99 ideas
| 13734 | Modern Quinean metaphysics is about what exists, but Aristotelian metaphysics asks about grounding [Schaffer,J] |
| Full Idea: On the now dominant Quinean view, metaphysics is about what there is (such as properties, meanings and numbers). I will argue for the revival of a more traditional Aristotelian view, on which metaphysics is about what grounds what. | |
| From: Jonathan Schaffer (On What Grounds What [2009], Intro) | |
| A reaction: I find that an enormously helpful distinction, and support the Aristotelian view. Schaffer's general line is that what exists is fairly uncontroversial and dull, but the interesting truths about the world emerge when we grasp its structure. |
| 13751 | If you tore the metaphysics out of philosophy, the whole enterprise would collapse [Schaffer,J] |
| Full Idea: Traditional metaphysics is so tightly woven into the fabric of philosophy that it cannot be torn out without the whole tapestry unravelling. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.3) | |
| A reaction: I often wonder why the opponents of metaphysics still continue to do philosophy. I don't see how you address questions of ethics, or philosophy of mathematics (etc) without coming up against highly general and abstract over-questions. |
| 14600 | Analysis aims at secure necessary and sufficient conditions [Schaffer,J] |
| Full Idea: An analysis is an attempt at providing finite, non-circular, and intuitively adequate necessary and sufficient conditions. | |
| From: Jonathan Schaffer (Causation and Laws of Nature [2008], 3) | |
| A reaction: Specifying the 'conditions' for something doesn't seem to quite add up to telling you what the thing is. A trivial side-effect might qualify as a sufficient condition for something, if it always happens. |
| 13743 | We should not multiply basic entities, but we can have as many derivative entities as we like [Schaffer,J] |
| Full Idea: Occam's Razor should only be understood to concern substances: do not multiply basic entities without necessity. There is no problem with the multiplication of derivative entities - they are an 'ontological free lunch'. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
| A reaction: The phrase 'ontological free lunch' comes from Armstrong. This is probably what Occam meant. A few extra specks of dust, or even a few more numbers (thank you, Cantor!) don't seem to challenge the principle. |
| 14603 | 'Reification' occurs if we mistake a concept for a thing [Schaffer,J] |
| Full Idea: 'Reification' occurs when a mere concept is mistaken for a thing. We seem generally prone to this sort of error. | |
| From: Jonathan Schaffer (Causation and Laws of Nature [2008], 3.1) | |
| A reaction: Personally I think we should face up to the fact that this is the only way we can think about generalised or abstract entities, and stop thinking of it as an 'error'. We have evolved to think well about objects, so we translate everything that way. |
| 14607 | T adds □p→p for reflexivity, and is ideal for modeling lawhood [Schaffer,J] |
| Full Idea: System T is a normal modal system augmented with the reflexivity-generating axiom □p→p, and is, I think, the best modal logic for modeling lawhood. | |
| From: Jonathan Schaffer (Causation and Laws of Nature [2008], n46) | |
| A reaction: Schaffer shows in the article why transitivity would not be appropriate for lawhood. |
| 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. |
| 10373 | Logical form can't dictate metaphysics, as it may propose an undesirable property [Schaffer,J] |
| Full Idea: Logical form should not have the last word in metaphysics, since it might predicate a property that we have theoretical reason to reject. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 1.3.1) | |
| A reaction: These kind of warnings need to be sounded all the time, to prevent logicians and language experts from pitching their tents in the middle of metaphysics. They are welcome guests only, |
| 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. |
| 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) |
| 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) |
| 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) |
| 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) |
| 13741 | If 'there are red roses' implies 'there are roses', then 'there are prime numbers' implies 'there are numbers' [Schaffer,J] |
| Full Idea: We can automatically infer 'there are roses' from 'there are red roses' (with no shift in the meaning of 'roses'). Likewise one can automatically infer 'there are numbers' from 'there are prime numbers'. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
| A reaction: He similarly observes that the atheist's 'God is a fictional character' implies 'there are fictional characters'. Schaffer is not committing to a strong platonism with his claim - merely that the existence of numbers is hardly worth disputing. |
| 14604 | If a notion is ontologically basic, it should be needed in our best attempt at science [Schaffer,J] |
| Full Idea: Science represents our best systematic understanding of the world, and if a certain notion proves unneeded in our best attempt at that, this provides strong evidence that what this notion concerns is not ontologically basic. | |
| From: Jonathan Schaffer (Causation and Laws of Nature [2008], 3.2) | |
| A reaction: But is the objective of science to find out what is 'ontologically basic'? If scientists can't get a purchase on a question, they have no interest in it. What are electrons made of? |
| 13748 | Grounding is unanalysable and primitive, and is the basic structuring concept in metaphysics [Schaffer,J] |
| Full Idea: Grounding should be taken as primitive, as per the neo-Aristotelian approach. Grounding is an unanalyzable but needed notion - it is the primitive structuring conception of metaphysics. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.2) | |
| A reaction: [he cites K.Fine 1991] I find that this simple claim clarifies the discussions of Kit Fine, where you are not always quite sure what the game is. I agree fully with it. It makes metaphysics interesting, where cataloguing entities is boring. |
| 17304 | As causation links across time, grounding links the world across levels [Schaffer,J] |
| Full Idea: Grounding is something like metaphysical causation. Just as causation links the world across time, grounding links the world across levels. Grounding connects the more fundamental to the less fundamental, and thereby backs a certain form of explanation. | |
| From: Jonathan Schaffer (Grounding, Transitivity and Contrastivity [2012], Intro) | |
| A reaction: Obviously you need 'levels' for this, which we should take to be structural levels. |
| 17306 | If ground is transitive and irreflexive, it has a strict partial ordering, giving structure [Schaffer,J] |
| Full Idea: By treating grounding as transitive (and irreflexive), one generates a strict partial ordering that induces metaphysical structure. | |
| From: Jonathan Schaffer (Grounding, Transitivity and Contrastivity [2012], Intro) | |
| A reaction: Schaffer's paper goes on to attach the claim that grounding is transitive, but I didn't find his examples very convincing. |
| 14599 | Three types of reduction: Theoretical (of terms), Definitional (of concepts), Ontological (of reality) [Schaffer,J] |
| Full Idea: Theoretical reduction concerns terms found in a theory; Definitional reduction concerns concepts found in the mind; Ontological reduction is independent of how we conceptualize entities, or theorize about them, and is about reality. | |
| From: Jonathan Schaffer (Causation and Laws of Nature [2008], 1) | |
| A reaction: An Aristotelian definition refers to reality, rather than to our words or concepts. |
| 13747 | Supervenience is just modal correlation [Schaffer,J] |
| Full Idea: Supervenience is mere modal correlation. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.2) |
| 13744 | The cosmos is the only fundamental entity, from which all else exists by abstraction [Schaffer,J] |
| Full Idea: My preferred view is that there is only one fundamental entity - the whole concrete cosmos - from which all else exists by abstraction. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
| A reaction: This looks to me like weak anti-realism - that there are no natural 'joints' in nature - but I don't think Schaffer intends that. I take the joints to be fundamentals, which necessitates that the cosmos has parts. His 'abstraction' is clearly a process. |
| 10367 | There is only one fact - the True [Schaffer,J] |
| Full Idea: It can be argued that if all facts are logically equivalent, then there is only one fact - the True. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 1.1) | |
| A reaction: [he cites Davidson's 'Causal Relations', who cites Frege] This is the sort of bizarre stuff you end up with if you start from formal logic and work out to the world, instead of vice versa. |
| 13739 | Maybe categories are just the different ways that things depend on basic substances [Schaffer,J] |
| Full Idea: Maybe the categories are determined by the different grounding relations, ..so that categories just are the ways things depend on substances. ...Categories are places in the dependence ordering. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 1.3) |
| 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. |
| 14605 | Tropes are the same as events [Schaffer,J] |
| Full Idea: Tropes can be identified with events. | |
| From: Jonathan Schaffer (Causation and Laws of Nature [2008], n17) | |
| A reaction: This is presumably on the view of events, associated with Kim, as instantiations of properties. This idea is a new angle on tropes and events which had never occurred to me. |
| 14601 | Individuation aims to count entities, by saying when there is one [Schaffer,J] |
| Full Idea: Individuation principles are attempts to describe how to count entities in a given domain, by saying when there is one. | |
| From: Jonathan Schaffer (Causation and Laws of Nature [2008], 3) | |
| A reaction: At last, someone tells me what they mean by 'individuation'! So it is just saying what your units are prior to counting, followed (presumably) by successful counting. It seems to aim more at kinds than at particulars. |
| 14082 | No sortal could ever exactly pin down which set of particles count as this 'cup' [Schaffer,J] |
| Full Idea: Many decent candidates could the referent of this 'cup', differing over whether outlying particles are parts. No further sortal I could invoke will be selective enough to rule out all but one referent for it. | |
| From: Jonathan Schaffer (Deflationary Metaontology of Thomasson [2009], 3.1 n8) | |
| A reaction: I never had much faith in sortals for establishing individual identity, so this point comes as no surprise. The implication is strongly realist - that the cup has an identity which is permanently beyond our capacity to specify it. |
| 13742 | There exist heaps with no integral unity, so we should accept arbitrary composites in the same way [Schaffer,J] |
| Full Idea: I am happy to accept universal composition, on the grounds that there are heaps, piles etc with no integral unity, and that arbitrary composites are no less unified than heaps. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1 n11) | |
| A reaction: The metaphysical focus is then placed on what constitutes 'integral unity', which is precisely the question which most interested Aristotle. Clearly if there is nothing more to an entity than its components, scattering them isn't destruction. |
| 13752 | The notion of 'grounding' can explain integrated wholes in a way that mere aggregates can't [Schaffer,J] |
| Full Idea: The notion of grounding my capture a crucial mereological distinction (missing from classical mereology) between an integrated whole with genuine unity, and a mere aggregate. x is an integrated whole if it grounds its proper parts. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 3.1) | |
| A reaction: That gives a nice theoretical notion, but if you remove each of the proper parts, does x remain? Is it a bare particular? I take it that it will have to be an abstract principle, the one Aristotle was aiming at with his notion of 'form'. Schaffer agrees. |
| 14081 | Identities can be true despite indeterminate reference, if true under all interpretations [Schaffer,J] |
| Full Idea: There can be determinately true identity claims despite indeterminate reference of the terms flanking the identity sign; these will be identity claims true under all admissible interpretations of the flanking terms. | |
| From: Jonathan Schaffer (Deflationary Metaontology of Thomasson [2009], 3.1) | |
| A reaction: In informal contexts there might be problems with the notion of what is 'admissible'. Is 'my least favourite physical object' admissible? |
| 14606 | Only ideal conceivability could indicate what is possible [Schaffer,J] |
| Full Idea: The only plausible link from conceivability to possibility is via ideal conceivability. | |
| From: Jonathan Schaffer (Causation and Laws of Nature [2008], n22) | |
| A reaction: [He cites Chalmers 2002] I'm not sure what 'via' could mean here. Since I don't know any other way than attempted conceivability for assessing a possibility, I am a bit baffled by this idea. |
| 13749 | Belief in impossible worlds may require dialetheism [Schaffer,J] |
| Full Idea: One motivation for dialetheism is the view that there are impossible worlds. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.3) |
| 13740 | 'Moorean certainties' are more credible than any sceptical argument [Schaffer,J] |
| Full Idea: A 'Moorean certainty' is when something is more credible than any philosopher's argument to the contrary. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
| A reaction: The reference is to G.E. Moore's famous claim that the existence of his hand is more certain than standard sceptical arguments. It sounds empiricist, but they might be parallel rational truths, of basic logic or arithmetic. |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| Full Idea: Anaxarchus said that he was not even sure that he knew nothing. | |
| From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1 |
| 17308 | Explaining 'Adam ate the apple' depends on emphasis, and thus implies a contrast [Schaffer,J] |
| Full Idea: Explaining why ADAM ate the apple is a different matter from explaining why he ATE the apple, and from why he ate THE APPLE. ...In my view the best explanations incorporate ....contrastive information. | |
| From: Jonathan Schaffer (Grounding, Transitivity and Contrastivity [2012], 4.3.1) | |
| A reaction: But why are the contrasts Eve, or throwing it, or a pear? It occurs to me that this is wrong! The contrast is with anything else which could have gone in subject, verb or object position. It is a matter of categories, not of contrasts. |
| 17305 | I take what is fundamental to be the whole spatiotemporal manifold and its fields [Schaffer,J] |
| Full Idea: I myself would prefer to speak of what is fundamental in terms of the whole spatiotemporal manifold and the fields that permeate it, with parts counting as derivative of the whole. | |
| From: Jonathan Schaffer (Grounding, Transitivity and Contrastivity [2012], 4.1.1) | |
| A reaction: Not quite the Parmenidean One, since it has parts, but a nice try at updating the great man. Note the reference to 'fields', suggesting that this view is grounded in the physics rather than metaphysics. How many fields has it got? |
| 10359 | In causation there are three problems of relata, and three metaphysical problems [Schaffer,J] |
| Full Idea: The questions about causation concern their relata (in space-time, how fine-grained, how many?) and the metaphysics (distinguish causal sequences from others, the direction of causation, selecting causes among pre-conditions?). | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], Intro) | |
| A reaction: A very nice map (which has got me thinking about restructuring this database). I can't think of a better way to do philosophy than this (let's hear it for analysis - but the greatest role models for the approach are Aristotle and Aquinas). |
| 10372 | Causation may not be transitive; the last event may follow from the first, but not be caused by it [Schaffer,J] |
| Full Idea: It is not clear whether causation is transitive. For example, if a boulder roll's towards a hiker's head, causing the hiker to duck, which causes the hiker to survive, it does not seem that the rolling boulder causes the survival of the hiker. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 1.2) | |
| A reaction: Maybe survival is not an event or an effect. How many times have I survived in my life? We could, though, say that the hiker strained a muscle as he or she ducked. But then it is unclear whether the boulder caused the muscle-strain. |
| 10374 | There are at least ten theories about causal connections [Schaffer,J] |
| Full Idea: Theories of causal connection are: nomological subsumption, statistical correlation, counterfactual dependence, agential manipulability, contiguous change, energy flow, physical processes, property transference, primitivism and eliminativism. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 1.3.1) | |
| A reaction: Schaffer reduces these to probability and process. I prefer the latter. The first two are wrong, the third right but superficial, the fourth wrong, the fifth, sixth and seventh on the right lines, the eighth wrong, the ninth tempting, and the last wrong. |
| 17307 | Nowadays causation is usually understood in terms of equations and variable ranges [Schaffer,J] |
| Full Idea: The leading treatments of causation work within 'structural equation models', with events represented via variables each of which is allotted a range of permitted values, which constitute a 'contrast space'. | |
| From: Jonathan Schaffer (Grounding, Transitivity and Contrastivity [2012], 4.3.1) | |
| A reaction: Like Woodward's idea that causation is a graph, this seems to be a matter of plotting or formalising correlations between activities, which is a very Humean approach to causation. |
| 10366 | Causation transcends nature, because absences can cause things [Schaffer,J] |
| Full Idea: The main argument for causation being transcendent (rather than being immanent in nature) is that absences can be involved in causal relations. Thus a rock-climber is caused to survive by not falling. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 1.1) | |
| A reaction: I don't like that. The obvious strategy is to redescribe the events. Even being hit with a brick could be described as an 'absence of brick-prevention'. So not being hit by a brick can be described as 'presence of brick prevention'. |
| 10377 | Causation may not be a process, if a crucial part of the process is 'disconnected' [Schaffer,J] |
| Full Idea: One problem case for the process view of causation is 'disconnection'. If a brick breaks a window by being fired from a catapult, a latch is released which was preventing the catapult from firing, so the 'process' is just internal to the catapult. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 2.1.1) | |
| A reaction: Schaffer says the normal reply is to deny that the catch-releasing is genuinely causal. I would have thought we should go more fine-grained, and identify linked components of the causal process. |
| 10378 | A causal process needs to be connected to the effect in the right way [Schaffer,J] |
| Full Idea: A problem case for the process view of causation is 'misconnection'. A process may be connected to an effect, without being causal, as when someone watches an act of vandalism in dismay. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 2.1.1) | |
| A reaction: This is a better objection to the process view than Idea 10377. If I push a window with increasing force until it breaks, the process is continuous, but it suddenly becomes a cause. |
| 10382 | Causation can't be a process, because a process needs causation as a primitive [Schaffer,J] |
| Full Idea: It might be that if causation is said to be a process, then a process is nothing more than a causal sequence, so that causation is primitive. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 2.1.2) | |
| A reaction: This again is tempting (as well as the primitivist view of probabilistic causation). If one tries to define a process as mere chronology, then the causal and accidental are indistinguishable. I take the label 'primitive' to be just our failure. |
| 10375 | At least four rivals have challenged the view that causal direction is time direction [Schaffer,J] |
| Full Idea: The traditional view that the direction of causation is the direction of time has been challenged, by the direction of forking, by overdetermination, by independence, and by manipulation, which all seem to be one-directional features. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 1.3.1) | |
| A reaction: Personally I incline to the view that time is prior, and fixes the direction of causation. I'm not sure that 'backward causation' can be stated coherently, even if it is metaphysically or naturally possible. |
| 10389 | Causal order must be temporal, or else causes could be blocked, and time couldn't be explained [Schaffer,J] |
| Full Idea: Reasons for causal order being temporal order are that otherwise the effect might occur but the cause then get prevented, ..and that they must be the same, because the temporal order can only be analysed in terms of the causal order. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 2.2) | |
| A reaction: If one took both time and causation as primitive, then the second argument would be void. The first argument, though, sounds pretty overwhelming to me. |
| 10390 | Causal order is not temporal, because of time travel, and simultanous, joint or backward causes [Schaffer,J] |
| Full Idea: Reasons for denying that causal order is temporal order are that time travel seems possible, that cause and effect can be simultaneous, because joint effects have temporal order without causal connection, and because backward causation may exist. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 2.2) | |
| A reaction: The possibility of time travel and backward causation can clearly be doubted, and certainly can't be grounds for one's whole metaphysics. The other two need careful analysis, but I think they can be answered. Causation is temporal. |
| 10380 | Causation is primitive; it is too intractable and central to be reduced; all explanations require it [Schaffer,J] |
| Full Idea: Primitivism arises from our failure to reduce causation, but also from causation being too central to reduce. The probability and process accounts are said to be inevitably circular, as they cannot be understood without reference to causation. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 2.1.2) | |
| A reaction: This is very tempting. The primitive view, though, must deal with the direction problem, which may suggest that time is even more primitive. Can we have a hierarchy of primitiveness? To be alive is to be causal. |
| 10385 | If causation is just observables, or part of common sense, or vacuous, it can't be primitive [Schaffer,J] |
| Full Idea: The three main objections to causation being primitive are that causation can't be anything more than what we observe, or that such a primitive is too spooky to be acceptable, or that primitivism leads to elimination of causation. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 2.1.2) | |
| A reaction: [summarised] I don't like the first (Humean) view. I suspect that anything which we finally decide has to be primitive (time, for example) is going to be left looking 'spooky', and I suspect that eliminativism is just Humeanism in disguise. |
| 10387 | The notion of causation allows understanding of science, without appearing in equations [Schaffer,J] |
| Full Idea: The concepts of 'event', 'law', 'cause' and 'explanation' are nomic concepts which serve to allow a systematic understanding of science; they do not themselves appear in the equations. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 2.1.2) | |
| A reaction: This is a criticism of Russell's attempt to eliminate causation from science. It shows that there has to be something we can call 'metascience', which is the province of philosophers, since scientists don't have much interest in it. |
| 10388 | Causation is utterly essential for numerous philosophical explanations [Schaffer,J] |
| Full Idea: Causation can't be eliminated if it is needed to explain persistence, explanation, disposition, perception, warrant, action, responsibility, mental functional role, conceptual content, and reference. It's elimination would be catastrophic. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 2.1.2) | |
| A reaction: [compressed list] I think I am going to vote for the view that causation is one of the primitives in the metaphysics of nature, so I have to agree with this. Most of the listed items, though, are controversial, so eliminativists are not defeated. |
| 10384 | If two different causes are possible in one set of circumstances, causation is primitive [Schaffer,J] |
| Full Idea: Causation seems to be primitive if the same laws and patterns of events might embody three different possible causes, as when two magicians cast the same successful spell, each with a 50% chance of success, and who was successful is unclear. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 2.1.2) | |
| A reaction: I'm cautious when the examples involve magic. It implies that the process that leads to the result will be impossible to observe, but if magic never really happens, then the patterns of events will always be different. |
| 10386 | If causation is primitive, it can be experienced in ourselves, or inferred as best explanation [Schaffer,J] |
| Full Idea: The view that causation is primitive can be defended against Humean critics by saying that causation can be directly observed in the will or our bodies, or that it can be inferred as the best explanation. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 2.1.2) | |
| A reaction: I like both views, and have just converted myself to the primitivist view of causation! I can't know the essence of a tree, because I am not a tree, but I can know the essence of causation. The Greek fascination with explaining movement is linked. |
| 10361 | Events are fairly course-grained (just saying 'hello'), unlike facts (like saying 'hello' loudly) [Schaffer,J] |
| Full Idea: Events are relatively coarse-grained, unlike facts; so the event of John's saying 'hello' seems to be the same event as John's saying 'hello' loudly, while they seem to be different facts. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 1) | |
| A reaction: The example seems good support for facts, since saying 'hello' loudly could have quite different effects from just saying 'hello'. I also incline temperamentally towards a fine-grained account, because it is more reductivist. |
| 10360 | Causal relata are events - or facts, features, tropes, states, situations or aspects [Schaffer,J] |
| Full Idea: The standard view make causal relata events (Davidson, Kim, Lewis), but there is considerable support for facts (Bennett, Mellor), and occasional support for features (Dretske), tropes (Campbell), states of affairs (Armstrong), and situations and aspects. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 1) | |
| A reaction: An event is presumed to be concrete, while a fact is more abstract (a proposition, perhaps). I'm always drawn to 'processes' (because they are good for discussing the mind), so an event, as a sort of natural process, looks good. |
| 10362 | One may defend three or four causal relata, as in 'c causes e rather than e*' [Schaffer,J] |
| Full Idea: The view that there are two causal relata is widely assumed but seldom defended. But the account based on 'effectual difference' says the form is 'c causes e rather than e*'. One might defend four relata, in 'c rather than c* causes e rather than e*'. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 1) | |
| A reaction: [compressed] This doesn't sound very plausible to me. How do you decide which is e*? If I lob a brick into the crowd, it hits Jim rather than - who? |
| 10368 | If causal relata must be in nature and fine-grained, neither facts nor events will do [Schaffer,J] |
| Full Idea: Theorists who reject both events and facts as causal relata do so because the relata must be immanent in nature, and thus not facts, but also fine-grained and thus not events. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 1.2) | |
|
A reaction:
Kim, however, offers a fine-grained account of events (as |
| 10383 | The relata of causation (such as events) need properties as explanation, which need causation! [Schaffer,J] |
| Full Idea: The primitivist about causation might say that the notion of an event (or other relata) cannot be understood without reference to causation, because properties themselves are individuated by their causal role. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 2.1.2) | |
| A reaction: Having enthusiastically embraced the causal view of properties (see Shoemaker and Ellis), I suddenly realise that I seem required to embrace primitivism about causation, which I hadn't anticipated! I've no immediate problem with that. |
| 10393 | Our selection of 'the' cause is very predictable, so must have a basis [Schaffer,J] |
| Full Idea: The main argument against saying that there is no basis for selecting the one cause of an event is that our selections are too predictable to be without a basis. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 2.3) | |
| A reaction: The problem is that we CAN, if we wish, whimsically pick out any pre-condition of an event for discussion (e.g. the railways before WW1). I would say that sensitivity to nature leads us to a moderately correct selection of 'the' cause. |
| 10394 | Selecting 'the' cause must have a basis; there is no causation without such a selection [Schaffer,J] |
| Full Idea: Another argument against the view that there is no basis for selecting 'the' cause is that we have no concept of causation without such a selection. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 2.3) | |
| A reaction: Good. Otherwise we could only state the conditions preceding an event, and then every event that occurred at any given moment in a region would have the same cause. How can 'the' cause be necessary, and yet capricious? |
| 10376 | The actual cause may make an event less likely than a possible more effective cause [Schaffer,J] |
| Full Idea: If Pam threw the brick that broke the window, then Bob (who refrained) might be a more reliable vandal, so that Pam's throw might have made the shattering less likely, so probability-raising is not necessary for causation. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 2.1) | |
| A reaction: That objection looks pretty conclusive to me. I take the probabilistic view to be a non-starter. |
| 10381 | All four probability versions of causation may need causation to be primitive [Schaffer,J] |
| Full Idea: All four probability versions of causation may need causation to be primitive: nomological - to distinguish laws from generalizations; statistical - to decide background; counterfactual - decide background; agent intervention - to understand intervention. | |
| From: Jonathan Schaffer (The Metaphysics of Causation [2007], 2.1.2) | |
| A reaction: I don't need much convincing that the probabilistic view is wrong. To just accept causation as primitive seems an awful defeat for philosophy. We should be able to characterise it, even if we cannot know its essence. |