118 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the spirit of metaphysics since Saul Kripke's work, though some people engaged in it seem to me to be trapped in an outdated linguistic view of the matter.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. |
| 224 | When questions are doubtful we should concentrate not on objects but on ideas of the intellect [Plato] |
| Full Idea: Doubtful questions should not be discussed in terms of visible objects or in relation to them, but only with reference to ideas conceived by the intellect. | |
| From: Plato (Parmenides [c.364 BCE], 135e) |
| 232 | Opposites are as unlike as possible [Plato] |
| Full Idea: Opposites are as unlike as possible. | |
| From: Plato (Parmenides [c.364 BCE], 159a) |
| 8937 | Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato] |
| Full Idea: Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic. | |
| From: comment on Plato (Parmenides [c.364 BCE]) by Georg W.F.Hegel - Phenomenology of Spirit Pref 71 | |
| A reaction: It is a long way from the analytic tradition of philosophy to be singling out a classic text for its 'artistic' achievement. Eventually we may even look back on, say, Kripke's 'Naming and Necessity' and see it in that light. |
| 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. |
| 10073 | There cannot be a set theory which is complete [Smith,P] |
| Full Idea: By Gödel's First Incompleteness Theorem, there cannot be a negation-complete set theory. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 01.3) | |
| A reaction: This means that we can never prove all the truths of a system of set theory. |
| 10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
| Full Idea: Going second-order in arithmetic enables us to prove new first-order arithmetical sentences that we couldn't prove before. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 23.4) | |
| A reaction: The wages of Satan, perhaps. We can prove things about objects by proving things about their properties and sets and functions. Smith says this fact goes all the way up the hierarchy. |
| 10075 | A 'partial function' maps only some elements to another set [Smith,P] |
| Full Idea: A 'partial function' is one which maps only some elements of a domain to elements in another set. For example, the reciprocal function 1/x is not defined for x=0. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1 n1) |
| 10074 | A 'total function' maps every element to one element in another set [Smith,P] |
| Full Idea: A 'total function' is one which maps every element of a domain to exactly one corresponding value in another set. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) |
| 10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
| Full Idea: If a function f maps the argument a back to a itself, so that f(a) = a, then a is said to be a 'fixed point' for f. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 20.5) |
| 10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
| Full Idea: The 'range' of a function is the set of elements in the output set that are values of the function for elements in the original set. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) | |
| A reaction: In other words, the range is the set of values that were created by the function. |
| 10605 | Two functions are the same if they have the same extension [Smith,P] |
| Full Idea: We count two functions as being the same if they have the same extension, i.e. if they pair up arguments with values in the same way. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 11.3) | |
| A reaction: So there's only one way to skin a cat in mathematical logic. |
| 10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
| Full Idea: The so-called Comprehension Schema ∃X∀x(Xx ↔ φ(x)) says that there is a property which is had by just those things which satisfy the condition φ. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 22.3) |
| 10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
| Full Idea: 'Theorem': given a derivation of the sentence φ from the axioms of the theory T using the background logical proof system, we will say that φ is a 'theorem' of the theory. Standard abbreviation is T |- φ. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) |
| 10602 | A 'natural deduction system' has no axioms but many rules [Smith,P] |
| Full Idea: A 'natural deduction system' will have no logical axioms but may rules of inference. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 09.1) | |
| A reaction: He contrasts this with 'Hilbert-style systems', which have many axioms but few rules. Natural deduction uses many assumptions which are then discharged, and so tree-systems are good for representing it. |
| 10613 | No nice theory can define truth for its own language [Smith,P] |
| Full Idea: No nice theory can define truth for its own language. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 21.5) | |
| A reaction: This leads on to Tarski's account of truth. |
| 10078 | An 'injective' ('one-to-one') function creates a distinct output element from each original [Smith,P] |
| Full Idea: An 'injective' function is 'one-to-one' - each element of the output set results from a different element of the original set. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) | |
| A reaction: That is, two different original elements cannot lead to the same output element. |
| 10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
| Full Idea: A 'bijective' function has 'one-to-one correspondence' - it is both surjective and injective, so that every element in each of the original and the output sets has a matching element in the other. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) | |
| A reaction: Note that 'injective' is also one-to-one, but only in the one direction. |
| 10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
| Full Idea: A 'surjective' function is 'onto' - the whole of the output set results from the function being applied to elements of the original set. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) |
| 10070 | If everything that a theory proves is true, then it is 'sound' [Smith,P] |
| Full Idea: If everything that a theory proves must be true, then it is a 'sound' theory. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 01.1) |
| 10086 | Soundness is true axioms and a truth-preserving proof system [Smith,P] |
| Full Idea: Soundness is normally a matter of having true axioms and a truth-preserving proof system. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) | |
| A reaction: The only exception I can think of is if a theory consisted of nothing but the axioms. |
| 10596 | A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P] |
| Full Idea: A theory is 'sound' iff every theorem of it is true (i.e. true on the interpretation built into its language). Soundness is normally a matter of having true axioms and a truth-preserving proof system. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) |
| 10598 | A theory is 'negation complete' if it proves all sentences or their negation [Smith,P] |
| Full Idea: A theory is 'negation complete' if it decides every sentence of its language (either the sentence, or its negation). | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) |
| 10597 | 'Complete' applies both to whole logics, and to theories within them [Smith,P] |
| Full Idea: There is an annoying double-use of 'complete': a logic may be semantically complete, but there may be an incomplete theory expressed in it. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) |
| 10069 | A theory is 'negation complete' if one of its sentences or its negation can always be proved [Smith,P] |
| Full Idea: Logicians say that a theory T is '(negation) complete' if, for every sentence φ in the language of the theory, either φ or ¬φ is deducible in T's proof system. If this were the case, then truth could be equated with provability. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 01.1) | |
| A reaction: The word 'negation' seems to be a recent addition to the concept. Presumable it might be the case that φ can always be proved, but not ¬φ. |
| 10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
| Full Idea: There are two routes to Incompleteness results. One goes via the semantic assumption that we are dealing with sound theories, using a result about what they can express. The other uses the syntactic notion of consistency, with stronger notions of proof. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 18.1) |
| 10080 | 'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P] |
| Full Idea: An 'effectively decidable' (or 'computable') algorithm will be step-by-small-step, with no need for intuition, or for independent sources, with no random methods, possible for a dumb computer, and terminates in finite steps. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.2) | |
| A reaction: [a compressed paragraph] |
| 10087 | A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P] |
| Full Idea: A theory is 'decidable' iff there is a mechanical procedure for determining whether any sentence of its language can be proved. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) | |
| A reaction: Note that it doesn't actually have to be proved. The theorems of the theory are all effectively decidable. |
| 10088 | Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P] |
| Full Idea: Any consistent, axiomatized, negation-complete formal theory is decidable. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.6) |
| 10081 | A set is 'enumerable' is all of its elements can result from a natural number function [Smith,P] |
| Full Idea: A set is 'enumerable' iff either the set is empty, or there is a surjective function to the set from the set of natural numbers, so that the set is in the range of that function. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.3) |
| 10083 | A set is 'effectively enumerable' if a computer could eventually list every member [Smith,P] |
| Full Idea: A set is 'effectively enumerable' if an (idealised) computer could be programmed to generate a list of its members such that any member will eventually be mentioned (even if the list is empty, or without end, or contains repetitions). | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.4) |
| 10084 | A finite set of finitely specifiable objects is always effectively enumerable (e.g. primes) [Smith,P] |
| Full Idea: A finite set of finitely specifiable objects is always effectively enumerable (for example, the prime numbers). | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.4) |
| 10085 | The set of ordered pairs of natural numbers <i,j> is effectively enumerable [Smith,P] |
| Full Idea: The set of ordered pairs of natural numbers (i,j) is effectively enumerable, as proven by listing them in an array (across: <0,0>, <0,1>, <0,2> ..., and down: <0,0>, <1,0>, <2,0>...), and then zig-zagging. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.5) |
| 10601 | The thorems of a nice arithmetic can be enumerated, but not the truths (so they're diffferent) [Smith,P] |
| Full Idea: The theorems of any properly axiomatized theory can be effectively enumerated. However, the truths of any sufficiently expressive arithmetic can't be effectively enumerated. Hence the theorems and truths of arithmetic cannot be the same. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 05 Intro) |
| 10600 | Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P] |
| Full Idea: Whether a property is 'expressible' in a given theory depends on the richness of the theory's language. Whether the property can be 'captured' (or 'represented') by the theory depends on the richness of the axioms and proof system. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 04.7) |
| 13986 | Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle] |
| Full Idea: Plato (in 'Parmenides') shows that the theory that 'Eide' are substances, and Kant that space and time are substances, and Bradley that relations are substances, all lead to aninomies. | |
| From: report of Plato (Parmenides [c.364 BCE]) by Gilbert Ryle - Are there propositions? 'Objections' |
| 14150 | Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato] |
| Full Idea: Plato's 'Parmenides' is perhaps the best collection of antinomies ever made. | |
| From: comment on Plato (Parmenides [c.364 BCE]) by Bertrand Russell - The Principles of Mathematics §337 |
| 10599 | For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P] |
| Full Idea: For prime numbers we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))). That is, the only way to multiply two numbers and a get a prime is if one of them is 1. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 04.5) |
| 10610 | The reals contain the naturals, but the theory of reals doesn't contain the theory of naturals [Smith,P] |
| Full Idea: It has been proved (by Tarski) that the real numbers R is a complete theory. But this means that while the real numbers contain the natural numbers, the pure theory of real numbers doesn't contain the theory of natural numbers. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 18.2) |
| 10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
| Full Idea: The truths of arithmetic are just the true equations involving particular numbers, and universally quantified versions of such equations. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 27.7) | |
| A reaction: Must each equation be universally quantified? Why can't we just universally quantify over the whole system? |
| 10608 | The number of Fs is the 'successor' of the Gs if there is a single F that isn't G [Smith,P] |
| Full Idea: The number of Fs is the 'successor' of the number of Gs if there is an object which is an F, and the remaining things that are F but not identical to the object are equinumerous with the Gs. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 14.1) |
| 10618 | All numbers are related to zero by the ancestral of the successor relation [Smith,P] |
| Full Idea: All numbers are related to zero by the ancestral of the successor relation. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 23.5) | |
| A reaction: The successor relation only ties a number to the previous one, not to the whole series. Ancestrals are a higher level of abstraction. |
| 10849 | Baby arithmetic covers addition and multiplication, but no general facts about numbers [Smith,P] |
| Full Idea: Baby Arithmetic 'knows' the addition of particular numbers and multiplication, but can't express general facts about numbers, because it lacks quantification. It has a constant '0', a function 'S', and functions '+' and 'x', and identity and negation. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 08.1) |
| 10850 | Baby Arithmetic is complete, but not very expressive [Smith,P] |
| Full Idea: Baby Arithmetic is negation complete, so it can prove every claim (or its negation) that it can express, but it is expressively extremely impoverished. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 08.3) |
| 10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
| Full Idea: We can beef up Baby Arithmetic into Robinson Arithmetic (referred to as 'Q'), by restoring quantifiers and variables. It has seven generalised axioms, plus standard first-order logic. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 08.3) |
| 10852 | Robinson Arithmetic (Q) is not negation complete [Smith,P] |
| Full Idea: Robinson Arithmetic (Q) is not negation complete | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 08.4) |
| 10068 | Natural numbers have zero, unique successors, unending, no circling back, and no strays [Smith,P] |
| Full Idea: The sequence of natural numbers starts from zero, and each number has just one immediate successor; the sequence continues without end, never circling back on itself, and there are no 'stray' numbers, lurking outside the sequence. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 01.1) | |
| A reaction: These are the characteristics of the natural numbers which have to be pinned down by any axiom system, such as Peano's, or any more modern axiomatic structures. We are in the territory of Gödel's theorems. |
| 10603 | The logic of arithmetic must quantify over properties of numbers to handle induction [Smith,P] |
| Full Idea: If the logic of arithmetic doesn't have second-order quantifiers to range over properties of numbers, how can it handle induction? | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 10.1) |
| 10848 | Multiplication only generates incompleteness if combined with addition and successor [Smith,P] |
| Full Idea: Multiplication in itself isn't is intractable. In 1929 Skolem showed a complete theory for a first-order language with multiplication but lacking addition (or successor). Multiplication together with addition and successor produces incompleteness. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 10.7 n8) |
| 10604 | Incompleteness results in arithmetic from combining addition and successor with multiplication [Smith,P] |
| Full Idea: Putting multiplication together with addition and successor in the language of arithmetic produces incompleteness. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 10.7) | |
| A reaction: His 'Baby Arithmetic' has all three and is complete, but lacks quantification (p.51) |
| 16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
| Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it. | |
| From: Plato (Parmenides [c.364 BCE], 144a) | |
| A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed. |
| 229 | The one was and is and will be and was becoming and is becoming and will become [Plato] |
| Full Idea: The one was and is and will be and was becoming and is becoming and will become. | |
| From: Plato (Parmenides [c.364 BCE], 155d) |
| 21821 | Plato's Parmenides has a three-part theory, of Primal One, a One-Many, and a One-and-Many [Plato, by Plotinus] |
| Full Idea: The Platonic Parmenides is more exact [than Parmenides himself]; the distinction is made between the Primal One, a strictly pure Unity, and a secondary One which is a One-Many, and a third which is a One-and-Many. | |
| From: report of Plato (Parmenides [c.364 BCE]) by Plotinus - The Enneads 5.1.08 | |
| A reaction: Plotinus approves of this three-part theory. Parmenides has the problem that the highest Being contains no movement. By placing the One outside Being you can give it powers which an existent thing cannot have. Cf the concept of God. |
| 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. |
| 221 | Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato] |
| Full Idea: The absolute good and the beautiful and all which we conceive to be absolute ideas are unknown to us. | |
| From: Plato (Parmenides [c.364 BCE], 134c) |
| 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. |
| 10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
| Full Idea: The 'ancestral' of a relation is that relation which holds when there is an indefinitely long chain of things having the initial relation. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 23.5) | |
| A reaction: The standard example is spotting the relation 'ancestor' from the receding relation 'parent'. This is a sort of abstraction derived from a relation which is not equivalent (parenthood being transitive but not reflexive). The idea originated with Frege. |
| 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. |
| 223 | If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato] |
| Full Idea: If a person denies that the idea of each thing is always the same, he will utterly destroy the power of carrying on discussion. | |
| From: Plato (Parmenides [c.364 BCE], 135c) |
| 227 | You must always mean the same thing when you utter the same name [Plato] |
| Full Idea: You must always mean the same thing when you utter the same name. | |
| From: Plato (Parmenides [c.364 BCE], 147d) |
| 210 | It would be absurd to think there were abstract Forms for vile things like hair, mud and dirt [Plato] |
| Full Idea: Are there abstract ideas for such things as hair, mud and dirt, which are particularly vile and worthless? That would be quite absurd. | |
| From: Plato (Parmenides [c.364 BCE], 130d) |
| 220 | The concept of a master includes the concept of a slave [Plato] |
| Full Idea: Mastership in the abstract is mastership of slavery in the abstract. | |
| From: Plato (Parmenides [c.364 BCE], 133e) |
| 211 | If admirable things have Forms, maybe everything else does as well [Plato] |
| Full Idea: It is troubling that if admirable things have abstract ideas, then perhaps everything else must have ideas as well. | |
| From: Plato (Parmenides [c.364 BCE], 130d) |
| 219 | If absolute ideas existed in us, they would cease to be absolute [Plato] |
| Full Idea: None of the absolute ideas exists in us, because then it would no longer be absolute. | |
| From: Plato (Parmenides [c.364 BCE], 133c) |
| 228 | Greatness and smallness must exist, to be opposed to one another, and come into being in things [Plato] |
| Full Idea: These two ideas, greatness and smallness, exist, do they not? For if they did not exist, they could not be opposites of one another, and could not come into being in things. | |
| From: Plato (Parmenides [c.364 BCE], 149e) |
| 16151 | Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M] |
| Full Idea: It seems to me that Plato in the later dialogues, beginning with the second half of 'Parmenides', wants to substitute a theory of genera and theory of principles that constitute these genera for the earlier theory of forms. | |
| From: report of Plato (Parmenides [c.364 BCE]) by Michael Frede - Title, Unity, Authenticity of the 'Categories' V | |
| A reaction: My theory is that the later Plato came under the influence of the brilliant young Aristotle, and this idea is a symptom of it. The theory of 'principles' sounds like hylomorphism to me. |
| 218 | Participation is not by means of similarity, so we are looking for some other method of participation [Plato] |
| Full Idea: Participation is not by means of likeness, so we must seek some other method of participation. | |
| From: Plato (Parmenides [c.364 BCE], 133a) |
| 213 | Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato] |
| Full Idea: Just as day is in many places at once, but not separated from itself, so each idea might be in all its participants at once. | |
| From: Plato (Parmenides [c.364 BCE], 131b) |
| 216 | If things are made alike by participating in something, that thing will be the absolute idea [Plato] |
| Full Idea: That by participation in which like things are made like, will be the absolute idea, will it not? | |
| From: Plato (Parmenides [c.364 BCE], 132e) |
| 215 | If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato] |
| Full Idea: If all things partake of ideas, must either everything be made of thoughts and everything thinks, or everything is thought, and so can't think? | |
| From: Plato (Parmenides [c.364 BCE], 132c) |
| 212 | The whole idea of each Form must be found in each thing which participates in it [Plato] |
| Full Idea: The whole idea of each form (of beauty, justice etc) must be found in each thing which participates in it. | |
| From: Plato (Parmenides [c.364 BCE], 131a) |
| 217 | Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [Plato] |
| Full Idea: It is impossible for anything to be like an absolute idea, because a third idea will appear to make them alike, and if that is like anything, it will lead to another idea, and so on. | |
| From: Plato (Parmenides [c.364 BCE], 133a) |
| 214 | If absolute greatness and great things are seen as the same, another thing appears which makes them seem great [Plato] |
| Full Idea: If you regard the absolute great and the many great things in the same way, will not another appear beyond, by which all these must appear to be great? | |
| From: Plato (Parmenides [c.364 BCE], 132a) |
| 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. |
| 15851 | Parts must belong to a created thing with a distinct form [Plato] |
| Full Idea: The part would not be the part of many things or all, but of some one character ['ideas'] and of some one thing, which we call a 'whole', since it has come to be one complete [perfected] thing composed [created] of all. | |
| From: Plato (Parmenides [c.364 BCE], 157d) | |
| A reaction: A serious shot by Plato at what identity is. Harte quotes it (125) and shows that 'character' is Gk 'idea', and 'composed' will translate as 'created'. 'Form' links this Platonic passage to Aristotle's hylomorphism. |
| 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. |
| 15846 | In Parmenides, if composition is identity, a whole is nothing more than its parts [Plato, by Harte,V] |
| Full Idea: At the heart of the 'Parmenides' puzzles about composition is the thesis that composition is identity. Considered thus, a whole adds nothing to an ontology that already includes its parts | |
| From: report of Plato (Parmenides [c.364 BCE]) by Verity Harte - Plato on Parts and Wholes 2.5 | |
| A reaction: There has to be more to a unified identity that mere proximity of the parts. When do parts come together, and when do they actually 'compose' something? |
| 15849 | Plato says only a one has parts, and a many does not [Plato, by Harte,V] |
| Full Idea: In 'Parmenides' it is argued that a part cannot be part of a many, but must be part of something one. | |
| From: report of Plato (Parmenides [c.364 BCE], 157c) by Verity Harte - Plato on Parts and Wholes 3.2 | |
| A reaction: This looks like the right way to go with the term 'part'. We presuppose a unity before we even talk of its parts, so we can't get into contradictions and paradoxes about their relationships. |
| 15850 | Anything which has parts must be one thing, and parts are of a one, not of a many [Plato] |
| Full Idea: The whole of which the parts are parts must be one thing composed of many; for each of the parts must be part, not of a many, but of a whole. | |
| From: Plato (Parmenides [c.364 BCE], 157c) | |
| A reaction: This is a key move of metaphysics, and we should hang on to it. The other way madness lies. |
| 13259 | It seems that the One must be composed of parts, which contradicts its being one [Plato] |
| Full Idea: The One must be composed of parts, both being a whole and having parts. So on both grounds the One would thus be many and not one. But it must be not many, but one. So if the One will be one, it will neither be a whole, nor have parts. | |
| From: Plato (Parmenides [c.364 BCE], 137c09), quoted by Kathrin Koslicki - The Structure of Objects 5.2 | |
| A reaction: This is the starting point for Plato's metaphysical discussion of objects. It seems to begin a line of thought which is completed by Aristotle, surmising that only an essential structure can bestow identity on a bunch of parts. |
| 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. |
| 15847 | Two things relate either as same or different, or part of a whole, or the whole of the part [Plato] |
| Full Idea: Everything is surely related to everything as follows: either it is the same or different; or, if it is not the same or different, it would be related as part to whole or as whole to part. | |
| From: Plato (Parmenides [c.364 BCE], 146b) | |
| A reaction: This strikes me as a really helpful first step in trying to analyse the nature of identity. Two things are either two or (actually) one, or related mereologically. |
| 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! |
| 222 | Only a great person can understand the essence of things, and an even greater person can teach it [Plato] |
| Full Idea: Only a man of very great natural gifts will be able to understand that everything has a class and absolute essence, and an even more wonderful man can teach this. | |
| From: Plato (Parmenides [c.364 BCE], 135a) |
| 225 | The unlimited has no shape and is endless [Plato] |
| Full Idea: The unlimited partakes neither of the round nor of the straight, because it has no ends nor edges. | |
| From: Plato (Parmenides [c.364 BCE], 137e) |
| 233 | Some things do not partake of the One [Plato] |
| Full Idea: The others cannot partake of the one in any way; they can neither partake of it nor of the whole. | |
| From: Plato (Parmenides [c.364 BCE], 159d) | |
| A reaction: Compare Idea 231 |
| 2062 | The only movement possible for the One is in space or in alteration [Plato] |
| Full Idea: If the One moves it either moves spatially or it is altered, since these are the only motions. | |
| From: Plato (Parmenides [c.364 BCE], 138b) |
| 231 | Everything partakes of the One in some way [Plato] |
| Full Idea: The others are not altogether deprived of the one, for they partake of it in some way. | |
| From: Plato (Parmenides [c.364 BCE], 157c) | |
| A reaction: Compare Idea 233. |
| 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. |
| 234 | We couldn't discuss the non-existence of the One without knowledge of it [Plato] |
| Full Idea: There must be knowledge of the one, or else not even the meaning of the words 'if the one does not exist' would be known. | |
| From: Plato (Parmenides [c.364 BCE], 160d) |