99 ideas
| 7001 | If you begin philosophy with language, you find yourself trapped in it [Heil] |
| Full Idea: If you start with language and try to work your way outwards, you will never get outside language. | |
| From: John Heil (From an Ontological Point of View [2003], Pref) | |
| A reaction: This voices my pessimism about the linguistic approach to philosophy (and I don't just mean analysis of ordinary language), though I wonder if the career of (say) John Searle is a counterexample. |
| 7038 | A theory with few fundamental principles might still posit a lot of entities [Heil] |
| Full Idea: It could well turn out that a simpler theory - a theory with fewer fundamental principles - posits more entities than a more complex competitor. | |
| From: John Heil (From an Ontological Point of View [2003], 13.6) | |
| A reaction: See also Idea 4036. The point here is that you can't simply translate Ockham as 'keep it simple', as there are different types of simplicity. The best theory will negotiate a balance between entities and principles. |
| 7037 | Parsimony does not imply the world is simple, but that our theories should try to be [Heil] |
| Full Idea: A commitment to parsimony is not a commitment to a conception of the world as simple. The idea, rather, is that we should not complicate our theories about the world unnecessarily. | |
| From: John Heil (From an Ontological Point of View [2003], 13.6) | |
| A reaction: In other words, Ockham's Razor is about us, not about the world. It would be absurd to make the a priori assumption that the world has to be simple. Are we, though, creating bad theories by insisting that they should be simple? |
| 9955 | Contextual definitions replace a complete sentence containing the expression [George/Velleman] |
| Full Idea: A contextual definition shows how to analyse an expression in situ, by replacing a complete sentence (of a particular form) in which the expression occurs by another in which it does not. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: This is a controversial procedure, which (according to Dummett) Frege originally accepted, and later rejected. It might not be the perfect definition that replacing just the expression would give you, but it is a promising step. |
| 10031 | Impredicative definitions quantify over the thing being defined [George/Velleman] |
| Full Idea: When a definition contains a quantifier whose range includes the very entity being defined, the definition is said to be 'impredicative'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: Presumably they are 'impredicative' because they do not predicate a new quality in the definiens, but make use of the qualities already known. |
| 7004 | The view that truth making is entailment is misguided and misleading [Heil] |
| Full Idea: I argue that the widely held view that truth making is to be understood as entailment is misguided in principle and potentially misleading. | |
| From: John Heil (From an Ontological Point of View [2003], Intro) | |
| A reaction: If reality was just one particle, what would entail the truths about it? Suppose something appears to be self-evident true about reality, but no one can think of any entailments to derive it? Do we assume a priori that they are possible? |
| 10098 | The 'power set' of A is all the subsets of A [George/Velleman] |
| Full Idea: The 'power set' of A is all the subsets of A. P(A) = {B : B ⊆ A}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10099 | The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}} [George/Velleman] |
| Full Idea: The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}}. The existence of this set is guaranteed by three applications of the Axiom of Pairing. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: See Idea 10100 for the Axiom of Pairing. |
| 10101 |
Cartesian Product A x B: the set of all ordered pairs |
| Full Idea: The 'Cartesian Product' of any two sets A and B is the set of all ordered pairs <a, b> in which a ∈ A and b ∈ B, and it is denoted as A x B. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10103 | Grouping by property is common in mathematics, usually using equivalence [George/Velleman] |
| Full Idea: The idea of grouping together objects that share some property is a common one in mathematics, ...and the technique most often involves the use of equivalence relations. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10104 | 'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman] |
| Full Idea: A relation is an equivalence relation if it is reflexive, symmetric and transitive. The 'same first letter' is an equivalence relation on the set of English words. Any relation that puts a partition into clusters will be equivalence - and vice versa. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This is a key concept in the Fregean strategy for defining numbers. |
| 10096 | Even the elements of sets in ZFC are sets, resting on the pure empty set [George/Velleman] |
| Full Idea: ZFC is a theory concerned only with sets. Even the elements of all of the sets studied in ZFC are also sets (whose elements are also sets, and so on). This rests on one clearly pure set, the empty set Φ. ..Mathematics only needs pure sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This makes ZFC a much more metaphysically comfortable way to think about sets, because it can be viewed entirely formally. It is rather hard to disentangle a chair from the singleton set of that chair. |
| 10097 | Axiom of Extensionality: for all sets x and y, if x and y have the same elements then x = y [George/Velleman] |
| Full Idea: The Axiom of Extensionality says that for all sets x and y, if x and y have the same elements then x = y. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This seems fine in pure set theory, but hits the problem of renates and cordates in the real world. The elements coincide, but the axiom can't tell you why they coincide. |
| 10100 | Axiom of Pairing: for all sets x and y, there is a set z containing just x and y [George/Velleman] |
| Full Idea: The Axiom of Pairing says that for all sets x and y, there is a set z containing x and y, and nothing else. In symbols: ∀x∀y∃z∀w(w ∈ z ↔ (w = x ∨ w = y)). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: See Idea 10099 for an application of this axiom. |
| 17900 | The Axiom of Reducibility made impredicative definitions possible [George/Velleman] |
| Full Idea: The Axiom of Reducibility ...had the effect of making impredicative definitions possible. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10109 | ZFC can prove that there is no set corresponding to the concept 'set' [George/Velleman] |
| Full Idea: Sets, unlike extensions, fail to correspond to all concepts. We can prove in ZFC that there is no set corresponding to the concept 'set' - that is, there is no set of all sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: This is rather an important point for Frege. However, all concepts have extensions, but they may be proper classes, rather than precisely defined sets. |
| 7035 | God does not create the world, and then add the classes [Heil] |
| Full Idea: It is hard to see classes as an 'addition of being'; God does not create the world, and then add the classes. | |
| From: John Heil (From an Ontological Point of View [2003], 13.4 n6) | |
| A reaction: This seems right. We may be tempted into believing in the reality of classes when considering maths, but it seems utterly implausible when considering trees or cows. |
| 10108 | As a reduction of arithmetic, set theory is not fully general, and so not logical [George/Velleman] |
| Full Idea: The problem with reducing arithmetic to ZFC is not that this theory is inconsistent (as far as we know it is not), but rather that is not completely general, and for this reason not logical. For example, it asserts the existence of sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: Note that ZFC has not been proved consistent. |
| 10111 | Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman] |
| Full Idea: A hallmark of our realist stance towards the natural world is that we are prepared to assert the Law of Excluded Middle for all statements about it. For all statements S, either S is true, or not-S is true. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: Personally I firmly subscribe to realism, so I suppose I must subscribe to Excluded Middle. ...Provided the statement is properly formulated. Or does liking excluded middle lead me to realism? |
| 10129 | A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman] |
| Full Idea: A 'model' of a theory is an assignment of meanings to the symbols of its language which makes all of its axioms come out true. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: If the axioms are all true, and the theory is sound, then all of the theorems will also come out true. |
| 10105 | Differences between isomorphic structures seem unimportant [George/Velleman] |
| Full Idea: Mathematicians tend to regard the differences between isomorphic mathematical structures as unimportant. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This seems to be a pointer towards Structuralism as the underlying story in mathematics. The intrinsic character of so-called 'objects' seems unimportant. How theories map onto one another (and onto the world?) is all that matters? |
| 10119 | Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman] |
| Full Idea: Consistency is a purely syntactic property, unlike the semantic property of soundness. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10126 | A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman] |
| Full Idea: If there is a sentence such that both the sentence and its negation are theorems of a theory, then the theory is 'inconsistent'. Otherwise it is 'consistent'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) |
| 10120 | Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman] |
| Full Idea: Soundness is a semantic property, unlike the purely syntactic property of consistency. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10127 | A 'complete' theory contains either any sentence or its negation [George/Velleman] |
| Full Idea: If there is a sentence such that neither the sentence nor its negation are theorems of a theory, then the theory is 'incomplete'. Otherwise it is 'complete'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: Interesting questions are raised about undecidable sentences, irrelevant sentences, unknown sentences.... |
| 10106 | Rational numbers give answers to division problems with integers [George/Velleman] |
| Full Idea: We can think of rational numbers as providing answers to division problems involving integers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Cf. Idea 10102. |
| 10102 | The integers are answers to subtraction problems involving natural numbers [George/Velleman] |
| Full Idea: In defining the integers in set theory, our definition will be motivated by thinking of the integers as answers to subtraction problems involving natural numbers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Typical of how all of the families of numbers came into existence; they are 'invented' so that we can have answers to problems, even if we can't interpret the answers. It it is money, we may say the minus-number is a 'debt', but is it? Cf Idea 10106. |
| 10107 | Real numbers provide answers to square root problems [George/Velleman] |
| Full Idea: One reason for introducing the real numbers is to provide answers to square root problems. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Presumably the other main reasons is to deal with problems of exact measurement. It is interesting that there seem to be two quite distinct reasons for introducing the reals. Cf. Ideas 10102 and 10106. |
| 9946 | Logicists say mathematics is applicable because it is totally general [George/Velleman] |
| Full Idea: The logicist idea is that if mathematics is logic, and logic is the most general of disciplines, one that applies to all rational thought regardless of its content, then it is not surprising that mathematics is widely applicable. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: Frege was keen to emphasise this. You are left wondering why pure logic is applicable to the physical world. The only account I can give is big-time Platonism, or Pythagoreanism. Logic reveals the engine-room of nature, where the design is done. |
| 10125 | The classical mathematician believes the real numbers form an actual set [George/Velleman] |
| Full Idea: Unlike the intuitionist, the classical mathematician believes in an actual set that contains all the real numbers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 17899 | Second-order induction is stronger as it covers all concepts, not just first-order definable ones [George/Velleman] |
| Full Idea: The first-order version of the induction axiom is weaker than the second-order, because the latter applies to all concepts, but the first-order applies only to concepts definable by a formula in the first-order language of number theory. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7 n7) |
| 10128 | The Incompleteness proofs use arithmetic to talk about formal arithmetic [George/Velleman] |
| Full Idea: The idea behind the proofs of the Incompleteness Theorems is to use the language of Peano Arithmetic to talk about the formal system of Peano Arithmetic itself. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: The mechanism used is to assign a Gödel Number to every possible formula, so that all reasonings become instances of arithmetic. |
| 17902 | A successor is the union of a set with its singleton [George/Velleman] |
| Full Idea: For any set x, we define the 'successor' of x to be the set S(x) = x U {x}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This is the Fregean approach to successor, where the Dedekind approach takes 'successor' to be a primitive. Frege 1884:§76. |
| 10133 | Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle [George/Velleman] |
| Full Idea: The derivability of Peano's Postulates from Hume's Principle in second-order logic has been dubbed 'Frege's Theorem', (though Frege would not have been interested, because he didn't think Hume's Principle gave an adequate definition of numebrs). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8 n1) | |
| A reaction: Frege said the numbers were the sets which were the extensions of the sets created by Hume's Principle. |
| 10130 | Set theory can prove the Peano Postulates [George/Velleman] |
| Full Idea: The Peano Postulates can be proven in ZFC. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) |
| 10089 | Talk of 'abstract entities' is more a label for the problem than a solution to it [George/Velleman] |
| Full Idea: One might well wonder whether talk of abstract entities is less a solution to the empiricist's problem of how a priori knowledge is possible than it is a label for the problem. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Intro) | |
| A reaction: This pinpoints my view nicely. What the platonist postulates is remote, bewildering, implausible and useless! |
| 10131 | If mathematics is not about particulars, observing particulars must be irrelevant [George/Velleman] |
| Full Idea: As, in the logicist view, mathematics is about nothing particular, it is little wonder that nothing in particular needs to be observed in order to acquire mathematical knowledge. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002]) | |
| A reaction: At the very least we can say that no one would have even dreamt of the general system of arithmetic is they hadn't had experience of the particulars. Frege thought generality ensured applicability, but extreme generality might entail irrelevance. |
| 10092 | In the unramified theory of types, the types are objects, then sets of objects, sets of sets etc. [George/Velleman] |
| Full Idea: In the unramified theory of types, all objects are classified into a hierarchy of types. The lowest level has individual objects that are not sets. Next come sets whose elements are individuals, then sets of sets, etc. Variables are confined to types. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: The objects are Type 0, the basic sets Type 1, etc. |
| 10094 | The theory of types seems to rule out harmless sets as well as paradoxical ones. [George/Velleman] |
| Full Idea: The theory of types seems to rule out harmless sets as well as paradoxical ones. If a is an individual and b is a set of individuals, then in type theory we cannot talk about the set {a,b}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Since we cheerfully talk about 'Cicero and other Romans', this sounds like a rather disasterous weakness. |
| 10095 | Type theory has only finitely many items at each level, which is a problem for mathematics [George/Velleman] |
| Full Idea: A problem with type theory is that there are only finitely many individuals, and finitely many sets of individuals, and so on. The hierarchy may be infinite, but each level is finite. Mathematics required an axiom asserting infinitely many individuals. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Most accounts of mathematics founder when it comes to infinities. Perhaps we should just reject them? |
| 17901 | Type theory prohibits (oddly) a set containing an individual and a set of individuals [George/Velleman] |
| Full Idea: If a is an individual and b is a set of individuals, then in the theory of types we cannot talk about the set {a,b}, since it is not an individual or a set of individuals, ...but it is hard to see what harm can come from it. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10114 | Bounded quantification is originally finitary, as conjunctions and disjunctions [George/Velleman] |
| Full Idea: In the first instance all bounded quantifications are finitary, for they can be viewed as abbreviations for conjunctions and disjunctions. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) | |
| A reaction: This strikes me as quite good support for finitism. The origin of a concept gives a good guide to what it really means (not a popular view, I admit). When Aristotle started quantifying, I suspect of he thought of lists, not totalities. |
| 10134 | Much infinite mathematics can still be justified finitely [George/Velleman] |
| Full Idea: It is possible to use finitary reasoning to justify a significant part of infinitary mathematics. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8) | |
| A reaction: This might save Hilbert's project, by gradually accepting into the fold all the parts which have been giving a finitist justification. |
| 10123 | The intuitionists are the idealists of mathematics [George/Velleman] |
| Full Idea: The intuitionists are the idealists of mathematics. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10124 | Gödel's First Theorem suggests there are truths which are independent of proof [George/Velleman] |
| Full Idea: For intuitionists, truth is not independent of proof, but this independence is precisely what seems to be suggested by Gödel's First Incompleteness Theorem. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8) | |
| A reaction: Thus Gödel was worse news for the Intuitionists than he was for Hilbert's Programme. Gödel himself responded by becoming a platonist about his unprovable truths. |
| 7017 | The reductionist programme dispenses with levels of reality [Heil] |
| Full Idea: The reductionist programme dispenses with levels of reality. | |
| From: John Heil (From an Ontological Point of View [2003], 04.3) | |
| A reaction: Fodor, for example, claims that certain causal laws only operate at high levels of reality. I agree with Heil's idea - the notion that there are different realities around here that don't connect properly to one another is philosopher's madness. |
| 7003 | There are levels of organisation, complexity, description and explanation, but not of reality [Heil] |
| Full Idea: We should accept levels of organisation, levels of complexity, levels of description, and levels of explanation, but not the levels of reality favoured by many anti-reductionists. The world is then ontologically, but not analytically, reductive. | |
| From: John Heil (From an Ontological Point of View [2003], Intro) | |
| A reaction: This sounds right to me. The crunch questions seem to be whether the boundaries at higher levels of organisation exist lower down, and whether the causal laws of the higher levels can be translated without remainder into lower level laws. |
| 7045 | Realism says some of our concepts 'cut nature at the joints' [Heil] |
| Full Idea: Realism is sometimes said to involve a commitment to the idea that certain of our concepts, those with respect to which we are realists, 'carve reality at the joints'. | |
| From: John Heil (From an Ontological Point of View [2003], 14.11) | |
| A reaction: Clearly not all concepts cut nature at the joints (e.g. we have concepts of things we know to be imaginary). Personally I am committed to this view of realism. I try very hard to use concepts that cut accurately; why shouldn't I sometimes succeed? |
| 7065 | Anti-realists who reduce reality to language must explain the existence of language [Heil] |
| Full Idea: Anti-realist philosophers, and those who hope to reduce metaphysics to (or replace it with) the philosophy of language, owe the rest of us an account of the ontology of language. | |
| From: John Heil (From an Ontological Point of View [2003], 20.6) | |
| A reaction: A nice turning-the-tables question. In all accounts of relativism, x is usually said to be relative to y. You haven't got proper relativism if you haven't relativised both x and y. But relativised them to what? Nietzsche's 'perspectivism' (Idea 4420)? |
| 7020 | Concepts don't carve up the world, which has endless overlooked or ignored divisions [Heil] |
| Full Idea: Concepts do not 'carve up' the world; the world already contains endless divisions, most of which we remain oblivious to or ignore. | |
| From: John Heil (From an Ontological Point of View [2003], 05.3) | |
| A reaction: Concepts could still carve up the world, without ever aspiring to do a complete job. We carve up the aspects that interest us, but the majority of the carving is in response to natural divisions, not whimsical conventions. |
| 7007 | I think of properties as simultaneously dispositional and qualitative [Heil] |
| Full Idea: Some philosophers who accept that properties are intrinsic features of objects regard them as pure powers, pure dispositionalities; I prefer to think of properties as simultaneously dispositional and qualitative. | |
| From: John Heil (From an Ontological Point of View [2003], Intro) | |
| A reaction: I am uneasy about 'qualitative' as a category, and am inclined to reduce it to being a dispositional power to cause primary and secondary qualities in observers. Roughness is only a power, not a quality, if there are no observers. |
| 7015 | A predicate applies truly if it picks out a real property of objects [Heil] |
| Full Idea: When a predicate applies truly to an object, it does so in virtue of designating a property possessed by that object and by every object to which the predicate truly applies (or would apply). | |
| From: John Heil (From an Ontological Point of View [2003], 03.3) | |
| A reaction: I am sympathetic to Heil's aim of shifting our attention from arbitrary predicates to natural properties, but it won't avoid Fodor's problem (Idea 7014) that all kinds of whimsical predicates will apply 'truly', but fail to pick out anything significant. |
| 7042 | A theory of universals says similarity is identity of parts; for modes, similarity is primitive [Heil] |
| Full Idea: The friend of universals has an account of similarity relations as relations of identity and partial identity; the friend of modes must regard similarity relations as primitive and irreducible. | |
| From: John Heil (From an Ontological Point of View [2003], 14.5) | |
| A reaction: We always seem to be able to ask 'in what respect' a similarity occurs. If similarity is 'primitive and irreducible', we should not be able to analyse and explain a similarity, yet we seem able to. I conclude that Heil is wrong. |
| 7023 | Powers or dispositions are usually seen as caused by lower-level qualities [Heil] |
| Full Idea: The modern default position on dispositionality is that powers or dispositions are higher-level properties objects possess by virtue of those objects' possession of lower-level qualitative (categorical) properties. | |
| From: John Heil (From an Ontological Point of View [2003], 09.2) | |
| A reaction: The new idea which is being floated by Heil, and which I prefer, is that dispositions or powers are basic. A 'quality' is a much more dubious entity than a power. |
| 7025 | Are a property's dispositions built in, or contingently added? [Heil] |
| Full Idea: There is a dispute over whether a property's dispositionality is built into the property or whether it is a contingent add-on. | |
| From: John Heil (From an Ontological Point of View [2003], 09.4) | |
| A reaction: Put that way, the idea that it is built in seems much more plausible. If it is an add-on, an explanation of why that disposition is added to that particular property seems required. If it is built in, it seems legitimate to accept it as a brute fact. |
| 7034 | Universals explain one-over-many relations, and similar qualities, and similar behaviour [Heil] |
| Full Idea: Universals can explain the one-over-many problem, and easily explain similarity relations between objects, and explain the similar behaviour of similar objects. | |
| From: John Heil (From an Ontological Point of View [2003], 13.1) | |
| A reaction: A useful summary. If you accept it, you seem to be faced with a choice between Plato (who has universals existing independently of particulars) and Armstrong (who makes them real, but existing only in particulars). |
| 7039 | How could you tell if the universals were missing from a world of instances? [Heil] |
| Full Idea: Imagine a pair of worlds, one in which there are the universals and their instances and one in which there are just the instances (a world of modes). How would the absence of universals make itself felt? | |
| From: John Heil (From an Ontological Point of View [2003], 13.7) | |
| A reaction: A nice question for Plato, very much in the spirit of Aristotle's string of questions. Compare 'suppose the physics remained, but someone removed the laws'. Either chaos ensues, or you realise they were redundant. Same with Forms. |
| 7009 | Similarity among modes will explain everthing universals were for [Heil] |
| Full Idea: My contention is that similarity among modes can do the job universals are conventionally postulated to do. | |
| From: John Heil (From an Ontological Point of View [2003], Intro) | |
| A reaction: See Idea 4441 for Russell's nice objection to this view. The very process by which we observes similarities (as assess their degrees) needs to be explained by any adequate theory of properties or universals. |
| 7041 | Similar objects have similar properties; properties are directly similar [Heil] |
| Full Idea: Objects are similar by virtue of possessing similar properties; properties, in contrast, are not similar in virtue of anything. | |
| From: John Heil (From an Ontological Point of View [2003], 14.2) | |
| A reaction: I am not sure if I can understand the concept of similarity if there is no answer to the question 'In what respect?' I suppose David Hume is happy to take resemblance as given and basic, but it could be defined as 'sharing identical properties'. |
| 7032 | Objects join sets because of properties; the property is not bestowed by set membership [Heil] |
| Full Idea: The set of red objects is the set of objects possessing a property: being red. Objects are members of the set in virtue of possessing this property; they do not possess the property in virtue of belonging to the set. | |
| From: John Heil (From an Ontological Point of View [2003], 12.2) | |
| A reaction: This seems to be a very effective denial of the claim that universals are sets. However, if 'being a Londoner' counts as a property, you can only have it by joining the London set. Being tall is more fundamental than being a Londoner. |
| 7008 | Trope theorists usually see objects as 'bundles' of tropes [Heil] |
| Full Idea: Philosophers identifying themselves as trope theorists have, by and large, accepted some form of the 'bundle theory' of objects: an object is a bundle of compresent tropes. | |
| From: John Heil (From an Ontological Point of View [2003], Intro) | |
| A reaction: This view eliminates anything called 'matter' or 'substance' or a 'bare particular'. I think I agree with Heil that this doesn't give a coherent picture, as properties seem to be 'of' something, and bundles always raise the question of what unites them. |
| 7018 | Objects are substances, which are objects considered as the bearer of properties [Heil] |
| Full Idea: I think of objects as substances, and a substance is an object considered as a bearer of properties. | |
| From: John Heil (From an Ontological Point of View [2003], 04.2) | |
| A reaction: This is an area of philosophy I always find disconcerting, where an account of how we should see objects seems to have no connection at all to what physicists report about objects. 'Considered as' seems to make substances entirely conventional. |
| 7019 | Maybe there is only one substance, space-time or a quantum field [Heil] |
| Full Idea: It would seem distinctly possible that there is but a single substance: space-time or some all-encompassing quantum field. | |
| From: John Heil (From an Ontological Point of View [2003], 05.2) | |
| A reaction: This would at least meet my concern that philosophers' 'substances' don't seem to connect to what physicists talk about. I wonder if anyone knows what a 'quantum field' is? The clash between relativity and quantum theory is being alluded to. |
| 7046 | Rather than 'substance' I use 'objects', which have properties [Heil] |
| Full Idea: I prefer the more colloquial 'object' to the traditional term 'substance'. An object can be regarded as a possessor of properties: as something that is red, spherical and pungent, for instance. | |
| From: John Heil (From an Ontological Point of View [2003], 15.3) | |
| A reaction: A nice move, but it seems to beg the question of 'what is it that has the properties?' Objects and substances do two different jobs in our ontology. Heil is just refusing to discuss what it is that has properties. |
| 7047 | Statues and bronze lumps have discernible differences, so can't be identical [Heil] |
| Full Idea: Applications of the principle of the indiscernibility of identicals apparently obliges us to distinguish the statue and the lump of bronze making it up. | |
| From: John Heil (From an Ontological Point of View [2003], 16.3) | |
| A reaction: In other words, statues and lumps of bronze have different properties. It is a moot point, though, whether there are any discernible differences between that statue at time t and its constituting lump of bronze at time t. |
| 7048 | Do we reduce statues to bronze, or eliminate statues, or allow statues and bronze? [Heil] |
| Full Idea: Must we choose between reductionism (the statue is the lump of bronze), eliminativism (there are no statues, only statue-shaped lumps of bronze), and a commitment to coincident objects? | |
| From: John Heil (From an Ontological Point of View [2003], 16.5) | |
| A reaction: (Heil goes on to offer his own view). Coincident objects sounds the least plausible view. Modern statues are only statues if we see them that way, but a tree is definitely a tree. Trenton Merricks is good on eliminativism. |
| 7030 | Properties don't possess ways they are, because that just is the property [Heil] |
| Full Idea: Objects possess properties, but I am sceptical of the idea that properties possess properties; just as a property is a way some object is, a property of a property would be a way a property is, but that is just the property itself. | |
| From: John Heil (From an Ontological Point of View [2003], 12.1) | |
| A reaction: This is quite a good defence of the idea that properties are qualities as well as dispositions. However, if we make the qualities of properties into secondary qualities, and the dispositions into primary qualities, the absurdity melts away. |
| 7028 | If properties were qualities without dispositions, they would be undetectable [Heil] |
| Full Idea: A pure quality, a property altogether lacking in dispositionality, would be undetectable and would, in one obvious sense, make no difference to its possessor. | |
| From: John Heil (From an Ontological Point of View [2003], 11.4) | |
| A reaction: This seems to be a very forceful and simple reason why we cannot view properties simply as qualities of things. Heil wants properties to be dispositions and qualities; personally I would vote for them just being dispositions or powers. |
| 7029 | Can we distinguish the way a property is from the property? [Heil] |
| Full Idea: It is not clear to me that we easily distinguish ways a property is from the property itself. | |
| From: John Heil (From an Ontological Point of View [2003], 11.6) | |
| A reaction: To defend properties as qualities, he is confusing ontology and epistemology. Presumably he means by 'ways a property is' what I would prefer to call 'ways a property seems to be'. I don't believe a smell is simply what it seems to be. |
| 7051 | Objects only have secondary qualities because they have primary qualities [Heil] |
| Full Idea: Secondary qualities are not distinct from primary qualities: an object's possession of a given secondary quality is a matter of its possession of certain complex primary qualities. | |
| From: John Heil (From an Ontological Point of View [2003], 17.3) | |
| A reaction: The bottom line here is that, if essentialism is right, colours are not properties at all (see Idea 5456). Heil wants to subsume secondary properties within primary properties. I think we should sharply distinguish them. |
| 7044 | Secondary qualities are just primary qualities considered in the light of their effect on us [Heil] |
| Full Idea: Secondary qualities are just ordinary properties - roughly, Locke's primary qualities - considered in the light of their effects on us. | |
| From: John Heil (From an Ontological Point of View [2003], 14.10) | |
| A reaction: Unconvincing. If they only acquire their ontological status as primary qualities if they have to be considered in relation to something (us), then that is not a primary quality. |
| 7052 | Colours aren't surface properties, because of radiant sources and the colour of the sky [Heil] |
| Full Idea: Theories that take colours to be properties of the surfaces of objects have difficulty accounting for a host of phenomena including coloured light emitted by radiant sources and so-called film colours (the colour of the sky, for instance). | |
| From: John Heil (From an Ontological Point of View [2003], 17.4) | |
| A reaction: Personally I never thought that colours might be actual properties of surfaces, but it is nice to have spelled out a couple of instances that make it very implausible. Neon and sodium lights I take to be examples of the first case. |
| 7053 | Treating colour as light radiation has the implausible result that tomatoes are not red [Heil] |
| Full Idea: Theories that tie colours to features of light radiation deal with radiant and diffused colours, but yield implausible results for objects; tomatoes are not red, on such a view, but merely reflect red light. | |
| From: John Heil (From an Ontological Point of View [2003], 17.4) | |
| A reaction: I see absolutely no problem with the philosophical denial that tomatoes are actually red, while continuing to use 'red' of tomatoes in the normal way. When we analyse our processes of knowledge acquisition, we must give up 'common sense'. |
| 7066 | If the world is just texts or social constructs, what are texts and social constructs? [Heil] |
| Full Idea: For those who regard the world as text or a social construct, are texts and social constructs real entities? If they are, what are they? | |
| From: John Heil (From an Ontological Point of View [2003], 20.6) | |
| A reaction: A nice turn-the-tables question. The oldest attacks of all on scepticism and relativism consist of showing that the positions themselves rest on knowledge or truth. Nietzsche may be the best model for relativists. E.g. Idea 4420. |
| 7021 | If the world is theory-dependent, the theories themselves can't be theory-dependent [Heil] |
| Full Idea: If the world is somehow theory-dependent, this implies, on pain of a regress, that theories are not theory-dependent. | |
| From: John Heil (From an Ontological Point of View [2003], 06.4) | |
| A reaction: I am not sure where this puts the ontology of theories, but this is a nice question, of a type which never seems to occur to your more simple-minded relativist. |
| 7026 | Science is sometimes said to classify powers, neglecting qualities [Heil] |
| Full Idea: The sciences are sometimes said to be in the business of identifying and classifying powers; the mass of an electron, its spin and charge, could be regarded as powers possessed by the electron; science is silent on an electron's qualities. | |
| From: John Heil (From an Ontological Point of View [2003], 11.2) | |
| A reaction: Heil raises the possibility that qualities are real, despite the silence of science; he wants colour to be a real quality. I like the simpler version of science. Qualities are the mental effects of powers; there exist substances, powers and effects. |
| 7060 | One form of explanation is by decomposition [Heil] |
| Full Idea: One form of explanation is by decomposition. | |
| From: John Heil (From an Ontological Point of View [2003], 19.8) | |
| A reaction: This is a fancy word for taking it apart, presumably to see how it works, which implies a functional explanation, rather than to see what it is made of, which seeks an ontological explanation. Simply 'decomposing' something wouldn't in itself explain. |
| 7010 | Dispositionality provides the grounding for intentionality [Heil] |
| Full Idea: Dispositionality provides the grounding for intentionality. | |
| From: John Heil (From an Ontological Point of View [2003], Intro) | |
| A reaction: This is a view with which I am sympathetic, though I am not sure if it explains anything. It would be necessary to identify a disposition of basic matter that could be built up into the disposition of a brain to think about things. |
| 7054 | Intentionality now has internalist (intrinsic to thinkers) and externalist (environment or community) views [Heil] |
| Full Idea: Nowadays philosophers concerned with intentionality divide into two camps. Internalists epitomise a traditional approach to thought, as intrinsic features of thinkers; externalists say it depends on contextual factors (environment or community). | |
| From: John Heil (From an Ontological Point of View [2003], 18.2) | |
| A reaction: This is basic to understanding modern debates (those that grow out of Putnam's Twin Earth). Externalism is fashionable, but I am reluctant to shake off my quaint internalism. Start by separating strict and literal meaning from speaker's meaning. |
| 7011 | Qualia are not extra appendages, but intrinsic ingredients of material states and processes [Heil] |
| Full Idea: Properties of conscious experience, the so-called qualia, are not dangling appendages to material states and processes but intrinsic ingredients of those states and processes. | |
| From: John Heil (From an Ontological Point of View [2003], Intro) | |
| A reaction: Personally I am inclined to the view that qualia are intrinsic to the processes and NOT to the 'states'. Heil must be right, though. I am sure qualia are not just epiphenomena - they are too useful. |
| 7061 | Philosophers' zombies aim to show consciousness is over and above the physical world [Heil] |
| Full Idea: Philosophers' zombies (invented by Robert Kirk) differ from the zombies of folklore; they are intended to make clear the idea that consciousness is an addition of being, something 'over and above' the physical world. | |
| From: John Heil (From an Ontological Point of View [2003], 20.1 n1) | |
| A reaction: The famous defender of zombies is David Chalmers. You can't believe in zombies if you believe (as I do) that 'the physical entails the mental'. Could there be redness without something that is red? If consciousness is extra, what is conscious? |
| 7063 | Zombies are based on the idea that consciousness relates contingently to the physical [Heil] |
| Full Idea: The possibility of zombies is founded on the idea that consciousness is related contingently to physical states and processes. | |
| From: John Heil (From an Ontological Point of View [2003], 20.3) | |
| A reaction: The question is, how do you decide whether the relationship is contingent or necessary? Hence the interest in whether conceivability entails possibility. Kripke attacks the idea of contingent identity, pointing towards necessity, and away from zombies. |
| 7064 | Functionalists deny zombies, since identity of functional state means identity of mental state [Heil] |
| Full Idea: Functionalists deny that zombies are possible since states of mind (including conscious states) are purely functional states. If two agents are in the same functional state, regardless of qualitative difference, they are in the same mental state. | |
| From: John Heil (From an Ontological Point of View [2003], 20.5) | |
| A reaction: In its 'brief' form this idea begins to smell of tautology. Only the right sort of functional state would entail a mental state, and how else can that functional state be defined, apart from its leading to a mental state? |
| 7027 | Functionalists say objects can be the same in disposition but differ in quality [Heil] |
| Full Idea: A central tenet of functionalism is that objects can be dispositionally indiscernible but differ qualitatively as much as you please. | |
| From: John Heil (From an Ontological Point of View [2003], 11.3) | |
| A reaction: This refers to the multiple realisability of functions. Presumably we reconcile essentialism with the functionalist view by saying that dispositions result from combinations of qualities. A unique combination of qualities will necessitate a disposition. |
| 7062 | Functionalism cannot explain consciousness just by functional organisation [Heil] |
| Full Idea: Functionalism has been widely criticized on the grounds that it is implausible to think that functional organization alone could suffice for conscious experience. | |
| From: John Heil (From an Ontological Point of View [2003], 20.2) | |
| A reaction: He cites Block's 'Chinese Mind' as an example. The obvious reply is that you can't explain consciousness with a lump of meat, or with behaviour, or with an anomalous property, or even with a non-physical substance. |
| 7059 | The 'explanatory gap' is used to say consciousness is inexplicable, at least with current concepts [Heil] |
| Full Idea: The expression 'explanatory gap' was coined by Joseph Levine in 1983. McGinn and Chalmers have invoked it in defence of the view that consciousness is physically inexplicable, and Nagel that it is inexplicable given existing conceptual resources. | |
| From: John Heil (From an Ontological Point of View [2003], 19.8 n14) | |
| A reaction: Coining a few concepts isn't going to help, but discovering more about the brain might. With computer simulations we will 'see' more of the physical end of thought. Psychologists may break thought down into physically more manageable components. |
| 7012 | If a car is a higher-level entity, distinct from its parts, how could it ever do anything? [Heil] |
| Full Idea: If we regard a Volvo car as a higher-level entity with its own independent reality, something distinct from its constituents (arranged in particular ways and variously connected to other things), we render mysterious how Volvos could do anything at all. | |
| From: John Heil (From an Ontological Point of View [2003], 02.3) | |
| A reaction: This seems to me perhaps the key reason why we have to be reductionists. The so-called 'bridge laws' from mind to brain are not just needed to explain the mind, they are also essential to show how a mind would cause behaviour. |
| 7043 | Multiple realisability is actually one predicate applying to a diverse range of properties [Heil] |
| Full Idea: Cases of multiple realisability are typically cases in which some predicate ('is red', 'is in pain') applies to an object in virtue of that object's possession of any of a diverse range of properties. | |
| From: John Heil (From an Ontological Point of View [2003], 14.8) | |
| A reaction: If the properties are diverse, why does one predicate apply to them? I take it that in the case of the pain, the predicate is ambiguous in applying to the behaviour or the phenomenal property. Same behaviour is possible with many qualia. |
| 7058 | Externalism is causal-historical, or social, or biological [Heil] |
| Full Idea: Some externalists focus on causal-historical connections, others emphasise social matters (especially thinkers' linguistic communities), still others focus on biological function. | |
| From: John Heil (From an Ontological Point of View [2003], 18.5 n6) | |
| A reaction: Helpful. The social view strikes me as the one to take most seriously (allowing for contextual views of justification, and for the social role of experts). The problem is to combine the social view with realism and a robust view of truth. |
| 7057 | Intentionality is based in dispositions, which are intrinsic to agents, suggesting internalism [Heil] |
| Full Idea: I suggest that intentionality is grounded in the dispositionalities of agents. Dispositions are intrinsic to agents, so this places me on the side of the internalists and against the externalists. | |
| From: John Heil (From an Ontological Point of View [2003], 18.4) | |
| A reaction: I think this is a key idea, and the right view. The key question is whether we see intentionality as active or passive. The externalist view seems to see the brain as a passive organ which the world manipulates. If the brain is active, what is it doing? |
| 10110 | Corresponding to every concept there is a class (some of them sets) [George/Velleman] |
| Full Idea: Corresponding to every concept there is a class (some classes will be sets, the others proper classes). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) |
| 7013 | The Picture Theory claims we can read reality from our ways of speaking about it [Heil] |
| Full Idea: The theory of language which I designate the 'Picture Theory' says that language pictures reality in roughly the sense that we can 'read off' features of reality from our ways of speaking about it. | |
| From: John Heil (From an Ontological Point of View [2003], 03.2) | |
| A reaction: Heil, quite rightly, attacks this view very strongly. I think of it as the great twentieth century philosophical heresy, that leads to shocking views like relativism and anti-realism. |
| 7002 | If propositions are states of affairs or sets of possible worlds, these lack truth values [Heil] |
| Full Idea: When pressed, philosophers will describe propositions as states of affairs or sets of possible worlds. But wait! Neither sets of possible worlds nor states of affairs - electrons being negatively charged, for instance - have truth values. | |
| From: John Heil (From an Ontological Point of View [2003], Intro) | |
| A reaction: I'm not sure that I see a problem. A pure proposition, expressed as, say "there is a giraffe on the roof" only acquires a truth value at the point where you assert it or believe it. There IS a possible world where there is a giraffe on the roof. |
| 20416 | By 1790 aestheticians were mainly trying to explain individual artistic genius [Kemp] |
| Full Idea: By 1790 the idea that a central task for the aesthetician was to explain or at least adequately to describe the phenomenon of the individual artistic genius had definitely taken hold. | |
| From: Gary Kemp (Croce and Collingwood [2012], Intro) | |
| A reaction: Hence when Kant and Hegel write about art, though are only really thinking of the greatest art (which might be in touch with the sublime or Spirit etc.). Nowadays I think we expect accounts of art to cover modest amateur efforts as well. |
| 20417 | Expression can be either necessary for art, or sufficient for art (or even both) [Kemp] |
| Full Idea: Seeing art as expression has two components: 1) if something is a work of art, then it is expressive, 2) if something is expressive, then it is a work of art. So expression can be necessary or sufficient for art. (or both, for Croce and Collingwood). | |
| From: Gary Kemp (Croce and Collingwood [2012], 1) | |
| A reaction: I take the idea that art 'expresses' the feelings of an artist to be false. Artists are more like actors. Nearly all art has some emotional impact, which is of major importance, but I don't think 'expression' is a very good word for that. |
| 20419 | We don't already know what to express, and then seek means of expressing it [Kemp] |
| Full Idea: One cannot really know, or be conscious of, what it is that one is going to express, and then set about expressing it; indeed if one is genuinely conscious of it then one has already expressed it. | |
| From: Gary Kemp (Croce and Collingwood [2012], 1) | |
| A reaction: That pretty conclusively demolishes the idea that art is expression. I picture Schubert composing at the piano: he doesn't feel an emotion, and then hunt for its expression on the keyboard; he seeks out expressive phrases by playing. |
| 20418 | The horror expressed in some works of art could equallly be expressed by other means [Kemp] |
| Full Idea: The horror or terror of Edvard Much's 'The Scream' could in principle be expressed by different paintings, or even by works of music. | |
| From: Gary Kemp (Croce and Collingwood [2012], 1) | |
| A reaction: A very good simple point against the idea that the point of art is expression. It leaves out the very specific nature of each work of art! |
| 7016 | The standard view is that causal sequences are backed by laws, and between particular events [Heil] |
| Full Idea: The notion that every causal sequence if backed by a law, like the idea that causation is a relation among particular events, forms a part of philosophy's Humean heritage. | |
| From: John Heil (From an Ontological Point of View [2003], 04.3) | |
| A reaction: This nicely pinpoints a view that needs to come under attack. I take the view that there are no 'laws' - other than the regularities in behaviour that result from the interaction of essential dispositional properties. Essences don't need laws. |
| 7036 | The real natural properties are sparse, but there are many complex properties [Heil] |
| Full Idea: I am sympathetic to the idea that the real properties are 'sparse'; ...but if, in counting kinds of property, we include complex properties as well as simple properties, the image of sparseness evaporates. | |
| From: John Heil (From an Ontological Point of View [2003], 13.4) | |
| A reaction: This seems right to me, and invites the obvious question of which are the sparse real properties. Presumably we let the physicists tell us that, though Heil wants to include qualities like phenomenal colour, which physicists ignore. |