77 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?) |
| 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. |
| 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? |
| 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. |
| 10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
| Full Idea: Three traditional names for rules are 'Simplification' (P from 'P and Q'), 'Addition' ('P or Q' from P), and 'Disjunctive Syllogism' (Q from 'P or Q' and 'not-P'). | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
| Full Idea: In S4 necessity is said to be informal 'provability', and in S5 it is said to be 'true in every possible world'. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.4) | |
| A reaction: It seems that the S4 version is proof-theoretic, and the S5 version is semantic. |
| 11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read] |
| Full Idea: In fuzzy logic, besides fuzzy predicates, which define fuzzy sets, there are also fuzzy quantifiers (such as 'most' and 'few') and fuzzy modifiers (such as 'usually'). | |
| From: Stephen Read (Thinking About Logic [1995], Ch.7) |
| 11011 | Same say there are positive, negative and neuter free logics [Read] |
| Full Idea: It is normal to classify free logics into three sorts; positive free logics (some propositions with empty terms are true), negative free logics (they are false), and neuter free logics (they lack truth-value), though I find this unhelpful and superficial. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.5) |
| 11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
| Full Idea: Hard-headed realism tends to embrace the full Comprehension Principle, that every well-defined concept determines a set. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.8) | |
| A reaction: This sort of thing gets you into trouble with Russell's paradox (though that is presumably meant to be excluded somehow by 'well-defined'). There are lots of diluted Comprehension Principles. |
| 10986 | Not all validity is captured in first-order logic [Read] |
| Full Idea: We must recognise that first-order classical logic is inadequate to describe all valid consequences, that is, all cases in which it is impossible for the premisses to be true and the conclusion false. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: This is despite the fact that first-order logic is 'complete', in the sense that its own truths are all provable. |
| 10972 | The non-emptiness of the domain is characteristic of classical logic [Read] |
| Full Idea: The non-emptiness of the domain is characteristic of classical logic. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
| Full Idea: For the realist, study of semantic structures comes before study of proofs. In higher-order logic is has to, for the logics are incomplete. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.9) | |
| A reaction: This seems to be an important general observation about any incomplete system, such as Peano arithmetic. You may dream the old rationalist dream of starting from the beginning and proving everything, but you can't. Start with truth and meaning. |
| 10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
| Full Idea: Those who believe mathematics goes beyond logic use that fact to argue that classical logic is right to exclude second-order logic. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read] |
| Full Idea: A theory of logical consequence, while requiring a conceptual analysis of consequence, also searches for a set of techniques to determine the validity of particular arguments. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square [Read] |
| Full Idea: If classical logic insists that logical consequence is just a matter of the form, we fail to include as valid consequences those inferences whose correctness depends on the connections between non-logical terms (such as 'round' and 'square'). | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: He suggests that an inference such as 'round, so not square' should be labelled as 'materially valid'. |
| 10973 | A theory is logically closed, which means infinite premisses [Read] |
| Full Idea: A 'theory' is any logically closed set of propositions, ..and since any proposition has infinitely many consequences, including all the logical truths, so that theories have infinitely many premisses. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: Read is introducing this as the essential preliminary to an account of the Compactness Theorem, which relates these infinite premisses to the finite. |
| 11007 | Quantifiers are second-order predicates [Read] |
| Full Idea: Quantifiers are second-order predicates. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.5) | |
| A reaction: [He calls this 'Frege's insight'] They seem to be second-order in Tarski's sense, that they are part of a metalanguage about the sentence, rather than being a part of the sentence. |
| 10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
| Full Idea: The defining factor of second-order logic is that, while the domain of its individual variables may be arbitrary, the range of the first-order variables is all the properties of the objects in its domain (or, thinking extensionally, of the sets objects). | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: The key point is that the domain is 'all' of the properties. How many properties does an object have. You need to decide whether you believe in sparse or abundant properties (I vote for very sparse indeed). |
| 10971 | A logical truth is the conclusion of a valid inference with no premisses [Read] |
| Full Idea: Logical truth is a degenerate, or extreme, case of consequence. A logical truth is the conclusion of a valid inference with no premisses, or a proposition in the premisses of an argument which is unnecessary or may be suppressed. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 10988 | Any first-order theory of sets is inadequate [Read] |
| Full Idea: Any first-order theory of sets is inadequate because of the Löwenheim-Skolem-Tarski property, and the consequent Skolem paradox. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: The limitation is in giving an account of infinities. |
| 10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
| Full Idea: Classical logical consequence is compact, which means that any consequence of an infinite set of propositions (such as a theory) is a consequence of some finite subset of them. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 10975 | Compactness does not deny that an inference can have infinitely many premisses [Read] |
| Full Idea: Compactness does not deny that an inference can have infinitely many premisses. It can; but classically, it is valid if and only if the conclusion follows from a finite subset of them. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read] |
| Full Idea: Compact consequence undergenerates - there are intuitively valid consequences which it marks as invalid, such as the ω-rule, that if A holds of the natural numbers, then 'for every n, A(n)', but the proof of that would be infinite, for each number. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 10976 | Compactness makes consequence manageable, but restricts expressive power [Read] |
| Full Idea: Compactness is a virtue - it makes the consequence relation more manageable; but it is also a limitation - it limits the expressive power of the logic. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: The major limitation is that wholly infinite proofs are not permitted, as in Idea 10977. |
| 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. |
| 11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
| Full Idea: It cannot be self-reference alone that is at fault. Rather, what seems to cause the problems in the paradoxes is the combination of self-reference with falsity. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.6) |
| 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 |
| 11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
| Full Idea: Every potential infinity seems to suggest an actual infinity - e.g. generating successors suggests they are really all there already; cutting the line suggests that the point where the cut is made is already in place. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.8) | |
| A reaction: Finding a new gambit in chess suggests it was there waiting for us, but we obviously invented chess. Daft. |
| 10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
| Full Idea: Second-order arithmetic is categorical - indeed, there is a single formula of second-order logic whose only model is the standard model ω, consisting of just the natural numbers, with all of arithmetic following. It is nevertheless incomplete. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: This is the main reason why second-order logic has a big fan club, despite the logic being incomplete (as well as the arithmetic). |
| 10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
| Full Idea: Second-order arithmetic can rule out the non-standard models (with non-standard numbers). Its induction axiom crucially refers to 'any' property, which gives the needed categoricity for the models. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 10997 | Von Neumann numbers are helpful, but don't correctly describe numbers [Read] |
| Full Idea: The Von Neumann numbers have a structural isomorphism to the natural numbers - each number is the set of all its predecessors, so 2 is the set of 0 and 1. This helps proofs, but is unacceptable. 2 is not a set with two members, or a member of 3. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.4) |
| 11016 | Would a language without vagueness be usable at all? [Read] |
| Full Idea: We must ask whether a language without vagueness would be usable at all. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.7) | |
| A reaction: Popper makes a similar remark somewhere, with which I heartily agreed. This is the idea of 'spreading the word' over the world, which seems the right way of understanding it. |
| 11019 | Supervaluations say there is a cut-off somewhere, but at no particular place [Read] |
| Full Idea: The supervaluation approach to vagueness is to construe vague predicates not as ones with fuzzy borderlines and no cut-off, but as having a cut-off somewhere, but in no particular place. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.7) | |
| A reaction: Presumably you narrow down the gap by supervaluation, then split the difference to get a definite value. |
| 11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read] |
| Full Idea: A 'supervaluation' says a proposition is true if it is true in all classical extensions of the original partial valuation. Thus 'A or not-A' has no valuation for an empty name, but if 'extended' to make A true or not-true, not-A always has opposite value. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.5) |
| 11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations [Read] |
| Full Idea: In supervaluations, the Law of Identity has no value for empty names, and remains so if extended. The Indiscernibility of Identicals also fails if extending it for non-denoting terms, where Fa comes out true and Fb false. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.5) |
| 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]. |
| 18431 | Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards] |
| Full Idea: Simons's 'nuclear' option blends features of the substratum and bundle theories. First we have tropes collected by virtue of their internal relations, forming the essential kernel or nucleus. This nucleus then bears the non-essential tropes. | |
| From: report of Peter Simons (Particulars in Particular Clothing [1994], p.567) by Douglas Edwards - Properties 3.5 | |
| A reaction: [compression of Edwards's summary] This strikes me as being a remarkably good theory. I am not sure of the ontological status of properties, such that they can (unaided) combine to make part of an object. What binds the non-essentials? |
| 10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
| Full Idea: The haecceitist (a neologism coined by Duns Scotus, pronounced 'hex-ee-it-ist', meaning literally 'thisness') believes that each thing has an individual essence, a set of properties which are essential to it. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.4) | |
| A reaction: This seems to be a difference of opinion over whether a haecceity is a set of essential properties, or a bare particular. The key point is that it is unique to each entity. |
| 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. |
| 11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
| Full Idea: The equation of 'necessity' with 'true in every possible world' is known as the S5 conception, corresponding to the strongest of C.I.Lewis's five modal systems. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.4) | |
| A reaction: Are the worlds naturally, or metaphysically, or logically possible? |
| 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? |
| 10989 | The standard view of conditionals is that they are truth-functional [Read] |
| Full Idea: The standard view of conditionals is that they are truth-functional, that is, that their truth-values are determined by the truth-values of their constituents. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.3) |
| 11017 | Some people even claim that conditionals do not express propositions [Read] |
| Full Idea: Some people even claim that conditionals do not express propositions. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.7) | |
| A reaction: See Idea 14283, where this appears to have been 'proved' by Lewis, and is not just a view held by some people. |
| 10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
| Full Idea: The point of conditionals is to show that one will accept modus ponens. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.3) | |
| A reaction: [He attributes this idea to Frank Jackson] This makes the point, against Grice, that the implication of conditionals is not conversational but a matter of logical convention. See Idea 21396 for a very different view. |
| 10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
| Full Idea: The modal Platonist denies that knowledge always depends on a causal relation. The reality of possible worlds is an ontological requirement, to secure the truth-values of modal propositions. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: [Reply to Idea 10982] This seems to be a case of deriving your metaphyics from your semantics, of which David Lewis seems to be guilty, and which strikes me as misguided. |
| 10982 | How can modal Platonists know the truth of a modal proposition? [Read] |
| Full Idea: If modal Platonism was true, how could we ever know the truth of a modal proposition? | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: I take this to be very important. Our knowledge of modal truths must depend on our knowledge of the actual world. The best answer seems to involve reference to the 'powers' of the actual world. A reply is in Idea 10983. |
| 10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read] |
| Full Idea: There are two main forms of actualism: reductionism, which seeks to construct possible worlds out of some more mundane material; and moderate realism, in which the actual concrete world is contrasted with abstract, but none the less real, possible worlds. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.4) | |
| A reaction: I am a reductionist, as I do not take abstractions to be 'real' (precisely because they have been 'abstracted' from the things that are real). I think I will call myself a 'scientific modalist' - we build worlds from possibilities, discovered by science. |
| 10981 | A possible world is a determination of the truth-values of all propositions of a domain [Read] |
| Full Idea: A possible world is a complete determination of the truth-values of all propositions over a certain domain. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: Even if the domain is very small? Even if the world fitted the logic nicely, but was naturally impossible? |
| 11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read] |
| Full Idea: If each possible world constitutes a concrete reality, then no object can be present in more than one world - objects may have 'counterparts', but cannot be identical with them. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.4) | |
| A reaction: This explains clearly why in Lewis's modal realist scheme he needs counterparts instead of rigid designation. Sounds like a slippery slope. If you say 'Humphrey might have won the election', who are you talking about? |
| 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. |
| 10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
| Full Idea: Ways things might be are real, but only when abstracted from the actual way things are. They are brought out and distinguished by the mind, by abstraction, but are not dependent on mind for their existence. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.4) | |
| A reaction: To me this just flatly contradicts itself. The idea that the mind can 'bring something out' by its operations, with the result being then accepted as part of reality is nonsense on stilts. What is real is the powers that make the possibilities. |
| 11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
| Full Idea: A problem with compositionality is negative existential propositions. If some of the terms of the proposition are empty, and don't refer, then compositionality implies that the whole will lack meaning too. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.5) | |
| A reaction: I don't agree. I don't see why compositionality implies holism about sentence-meaning. If I say 'that circular square is a psychopath', you understand the predication, despite being puzzled by the singular term. |
| 10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
| Full Idea: A proposition makes an object out of what is said or expressed by the utterance of a certain sort of sentence, namely, one in the indicative mood which makes sense and doesn't fail in its references. It can then be an object of thought and belief. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.1) | |
| A reaction: Nice, but two objections: I take it to be crucial to propositions that they eliminate ambiguities, and I take it that animals are capable of forming propositions. Read seems to regard them as fictions, but I take them to be brain events. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |