68 ideas
| 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the spirit of metaphysics since Saul Kripke's work, though some people engaged in it seem to me to be trapped in an outdated linguistic view of the matter.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. |
| 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. |
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| Full Idea: Dedkind gave a rigorous proof of the principle of definition by recursion, permitting recursive definitions of addition and multiplication, and hence proofs of the familiar arithmetical laws. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 13 'Deriv' |
| 10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
| Full Idea: A set is 'Dedekind-infinite' iff there exists a one-to-one function that maps a set into a proper subset of itself. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §64) by E Reck / M Price - Structures and Structuralism in Phil of Maths n 7 | |
| A reaction: Sounds as if it is only infinite if it is contradictory, or doesn't know how big it is! |
| 22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
| Full Idea: Dedekind had an interesting proof of the Axiom of Infinity. He held that I have an a priori grasp of the idea of my self, and that every idea I can form the idea of that idea. Hence there are infinitely many objects available to me a priori. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], no. 66) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 12 'Numb' | |
| A reaction: Who said that Descartes' Cogito was of no use? Frege endorsed this, as long as the ideas are objective and not subjective. |
| 10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
| Full Idea: Dedekind plainly had fusions, not collections, in mind when he avoided the empty set and used the same symbol for membership and inclusion - two tell-tale signs of a mereological conception. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], 2-3) by Michael Potter - Set Theory and Its Philosophy 02.1 | |
| A reaction: Potter suggests that mathematicians were torn between mereology and sets, and eventually opted whole-heartedly for sets. Maybe this is only because set theory was axiomatised by Zermelo some years before Lezniewski got to mereology. |
| 9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
| Full Idea: Numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref) | |
| A reaction: Does this fit real numbers and complex numbers, as well as natural numbers? Frege was concerned by the lack of objectivity in this sort of view. What sort of arithmetic might the Martians have created? Numbers register sameness too. |
| 10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
| Full Idea: It was primarily Dedekind's accomplishment to define the integers, rationals and reals, taking only the system of natural numbers for granted. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by A.George / D.J.Velleman - Philosophies of Mathematics Intro |
| 7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
| Full Idea: Dedekind said that the notion of order, rather than that of quantity, is the central notion in the definition of number. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4 | |
| A reaction: Compare Aristotle's nice question in Idea 646. My intuition is that quantity comes first, because I'm not sure HOW you could count, if you didn't think you were changing the quantity each time. Why does counting go in THAT particular order? Cf. Idea 8661. |
| 17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
| Full Idea: Dedekind and Cantor said the cardinals may be defined in terms of the ordinals: The cardinal number of a set S is the least ordinal onto whose predecessors the members of S can be mapped one-one. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 5 |
| 14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
| Full Idea: Dedekind's ordinals are not essentially either ordinals or cardinals, but the members of any progression whatever. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §243 | |
| A reaction: This is part of Russell's objection to Dedekind's structuralism. The question is always why these beautiful structures should actually be considered as numbers. I say, unlike Russell, that the connection to counting is crucial. |
| 17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
| Full Idea: It then only remained to discover its true origin in the elements of arithmetic and thus at the same time to secure a real definition of the essence of continuity. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], Intro) | |
| A reaction: [He seeks the origin of the theorem that differential calculus deals with continuous magnitude, and he wants an arithmetical rather than geometrical demonstration; the result is his famous 'cut']. |
| 10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
| Full Idea: Whenever we have to do a cut produced by no rational number, we create a new, an irrational number, which we regard as completely defined by this cut. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], §4) | |
| A reaction: Fine quotes this to show that the Dedekind Cut creates the irrational numbers, rather than hitting them. A consequence is that the irrational numbers depend on the rational numbers, and so can never be identical with any of them. See Idea 10573. |
| 14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
| Full Idea: Dedekind set up the axiom that the gap in his 'cut' must always be filled …The method of 'postulating' what we want has many advantages; they are the same as the advantages of theft over honest toil. Let us leave them to others. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - Introduction to Mathematical Philosophy VII | |
| A reaction: This remark of Russell's is famous, and much quoted in other contexts, but I have seen the modern comment that it is grossly unfair to Dedekind. |
| 18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
| Full Idea: One view, favoured by Dedekind, is that the cut postulates a real number for each cut in the rationals; it does not identify real numbers with cuts. ....A view favoured by later logicists is simply to identify a real number with a cut. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4 | |
| A reaction: Dedekind is the patriarch of structuralism about mathematics, so he has little interest in the existenc of 'objects'. |
| 18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
| Full Idea: Of my theory of irrationals you say that the irrational number is nothing else than the cut itself, whereas I prefer to create something new (different from the cut), which corresponds to the cut. We have the right to claim such a creative power. | |
| From: Richard Dedekind (Letter to Weber [1888], 1888 Jan), quoted by Stewart Shapiro - Philosophy of Mathematics 5.4 | |
| A reaction: Clearly a cut will not locate a unique irrational number, so something more needs to be done. Shapiro remarks here that for Dedekind numbers are objects. |
| 9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
| Full Idea: If we scrutinize closely what is done in counting an aggregate of things, we see the ability of the mind to relate things to things, to let a thing correspond to a thing, or to represent a thing by a thing, without which no thinking is possible. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref) | |
| A reaction: I don't suppose it occurred to Dedekind that he was reasserting Hume's observation about the fundamental psychology of thought. Is the origin of our numerical ability of philosophical interest? |
| 17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
| Full Idea: I regard the whole of arithmetic as a necessary, or at least natural, consequence of the simplest arithmetic act, that of counting, and counting itself is nothing else than the successive creation of the infinite series of positive integers. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], §1) | |
| A reaction: Thus counting roots arithmetic in the world, the successor operation is the essence of counting, and the Dedekind-Peano axioms are built around successors, and give the essence of arithmetic. Unfashionable now, but I love it. Intransitive counting? |
| 9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
| Full Idea: A system S is said to be infinite when it is similar to a proper part of itself. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], V.64) |
| 18087 | If x changes by less and less, it must approach a limit [Dedekind] |
| Full Idea: If in the variation of a magnitude x we can for every positive magnitude δ assign a corresponding position from and after which x changes by less than δ then x approaches a limiting value. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], p.27), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.7 | |
| A reaction: [Kitcher says he 'showed' this, rather than just stating it] |
| 13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
| Full Idea: Dedekind's natural numbers: an object is in a set (0 is a number), a function sends the set one-one into itself (numbers have unique successors), the object isn't a value of the function (it isn't a successor), plus induction. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William D. Hart - The Evolution of Logic 5 | |
| A reaction: Hart notes that since this refers to sets of individuals, it is a second-order account of numbers, what we now call 'Second-Order Peano Arithmetic'. |
| 18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
| Full Idea: Dedekind's idea is that the set of natural numbers has zero as a member, and also has as a member the successor of each of its members, and it is the smallest set satisfying this condition. It is the intersection of all sets satisfying the condition. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4 |
| 18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
| Full Idea: It is Dedekind's categoricity result that convinces most of us that he has articulated our implicit conception of the natural numbers, since it entitles us to speak of 'the' domain (in the singular, up to isomorphism) of natural numbers. | |
| From: comment on Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ian Rumfitt - The Boundary Stones of Thought 9.1 | |
| A reaction: The main rival is set theory, but that has an endlessly expanding domain. He points out that Dedekind needs second-order logic to achieve categoricity. Rumfitt says one could also add to the 1st-order version that successor is an ancestral relation. |
| 14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
| Full Idea: Dedekind proves mathematical induction, while Peano regards it as an axiom, ...and Peano's method has the advantage of simplicity, and a clearer separation between the particular and the general propositions of arithmetic. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §241 |
| 8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
| Full Idea: Dedekind is the philosopher-mathematician with whom the structuralist conception originates. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §3 n13) by Fraser MacBride - Structuralism Reconsidered | |
| A reaction: Hellman says the idea grew naturally out of modern mathematics, and cites Hilbert's belief that furniture would do as mathematical objects. |
| 9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
| Full Idea: Dedekindian abstraction says mathematical objects are 'positions' in a model, while Cantorian abstraction says they are the result of abstracting on structurally similar objects. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Kit Fine - Cantorian Abstraction: Recon. and Defence §6 | |
| A reaction: The key debate among structuralists seems to be whether or not they are committed to 'objects'. Fine rejects the 'austere' version, which says that objects have no properties. Either version of structuralism can have abstraction as its basis. |
| 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. |
| 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? |
| 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. |
| 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. |
| 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. |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| Full Idea: A thing (an object of our thought) is completely determined by all that can be affirmed or thought concerning it. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], I.1) | |
| A reaction: How could you justify this as an observation? Why can't there be unthinkable things (even by God)? Presumably Dedekind is offering a stipulative definition, but we may then be confusing epistemology with ontology. |
| 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. |
| 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! |
| 9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
| Full Idea: By applying the operation of abstraction to a system of objects isomorphic to the natural numbers, Dedekind believed that we obtained the abstract system of natural numbers, each member having only properties consequent upon its position. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Dummett - The Philosophy of Mathematics | |
| A reaction: Dummett is scornful of the abstractionism. He cites Benacerraf as a modern non-abstractionist follower of Dedekind's view. There seems to be a suspicion of circularity in it. How many objects will you abstract from to get seven? |
| 9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
| Full Idea: If in an infinite system, set in order, we neglect the special character of the elements, simply retaining their distinguishability and their order-relations to one another, then the elements are the natural numbers, created by the human mind. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], VI.73) | |
| A reaction: [compressed] This is the classic abstractionist view of the origin of number, but with the added feature that the order is first imposed, so that ordinals remain after the abstraction. This, of course, sounds a bit circular, as well as subjective. |
| 9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
| Full Idea: Dedekind's conception is psychologistic only if that is the only way to understand the abstraction that is involved, which it is not. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William W. Tait - Frege versus Cantor and Dedekind IV | |
| A reaction: This is a very important suggestion, implying that we can retain some notion of abstractionism, while jettisoning the hated subjective character of private psychologism, which seems to undermine truth and logic. |
| 5845 | Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon] |
| Full Idea: Niceratus said that his father, because he was concerned to make him a good man, made him learn the whole works of Homer, and he could still repeat by heart the entire 'Iliad' and 'Odyssey'. | |
| From: Xenophon (Symposium [c.391 BCE], 3.5) | |
| A reaction: This clearly shows the status which Homer had in the teaching of morality in the time of Socrates, and it is precisely this acceptance of authority which he was challenging, in his attempts to analyse the true basis of virtue |
| 5833 | Education is the greatest of human goods [Xenophon] |
| Full Idea: Education is the greatest of human goods. | |
| From: Xenophon (Apology of Socrates [c.392 BCE], 22) | |
| A reaction: Of course, one might ask what education is for, and arrive at a greater good. If you ask what is the greatest good which a society can provide for you, or which you can give to your children, this seems to me a good answer. |
| 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. |