58 ideas
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. |
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... |
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 in which a∈A and b∈B [George/Velleman] |
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. |
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). |
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. |
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. |
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? |
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. |
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.... |
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. |
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) |
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. |
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. |
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) |
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? |
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. |
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. |
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. |
8978 | Events are made of other things, and are not fundamental to ontology [Bennett] |
Full Idea: Events are not basic items in the universe; they should not be included in any fundamental ontology...all the truths about them are entailed by and explained and made true by truths that do not involve the event concept. | |
From: Jonathan Bennett (Events and Their Names [1988], p.12), quoted by Peter Simons - Events 3.1 | |
A reaction: Given the variable time spans of events, their ability to coincide, their ability to contain no motion, their blatantly conventional component, and their recalcitrance to individuation, I say Bennett is right. |
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. |
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) |
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'. |
10364 | Facts are about the world, not in it, so they can't cause anything [Bennett] |
Full Idea: Facts are not the sort of item that can cause anything. A fact is a true proposition (they say); it is not something in the world but is rather something about the world. | |
From: Jonathan Bennett (Events and Their Names [1988], p.22), quoted by Jonathan Schaffer - The Metaphysics of Causation 1.1 | |
A reaction: Compare 10361. Good argument, but maybe 'fact' is ambiguous. See Idea 10365. Events are said to be more concrete, and so can do the job, but their individuation also seems to depend on a description (as Davidson has pointed out). |
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? |