51 ideas
12274 | Begin examination with basics, and subdivide till you can go no further [Aristotle] |
Full Idea: The examination must be carried on and begin from the primary classes and then go on step by step until further division is impossible. | |
From: Aristotle (Topics [c.331 BCE], 109b17) | |
A reaction: This is a good slogan for the analytic approach to thought. I take Aristotle (or possibly Socrates) to be the father of analysis, not Frege (though see Idea 9840). (He may be thinking of the tableau method of proof). |
12260 | Dialectic starts from generally accepted opinions [Aristotle] |
Full Idea: Reasoning is dialectical which reasons from generally accepted opinions. | |
From: Aristotle (Topics [c.331 BCE], 100a30) | |
A reaction: This is right at the heart of Aristotle's philosophical method, and Greek thinking generally. There are nice modern debates about 'folk' understanding, derived from science (e.g. quantum theory) which suggest that starting from normal views is a bad idea. |
12291 | There can't be one definition of two things, or two definitions of the same thing [Aristotle] |
Full Idea: There cannot possibly be one definition of two things, or two definitions of the same thing. | |
From: Aristotle (Topics [c.331 BCE], 154a11) | |
A reaction: The second half of this is much bolder and more controversial, and plenty of modern thinkers would flatly reject it. Are definitions contextual, that is, designed for some specific human purpose. Must definitions be of causes? |
12292 | Definitions are easily destroyed, since they can contain very many assertions [Aristotle] |
Full Idea: A definition is the easiest of all things to destroy; for, since it contains many assertions, the opportunities which it offers are very numerous, and the more abundant the material, the more quickly the reasoning can set to work. | |
From: Aristotle (Topics [c.331 BCE], 155a03) | |
A reaction: I quote this to show that Aristotle expected many definitions to be very long affairs (maybe even of book length?) |
12261 | Differentia are generic, and belong with genus [Aristotle] |
Full Idea: The differentia, being generic in character, should be ranged with the genus. | |
From: Aristotle (Topics [c.331 BCE], 101b18) | |
A reaction: This does not mean that naming the differentia amounts to mere classification. I presume we can only state individual differences by using a language which is crammed full of universals. |
12263 | 'Genus' is part of the essence shared among several things [Aristotle] |
Full Idea: A 'genus' is that which is predicated in the category of essence of several things which differ in kind. | |
From: Aristotle (Topics [c.331 BCE], 102a32) | |
A reaction: Hence a genus is likely to be expressed by a universal, a one-over-many. A particular will be a highly individual collection of various genera, but what ensures the uniqueness of each thing, if they are indiscernible? |
12272 | We describe the essence of a particular thing by means of its differentiae [Aristotle] |
Full Idea: We usually isolate the appropriate description of the essence of a particular thing by means of the differentiae which are peculiar to it. | |
From: Aristotle (Topics [c.331 BCE], 108b05) | |
A reaction: I take this to be important for showing the definition is more than mere categorisation. A good definition homes in the particular, by gradually narrowing down the differentiae. |
12279 | The differentia indicate the qualities, but not the essence [Aristotle] |
Full Idea: No differentia indicates the essence [ti estin], but rather some quality, such as 'pedestrian' or 'biped'. | |
From: Aristotle (Topics [c.331 BCE], 122b17) | |
A reaction: We must disentangle this, since essence is what is definable, and definition seems to give us the essence, and yet it appears that definition only requires genus and differentia. Differentiae seem to be both generic and fine-grained. See Idea 12280! |
12283 | In definitions the first term to be assigned ought to be the genus [Aristotle] |
Full Idea: In definitions the first term to be assigned ought to be the genus. | |
From: Aristotle (Topics [c.331 BCE], 132a12) | |
A reaction: We mustn't be deluded into thinking that nothing else is required. I take the increasing refinement of differentiae to be where the real action is. The genus gives you 70% of the explanation. |
12289 | The genera and the differentiae are part of the essence [Aristotle] |
Full Idea: The genera and the differentiae are predicated in the category of essence. | |
From: Aristotle (Topics [c.331 BCE], 153a19) | |
A reaction: The definition is words, and the essence is real, so our best definition might not fully attain to the essence. Aristotle has us reaching out to the world through our definitions. |
12285 | The definition is peculiar to one thing, not common to many [Aristotle] |
Full Idea: The definition ought to be peculiar to one thing, not common to many. | |
From: Aristotle (Topics [c.331 BCE], 149b24) | |
A reaction: I take this to be very important, against those who think that definition is no more than mere categorisation. To explain, you must get down to the level of the individual. We must explain that uniquely docile tiger. |
9921 | 'True' is only occasionally useful, as in 'everything Fermat believed was true' [Burgess/Rosen] |
Full Idea: In the disquotational view of truth, what saves truth from being wholly redundant and so wholly useless, is mainly that it provides an ability to state generalisations like 'Everything Fermat believed was true'. | |
From: JP Burgess / G Rosen (A Subject with No Object [1997], I.A.2.c) | |
A reaction: Sounds like the thin end of the wedge. Presumably we can infer that the first thing Fermat believed on his last Christmas Day was true. |
9924 | Modal logic gives an account of metalogical possibility, not metaphysical possibility [Burgess/Rosen] |
Full Idea: If you want a logic of metaphysical possibility, the existing literature was originally developed to supply a logic of metalogical possibility, and still reflects its origins. | |
From: JP Burgess / G Rosen (A Subject with No Object [1997], II.B.3.b) | |
A reaction: This is a warning shot (which I don't fully understand) to people like me, who were beginning to think they could fill their ontology with possibilia, which could then be incorporated into the wider account of logical thinking. Ah well... |
9933 | The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set [Burgess/Rosen] |
Full Idea: The paradoxes only seem to arise in connection with Frege's logical notion of extension or class, not Cantor's mathematical notion of set. Cantor never assumed that every condition determines a set. | |
From: JP Burgess / G Rosen (A Subject with No Object [1997], III.C.1.b) | |
A reaction: This makes the whole issue a parochial episode in the history of philosophy, not a central question. Cantor favoured some sort of abstractionism (see Kit Fine on the subject). |
9928 | Mereology implies that acceptance of entities entails acceptance of conglomerates [Burgess/Rosen] |
Full Idea: Mereology has ontological implications. The acceptance of some initial entities involves the acceptance of many further entities, arbitrary wholes having the entities as parts. It must accept conglomerates. Geometric points imply geometric regions. | |
From: JP Burgess / G Rosen (A Subject with No Object [1997], II.C.1.b) | |
A reaction: Presumably without the wholes being entailed by the parts, there is no subject called 'mereology'. But if the conglomeration is unrestricted, there is not much left to be said. 'Restricted' composition (by nature?) sounds a nice line. |
9926 | A relation is either a set of sets of sets, or a set of sets [Burgess/Rosen] |
Full Idea: While in general a relation is taken to be a set of ordered pairs <u, v> = {{u}, {u, v}}, and hence a set of sets of sets, in special cases a relation can be represented by a set of sets. | |
From: JP Burgess / G Rosen (A Subject with No Object [1997], II.C.1.a) | |
A reaction: [See book for their examples, which are <, symmetric, and arbitrary] The fact that a relation (or anything else) can be represented in a certain way should never ever be taken to mean that you now know what the thing IS. |
11261 | Puzzles arise when reasoning seems equal on both sides [Aristotle] |
Full Idea: The equality of opposite reasonings is the cause of aporia; for it is when we reason on both [sides of a question] and it appears to us that everything can come about either way, that we are in a state of aporia about which of the two ways to take up. | |
From: Aristotle (Topics [c.331 BCE], 145b17), quoted by Vassilis Politis - Aristotle and the Metaphysics 3.1 | |
A reaction: Other philosophers give up on the subject in this situation, but I love Aristotle because he takes this to be the place where philosophy begins. |
9932 | The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen] |
Full Idea: Recent commentators have de-emphasised the set paradoxes because they play no prominent part in motivating the most articulate and active opponents of set theory, such as Kronecker (constructivism) or Brouwer (intuitionism), or Weyl (predicativism). | |
From: JP Burgess / G Rosen (A Subject with No Object [1997], III.C.1.b) | |
A reaction: This seems to be a sad illustration of the way most analytical philosophers have to limp along behind the logicians and mathematicians, arguing furiously about problems that have largely been abandoned. |
9923 | We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen] |
Full Idea: The modal strategy for numbers is to replace assumptions about the actual existence of numbers by assumptions about the possible existence of numbers | |
From: JP Burgess / G Rosen (A Subject with No Object [1997], II.B.3.a) | |
A reaction: This seems to be quite a good way of dealing with very large numbers and infinities. It is not clear whether 5 is so regularly actualised that we must consider it as permanent, or whether it is just a prominent permanent possibility. |
12273 | Unit is the starting point of number [Aristotle] |
Full Idea: They say that the unit [monada] is the starting point of number (and the point the starting-point of a line). | |
From: Aristotle (Topics [c.331 BCE], 108b30) | |
A reaction: Yes, despite Frege's objections in the early part of the 'Grundlagen' (1884). I take arithmetic to be rooted in counting, despite all abstract definitions of number by Frege and Dedekind. Identity gives the unit, which is countable. See also Topics 141b9 |
9925 | Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen] |
Full Idea: Usually structuralism and nominalism are considered rivals. But structuralism can also be the first step in a strategy of nominalist reconstrual or paraphrase. | |
From: JP Burgess / G Rosen (A Subject with No Object [1997], II.C.0) | |
A reaction: Hellman and later Chihara seem to be the main proponents of nominalist structuralism. My sympathies lie with this strategy. Are there objects at the nodes of the structure, or is the structure itself platonic? Mill offers a route. |
9934 | Number words became nouns around the time of Plato [Burgess/Rosen] |
Full Idea: The transition from using number words purely as adjectives to using them extensively as nouns has been traced to 'around the time of Plato'. | |
From: JP Burgess / G Rosen (A Subject with No Object [1997], III.C.2.a) | |
A reaction: [The cite Kneale and Kneale VI,§2 for this] It is just too tempting to think that in fact Plato (and early Platonists) were totally responsible for this shift, since the whole reification of numbers seems to be inherently platonist. |
9918 | Abstract/concrete is a distinction of kind, not degree [Burgess/Rosen] |
Full Idea: The distinction of abstract and concrete is one of kind and not degree. | |
From: JP Burgess / G Rosen (A Subject with No Object [1997], I.A.1.a) | |
A reaction: I think I must agree with this. If there is a borderline, it would be in particulars that seem to have an abstract aspect to them. A horse involves the abstraction of being a horse, and it involves be one horse. |
9929 | Much of what science says about concrete entities is 'abstraction-laden' [Burgess/Rosen] |
Full Idea: Much of what science says about concrete entities is 'abstraction-laden'. | |
From: JP Burgess / G Rosen (A Subject with No Object [1997], III.A.1.d) | |
A reaction: Not just science. In ordinary conversation we continually refer to particulars using so-called 'universal' predicates and object-terms, which are presumably abstractions. 'I've just seen an elephant'. |
9927 | Mathematics has ascended to higher and higher levels of abstraction [Burgess/Rosen] |
Full Idea: In mathematics, since the beginning of the nineteenth century, there has been an ascent to higher and higher levels of abstraction. | |
From: JP Burgess / G Rosen (A Subject with No Object [1997], II.C.1.b) | |
A reaction: I am interested in clarifying what this means, which might involve the common sense and psychological view of the matter, as well as some sort of formal definition in terms of equivalence (or whatever). |
9930 | Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas [Burgess/Rosen] |
Full Idea: There is a scale of abstractness that leads downwards from sets through attributes to formulas as abstract types and on to formulas as abstract tokens. | |
From: JP Burgess / G Rosen (A Subject with No Object [1997], III.B.2.c) | |
A reaction: Presumably the 'abstract tokens' at the bottom must have some interpretation, to support the system. Presumably one can keep going upwards, through sets of sets of sets. |
12267 | There are ten categories: essence, quantity, quality, relation, place, time, position, state, activity, passivity [Aristotle] |
Full Idea: The four main types of predicates fall into ten categories: essence, quantity, quality, relation, place, time, position, state, activity, passivity. | |
From: Aristotle (Topics [c.331 BCE], 103b20) | |
A reaction: These are the standard ten categories of Aristotle. He is notable for the divisions not being sharp, and ten being a rough total. He is well aware of the limits of precision in such matters. |
12282 | An individual property has to exist (in past, present or future) [Aristotle] |
Full Idea: If it does not at present exist, or, if it has not existed in the past, or if it is not going to exist in the future, it will not be a property [idion] at all. | |
From: Aristotle (Topics [c.331 BCE], 129a27) | |
A reaction: This seems to cramp our style in counterfactual discussion. Can't we even mention an individual property if we believe that it will never exist. Utopian political discussion will have to cease! |
12264 | An 'accident' is something which may possibly either belong or not belong to a thing [Aristotle] |
Full Idea: An 'accident' [sumbebekos] is something which may possibly either belong or not belong to any one and the self-same thing, such as 'sitting posture' or 'whiteness'. This is the best definition, because it tells us the essential meaning of the term itself. | |
From: Aristotle (Topics [c.331 BCE], 102b07) | |
A reaction: Thus a car could be red, or not red. Accidents are contingent. It does not follow that necessary properties are essential (see Idea 12262). There are accidents [sumbebekos], propria [idion] and essences [to ti en einai]. |
12280 | Genus gives the essence better than the differentiae do [Aristotle] |
Full Idea: In assigning the essence [ti estin], it is more appropriate to state the genus than the differentiae; for he who describes 'man' as an 'animal' indicates his essence better than he who describes him as 'pedestrian'. | |
From: Aristotle (Topics [c.331 BCE], 128a24) | |
A reaction: See Idea 12279. This idea is only part of the story. My reading of this is simply that assigning a genus gives more information. We learn more about him when we say he is a man than when we say he is Socrates. |
13269 | In the case of a house the parts can exist without the whole, so parts are not the whole [Aristotle] |
Full Idea: In the case of a house, where the process of compounding the parts is obvious, though the parts exist, there is no reason why the whole should not be non-existent, and so the parts are not the same as the whole. | |
From: Aristotle (Topics [c.331 BCE], 150a19) | |
A reaction: Compare buying a piece of furniture, and being surprised to discover, when it is delivered, that it is self-assembly. This idea is a simple refutation of the claims of classical mereology, that wholes are just some parts. Aristotle uses modal claims. |
12284 | Everything that is has one single essence [Aristotle] |
Full Idea: Everything that is has one single essence [en esti to einai]. | |
From: Aristotle (Topics [c.331 BCE], 141a36) | |
A reaction: Does this include vague objects, and abstract 'objects'? Sceptics might ask what grounds this claim. Does Dr Jeckyll have two essences? |
12262 | An 'idion' belongs uniquely to a thing, but is not part of its essence [Aristotle] |
Full Idea: A property [idion] is something which does not show the essence of a thing but belongs to it alone. ...No one calls anything a property which can possibly belong to something else. | |
From: Aristotle (Topics [c.331 BCE], 102a18) | |
A reaction: [See Charlotte Witt 106 on this] 'Property' is clearly a bad translation for such an individual item. Witt uses 'proprium', which is a necessary but nonessential property of something. Necessity is NOT the hallmark of essence. See Idea 12266. |
12290 | Destruction is dissolution of essence [Aristotle] |
Full Idea: Destruction is a dissolution of essence. | |
From: Aristotle (Topics [c.331 BCE], 153b30) | |
A reaction: [plucked from context!] I can't think of a better way to define destruction, in order to distinguish it from damage. A vase is destroyed when its essential function cannot be recovered. |
12286 | If two things are the same, they must have the same source and origin [Aristotle] |
Full Idea: When things are absolutely the same, their coming-into-being and destruction are also the same and so are the agents of their production and destruction. | |
From: Aristotle (Topics [c.331 BCE], 152a02) | |
A reaction: Thus Queen Elizabeth II has to be the result of that particular birth, and from those particular parents, as Kripke says? The inverse may not be true. Do twins have a single origin? Things that fission and then re-fuse differently? etc |
12266 | 'Same' is mainly for names or definitions, but also for propria, and for accidents [Aristotle] |
Full Idea: 'The same' is employed in several senses: its principal sense is for same name or same definition; a second sense occurs when sameness is applied to a property [idiu]; a third sense is applied to an accident. | |
From: Aristotle (Topics [c.331 BCE], 103a24-33) | |
A reaction: [compressed] 'Property' is better translated as 'proprium' - a property unique to a particular thing, but not essential - see Idea 12262. Things are made up of essence, propria and accidents, and three ways of being 'the same' are the result. |
12287 | Two identical things have the same accidents, they are the same; if the accidents differ, they're different [Aristotle] |
Full Idea: If two things are the same then any accident of one must also be an accident of the other, and, if one of them is an accident of something else, so must the other be also. For, if there is any discrepancy on these points, obviously they are not the same. | |
From: Aristotle (Topics [c.331 BCE], 152a36) | |
A reaction: So what is always called 'Leibniz's Law' should actually be 'Aristotle's Law'! I can't see anything missing from the Aristotle version, but then, since most people think it is pretty obvious, you would expect the great stater of the obvious to get it. |
12288 | Numerical sameness and generic sameness are not the same [Aristotle] |
Full Idea: Things which are the same specifically or generically are not necessarily the same or cannot possibly be the same numerically. | |
From: Aristotle (Topics [c.331 BCE], 152b32) | |
A reaction: See also Idea 12266. This looks to me to be a pretty precise anticipation of Peirce's type/token distinction, but without the terminology. It is reassuring that Aristotle spotted it, as that makes it more likely to be a genuine distinction. |
12259 | Reasoning is when some results follow necessarily from certain claims [Aristotle] |
Full Idea: Reasoning [sullogismos] is a discussion in which, certain things having been laid down, something other than these things necessarily results through them. | |
From: Aristotle (Topics [c.331 BCE], 100a25) | |
A reaction: This is cited as the standard statement of the nature of logical necessity. One might challenge either the very word 'necessary', or the exact sense of the word employed here. Is it, in fact, metaphysical, or merely analytic? |
12271 | Induction is the progress from particulars to universals [Aristotle] |
Full Idea: Induction is the progress from particulars to universals; if the skilled pilot is the best pilot and the skilled charioteer the best charioteer, then, in general, the skilled man is the best man in any particular sphere. | |
From: Aristotle (Topics [c.331 BCE], 105a15) | |
A reaction: It is a bit unclear whether we are deriving universal concepts, or merely general truths. Need general truths be absolute or necessary truths? Presumably occasionally the best person is not the most skilled, as in playing a musical instrument. |
12293 | We say 'so in cases of this kind', but how do you decide what is 'of this kind'? [Aristotle] |
Full Idea: When it is necessary to establish the universal, people use the expression 'So in all cases of this kind'; but it is one of the most difficult tasks to define which of the terms proposed are 'of this kind' and which are not. | |
From: Aristotle (Topics [c.331 BCE], 157a25) | |
A reaction: It is particularly hard if induction is expressed as the search for universals, since the kind presumably is the universal, so the universal must be known before the induction can apply, which really is the most frightful nuisance for truth-seekers. |
9919 | The old debate classified representations as abstract, not entities [Burgess/Rosen] |
Full Idea: The original debate was over abstract ideas; thus it was mental (or linguistic) representations that were classified as abstract or otherwise, and not the entities represented. | |
From: JP Burgess / G Rosen (A Subject with No Object [1997], I.A.1.b) | |
A reaction: This seems to beg the question of whether there are any such entities. It is equally plausible to talk of the entities that are 'constructed', rather than 'represented'. |
20739 | Levinas took 'first philosophy' to begin with seeing the vulnerable faces of others [Levinas, by Aho] |
Full Idea: Levinas forwarded a notion of 'ethics as first philosophy' that begins from the concete exposure and openness to 'the face' of the other, an experience of vulnerability and suffering that undercuts our ordinary egoistic and objectifying tendencies. | |
From: report of Emmanuel Levinas (works [1956]) by Kevin Aho - Existentialism: an introduction 1 'Existentialism' | |
A reaction: Iris Murdoch speaks of seeing a falcon in flight as having a similar effect of diminishing the ego. If the main focus is on potential 'suffering' does this eventually cash out as utilitarianism? I bet not! |
12276 | Justice and self-control are better than courage, because they are always useful [Aristotle] |
Full Idea: Justice [dikaiosune] and self-control [sophrosune] are preferable to courage, for the first two are always useful, but courage only sometimes. | |
From: Aristotle (Topics [c.331 BCE], 117a36) | |
A reaction: One could challenge his criterion. What of something which is absolutely vital on occasions, against something which is very mildly useful all the time? You may survive without justice, but not without courage. Compare Idea 12277. |
12277 | Friendship is preferable to money, since its excess is preferable [Aristotle] |
Full Idea: Friendship is preferable to money; for excess of friendship is preferable to excess of money. | |
From: Aristotle (Topics [c.331 BCE], 118b07) | |
A reaction: Compare Idea 12276, which gives a different criterion for choosing between virtues. This idea is an interesting qualification of the doctrine of the mean. |
12275 | We value friendship just for its own sake [Aristotle] |
Full Idea: We value friendship for its own sake, even if we are not likely to get anything else from it. | |
From: Aristotle (Topics [c.331 BCE], 117a03) | |
A reaction: In 'Ethics' he distinguishes some friendships which don't meet this requirement. Presumably true friendships survive all vicissitudes (except betrayal), but that makes such things fairly rare. |
12281 | Man is intrinsically a civilized animal [Aristotle] |
Full Idea: It is an essential [kath' auto] property of man to be 'by nature a civilized animal'. | |
From: Aristotle (Topics [c.331 BCE], 128b17) | |
A reaction: I take this, along with man being intrinsically rational, to be the foundation of Aristotelian ethics. Given that we are civilized, self-evident criteria emerge for how to be good at it. A good person is, above all, a good citizen. |
20445 | Levinas says Marxism is the replacement of individualist ethics, by solidarity and sociality [Levinas, by Critchley] |
Full Idea: For Levinas, Marxism is the absorption of the ethical in the socioeconomic, and so it is the disappearance of the face-to-face relation and the privileging of relations of solidarity and anonymous sociality, which he calls 'socialism'. | |
From: report of Emmanuel Levinas (works [1956]) by Simon Critchley - Impossible Objects: interviews 1 | |
A reaction: Startling, if you are not used to this sort of thing. If you are in trouble, I should help you, not because you are you, or a human being, but because you are a member of my group? So what about the Good Samaritan? Or solidarity with humanity? Animals? |
12265 | All water is the same, because of a certain similarity [Aristotle] |
Full Idea: Any water is said to be specifically the same as any other water because it has a certain similarity to it. | |
From: Aristotle (Topics [c.331 BCE], 103a20) | |
A reaction: (Cf. Idea 8153) It take this to be the hallmark of a natural kind, and we should not lose sight of it in the midst of discussions about rigid designation and essential identity. Tigers are only a natural kind insofar as they are indistinguishable. |
9922 | If space is really just a force-field, then it is a physical entity [Burgess/Rosen] |
Full Idea: According to many philosophical commentators, a force-field must be considered to be a physical entity, and as the distinction between space and the force-field may be considered to be merely verbal, space itself may be considered to be a physical entity. | |
From: JP Burgess / G Rosen (A Subject with No Object [1997], II.A.1) | |
A reaction: The ontology becomes a bit odd if we cheerfully accept that space is physical, but then we can't give the same account of time. I'm not sure how time could be physical. What's it made of? |
12278 | 'Being' and 'oneness' are predicated of everything which exists [Aristotle] |
Full Idea: 'Being' and 'oneness' are predicated of everything which exists. | |
From: Aristotle (Topics [c.331 BCE], 121a18) | |
A reaction: Is 'oneness' predicated of water? So existence always was a predicate, it seems, until Kant told us it wasn't. That existence is a quantifier, not a predicate, seems to be up for question again these days. |