are picking out. |
| 18367 | A true existence statement has its truth caused by the existence of the thing [Aristotle] |
| Full Idea: Whereas the true statement [that there is a man] is in no way the cause of the actual thing's existence, the actual thing does seem in some way the cause of the statement's being true. | |
| From: Aristotle (Categories [c.331 BCE], 14b18) | |
| A reaction: Armstrong offers this as the earliest statement of the truthmaker principle. Notice the cautious qualification 'seem in some way'. The truthmaker dependence seems even clearer in falsemaking, where the death of the man falsifies the statement. |
| 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) |
| 11033 | Predications of predicates are predications of their subjects [Aristotle] |
| Full Idea: Whenever one thing is predicated of another as of a subject, all things said of what is predicated will be said of the subject also. | |
| From: Aristotle (Categories [c.331 BCE], 01b10) |
| 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. |
| 11044 | One is prior to two, because its existence is implied by two [Aristotle] |
| Full Idea: One is prior to two because if there are two it follows at once that there is one, whereas if there is one there is not necessarily two. | |
| From: Aristotle (Categories [c.331 BCE], 14a29) | |
| A reaction: The axiomatic introduction of a 'successor' to a number does not seem to introduce this notion of priority, based on inclusiveness. Introducing order by '>' also does not seem to indicate any logical priority. |
| 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') |
| 11042 | Parts of a line join at a point, so it is continuous [Aristotle] |
| Full Idea: A line is a continuous quantity. For it is possible to find a common boundary at which its parts join together, a point. | |
| From: Aristotle (Categories [c.331 BCE], 04b33) | |
| A reaction: This appears to be the essential concept of a Dedekind cut. It seems to be an open question whether a cut defines a unique number, but a boundary seems to be intrinsically unique. Aristotle wins again. |
| 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'? |
| 11041 | Some quantities are discrete, like number, and others continuous, like lines, time and space [Aristotle] |
| Full Idea: Of quantities, some are discrete, others continuous. ...Discrete are number and language; continuous are lines, surfaces, bodies, and also, besides these, time and place. | |
| From: Aristotle (Categories [c.331 BCE], 04b20) | |
| A reaction: This distinction seems to me to be extremely illuminating, when comparing natural numbers with real numbers, and it is the foundation of the Greek view of mathematics. |
| 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. |
| 11286 | Primary being must be more than mere indeterminate ultimate subject of predication [Politis on Aristotle] |
| Full Idea: He criticises his 'Categories' view, because if primary being is simply the ultimate subject of predication the primary being is, in virtue of itself, something indeterminate; it would be a necessary but not a sufficient condition for primary being. | |
| From: comment on Aristotle (Categories [c.331 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 7.5 | |
| A reaction: Thus, Politis argues, primary being is essence in the later work. The words 'substance' and 'ousia' cause confusion here, and must be watched closely. Wedin argues that Aristotle merely develops his 'Categories' view, but most disagree. |
| 1700 | There are six kinds of change: generation, destruction, increase, diminution, alteration, change of place [Aristotle] |
| Full Idea: There are six kinds of change: generation, destruction, increase, diminution, alteration, change of place. A change in our affections would be an example of alteration. | |
| From: Aristotle (Categories [c.331 BCE], 15a13) |
| 1699 | A thing is prior to another if it implies its existence [Aristotle] |
| Full Idea: That from which the implication of existence does not hold reciprocally is thought to be prior. | |
| From: Aristotle (Categories [c.331 BCE], 14a32) | |
| A reaction: shadows and objects |
| 18366 | Of interdependent things, the prior one causes the other's existence [Aristotle] |
| Full Idea: For of things which reciprocate as to implication of existence, that which is in some way the cause of the other's existence might reasonably by called prior by nature. | |
| From: Aristotle (Categories [c.331 BCE], 14b12) | |
| A reaction: Not so clear when you seek examples. The bus is prior to its redness, but you can't have a colourless bus, so being coloured is prior to being a bus. Aristotle's example is a man being prior to the truths about him. |
| 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. |
| 3311 | The categories (substance, quality, quantity, relation, action, passion, place, time) peter out inconsequentially [Benardete,JA on Aristotle] |
| Full Idea: The Aristotelian schedule of categories - substance, quality, quantity, relation, action, passion, place, time, and so forth - appears to peter out inconsequentially. | |
| From: comment on Aristotle (Categories [c.331 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.7 | |
| A reaction: Compare Idea 5544 for Kant's attempt to classify categories. Personally I like the way Aristotle's 'peter out'. That seems to me a more plausible character for good metaphysics. |
| 11035 | There are ten basic categories for thinking about things [Aristotle] |
| Full Idea: Of things said without any combination, each signifies either substance or quantity or qualification or a relative or where or when or being-in-a-position or having or doing or being-affected. | |
| From: Aristotle (Categories [c.331 BCE], 01b25) | |
| A reaction: This sums up the earlier of Aristotle's two metaphysical view, and each of this categories is discussed in the present text. |
| 13121 | Substance,Quantity,Quality,Relation,Place,Time,Being-in-a-position,Having,Doing,Being affected [Aristotle, by Westerhoff] |
| Full Idea: Aristotle's list of ten categories proved to be the most influential scheme found in his works: Substance, Quantity, Quality, Relation, Place, Time, Being-in-a-position, Having, Doing, Being affected. | |
| From: report of Aristotle (Categories [c.331 BCE]) by Jan Westerhoff - Ontological Categories §01 |
| 16116 | Aristotle derived categories as answers to basic questions about nature, size, quality, location etc. [Aristotle, by Gill,ML] |
| Full Idea: Aristotle seems to have worked out his list of categories by considering various questions that one might ask about a particular object, such as What is it? How big is it? How is it qualified? And Where is it? | |
| From: report of Aristotle (Categories [c.331 BCE]) by Mary Louise Gill - Aristotle on Substance | |
| A reaction: Of course, to think of his questions, Aristotle already had categories in his mind. How would he approach a proposal to recategorise reality more efficiently? |
| 21345 | Aristotle said relations are not substances, so (if they exist) they must be accidents [Aristotle, by Heil] |
| Full Idea: Aristotle categorised relations as accidents - Socrates's whiteness, the sphericity of this ball - entities dependent on substances. Relations are not substances, so they must be, if anything at all, accidents. | |
| From: report of Aristotle (Categories [c.331 BCE], §7) by John Heil - Relations 'Historical' | |
| A reaction: Heil says this thought encouraged anti-realist views of relations, which became the norm until Russell. |
| 16155 | Aristotle promoted the importance of properties and objects (rather than general and particular) [Aristotle, by Frede,M] |
| Full Idea: In 'Categories' Aristotle is taking a first step in making the distinction between objects and properties central to ontology. This plays virtually no role in Plato, and was overshadowed by the distinction between general and particular. | |
| From: report of Aristotle (Categories [c.331 BCE]) by Michael Frede - Individuals in Aristotle I | |
| A reaction: Frede says he gets in a tangle because he mixes the earlier and the new views. Because we are nowadays in a total muddle about properties, I'm thinking we should go back to the earlier view! Modern commentators make him a trope theorist. |
| 11032 | Some things said 'of' a subject are not 'in' the subject [Aristotle] |
| Full Idea: Of things there are, some are said of a subject, but are not in any subject. For example, man is said of a subject, the individual man, but is not in any subject. | |
| From: Aristotle (Categories [c.331 BCE], 01a20) | |
| A reaction: See? 'Being a man' is not a property of a man! Only the properties which are 'in' the man are properties of the man. The rest are things which are said 'of' men, usually as classifications. A classification is not a property. |
| 11038 | We call them secondary 'substances' because they reveal the primary substances [Aristotle] |
| Full Idea: It is reasonable that, after the primary substances, their species and genera should be the only other things called (secondary) substances. For only they, of things predicated, reveal the primary substance. | |
| From: Aristotle (Categories [c.331 BCE], 02b29) | |
| A reaction: This is the key passage in all of Aristotle for sortal essentialists like Wiggins, especially the word 'only'. I take it that this observation is superseded by the Metaphysics. Definition is the route to substance (which involves general terms). |
| 16739 | Four species of quality: states, capacities, affects, and forms [Aristotle, by Pasnau] |
| Full Idea: In Categories 8 there are four species of qualities: States and conditions, Natural capacities and incapacities, Affective qualities or affections, and Shape and external form. | |
| From: report of Aristotle (Categories [c.331 BCE], Ch.8) by Robert Pasnau - Metaphysical Themes 1274-1671 23.5 |
| 11037 | Colour must be in an individual body, or it is not embodied [Aristotle] |
| Full Idea: Colour is in body and therefore also in an individual body; for were it not in some individual body it would not be in body at all. | |
| From: Aristotle (Categories [c.331 BCE], 02b02) | |
| A reaction: This may be just a truism, or it may be the Aristotelian commitment to universals only existing if they are instantiated. |
| 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. |
| 16154 | Aristotle gave up his earlier notion of individuals, because it relied on universals [Aristotle, by Frede,M] |
| Full Idea: In 'Metaphysics' Aristotle abandons the notion of an individual which he had relied on in the 'Categories', since it presupposes that there are general things, that there are universals. | |
| From: report of Aristotle (Categories [c.331 BCE]) by Michael Frede - Individuals in Aristotle Intro | |
| A reaction: Ah, very illuminating. So all the way through we have a concept of individuals, first relying on universals, and then relying on hylomorphism? I suppose a bundle theory of individuals would need universals. |
| 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? |
| 12351 | Genus and species are substances, because only they reveal the primary substance [Aristotle, by Wedin] |
| Full Idea: The reason Aristotle gives for calling species and genera substances is that of what is predicated only they reveal what the primary substance is. | |
| From: report of Aristotle (Categories [c.331 BCE], 02b29-37) by Michael V. Wedin - Aristotle's Theory of Substance III.6 | |
| A reaction: Thus we should not be misled into thinking that the genus and species ARE the essence. We edge our way towards the essence of an individual by subdividing its categories. |
| 1694 | Substances have no opposites, and don't come in degrees (including if the substance is a man) [Aristotle] |
| Full Idea: There is nothing contrary to substances,…. and a substance does not admit of a more and a less. If this substance is a man, it will not be more a man or less a man either than itself or than another man. | |
| From: Aristotle (Categories [c.331 BCE], 03b33) |
| 16091 | Is primary substance just an ultimate subject, or some aspect of a complex body? [Aristotle, by Gill,ML] |
| Full Idea: 'Categories' treats something's being an ultimate subject as a test for being a primary substance, but it does not treat its primary objects as complex bodies consisting of matter and form. In that case, is the composite or a feature the ultimate subject? | |
| From: report of Aristotle (Categories [c.331 BCE]) by Mary Louise Gill - Aristotle on Substance Ch.1 | |
| A reaction: Gill is trying to throw light on the difference between 'Categories' and 'Metaphysics'. Once you have hylomorphism (form-plus-matter) you have a new difficulty in explaining unity. The answer is revealed once we understand 'form'. |
| 11280 | Primary being is 'that which lies under', or 'particular substance' [Aristotle, by Politis] |
| Full Idea: In 'Categories' Aristotle argues the primary being (proté ousia) is the ultimate subject of predication (to hupokeimenon, meaning 'that which lies under'), nowadays referred to as the 'particular substance' view. | |
| From: report of Aristotle (Categories [c.331 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 4.4 | |
| A reaction: Politis says that Aristotle shifts to the quite different view in 'Metaphysics', that primary being is essence, rather than mere subject of predication. |
| 11040 | A single substance can receive contrary properties [Aristotle] |
| Full Idea: It seems distinctive of substance that what is numerically one and the same is able to receive contraries. ...For example, an individual man - one and the same - becomes pale at one time and dark at another. | |
| From: Aristotle (Categories [c.331 BCE], 04a10/20) |
| 16140 | Secondary substances do have subjects, so they are not ultimate in the ontology [Aristotle, by Frede,M] |
| Full Idea: The concept of substance applies to secondary substances only with some deletions; ..it is not true that they have no subjects, and hence they are not ultimate subjects for all other elements of the ontology. | |
| From: report of Aristotle (Categories [c.331 BCE]) by Michael Frede - Title, Unity, Authenticity of the 'Categories' V | |
| A reaction: It increasingly strikes that to treat secondary substance (roughly, species) as essence is a shocking misreading of Aristotle. Frede says they are substances, because they do indeed 'underlie'. |
| 10965 | In earlier Aristotle the substances were particulars, not kinds [Aristotle, by Lawson-Tancred] |
| Full Idea: In 'Metaphysics' Aristotle changed his view, as in 'Categories' the substances, the basic realities, were particular items, notably individual men, horses, cabbages etc. | |
| From: report of Aristotle (Categories [c.331 BCE]) by Hugh Lawson-Tancred - Introductions to 'Metaphysics' p.178 | |
| A reaction: The charge is that having successfully rebelled against Plato, Aristotle gradually succumbed to his teacher's influence, and ended up with a more platonist view. For anti-platonists like myself, the 'Categories' seems to be the key text. |
| 11036 | A 'primary' substance is in each subject, with species or genera as 'secondary' substances [Aristotle] |
| Full Idea: A substance, in its most primary sense, is that which is neither said of a subject nor in a subject, e.g. the individual man or horse. The species in which things primarily called substances are, are called secondary substances, as are the genera. | |
| From: Aristotle (Categories [c.331 BCE], 02a11) | |
| A reaction: This distinction between 'primary' and 'secondary' substances is characteristic of Aristotle's earlier metaphysical view, with the later view (more unified and Platonic) in the 'Metaphysics'. |
| 8287 | Earlier Aristotle had objects as primary substances, but later he switched to substantial form [Aristotle, by Lowe] |
| Full Idea: In 'Categories' primary substances are individual concrete objects, such as a particular horse, whereas in 'Metaphysics' such things are combinations of matter and substantial form, with the latter being the primary substances. | |
| From: report of Aristotle (Categories [c.331 BCE]) by E.J. Lowe - The Possibility of Metaphysics 9.1 | |
| A reaction: Lowe claims there is no real difference. Aristotle came to think that matter was not part of primary substance, so the shift seems to be that substance was concrete, but then he decided it was abstract. Physicists will prefer 'Metaphysics'. |
| 12350 | Things are called 'substances' because they are subjects for everything else [Aristotle] |
| Full Idea: It is because the primary substances are subjects for everything else that they are called substances [ousiai] most strictly. | |
| From: Aristotle (Categories [c.331 BCE], 03a04) | |
| A reaction: This points to a rather minimal account of substance, as possibly the 'bare particular' which has no other role than to have properties. This expands in 'Metaphysics' to be matter which has form, making properties possible. |
| 11039 | A primary substance reveals a 'this', which is an individual unit [Aristotle] |
| Full Idea: Every substance seems to signify a certain 'this'. As regards the primary substances, it is indisputably true that each of them signifies a certain 'this'; for the thing revealed is individual and numerically one. | |
| From: Aristotle (Categories [c.331 BCE], 03b10) | |
| A reaction: The notion of 'primary' substance is confined to this earlier metaphysics of Aristotle. |
| 12361 | Primary substances are ontological in 'Categories', and explanatory in 'Metaphysics' [Aristotle, by Wedin] |
| Full Idea: The primacy of 'Categories' primary substances is a kind of ontological primacy, whereas the primacy of form is a kind of structural or explanatory primacy. | |
| From: report of Aristotle (Categories [c.331 BCE]) by Michael V. Wedin - Aristotle's Theory of Substance X.9 | |
| A reaction: 'Structural' and 'explanatory' sound very different, since the former sounds ontological and the latter epistemological (and more subjective). |
| 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. |
| 3315 | Aristotle denigrates the category of relation, but for modern absolutists self-relation is basic [Benardete,JA on Aristotle] |
| Full Idea: Aristotle denigrates the whole category of relations, but modern logical absolutists single out self-relation (in the mode of identity) as metaphysically privileged. | |
| From: comment on Aristotle (Categories [c.331 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.8 | |
| A reaction: I think this refers to Plantinga and Merrihew Adams, who make identity-with-itself the basic component of individual existences. |
| 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'. |
| 12349 | Only what can be said of many things is a predicable [Aristotle, by Wedin] |
| Full Idea: Aristotle reminds us that nothing is to count as predicable that cannot be said-of many things. | |
| From: report of Aristotle (Categories [c.331 BCE]) by Michael V. Wedin - Aristotle's Theory of Substance III.1 | |
| A reaction: Thus there wouldn't be any predicates if there were not universals. Could we have proper names for individual qualities (tropes), in the way that we have them for individual objects? |
| 11837 | Some predicates signify qualification of a substance, others the substance itself [Aristotle] |
| Full Idea: 'White' signifies nothing but a qualification, whereas the species ('man') and the genus ('animal') mark off the qualification of substance - they signify substance of a certain qualification. | |
| From: Aristotle (Categories [c.331 BCE], 03b18) | |
| A reaction: This is making a fundamental distinction between two different types of predication. I would describe them as one attributing a real property, and the other attributing a category (as a result of the properties). I don't think 'substance' helps here. |
| 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. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 11043 | It is not possible for fire to be cold or snow black [Aristotle] |
| Full Idea: It is not possible for fire to be cold or snow black. | |
| From: Aristotle (Categories [c.331 BCE], 12b01) |
| 1696 | Change goes from possession to loss (as in baldness), but not the other way round [Aristotle] |
| Full Idea: Change occurs from possession to privation, but from privation to possession is impossible; one who has gone blind does not recover sight nor does a bald man regain his hair nor does a toothless man grow new ones. | |
| From: Aristotle (Categories [c.331 BCE], 13a35) | |
| A reaction: Although this seems like an insight into entropy, it isn't an accurate observation, since trees lose their leaves, and then regain them in spring. Maybe somewhere men regrow their hair each spring. |
| 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') |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |