90 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. |
| 11912 | Substantive metaphysics says what a property is, not what a predicate means [Molnar] |
| Full Idea: The motto of what is presented here is 'less conceptual analysis, more metaphysics', where the distinction is equivalent to the distinction between saying what 'F' means and saying what being F is. | |
| From: George Molnar (Powers [1998], 1.1) | |
| A reaction: This seems to me to capture exactly the spirit of metaphysics since Saul Kripke's work, though some people engaged in it seem to me to be trapped in an outdated linguistic view of the matter. Molnar credits Locke as the source of his view. |
| 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? |
| 11920 | A real definition gives all the properties that constitute an identity [Molnar] |
| Full Idea: A real definition expresses the sum of the properties that constitute the identity of the thing defined. | |
| From: George Molnar (Powers [1998], 1.4.4) | |
| A reaction: This is a standard modern view among modern essentialists, and one which I believe can come into question. It seems to miss out the fact that an essence will also explain the possible functions and behaviours of a thing. Explanation seems basic. |
| 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) |
| 11919 | Ontological dependence rests on essential connection, not necessary connection [Molnar] |
| Full Idea: Ontological dependence is better understood in terms of an essential connection, rather than simply a necessary connection. | |
| From: George Molnar (Powers [1998], 1.4.4) | |
| A reaction: This seems to be an important piece in the essentialist jigsaw. Apart from essentialism, I can't think of any doctrine which offers any sort of explanation of the self-evident fact of certain ontological dependencies. |
| 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. |
| 11929 | The three categories in ontology are objects, properties and relations [Molnar] |
| Full Idea: The ontologically fundamental categories are three in number: Objects, Properties, and Relations. | |
| From: George Molnar (Powers [1998], 2 Intr) | |
| A reaction: We need second-order logic to quantify over all of these. The challenge to this view might be that it is static, and needs the addition of processes or events. Molnar rejects facts and states of affairs. |
| 11927 | Reflexive relations are syntactically polyadic but ontologically monadic [Molnar] |
| Full Idea: Reflexive relations are, and non-reflexive relations may be, monadic in the ontological sense although they are syntactically polyadic. | |
| From: George Molnar (Powers [1998], 1.4.5) | |
| A reaction: I find this a very helpful distinction, as I have never quite understood reflexive relations as 'relations', even in the most obvious cases, such as self-love or self-slaughter. |
| 11915 | If atomism is true, then all properties derive from ultimate properties [Molnar] |
| Full Idea: If a priori atomism is a true theory of the world, then all properties are derivative from ultimate properties. | |
| From: George Molnar (Powers [1998], 1.4.1) | |
| A reaction: Presumably there is a physicalist metaphysic underlying this, which means that even abstract properties derive ultimately from these physical atoms. Unless we want to postulate logical atoms, or monads, or some such weird thing. |
| 11916 | 'Being physical' is a second-order property [Molnar] |
| Full Idea: A property like 'being physical' is just a second-order property. ...It is not required as a first-order property. ...Higher-order properties earn their keep as necessity-makers. | |
| From: George Molnar (Powers [1998], 1.4.2) | |
| A reaction: I take this to be correct and very important. People who like 'abundant' properties don't make this distinction about orders (of levels of abstraction, I would say), so the whole hierarchy has an equal status in ontology, which is ridiculous. |
| 11956 | 'Categorical properties' are those which are not powers [Molnar] |
| Full Idea: The canonical name for a property that is a non-power is 'categorical property'. | |
| From: George Molnar (Powers [1998], 10.2) | |
| A reaction: Molnar objects that this implies that powers cannot be used categorically, and refuses to use the term. There seems to be uncertainty over whether the term refers to necessity, or to the ability to categorise. I'm getting confused myself. |
| 11928 | Are tropes transferable? If they are, that is a version of Platonism [Molnar] |
| Full Idea: Are tropes transferable? ...If tropes are not dependent on their bearers, that is a trope-theoretic version of Platonism. | |
| From: George Molnar (Powers [1998], 1.4.6) | |
| A reaction: These are the sort of beautifully simple questions that we pay philosophers to come up with. If they are transferable, what was the loose bond which connected them? If they aren't, then what individuates them? |
| 11933 | A power's type-identity is given by its definitive manifestation [Molnar] |
| Full Idea: A power's type-identity is given by its definitive manifestation. | |
| From: George Molnar (Powers [1998], 3.1) | |
| A reaction: Presumably there remains an I-know-not-what that lurks behind the manifestation, which is beyond our limits of cognizance. The ultimate reality of the world has to be unknowable. |
| 11932 | Powers have Directedness, Independence, Actuality, Intrinsicality and Objectivity [Molnar] |
| Full Idea: The basic features of powers are: Directedness (to some outcome); Independence (from their manifestations); Actuality (not mere possibilities); Intrinsicality (not relying on other objects) and Objectivity (rather than psychological). | |
| From: George Molnar (Powers [1998], 2.4) | |
| A reaction: [compression of his list] This offering is why Molnar's book is important, because no one else seems to get to grips with trying to pin down what a power is, and hence their role. |
| 11934 | The physical world has a feature very like mental intentionality [Molnar] |
| Full Idea: Something very much like mental intentionality is a pervasive and ineliminable feature of the physical world. | |
| From: George Molnar (Powers [1998], 3.2) | |
| A reaction: I like this, because it offers a continuous account of mind and world. The idea that intentionality is some magic ingredient that marks off a non-physical type of reality is nonsense. See Fodor's attempts to reduce intentionality. |
| 11947 | Dispositions and external powers arise entirely from intrinsic powers in objects [Molnar] |
| Full Idea: I propose a generalization: that all dispositional and extrinsic predicates that apply to an object, do so by virtue of intrinsic powers borne by the object. | |
| From: George Molnar (Powers [1998], 6.3) | |
| A reaction: This is the clearest statement of the 'powers' view of nature, and the one with which I agree. An interesting question is whether powers or objects are more basic in our ontology. Are objects just collections of causal powers? What has the power? |
| 11952 | The Standard Model suggest that particles are entirely dispositional, and hence are powers [Molnar] |
| Full Idea: In the Standard Model of physics the fundamental physical magnitudes are represented as ones whose whole nature is exhausted by the dispositionality, ..so there is a strong presumption that the properties of subatomic particles are powers. | |
| From: George Molnar (Powers [1998], 8.4.3) | |
| A reaction: A very nice point, because it asserts not merely that we should revise our metaphysic to endorse powers, but that we are actually already operating with exactly that view, in so far as we are physicalist. |
| 11953 | Some powers are ungrounded, and others rest on them, and are derivative [Molnar] |
| Full Idea: Some powers are grounded and some are not. ...All derivative powers ultimately derive from ungrounded powers. | |
| From: George Molnar (Powers [1998], 8.5.2) | |
| A reaction: It is tempting to use the term 'property' for the derivative powers, reserving 'power' for something which is basic. Molnar makes a plausible case, though. |
| 11943 | Dispositions can be causes, so they must be part of the actual world [Molnar] |
| Full Idea: Dispositions can be causes. What is not actual cannot be a cause or any part of a cause. Merely possible events are not actual, and that makes them causally impotent. The claim that powers are causally potent has strong initial plausibility. | |
| From: George Molnar (Powers [1998], 5) | |
| A reaction: [He credits Mellor 1974 for this idea] He will need to show how dispositions can be causes (other than, presumably, being anticipated or imagined by conscious minds), which he says he will do in Ch. 12. |
| 11939 | If powers only exist when actual, they seem to be nomadic, and indistinguishable from non-powers [Molnar] |
| Full Idea: Two arguments against Megaran Actualism are that it turns powers into nomads: they come and go, depending on whether they are being exercised or not. And it stops us from distinguishing between unexercised powers and absent powers. | |
| From: George Molnar (Powers [1998], 4.3.1) | |
| A reaction: See Idea 11938 for Megaran Actualism. Molnar takes these objections to be fairly decisive, but if the Megarans are denying the existence of latent powers, they aren't going to be bothered by nomadism or the lack of distinction. |
| 11914 | Platonic explanations of universals actually diminish our understanding [Molnar] |
| Full Idea: We understand less after a platonic explanation of universals than we understand before it was given. | |
| From: George Molnar (Powers [1998], 1.2) | |
| A reaction: That pretty much sums up my view, and it pretty well sums up my view of religion as well. I thought I understood what numbers were until Frege told me that they were abstract objects, some sort of higher-order set. |
| 11913 | For nominalists, predicate extensions are inexplicable facts [Molnar] |
| Full Idea: For the nominalist, belonging to the extension of a predicate is just an inexplicable ultimate fact. | |
| From: George Molnar (Powers [1998], 1.2) | |
| A reaction: I sometimes think of myself as a nominalist, but when it is summarised in Molnar's way I back off. He seem to be offering a third way, between platonic realism and nominalism. It is physical essentialist realism, I think. |
| 11962 | Nominalists only accept first-order logic [Molnar] |
| Full Idea: A nominalist will only countenance first-order logic. | |
| From: George Molnar (Powers [1998], 12.2.2) | |
| A reaction: This is because nominalist will not acknowledge properties as entities to be quantified over. Plural quantification seems to be a strategy for extending first-order logic while retaining nominalist sympathies. |
| 11917 | Structural properties are derivate properties [Molnar] |
| Full Idea: Structural properties are clear examples of derivative properties. | |
| From: George Molnar (Powers [1998], 1.4.3) | |
| A reaction: This is an important question in the debate. Presumably you can't just reduce structural properties to more basic ones, because one set of basic properties might appear in many different structures. Ellis defends structural properties in metaphysics. |
| 11955 | There are no 'structural properties', as properties with parts [Molnar] |
| Full Idea: There are no 'structural properties', if by that we mean a property that has properties as parts. | |
| From: George Molnar (Powers [1998], 9.1.2) | |
| A reaction: There do seem to be properties that result from arranging more basic properties in one way rather than another (e.g. arranging the metal in a knife to be 'sharp'). But I think Molnar is right that they are not part of basic ontology. |
| 11918 | The essence of a thing need not include everything that is necessarily true of it [Molnar] |
| Full Idea: Pre-theoretically it does not seem to be the case that what is essential to a thing includes everything that is necessarily true of that thing. | |
| From: George Molnar (Powers [1998], 1.4.4) | |
| A reaction: This seems to me to be true. The simple point, which I take to be obvious, is that essential properties must at the very least be in some way important, whereas necessities can be trivial. I favour the idea that the essences create the necessities. |
| 11963 | What is the truthmaker for a non-existent possible? [Molnar] |
| Full Idea: What is the nature of the truthmaker for 'It is possible that p' in cases where p itself is false? | |
| From: George Molnar (Powers [1998], 12.2.2) | |
| A reaction: Molnar mentions three views: there is a different type of being for possibilia (Meinong), or possibilia exist, or possibilia are merely represented. The third view is obviously correct, though I presume possibilia to be based on actual powers. |
| 11984 | Asserting a possible property is to say it would have had the property if that world had been actual [Plantinga] |
| Full Idea: To say than x has a property in a possible world is simply to say that x would have had the property if that world had been actual. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], I) | |
| A reaction: Plantinga tries to defuse all the problems with identity across possible worlds, by hanging on to subjunctive verbs and modal modifiers. The point, though, was to explain these, or at least to try to give their logical form. |
| 11980 | A possible world is a maximal possible state of affairs [Plantinga] |
| Full Idea: A possible world is just a maximal possible state of affairs. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], I) | |
| A reaction: The key point here is that Plantinga includes the word 'possible' in his definition. Possibility defines the worlds, and so worlds cannot be used on their own to define possibility. |
| 11982 | If possible Socrates differs from actual Socrates, the Indiscernibility of Identicals says they are different [Plantinga] |
| Full Idea: If the Socrates of the actual world has snubnosedness but Socrates-in-W does not, this is surely inconsistent with the Indiscernibility of Identicals, a principle than which none sounder can be conceived. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], I) | |
| A reaction: However, we allow Socrates to differ over time while remaining the same Socrates, so some similar approach should apply here. In both cases we need some notion of what is essential to Socrates. But what unites aged 3 with aged 70? |
| 11983 | It doesn't matter that we can't identify the possible Socrates; we can't identify adults from baby photos [Plantinga] |
| Full Idea: We may say it makes no sense to say that Socrates exists at a world, if there is in principle no way of identifying him. ...But this is confused. To suppose Agnew was a precocious baby, we needn't be able to pick him from a gallery of babies. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], I) | |
| A reaction: This seems a good point, and yet we have a space-time line joining adult Agnew with baby Agnew, and no such causal link is available between persons in different possible worlds. What would be the criterion in each case? |
| 11985 | If individuals can only exist in one world, then they can never lack any of their properties [Plantinga] |
| Full Idea: The Theory of Worldbound Individuals contends that no object exists in more than one possible world; this implies the outrageous view that - taking properties in the broadest sense - no object could have lacked any property that it in fact has. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], II) | |
| A reaction: Leibniz is the best known exponent of this 'outrageous view', though Plantinga shows that Lewis may be seen in the same light, since only counterparts are found in possible worlds, not the real thing. The Theory does seem wrong. |
| 11986 | The counterparts of Socrates have self-identity, but only the actual Socrates has identity-with-Socrates [Plantinga] |
| Full Idea: While Socrates has no counterparts that lack self-identity, he does have counterparts that lack identity-with-Socrates. He alone has that - the property, that is, of being identical with the object that in fact instantiates Socrateity. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], II) | |
| A reaction: I am never persuaded by arguments which rest on such dubious pseudo-properties. Whether or not a counterpart of Socrates has any sort of identity with Socrates cannot be prejudged, as it would beg the question. |
| 11987 | Counterpart Theory absurdly says I would be someone else if things went differently [Plantinga] |
| Full Idea: It makes no sense to say I could have been someone else, yet Counterpart Theory implies not merely that I could have been distinct from myself, but that I would have been distinct from myself had things gone differently in even the most miniscule detail. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], II) | |
| A reaction: A counterpart doesn't appear to be 'me being distinct from myself'. We have to combine counterparts over possible worlds with perdurance over time. I am a 'worm' of time-slices. Anything not in that worm is not strictly me. |
| 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. |
| 11951 | Hume allows interpolation, even though it and extrapolation are not actually valid [Molnar] |
| Full Idea: In his 'shade of blue' example, Hume is (sensibly) endorsing a type of reasoning - interpolation - that is widely used by rational thinkers. Too bad that interpolation and extrapolation are incurably invalid. | |
| From: George Molnar (Powers [1998], 7.2.3) | |
| A reaction: Interpolation and extrapolation are two aspects of inductive reasoning which contribute to our notion of best explanation. Empiricism has to allow at least some knowledge which goes beyond strict direct experience. |
| 11936 | The two ways proposed to distinguish mind are intentionality or consciousness [Molnar] |
| Full Idea: There have only been two serious proposals for distinguishing mind from matter. One appeals to intentionality, as per Brentano and his medieval precursors. The other, harking back to Descartes, Locke and empiricism, uses the capacity for consciousness. | |
| From: George Molnar (Powers [1998], 3.5.3) | |
| A reaction: Personally I take both of these to be reducible, and hence have no place for 'minds' in my ontology. Focusing on Chalmers's 'Hard Question' was the shift from the intentionality view to the consciousness view which is now more popular. |
| 11935 | Physical powers like solubility and charge also have directedness [Molnar] |
| Full Idea: Contrary to the Brentano Thesis, physical powers, such as solubility or electromagnetic charge, also have that direction toward something outside themselves that is typical of psychological attributes. | |
| From: George Molnar (Powers [1998], 3.4) | |
| A reaction: I think this decisively undermines any strong thesis that 'intentionality is the mark of the mental'. I take thought to be just a fancy development of the physical powers of the physical world. |
| 11944 | Rule occasionalism says God's actions follow laws, not miracles [Molnar] |
| Full Idea: Rule occasionalists (Arnauld, Bayle) say that on their view the results of God's action are the nomic regularities of nature, and not a miracle. | |
| From: George Molnar (Powers [1998], 6.1) | |
| A reaction: This is clearly more plausible that Malebranche's idea that God constantly intervenes. I take it as a nice illustration of the fact that 'laws of nature' were mainly invented by us to explain how God could control his world. Away with them! |
| 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. |
| 11960 | Singular causation is prior to general causation; each aspirin produces the aspirin generalization [Molnar] |
| Full Idea: I take for granted the primacy of singular causation. A singular causal state of affairs is not constituted by a generalization. 'Aspirin relieves headache' is made true by 'This/that aspirin relieves this/that headache'. | |
| From: George Molnar (Powers [1998], 12.1) | |
| A reaction: [He cites Tooley for the opposite view] I wholly agree with Molnar, and am inclined to link it with the primacy of individual essences over kind essences. |
| 11937 | We should analyse causation in terms of powers, not vice versa [Molnar] |
| Full Idea: Causal analyses of powers pre-empt the correct account of causation in terms of powers. | |
| From: George Molnar (Powers [1998], 4.2.3) | |
| A reaction: I think this is my preferred view. The crucial point is that powers are active, so one is not needing to add some weird 'causation' ingredient to a world which would otherwise be passive and inert. That is a relic from the interventions of God. |
| 11954 | We should analyse causation in terms of powers [Molnar] |
| Full Idea: We should give up any causal analysis of powers, ..so we should try to analyse causation in terms of powers. | |
| From: George Molnar (Powers [1998], 8.5.3) | |
| A reaction: It may be hard to explain what powers are, or identify them, if you can't say that they cause things to happen. I am torn between Molnar's view, and the view that causation is primitive. |
| 11961 | Causal dependence explains counterfactual dependence, not vice versa [Molnar] |
| Full Idea: The counterfactual analysis is open to the Euthyphro objection: it is causal dependence that explains any counterfactual dependence rather than vice versa. | |
| From: George Molnar (Powers [1998], 12.1) | |
| A reaction: I take views like the counterfactual analysis of causation to arise from empiricists who are bizarrely reluctant to adopt plausible best explainations (such as powers and essences). |
| 11959 | Science works when we assume natural kinds have essences - because it is true [Molnar] |
| Full Idea: Investigations premissed on the assumption that natural kinds have essences, that in particular the fundamental natural kinds have only essential intrinsic properties, tend to be practically successful because the assumption is true. | |
| From: George Molnar (Powers [1998], 11.3) | |
| A reaction: The point is made against a pragmatist approach to the problem by Nancy Cartwright. I take the starting point for scientific essentialism to be an empirical observation, that natural kinds seem to be very very stable. See Idea 8153. |
| 9448 | Location in space and time are non-power properties [Molnar, by Mumford] |
| Full Idea: Molnar argues that some properties are non-powers, and he cites spatial location, spatial orientation, and temporal location. | |
| From: report of George Molnar (Powers [1998], 158-62) by Stephen Mumford - Laws in Nature 11.4 | |
| A reaction: Although you might say an event happened 'because' of an item on this list, this doesn't feel right to me. The ability to arrest someone is a power, but being at the scene of the crime isn't. It's an opportunity for a power. |
| 11930 | One essential property of a muon doesn't entail the others [Molnar] |
| Full Idea: The muon has mass 106.2 MeV, unit negative charge, and spin a half. The electron and tauon have unit negative charge, but electrons are 200 times less massive, and tauons 17 times more massive. Its essential properties are not mutually entailing. | |
| From: George Molnar (Powers [1998], 2.1) | |
| A reaction: This rejects a popular idea of scientific essentialism, that the essence is the set of properties which entail the non-essential properties (and not vice versa), a view which I had hitherto found rather appealing. |
| 11957 | It is contingent which kinds and powers exist in the world [Molnar] |
| Full Idea: It is a contingent matter that the world contains the exact natural kinds it does, and hence it is a contingent matter that it contains the very powers it does. | |
| From: George Molnar (Powers [1998], 10.3) | |
| A reaction: I take this to be correct (for all we know). It would be daft to claim that the regularities of the universe are necessarily that way, but it is not daft to say that the stuff of the universe necessitates the pattern of what happens. |
| 11921 | The laws of nature depend on the powers, not the other way round [Molnar] |
| Full Idea: What powers there are does not depend on what laws there are, but vice versa, what laws obtain in the world is a function of what powers are to be found in that world. | |
| From: George Molnar (Powers [1998], 1.4.5) | |
| A reaction: This old idea may well be the most important realisation of modern times. I take the 'law' view to be based on a religious view of the world (see Idea 5470). There is still room to believe in a divine creator of the bewildering underlying powers. |
| 11931 | Energy fields are discontinuous at the very small [Molnar] |
| Full Idea: We know that all energy fields are discontinuous below the distance measured by Planck's constant h. The physical world ultimately consists of discrete objects. | |
| From: George Molnar (Powers [1998], 2.2) | |
| A reaction: This is where quantum theory clashes with relativity, since the latter holds space to be a continuum. I'm not sure about Molnar's use of the word 'objects' here. |