114 ideas
| 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. |
| 9449 | The plausible Barcan formula implies modality in the actual world [Bird] |
| Full Idea: Modality in the actual world is the import of the Barcan formula, and there are good reasons for accepting the Barcan formula. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 1.2) | |
| A reaction: If you thought logic was irrelevant to metaphysics, this should make you think twice. |
| 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. |
| 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) |
| 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. |
| 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? |
| 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. |
| 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) |
| 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) |
| 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) |
| 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) |
| 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. |
| 9501 | If all existents are causally active, that excludes abstracta and causally isolated objects [Bird] |
| Full Idea: If one says that 'everything that exists is causally active', that rules out abstracta (notably sets and numbers), and it rules out objects that are causally isolated. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 5.5) | |
| A reaction: I like the principle. I take abstracta to be brain events, so they are causally active, within highly refined and focused brains, and if your physics is built on the notion of fields then I would think a 'causally isolated' object incoherent. |
| 9500 | If naturalism refers to supervenience, that leaves necessary entities untouched [Bird] |
| Full Idea: If one's naturalistic principles are formulated in terms of supervenience, then necessary entities are left untouched. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 5.5) | |
| A reaction: I take this to be part of the reason why some people like supervenience - that it leaves a pure 'space of reasons' which is unreachable from the flesh and blood inside a cranium. Personall I like the space of reasons, but I drop the 'pure'. |
| 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) |
| 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. |
| 9502 | There might be just one fundamental natural property [Bird] |
| Full Idea: The thought that there might be just one fundamental natural property is not that strange. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 6.3) | |
| A reaction: A nice variation on the Parmenides idea that only the One exists. Bird's point would refer to a possible unification of modern physics. We see, for example, the forces of electricity and of magnetism turning out to be the same force. |
| 9477 | Categorical properties are not modally fixed, but change across possible worlds [Bird] |
| Full Idea: Categorical properties do not have their dispositional characters modally fixed, but may change their dispositional characters (and their causal and nomic behaviour more generally) across different worlds. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.1) | |
| A reaction: This is the key ground for Bird's praiseworth opposition to categorical propertie. I take it to be a nonsense to call the category in which we place something a 'property' of that thing. A confusion of thought with reality. |
| 9490 | The categoricalist idea is that a property is only individuated by being itself [Bird] |
| Full Idea: In the categoricalist view, the essential properties of a natural property are limited to its essentially being itself and not some distinct property. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.1) | |
| A reaction: He associates this view with Lewis (modern regularity view) and Armstrong (nomic necessitation), and launches a splendid attack against it. I have always laughed at the idea that 'being Socrates' was one of the properties of Socrates. |
| 9495 | If we abstractly define a property, that doesn't mean some object could possess it [Bird] |
| Full Idea: The possibility of abstract definition does not show that we have defined a property that we can know, independently of any theory, that it is physically possible for some object to possess. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.2.3.1) | |
| A reaction: This is a naturalist resisting the idea that there is no more to a property than set-membership. I strongly agree. We need a firm notion of properties as features of the actual world; anything else should be called something like 'categorisations'. |
| 9492 | Categoricalists take properties to be quiddities, with no essential difference between them [Bird] |
| Full Idea: The categoricalist conception of properties takes them to be quiddities, which are primitive identities between fundamental qualities, having no difference with regard to their essence. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.5) | |
| A reaction: Compare 'haecceitism' about indentity of objects, though 'quidditism' sounds even less plausible. Bird attributes this view to Lewis and Armstrong, and makes it sound well daft. |
| 9503 | To name an abundant property is either a Fregean concept, or a simple predicate [Bird] |
| Full Idea: It isn't clear what it is to name an abundant property. One might reify them, as akin to Fregean concepts, or it might be equivalent to a simple predication. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 7.1.2) | |
| A reaction: 'Fregean concepts' would make them functions that purely link things (hence relational?). One suspects that people who actually treat abundant properties as part of their ontology (Lewis) are confusing natural properties with predicates. |
| 14540 | Only real powers are fundamental [Bird, by Mumford/Anjum] |
| Full Idea: Bird says only real powers are fundamental. | |
| From: report of Alexander Bird (Nature's Metaphysics [2007]) by S.Mumford/R.Lill Anjum - Getting Causes from Powers 1.5 | |
| A reaction: They disagree, and want higher-level properties in their ontology. I'm with Bird, except that something must exist to have the powers. Powers are fundamental to all the activity of nature, and are intrinsic to the stuff which constitutes nature. |
| 9450 | If all properties are potencies, and stimuli and manifestation characterise them, there is a regress [Bird] |
| Full Idea: Potencies are characterized in terms of their stimulus and manifestation properties, then if potencies are the only properties then these properties are also potencies, and must be characterized by yet further properties, leading to a vicious regress. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 1.2) | |
| A reaction: This is cited as the most popular objection to the dispositional account of properties. |
| 9498 | The essence of a potency involves relations, e.g. mass, to impressed force and acceleration [Bird] |
| Full Idea: The essence of a potency involves a relation to something else; if inertial mass is a potency then its essence involves a relation to a stimulus property (impressed force) and a manifestation property (acceleration). | |
| From: Alexander Bird (Nature's Metaphysics [2007], 5.3.3) | |
| A reaction: It doesn't seem quite right to say that the relations are part of the essence, if they might not occur, but some other relations might happen in their place. An essence is what makes a relation possible (like being good-looking). |
| 9474 | A disposition is finkish if a time delay might mean the manifestation fizzles out [Bird] |
| Full Idea: Finkish dispositions arise because the time delay between stimulus and manifestation provides an opportunity for the disposition to go out of existence and so halt the process that would bring about the manifestation. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 2.2.3) | |
| A reaction: This is a problem for the conditional analysis of dispositions; there may be a disposition, but it never reaches manifestation. Bird rightly points us towards actual powers rather than dispositions that need manifestation. |
| 9475 | A robust pot attached to a sensitive bomb is not fragile, but if struck it will easily break [Bird] |
| Full Idea: If a robust iron pot is attached to a bomb with a sensitive detonator. If the pot is struck, the bomb will go off, so they counterfactual 'if the pot were struck it would break' is true, but it is not a fragile pot. This is a 'mimic' of the disposition. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 2.2.5.1) | |
| A reaction: A very nice example, showing that a true disposition would have to be an internal feature (a power) of the pot itself, not a mere disposition to behave. The problem is these pesky empiricists, who want to reduce it all to what is observable. |
| 9499 | Megarian actualists deny unmanifested dispositions [Bird] |
| Full Idea: The Megarian actualist denies that a disposition can exist without being manifested. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 5.4) | |
| A reaction: I agree with Bird that this extreme realism seems wrong. As he puts it (p.109), "unrealized possibilities must be part of the actual world". This commitment is beginning to change my understanding of the world I am looking at. |
| 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) |
| 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) |
| 9486 | Why should a universal's existence depend on instantiation in an existing particular? [Bird] |
| Full Idea: An instantiation condition seems to be a failure of nerve as regards realism about universals. If universals really are entities in their own right, why should their existence depend upon a relationship with existing particulars? | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.2.2) | |
| A reaction: I like this challenge, which seems to leave fans of universals no option but full-blown Platonism, which most of them recognise as being deeply implausible. |
| 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. |
| 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) |
| 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) |
| 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) |
| 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) |
| 9472 | Resemblance itself needs explanation, presumably in terms of something held in common [Bird] |
| Full Idea: The realist view of resemblance nominalism is that it is resemblance that needs explaining. When there is resemblance it is natural to want to explain it, in terms of something held in common. Explanations end somewhere, but not with resemblance. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 2.1.2) | |
| A reaction: I smell a regress. If a knife and a razor resemble because they share sharpness, you have to see that the sharp phenomenon falls within the category of 'sharpness' before you can make the connection, which is spotting its similarity. |
| 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. |
| 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. |
| 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. |
| 9482 | If the laws necessarily imply p, that doesn't give a new 'nomological' necessity [Bird] |
| Full Idea: It does not add to the kinds of necessity to say that p is 'nomologically necessary' iff (the laws of nature → p) is metaphysically necessary. That trick of construction could be pulled for 'feline necessity' (true in all worlds that contain cats). | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.1.2) | |
| A reaction: I love it! Bird seems to think that the only necessity is 'metaphysical' necessity, true in all possible worlds, and he is right. The question arises in modal logic, though, of the accessibility between worlds (which might give degrees of necessity?). |
| 9481 | Logical necessitation is not a kind of necessity; George Orwell not being Eric Blair is not a real possibility [Bird] |
| Full Idea: I do not regard logical necessitation as a kind of necessity. It is logically possible that George Orwell is not Eric Blair, but in what sense is this any kind of possibility? It arises from having two names, but that confers no genuine possibility. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.1.2) | |
| A reaction: How refreshing. All kinds of concepts like this are just accepted by philosophers as obvious, until someone challenges them. The whole undergrowth of modal thinking needs a good flamethrower taken to it. |
| 9505 | Empiricist saw imaginability and possibility as close, but now they seem remote [Bird] |
| Full Idea: Whereas the link between imaginability and possibility was once held, under the influence of empiricism, to be close, it is now widely held to be very remote. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 8) | |
| A reaction: Tim Williamson nicely argues the opposite - that assessment of possibility is an adjunct of our ability to think counterfactually, which is precisely an operation of the imagination. Big error is possible, but how else could we do it? |
| 9491 | Haecceitism says identity is independent of qualities and without essence [Bird] |
| Full Idea: The core of haecceitism is the view that the transworld identity of particulars does not supervene on their qualitative features. ...The simplest expression of it is that particulars lack essential properties. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.2.1) | |
| A reaction: This seems to be something the 'bare substratum' account of substance (associated with Locke). You are left with the difficulty of how to individuate an instance of the haecceity, as opposed to the bundle of properties attached to it. |
| 9487 | We can't reject all explanations because of a regress; inexplicable A can still explain B [Bird] |
| Full Idea: Some regard the potential regress of explanations as a reason to think that the very idea of explanation is illusory. This is a fallacy; it is not a necessary condition on A's explaining B that we have an explanation for A also. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.2.4) | |
| A reaction: True, though to say 'B is explained by A, but A is totally baffling' is not the account we are dreaming of. And the explanation would certainly fail if we could say nothing at all about A, apart from naming it. |
| 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. |
| 9493 | We should explain causation by powers, not powers by causation [Bird] |
| Full Idea: The notion of 'causal power' is not to be analysed in terms of causation; if anything, the relationship is the reverse. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.2.1 n71) | |
| A reaction: It is a popular view these days to take causation as basic (as opposed to the counterfactual account), but I prefer this view. If anything is basic in nature, it is the dynamic force in the engine room, which is the active powers of substances. |
| 9494 | Singularism about causes is wrong, as the universals involved imply laws [Bird] |
| Full Idea: While singularists about causation might think that a particular has its causal powers independently of law, it is difficult to see how a universal could have or confer causal powers without generating what we would naturally think of as a law. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.2.1 n71) | |
| A reaction: This is a middle road between the purely singularist account (Anscombe) and the fully nomological account. We might say that a caused event will be 'involved in law-like behaviour', without attributing the cause to a law. |
| 9507 | Laws are explanatory relationships of things, which supervene on their essences [Bird] |
| Full Idea: The laws of a domain are the fundamental, general explanatory relationships between kinds, quantities, and qualities of that domain, that supervene upon the essential natures of those things. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 10.1) | |
| A reaction: This is the scientific essentialist view of laws [see entries there, in 'Laws of Nature']. There seems uncertainty between 'kinds' and 'qualities' (with 'quantities' looking like a category mistake). I vote, with Ellis, for natural kinds as the basis. |
| 9488 | Laws are either disposition regularities, or relations between properties [Bird] |
| Full Idea: Instead of viewing laws as regular relationships between dispositional properties and stimulus-manifestation, they can be conceived of as a relation between properties. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.4) | |
| A reaction: Bird offers these as the two main views, with the first coming from scientific essentialism, and the second from Armstrong's account of universals. Personally I favour the first, but Bird suggests that powers give the best support for both views. |
| 9496 | That other diamonds are hard does not explain why this one is [Bird] |
| Full Idea: The fact that some other diamonds are hard does not explain why this diamond is hard. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.3.2) | |
| A reaction: A very nice aphorism! It pinpoints the whole error of trying to explain the behaviour of the world by citing laws. Why should this item obey that law? Bird prefers 'powers', and so do I. |
| 9479 | Dispositional essentialism says laws (and laws about laws) are guaranteed regularities [Bird] |
| Full Idea: For the regularity version of dispositional essentialism about laws, laws are those regularities whose truth is guaranteed by the essential dispositional nature of one or more of the constituents. Regularities that supervene on such laws are also laws. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.1.2) | |
| A reaction: Even if you accept necessary behaviour resulting from essential dispositions, you still need to distinguish the important regularities from the accidental ones, so the word 'guarantee' is helpful, even if it raises lots of difficulties. |
| 9473 | Laws cannot offer unified explanations if they don't involve universals [Bird] |
| Full Idea: Laws, or what flow from them, are supposed to provide a unified explanation of the behaviours of particulars. Without universals the explanation of the behaviours of things lacks the required unity. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 2.1.2) | |
| A reaction: Sounds a bit question-begging? Gravity seems fairly unified, whereas the frequency of London buses doesn't. Maybe I could unify bus-behaviour by positing a few new universals? The unity should first be in the phenomena, not in the explanation. |
| 9484 | If the universals for laws must be instantiated, a vanishing particular could destroy a law [Bird] |
| Full Idea: If universals exist only where and when they are instantiated, this make serious trouble for the universals view of laws. It would be most odd if a particular, merely by changing its properties, could cause a law to go out of existence. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.2.2) | |
| A reaction: This sounds conclusive. He notes that this is probably why Armstrong does not adopt this view (though Lowe seems to favour it). Could there be a possible property (and concomitant law) which was never ever instantiated? |
| 9506 | Salt necessarily dissolves in water, because of the law which makes the existence of salt possible [Bird] |
| Full Idea: We cannot have a world where it is true both that salt exists (which requires Coulomb's Law to be true), and that it fails to dissolve in water (which requires Coulomb's Law to be false). So the dissolving is necessary even if the Law is contingent. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 8.2) | |
| A reaction: Excellent. It is just like the bonfire on the Moon (imaginable through ignorance, but impossible). People who assert that the solubility of salt is contingent tend not to know much about chemistry. |
| 23713 | Most laws supervene on fundamental laws, which are explained by basic powers [Bird, by Friend/Kimpton-Nye] |
| Full Idea: According to Bird, non-fundamental laws supervene on fundamental laws, and so are ultimately explained by fundamental powers. | |
| From: report of Alexander Bird (Nature's Metaphysics [2007]) by Friend/Kimpton-Nye - Dispositions and Powers 3.6.1 | |
| A reaction: This looks like the picture I subscribe to. Roughly, fundamental laws are explained by powers, and non-fundamental laws are explained by properties, which are complexes of powers. 'Fundamental' may not be a precise term! |
| 9489 | Essentialism can't use conditionals to explain regularities, because of possible interventions [Bird] |
| Full Idea: The straightforward dispositional essentialist account of laws by subjunctive conditionals is false because dispositions typically suffer from finks and antidotes. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.4) | |
| A reaction: [Finks and antidotes intervene before a disposition can take effect] This seems very persuasive to me, and shows why you can't just explain laws as counterfactual or conditional claims. Explanation demands what underlies them. |
| 9504 | The relational view of space-time doesn't cover times and places where things could be [Bird] |
| Full Idea: The obvious problem with the simple relational view of space and time is that it fails to account for the full range of spatio-temporal possibility. There seem to be times and places where objects and events could be, but are not. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 7.3.2) | |
| A reaction: This view seems strongly supported by intuition. I certainly don't accept the views of physicists and cosmologists on the subject, because they seem to approach the whole thing too instrumentally. |
| 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) |