82 ideas
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| Full Idea: We are all post-Kantians, ...because Kant set an agenda for philosophy that we are still working through. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Hart says that the main agenda is set by Kant's desire to defend the principle of sufficient reason against Hume's attack on causation. I would take it more generally to be the assessment of metaphysics, and of a priori knowledge. |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| Full Idea: The real monuments of philosophy are its problems. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Presumably he means '....rather than its solutions'. No other subject would be very happy with that sort of claim. Compare Idea 8243. A complaint against analytic philosophy is that it has achieved no consensus at all. |
| 7950 | Philosophy tries to explain how the actual is possible, given that it seems impossible [Macdonald,C] |
| Full Idea: Philosophical problems are problems about how what is actual is possible, given that what is actual appears, because of some faulty argument, to be impossible. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: [She is discussing universals when she makes this comment] A very appealing remark, given that most people come into philosophy because of a mixture of wonder and puzzlement. It is a rather Wittgensteinian view, though, that we must cure our own ills. |
| 7923 | 'Did it for the sake of x' doesn't involve a sake, so how can ontological commitments be inferred? [Macdonald,C] |
| Full Idea: In 'She did it for the sake of her country' no one thinks that the expression 'the sake' refers to an individual thing, a sake. But given that, how can we work out what the ontological commitments of a theory actually are? | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.1) | |
| A reaction: For these sorts of reasons it rapidly became obvious that ordinary language analysis wasn't going to reveal much, but it is also a problem for a project like Quine's, which infers an ontology from the terms of a scientific theory. |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| Full Idea: By now, no education in abstract pursuits is adequate without some familiarity with sets. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: A heart-sinking observation for those who aspire to study metaphysics and modality. The question is, what will count as 'some' familiarity? Are only professional logicians now allowed to be proper philosophers? |
| 7933 | Don't assume that a thing has all the properties of its parts [Macdonald,C] |
| Full Idea: The fallacy of composition makes the erroneous assumption that every property of the things that constitute a thing is a property of the thing as well. But every large object is constituted by small parts, and every red object by colourless parts. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.5) | |
| A reaction: There are nice questions here like 'If you add lots of smallness together, why don't you get extreme smallness?' Colours always make bad examples in such cases (see Idea 5456). Distinctions are needed here (e.g. Idea 7007). |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| Full Idea: It is an ancient and honourable view that truth is correspondence to fact; Tarski showed us how to do without facts here. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This is a very interesting spin on Tarski, who certainly seems to endorse the correspondence theory, even while apparently inventing a new 'semantic' theory of truth. It is controversial how far Tarski's theory really is a 'correspondence' theory. |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| Full Idea: We explain truth for sentences in terms of satisfaction of formulae. The crux here is that for a sentence, either all sequences satisfy it or none do (with no middle ground). For formulae, some sequences may satisfy it and others not. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This is the hardest part of Tarski's theory of truth to grasp. |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| Full Idea: In any first-order language, there are infinitely many T-sentences. Since definitions should be finite, the agglomeration of all the T-sentences is not a definition of truth. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This may be a warning shot aimed at Davidson's extensive use of Tarski's formal account in his own views on meaning in natural language. |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| Full Idea: A 'conditional proof' licenses inferences to a conditional from a deduction of its consequent from its antecedent. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: That is, a proof can be enshrined in an arrow. |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| Full Idea: When a quantifier is attached to a variable, as in '∃(y)....', then it should be read as 'There exists an individual, call it y, such that....'. One should not read it as 'There exists a y such that...', which would attach predicate to quantifier. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: The point is to make clear that in classical logic the predicates attach to the objects, and not to some formal component like a quantifier. |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| Full Idea: It is set theory, and more specifically the theory of relations, that articulates order. | |
| From: William D. Hart (The Evolution of Logic [2010]) | |
| A reaction: It would seem that we mainly need set theory in order to talk accurately about order, and about infinity. The two come together in the study of the ordinal numbers. |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| Full Idea: The theory of types is a thing of the past. There is now nothing to choose between ZFC and NBG (Neumann-Bernays-Gödel). NF (Quine's) is a more specialized taste, but is a place to look if you want the universe. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| Full Idea: ∈ relates across layers (Plato is a member of his unit set and the set of people), while ⊆ relates within layers (the singleton of Plato is a subset of the set of people). This distinction only became clear in the 19th century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: Getting these two clear may be the most important distinction needed to understand how set theory works. |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| Full Idea: Without the empty set, disjoint sets would have no intersection, and we could not form a∩b without checking that a and b meet. This is an example of the utility of the empty set. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: A novice might plausibly ask why there should be an intersection for every pair of sets, if they have nothing in common except for containing this little puff of nothingness. But then what do novices know? |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| Full Idea: In the second half of the twentieth century there emerged the opinion that foundation is the heart of the way to do set theory. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: It is foundation which is the central axiom of the iterative conception of sets, where each level of sets is built on previous levels, and they are all 'well-founded'. |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| Full Idea: The usual statement of Foundation is that any nonempty set has a member disjoint from it. This phrasing is ordinal-free and closer to the primitives of ZFC. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| Full Idea: When a set is finite, we can prove it has a choice function (∀x x∈A → f(x)∈A), but we need an axiom when A is infinite and the members opaque. From infinite shoes we can pick a left one, but from socks we need the axiom of choice. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The socks example in from Russell 1919:126. |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| Full Idea: It follows from the Axiom of Choice that every set can be well-ordered. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: For 'well-ordered' see Idea 13460. Every set can be ordered with a least member. |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| Full Idea: It has been said (by Burt Dreben) that the only reason set theorists do not generally buy the view that V = L is that it would put them out of business by settling their open questions. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: Hart says V=L breaks with the interative conception of sets at level ω+1, which is countable is the constructible view, but has continuum many in the cumulative (iterative) hierarch. The constructible V=L view is anti-platonist. |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| Full Idea: 'Comprehension' is the assumption that every predicate has an extension. Naïve set theory is the theory whose axioms are extensionality and comprehension, and comprehension is thought to be its naivety. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: This doesn't, of course, mean that there couldn't be a more modest version of comprehension. The notorious difficulty come with the discovery of self-referring predicates which can't possibly have extensions. |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| Full Idea: That the iterative sets suffice for most of ZFC does not show they are necessary, nor is it evident that the set of operations has no fixed points (as 0 is a fixed point for square-of), and no infinitely descending chains (like negative integers). | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: People don't seem to worry that they aren't 'necessary', and further measures are possible to block infinitely descending chains. |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| Full Idea: We say that a binary relation R 'partially orders' a field A just in case R is irreflexive (so that nothing bears R to itself) and transitive. When the set is {a,b}, its subsets {a} and {b} are incomparable in a partial ordering. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| Full Idea: A partial ordering is a 'total ordering' just in case any two members of its field are comparable, that is, either a is R to b, or b is R to a, or a is b. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: See Idea 13457 for 'partial ordering'. The three conditions are known as the 'trichotomy' condition. |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| Full Idea: A total order 'well-orders' its field just in case any nonempty subset B of its field has an R-least member, that is, there is a b in B such that for any a in B different from b, b bears R to a. So less-than well-orders natural numbers, but not integers. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The natural numbers have a starting point, but the integers are infinite in both directions. In plain English, an order is 'well-ordered' if there is a starting point. |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| Full Idea: One of the glories of Von Neumann's theory of numbers is to define α < β to mean that α ∈ β. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| Full Idea: Some have claimed that sets should be rethought in terms of still more basic things, categories. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: [He cites F.William Lawvere 1966] It appears to the the context of foundations for mathematics that he has in mind. |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| Full Idea: All the main set theories deny that there is a set of which everything is a member. No interpretation has a domain with everything in it. So the universal quantifier never gets to mean everything all at once; 'all' does not mean all. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: Could you have an 'uncompleted' universal set, in the spirit of uncompleted infinities? In ordinary English we can talk about 'absolutely everything' - we just can't define a set of everything. Must we 'define' our domain? |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| Full Idea: The beginning of modern model theory was when Morley proved Los's Conjecture in 1962 - that a complete theory in a countable language categorical in one uncountable cardinal is categorical in all. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| Full Idea: Modern model theory investigates which set theoretic structures are models for which collections of sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: So first you must choose your set theory (see Idea 13497). Then you presumably look at how to formalise sentences, and then look at the really tricky ones, many of which will involve various degrees of infinity. |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| Full Idea: There is no developed methematics of models for second-order theories, so for the most part, model theory is about models for first-order theories. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| Full Idea: Models are ways the world might be from a first-order point of view. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| Full Idea: First-order logic is 'compact', which means that any logical consequence of a set (finite or infinite) of first-order sentences is a logical consequence of a finite subset of those sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| Full Idea: Berry's Paradox: by the least number principle 'the least number denoted by no description of fewer than 79 letters' exists, but we just referred to it using a description of 77 letters. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: I struggle with this. If I refer to 'an object to which no human being could possibly refer', have I just referred to something? Graham Priest likes this sort of idea. |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| Full Idea: The Burali-Forti Paradox was a crisis for Cantor's theory of ordinal numbers. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| Full Idea: In effect, the machinery introduced to solve the liar can always be rejigged to yield another version the liar. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: [He cites Hans Herzberger 1980-81] The machinery is Tarski's device of only talking about sentences of a language by using a 'metalanguage'. |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| Full Idea: We can show (using the axiom of choice) that the less-than relation, <, well-orders the ordinals, ...and that it partially orders the ordinals, ...and that it totally orders the ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| Full Idea: The axiom of infinity with separation yields a least limit ordinal, which is called ω. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| Full Idea: Since we can map the transfinite ordinals one-one into the infinite cardinals, there are at least as many infinite cardinals as transfinite ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| Full Idea: It is easier to generalize von Neumann's finite ordinals into the transfinite. All Zermelo's nonzero finite ordinals are singletons, but if ω were a singleton it is hard to see how if could fail to be the successor of its member and so not a limit. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| Full Idea: The real numbers were not isolated from geometry until the arithmetization of analysis during the nineteenth century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| Full Idea: Mathematical induction is a way to establish truths about the infinity of natural numbers by a finite proof. | |
| From: William D. Hart (The Evolution of Logic [2010], 5) | |
| A reaction: If there are truths about infinities, it is very tempting to infer that the infinities must therefore 'exist'. A nice, and large, question in philosophy is whether there can be truths without corresponding implications of existence. |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| Full Idea: There is a familiar comparison between Euclid (unique parallel) and 'spherical' geometry (no parallel) and 'saddle' geometry (several parallels). | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| Full Idea: The thesis that no existence proposition is analytic is one of the few constants in philosophical consciences, but there are many existence claims in mathematics, such as the infinity of primes, five regular solids, and certain undecidable propositions. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 7944 | Reduce by bridge laws (plus property identities?), by elimination, or by reducing talk [Macdonald,C] |
| Full Idea: There are four kinds of reduction: the identifying of entities of two theories by means of bridge or correlation laws; the elimination of entities in favour of the other theory; reducing by bridge laws and property identities; and merely reducing talk. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3 n5) | |
| A reaction: [She gives references] The idea of 'bridge laws' I regard with caution. If bridge laws are ceteris paribus, they are not much help, and if they are strict, or necessary, then there must be an underlying reason for that, which is probably elimination. |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| Full Idea: Jespersen calls a noun a mass word when it has no plural, does not take numerical adjectives, and does not take 'fewer'. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: Jespersen was a great linguistics expert. |
| 7938 | Relational properties are clearly not essential to substances [Macdonald,C] |
| Full Idea: In statements attributing relational properties ('Felix is my favourite cat'), it seems clear that the property truly attributed to the substance is not essential to it. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: A fairly obvious point, but an important one when mapping out (cautiously) what we actually mean by 'property'. However, maybe the relational property is essential: the ceiling is ('is' of predication!) above the room. |
| 7967 | Being taller is an external relation, but properties and substances have internal relations [Macdonald,C] |
| Full Idea: The relation of being taller than is an external relation, since it relates two independent material substances, but the relation of instantiation or exemplification is internal, in that it relates a substance with a property. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: An interesting revival of internal relations. To be plausible it would need clear notions of 'property' and 'substance'. We are getting a long way from physics, and I sense Ockham stropping his Razor. How do you individuate a 'relation'? |
| 7965 | Does the knowledge of each property require an infinity of accompanying knowledge? [Macdonald,C] |
| Full Idea: An object's being two inches long seems to guarantee an infinite number of other properties, such as being less than three inches long. If we must understand the second property to understand the first, then there seems to be a vicious infinite regress. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.2) | |
| A reaction: She dismisses this by saying that we don't need to know an infinity of numbers in order to count. I would say that we just need to distinguish between intrinsic and relational properties. You needn't know all a thing's relations to know the thing. |
| 7934 | Tropes are abstract (two can occupy the same place), but not universals (they have locations) [Macdonald,C] |
| Full Idea: Tropes are abstract entities, at least in the sense that more than one can be in the same place at the same time (e.g. redness and roundness). But they are not universals, because they have unique and particular locations. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: I'm uneasy about the reification involved in this kind of talk. Does a coin possess a thing called 'roundness', which then has to be individuated, identified and located? I am drawn to the two extreme views, and suspicious of compromise. |
| 7958 | Properties are sets of exactly resembling property-particulars [Macdonald,C] |
| Full Idea: Trope Nominalism says properties are classes or sets of exactly similar or resembling tropes, where tropes are what we might called 'property-tokens' or 'particularized properties'. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: We still seem to have the problem of 'resembling' here, and we certainly have the perennial problem of why any given particular should be placed in any particular set. See Idea 7959. |
| 7972 | Tropes are abstract particulars, not concrete particulars, so the theory is not nominalist [Macdonald,C] |
| Full Idea: Trope 'Nominalism' is not a version of nominalism, because tropes are abstract particulars, rather than concrete particulars. Of course, a trope account of the relations between particulars and their properties has ramifications for concrete particulars. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6 n16) | |
| A reaction: Cf. Idea 7971. At this point the boundary between nominalist and realist theories seems to blur. Possibly that is bad news for tropes. Not many dilemmas can be solved by simply blurring the boundary. |
| 7959 | How do a group of resembling tropes all resemble one another in the same way? [Macdonald,C] |
| Full Idea: The problem is how a group of resembling tropes can be of the same type, that is, that they can resemble one another in the same way. This problem is not settled simply by positing tropes. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: There seems to be a fundamental fact that there is no resemblance unless the respect of resemblance is specified. Two identical objects could still said to be different because of their locations. Is resemblance natural or conventional? Consider atoms. |
| 7960 | Trope Nominalism is the only nominalism to introduce new entities, inviting Ockham's Razor [Macdonald,C] |
| Full Idea: Of all the nominalist solutions, Trope Nominalism is the only one that tries to solve the problem at issue by introducing entities; all the others try to get by with concrete particulars and sets of them. This might invite Ockham's Razor. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: We could reply that tropes are necessities. The issue seems to be a key one, which is whether our fundamental onotology should include properties (in some form or other). I am inclined to exclude them (Ideas 3322, 3906, 4029). |
| 7951 | Numerical sameness is explained by theories of identity, but what explains qualitative identity? [Macdonald,C] |
| Full Idea: We can distinguish between numerical identity and qualitative identity. Numerical sameness is explained by a theory of identity, but what explains qualitative sameness? | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: The distinction is between type and token identity. Tokens are particulars, and types are sets, so her question comes down to the one of what entitles something to be a member of a set? Nothing, if sets are totally conventional, but they aren't. |
| 7964 | How can universals connect instances, if they are nothing like them? [Macdonald,C] |
| Full Idea: The 'one over many' problem is to explain how universals can unify their instances if they are wholly other than them. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: If universals are self-predicating (beauty is beautiful) then they have a massive amount in common, despite one being general. You then have the regress problem of explaining the beauty of the beautiful. Baffling regress, or baffling participation. |
| 7971 | Real Nominalism is only committed to concrete particulars, word-tokens, and (possibly) sets [Macdonald,C] |
| Full Idea: All real forms of Nominalism should hold that the only objects relevant to the explanation of generality are concrete particulars, words (i.e. word-tokens, not word-types), and perhaps sets. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6 n16) | |
| A reaction: The addition of sets seems controversial (see Idea 7970). The context is her rejection of the use of tropes in nominalist theories. I would doubt whether a theory still counted as nominalist if it admitted sets (e.g. Quine). |
| 7955 | Resemblance Nominalism cannot explain either new resemblances, or absence of resemblances [Macdonald,C] |
| Full Idea: Resemblance Nominalism cannot explain the fact that we know when and in what way new objects resemble old ones, and that we know when and in what ways new objects do not resemble old ones. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: It is not clear what sort of theory would be needed to 'explain' such a thing. Unless there is an explanation of resemblance waiting in the wings (beyond asserting that resemblance is a universal), then this is not a strong objection. |
| 7961 | A 'thing' cannot be in two places at once, and two things cannot be in the same place at once [Macdonald,C] |
| Full Idea: The so-called 'laws of thinghood' govern particulars, saying that one thing cannot be wholly present at different places at the same time, and two things cannot occupy the same place at the same time. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: Is this an empirical observation, or a tautology? Or might it even be a priori synthetic? What happens when two water drops or clouds merge? Or an amoeba fissions? In what sense is an image in two places at once? Se also Idea 2351. |
| 7926 | We 'individuate' kinds of object, and 'identify' particular specimens [Macdonald,C] |
| Full Idea: We can usefully refer to 'individuation conditions', to distinguish objects of that kind from objects not of that kind, and to 'identity conditions', to distinguish objects within that kind from one another. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.2) | |
| A reaction: So we individuate types or sets, and identify tokens or particulars. Sounds good. Should be in every philosopher's toolkit, and on every introductory philosophy course. |
| 7936 | Unlike bundles of properties, substances have an intrinsic unity [Macdonald,C] |
| Full Idea: Substances have a kind of unity that mere collocations of properties do not have, namely an instrinsic unity. So substances cannot be collocations - bundles - of properties. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: A team is a unity. Compare a similar thought, Idea 1395, about personal identity. How can something which is a pure unity have more than one property? What distinguishes substances? Why can't a substance have a certain property? |
| 7930 | The bundle theory of substance implies the identity of indiscernibles [Macdonald,C] |
| Full Idea: The bundle theory of substance requires unconditional commitment to the truth of the Principle of the Identity of Indiscernibles: that things that are alike with respect to all of their properties are identical. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: Since the identity of indiscernibles is very dubious (see Ideas 1365, 4476, 5746, 7928), this is bad news for the bundle theory. I suspect that all of these problems arise because no one seems to have a clear concept of a property. |
| 7932 | A phenomenalist cannot distinguish substance from attribute, so must accept the bundle view [Macdonald,C] |
| Full Idea: Commitment to the view that only what can be an object of possible sensory experience can exist eliminates the possibility of distinguishing between substance and attribute, leaving only one alternative, namely the bundle view. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: Phenomenalism strikes me as a paradigm case of confusing ontology with epistemology. Presumably physicists (even empiricist ones) are committed to the 'interior' of quarks and electrons, but no one expects to experience them. |
| 7937 | When we ascribe a property to a substance, the bundle theory will make that a tautology [Macdonald,C] |
| Full Idea: The bundle theory makes all true statements ascribing properties to substances uninformative, by making them logical truths. The property of being a feline animal is literally a constituent of a cat. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: The solution would seem to a distinction between accidental and essential properties. Compare 'that plane is red' with 'that plane has wings'. 'Of course it does - it's a plane'. We might still survive without a plane-substance. |
| 7939 | Substances persist through change, but the bundle theory says they can't [Macdonald,C] |
| Full Idea: Substances are capable of persisting through change, where this involves change in properties; but the bundle theory has the consequence that substances cannot survive change. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: Her example is an apple remaining an apple when it turns brown. It doesn't look, though, as if there is a precise moment when the apple-substance ceases. The end of an apple seems to be more a matter of a loss of crucial properties. |
| 7940 | A substance might be a sequence of bundles, rather than a single bundle [Macdonald,C] |
| Full Idea: Maybe a substance is not itself a bundle of properties, but a sum or sequence of bundles of properties, a bundle of bundles of properties (which 'perdures' rather than 'endures'). | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: There remains the problem of deciding when the bundle has drifted too far away from the original to perdure correctly. A caterpillar can turn into a butterfly (which is pretty bizarre!), but not into a cathedral. Why? She says this idea denies change. |
| 7948 | A statue and its matter have different persistence conditions, so they are not identical [Macdonald,C] |
| Full Idea: Because a statue and the lump of matter that constitute it have different persistence conditions, they are not identical. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.4) | |
| A reaction: Maybe being a statue is a relational property? All the relational properties of a thing will have different persistence conditions. Suppose I see a face in a bowl of sugar, and you don't? |
| 7929 | A substance is either a bundle of properties, or a bare substratum, or an essence [Macdonald,C] |
| Full Idea: The three main theories of substance are the bundle theory (Leibniz, Berkeley, Hume, Ayer), the bare substratum theory (Locke and Bergmann), and the essentialist theory. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: Macdonald defends the essentialist theory. The essentialist view immediately appeals to me. Properties must be OF something, and the something must have the power to produce properties. So there. |
| 7941 | Each substance contains a non-property, which is its substratum or bare particular [Macdonald,C] |
| Full Idea: A rival to the bundle theory says that, for each substance, there is a constituent of it that is not a property but is both essential and unique to it, this constituent being referred to as a 'bare particular' or 'substratum'. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: This doesn't sound promising. It is unclear what existence devoid of all properties could be like. How could it 'have' its properties if it was devoid of features (it seems to need property-hooks)? It is an ontological black hole. How do you prove it? |
| 7942 | The substratum theory explains the unity of substances, and their survival through change [Macdonald,C] |
| Full Idea: If there is a substratum or bare particular within a substance, this gives an explanation of the unity of substances, and it is something which can survive intact when a substance changes. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: [v. compressed wording] Many problems here. The one that strikes me is that when things change they sometimes lose their unity and identity, and that seems to be decided entirely from observation of properties, not from assessing the substratum. |
| 7943 | A substratum has the quality of being bare, and they are useless because indiscernible [Macdonald,C] |
| Full Idea: There seems to be no way of identifying a substratum as the bearer of qualities without qualifiying it as bare (having the property of being bare?), ..and they cannot be used to individuate things, because they are necessarily indiscernible. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: The defence would probably be a priori, claiming an axiomatic necessity for substrata in our thinking about the world, along with a denial that bareness is a property (any more than not being a contemporary of Napoleon is a property). |
| 7927 | At different times Leibniz articulated three different versions of his so-called Law [Macdonald,C] |
| Full Idea: There are three distinct versions of Leibniz's Law, all traced to remarks made by Leibniz: the Identity of Indiscernibles (same properties, same thing), the Indiscernibility of Identicals (same thing, same properties), and the Substitution Principle. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.2) | |
| A reaction: The best view seems to be to treat the second one as Leibniz's Law (and uncontroversially true), and the first one as being an interesting but dubious claim. |
| 7928 | The Identity of Indiscernibles is false, because it is not necessarily true [Macdonald,C] |
| Full Idea: One common argument to the conclusion that the Principle of the Identity of Indiscernibles is false is that it is not necessarily true. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.2 n32) | |
| A reaction: This sounds like a good argument. If you test the Principle with an example ('this butler is the murderer') then total identity does not seem to necessitate identity, though it strongly implies it (the butler may have a twin etc). |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| Full Idea: The conception of Frege is that self-evidence is an intrinsic property of the basic truths, rules, and thoughts expressed by definitions. | |
| From: William D. Hart (The Evolution of Logic [2010], p.350) | |
| A reaction: The problem is always that what appears to be self-evident may turn out to be wrong. Presumably the effort of arriving at a definition ought to clarify and support the self-evident ingredient. |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| Full Idea: In the case of the parallels postulate, Euclid's fifth axiom (the whole is greater than the part), and comprehension, saying was believing for a while, but what was said was false. This should make a shrewd philosopher sceptical about a priori knowledge. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Euclid's fifth is challenged by infinite numbers, and comprehension is challenged by Russell's paradox. I can't see a defender of the a priori being greatly worried about these cases. No one ever said we would be right - in doing arithmetic, for example. |
| 7947 | In continuity, what matters is not just the beginning and end states, but the process itself [Macdonald,C] |
| Full Idea: What matters to continuity is not just the beginning and end states of the process by which a thing persists, perhaps through change, but the process itself. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.4) | |
| A reaction: This strikes me as being a really important insight. Compare Idea 4931. If this is the key to understanding mind and personal identity, it means that the concept of a 'process' must be a central issue in ontology. How do you individuate a process? |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| Full Idea: A Fregean concept is a function that assigns to each object a truth value. So instead of the colour green, the concept GREEN assigns truth to each green thing, but falsity to anything else. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This would seem to immediately hit the renate/cordate problem, if there was a world in which all and only the green things happened to be square. How could Frege then distinguish the green from the square? Compare Idea 8245. |
| 8430 | Causal statements are used to explain, to predict, to control, to attribute responsibility, and in theories [Kim] |
| Full Idea: The function of causal statements is 1) to explain events, 2) for predictive usefulness, 3) to help control events, 4) with agents, to attribute moral responsibility, 5) in physical theory. We should judge causal theories by how they account for these. | |
| From: Jaegwon Kim (Causes and Counterfactuals [1973], p.207) | |
| A reaction: He suggests that Lewis's counterfactual theory won't do well on this test. I think the first one is what matters. Philosophy aims to understand, and that is achieved through explanation. Regularity and counterfactual theories explain very little. |
| 8396 | Many counterfactuals have nothing to do with causation [Kim, by Tooley] |
| Full Idea: Kim has pointed out that there are a number of counterfactuals that have nothing to do with causation. If John marries Mary, then if John had not existed he would not have married Mary, but that is not the cause of their union. | |
| From: report of Jaegwon Kim (Causes and Counterfactuals [1973], 5.2) by Michael Tooley - Causation and Supervenience | |
| A reaction: One might not think that this mattered, but it leaves the problem of distinguishing between the causal counterfactuals and the rest (and you mustn't mention causation when you are doing it!). |
| 8429 | Counterfactuals can express four other relations between events, apart from causation [Kim] |
| Full Idea: Counterfactuals can express 'analytical' dependency, or the fact that one event is part of another, or an action done by doing another, or (most interestingly) an event can determine another without causally determining it. | |
| From: Jaegwon Kim (Causes and Counterfactuals [1973], p.205) | |
| A reaction: [Kim gives example of each case] Counterfactuals can even express a relation that involves no dependency. Or they might just involve redescription, as in 'If Scott were still alive, then the author of "Waverley" would be too'. |
| 8428 | Causation is not the only dependency relation expressed by counterfactuals [Kim] |
| Full Idea: The sort of dependency expressed by counterfactual relations is considerably broader than strictly causal dependency, and causal dependency is only one among the heterogeneous group of dependency relationships counterfactuals can express. | |
| From: Jaegwon Kim (Causes and Counterfactuals [1973], p.205) | |
| A reaction: In 'If pigs could fly, one and one still wouldn't make three' there isn't even a dependency. Kim has opened up lines of criticism which make the counterfactual analysis of causation look very implausible to me. |
| 4781 | Many counterfactual truths do not imply causation ('if yesterday wasn't Monday, it isn't Tuesday') [Kim, by Psillos] |
| Full Idea: Kim gives a range of examples of counterfactual dependence without causation, as: 'if yesterday wasn't Monday, today wouldn't be Tuesday', and 'if my sister had not given birth, I would not be an uncle'. | |
| From: report of Jaegwon Kim (Causes and Counterfactuals [1973]) by Stathis Psillos - Causation and Explanation §3.3 | |
| A reaction: This is aimed at David Lewis. The objection seems like commonsense. "If you blink, the cat gets it". Causal claims involve counterfactuals, but they are not definitive of what causation is. |