82 ideas
| 19023 | Slippery slope arguments are challenges to show where a non-arbitrary boundary lies [Vetter] |
| Full Idea: Slippery slope arguments are not intended as demonstrative arguments, but rather as a challenge to show where a boundary is, and to show that the boundary is not arbitrary. | |
| From: Barbara Vetter (Potentiality [2015], 5.3.3) | |
| A reaction: [extracted from details of its context] You could respond by saying that a slippery slope levels off, rather than hitting a wall or plunging to perdition. |
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| Full Idea: Until the 1960s standard truth-table semantics were the only ones that there were. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.10.1) | |
| A reaction: The 1960s presumably marked the advent of possible worlds. |
| 19033 | Deontic modalities are 'ought-to-be', for sentences, and 'ought-to-do' for predicates [Vetter] |
| Full Idea: Deontic modality can be divided into sentence-modifying 'ought-to-be' modals, and predicate-modifying 'ought-to-do' modals. | |
| From: Barbara Vetter (Potentiality [2015], 6.9.2) | |
| A reaction: [She cites Brennan 1993] These two seem to correspond to what is 'good' (ought to be), and what is 'right' (ought to do). Since I like that distinction, I also like this one. |
| 19032 | S5 is undesirable, as it prevents necessities from having contingent grounds [Vetter] |
| Full Idea: Wedgwood (2007:220) argues that S5 is undesirable because it excludes that necessary truths may have contingent grounds. | |
| From: Barbara Vetter (Potentiality [2015], 6.4 n5) | |
| A reaction: Cameron defends the possibility of necessity grounded in contingency, against Blackburn's denial of it. It's interesting that we choose the logic on the basis of the metaphysics. Shouldn't there be internal reasons for a logic's correctness? |
| 19036 | The Barcan formula endorses either merely possible things, or makes the unactualised impossible [Vetter] |
| Full Idea: Subscribers to the Barcan formula must either be committed to the existence of mere possibilia (such as possible unicorns), or deny many unactualised possibilities of existence. | |
| From: Barbara Vetter (Potentiality [2015], 7.5) | |
| A reaction: It increasingly strikes me that the implications of the Barcan formula are ridiculous. Williamson is its champion, but I'm blowed if I can see why. What could a possible unicorn be like? Without them, must we say unicorns are impossible? |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
| Full Idea: 'dom R' indicates the 'domain' of a relation, that is, the set of all objects that are members of ordered pairs and that have that relation. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
| Full Idea: 'fld R' indicates the 'field' of a relation, that is, the set of all objects that are members of ordered pairs on either side of the relation. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
| Full Idea: 'ran R' indicates the 'range' of a relation, that is, the set of all objects that are members of ordered pairs and that are related to by the first objects. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
| Full Idea: We write F : A → B to indicate that A maps into B, that is, the domain of relating things is set A, and the things related to are all in B. If we add that F = B, then A maps 'onto' B. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
|
Full Idea:
F(x) is a 'function', which indicates the unique value which y takes in |
|
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| Full Idea: To know if A ∈ B, we look at the set A as a single object, and check if it is among B's members. But if we want to know whether A ⊆ B then we must open up set A and check whether its various members are among the members of B. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:04) | |
| A reaction: This idea is one of the key ideas to grasp if you are going to get the hang of set theory. John ∈ USA ∈ UN, but John is not a member of the UN, because he isn't a country. See Idea 12337 for a special case. |
| 9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
| Full Idea: A relation is 'symmetric' on a set if every ordered pair in the set has the relation in both directions. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
| Full Idea: A relation is 'transitive' on a set if the relation can be carried over from two ordered pairs to a third. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| Full Idea: The 'ordered pair' <x,y> is defined to be {{x}, {x,y}}; hence it can be proved that <u,v> = <x,y> iff u = x and v = y (given by Kuratowski in 1921). ...The definition is somewhat arbitrary, and others could be used. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:36) | |
| A reaction: This looks to me like one of those regular cases where the formal definitions capture all the logical behaviour of the concept that are required for inference, while failing to fully capture the concept for ordinary conversation. |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| Full Idea: A 'linear ordering' (or 'total ordering') on A is a binary relation R meeting two conditions: R is transitive (of xRy and yRz, the xRz), and R satisfies trichotomy (either xRy or x=y or yRx). | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:62) |
| 9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
| Full Idea: The 'powerset' of a set is all the subsets of a given set. Thus: PA = {x : x ⊆ A}. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
| Full Idea: Two sets are 'disjoint' iff their intersection is empty (i.e. they have no members in common). | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
| Full Idea: The 'domain' of a relation is the set of all objects that are members of ordered pairs that are members of the relation. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| Full Idea: A 'relation' is a set of ordered pairs. The ordering relation on the numbers 0-3 is captured by - in fact it is - the set of ordered pairs {<0,1>,<0,2>,<0,3>,<1,2>,<1,3>,<2,3>}. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) | |
| A reaction: This can't quite be a definition of order among numbers, since it relies on the notion of a 'ordered' pair. |
| 9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
| Full Idea: A 'function' is a relation which is single-valued. That is, for each object, there is only one object in the function set to which that object is related. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
| Full Idea: A function 'maps A into B' if the domain of relating things is set A, and the things related to are all in B. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
| Full Idea: A function 'maps A onto B' if the domain of relating things is set A, and the things related to are set B. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
| Full Idea: A relation is 'reflexive' on a set if every member of the set bears the relation to itself. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
| Full Idea: A relation satisfies 'trichotomy' on a set if every ordered pair is related (in either direction), or the objects are identical. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
| Full Idea: A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| Full Idea: Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ. A man with an empty container is better off than a man with nothing. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1.03) |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| Full Idea: It might be thought at first that the empty set would be a rather useless or even frivolous set to mention, but from the empty set by various set-theoretic operations a surprising array of sets will be constructed. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:02) | |
| A reaction: This nicely sums up the ontological commitments of mathematics - that we will accept absolutely anything, as long as we can have some fun with it. Sets are an abstraction from reality, and the empty set is the very idea of that abstraction. |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| Full Idea: Given any x we have the singleton {x}, which is defined by the pairing axiom to be {x,x}. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 2:19) | |
| A reaction: An interesting contrivance which is obviously aimed at keeping the axioms to a minimum. If you can do it intuitively with a new axiom, or unintuitively with an existing axiom - prefer the latter! |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| Full Idea: An 'equivalence relation' is a binary relation which is reflexive, and symmetric, and transitive. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| Full Idea: Equivalence classes will 'partition' a set. That is, it will divide it into distinct subsets, according to each relation on the set. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| Full Idea: It was observed by several people that for a satisfactory theory of ordinal numbers, Zermelo's axioms required strengthening. The Axiom of Replacement was proposed by Fraenkel and others, giving rise to the Zermelo-Fraenkel (ZF) axioms. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:15) |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| Full Idea: For functions, we know that for any y there exists an appropriate x, but we can't yet form a function H, as we have no way of defining one particular choice of x. Hence we need the axiom of choice. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:48) |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| Full Idea: The process is dubbed 'conversational implicature' when the inference is not from the content of what has been said, but from the fact that it has been said. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.7.3) |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| Full Idea: The point of logic is to give an account of the notion of validity,..in two standard ways: the semantic way says that a valid inference preserves truth (symbol |=), and the proof-theoretic way is defined in terms of purely formal procedures (symbol |-). | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.3..) | |
| A reaction: This division can be mirrored in mathematics, where it is either to do with counting or theorising about things in the physical world, or following sets of rules from axioms. Language can discuss reality, or play word-games. |
| 9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
| Full Idea: A is a logical truth (tautology) (|= A) iff it is a semantic consequence of the empty set of premises (φ |= A), that is, every interpretation makes A true. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.3.4) | |
| A reaction: So the final column of every line of the truth table will be T. |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| Full Idea: A truth assignment 'satisfies' a formula, or set of formulae, if it evaluates as True when all of its components have been assigned truth values. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.2) | |
| A reaction: [very roughly what Enderton says!] The concept becomes most significant when a large set of wff's is pronounced 'satisfied' after a truth assignment leads to them all being true. |
| 9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
| Full Idea: If every proof-theoretically valid inference is semantically valid (so that |- entails |=), the proof theory is said to be 'sound'. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.7) |
| 9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
| Full Idea: If every semantically valid inference is proof-theoretically valid (so that |= entails |-), the proof-theory is said to be 'complete'. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.7) |
| 9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
| Full Idea: If a wff is tautologically implied by a set of wff's, it is implied by a finite subset of them; and if every finite subset is satisfiable, then so is the whole set of wff's. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 2.5) | |
| A reaction: [Enderton's account is more symbolic] He adds that this also applies to models. It is a 'theorem' because it can be proved. It is a major theorem in logic, because it brings the infinite under control, and who doesn't want that? |
| 9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
| Full Idea: A set of expressions is 'decidable' iff there exists an effective procedure (qv) that, given some expression, will decide whether or not the expression is included in the set (i.e. doesn't contradict it). | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.7) | |
| A reaction: This is obviously a highly desirable feature for a really reliable system of expressions to possess. All finite sets are decidable, but some infinite sets are not. |
| 9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
| Full Idea: The Enumerability Theorem says that for a reasonable language, the set of valid wff's can be effectively enumerated. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 2.5) | |
| A reaction: There are criteria for what makes a 'reasonable' language (probably specified to ensure enumerability!). Predicates and functions must be decidable, and the language must be finite. |
| 19034 | The world is either a whole made of its parts, or a container which contains its parts [Vetter] |
| Full Idea: We can think of the world as a 'whole' that has everything as its parts, like raisins in a cake, or we can think of the world as a 'container', which is disjoint from everything there is, like a bottle containing water. | |
| From: Barbara Vetter (Potentiality [2015], 7.3) | |
| A reaction: [compressed] Space and time seem to have a special role here, and it is hard to think of any other candidates for being the 'container'. I think I will apply my 'what's it made of' test to ontology, and opt for the world as a 'whole'. |
| 19015 | Grounding can be between objects ('relational'), or between sentences ('operational') [Vetter] |
| Full Idea: 'Relational' grounding is between entities, best expressed by the two-place predicate 'x grounds y'. 'Operational' grounding is between sentences, best expressed by the two-place sentence operator read as 'because of' or 'in virtue of'. | |
| From: Barbara Vetter (Potentiality [2015], 1.6) |
| 19012 | The Humean supervenience base entirely excludes modality [Vetter] |
| Full Idea: Humean supervenience excludes modality - the whole modal package - from the supervenience base. The Humean world is, at root, thoroughly non-modal. | |
| From: Barbara Vetter (Potentiality [2015], 1.2) | |
| A reaction: This sums up my problem with David Lewis with perfect clarity. He is just excessively empirical. Hume himself also excluded modality from the basic impressions. Locke allows powerful essences (even if they are well hidden). |
| 19024 | A determinate property must be a unique instance of the determinable class [Vetter] |
| Full Idea: The crucial feature of the determinates / determinables relation is that to possess the determinable property, an object must possess exactly one of the determinate properties. | |
| From: Barbara Vetter (Potentiality [2015], 5.7.2) | |
| A reaction: This sounds like a determinable being a function, and the determinate being its output. If 'scarlet' is a determinate of the determinables 'red' or 'coloured', it is not obvious that there is only one possible shade of scarlet. This schema oversimplifies. |
| 17954 | Essence is a thing's necessities, but what about its possibilities (which may not be realised)? [Vetter] |
| Full Idea: Essence is, as it were, necessity rooted in things, ...but how about possibility rooted in things? ...Having the potential to Φ, unlike being essentially Φ, does not entail being actually Φ. | |
| From: Barbara Vetter (Essence and Potentiality [2010], §2) | |
| A reaction: To me this invites the question 'what is it about the entity which endows it with its rooted possibilities?' A thing has possibilities because it has a certain nature (at a given time). |
| 19021 | I have an 'iterated ability' to learn the violin - that is, the ability to acquire that ability [Vetter] |
| Full Idea: I do not have the ability to play the violin. Nor does my desk. Unlike my desk, however, I possess the ability to learn to play the violin - the ability, that is, to acquire the ability to play the violin. I have an 'iterated ability' to play the violin. | |
| From: Barbara Vetter (Potentiality [2015], 4.6) | |
| A reaction: An important idea, though the examples are more likely to come from human behaviour than from the non-human physical world. |
| 19016 | We should think of dispositions as 'to do' something, not as 'to do something, if ....' [Vetter] |
| Full Idea: We should think in terms of dispositions in terms of the manifestation alone - not as a disposition to ...if..., but as a disposition to ..., full stop. | |
| From: Barbara Vetter (Potentiality [2015], 1.7) | |
| A reaction: This way of individuating dispositions seems plausible. Some dispositions only have one trigger, but others have many. All sorts of things are inclined to trigger a human smile, but we are just disposed to smile. Some people smile at disasters. |
| 19017 | Nomological dispositions (unlike ordinary ones) have to be continually realised [Vetter] |
| Full Idea: Nomological dispositions such as electric charge seem different from ordinary dispositions. A particle's being electrically charged is not just a possibility of exerting a certain force. Rather, the particle has to exert a force in certain circumstances. | |
| From: Barbara Vetter (Potentiality [2015], 2.7) | |
| A reaction: I can only pull when there is something to pull, but a magnet seems to have a 'field' of attraction which is pullish in character. Does it detect something to pull (like a monad)? Can there be a force which has no object? |
| 19014 | How can spatiotemporal relations be understood in dispositional terms? [Vetter] |
| Full Idea: Spatiotemporal relations are a prime example of properties that are difficult to understand in dispositional terms. | |
| From: Barbara Vetter (Potentiality [2015], 1.6) | |
| A reaction: [Vetter refers to A.Bird 2007 Ch.8 for an attempt] One approach would be to question whether they are 'properties'. I don't think of relations as properties, even if they are predicates. Is space a property of something? |
| 17953 | Real definition fits abstracta, but not individual concrete objects like Socrates [Vetter] |
| Full Idea: I can understand the notion of real definition as applying to (some) abstact entities, but I have no idea how to apply it to a concrete object such as Socrates or myself. | |
| From: Barbara Vetter (Essence and Potentiality [2010], §1) | |
| A reaction: She is objecting to Kit Fine's account of essence, which is meant to be clearer than the normal account of essences based on necessities. Aristotle implies that definitions get fuzzy when you reach the level of the individual. |
| 17952 | Modal accounts make essence less mysterious, by basing them on the clearer necessity [Vetter] |
| Full Idea: The modal account was meant, I take it, to make the notion of essence less mysterious by basing it on the supposedly better understood notion of necessity. | |
| From: Barbara Vetter (Essence and Potentiality [2010], §1) |
| 19030 | Why does origin matter more than development; why are some features of origin more important? [Vetter] |
| Full Idea: Not every feature of an individual's origin is plausibly considered necessary, so we can distinguish two questions: 'why origin, rather than development?', and 'why these particular features of origin?'. | |
| From: Barbara Vetter (Potentiality [2015], 6.2) | |
| A reaction: [she cites P. Mackie 1998] The point is that exactly where someone was born doesn't seem vital. If it is nothing more than that every contingent object must have an origin, that is not very exciting. |
| 19040 | We take origin to be necessary because we see possibilities as branches from actuality [Vetter] |
| Full Idea: The plausibility of the necessity of origin is a symptom of our general tendency to think of possibility in terms of the 'branching model' - that unactualised possibilities must branch off from actuality, at some point. | |
| From: Barbara Vetter (Potentiality [2015], 7.9) | |
| A reaction: [she cites P. Mackie 1998] It is hard to see how we could flatly deny some possibilities which had absolutely no connection with actuality, and were probably quite unimaginable for us. |
| 19008 | The modern revival of necessity and possibility treated them as special cases of quantification [Vetter] |
| Full Idea: Necessity and possibility had a revival with the development of modal logic, treating them as special cases of the existential and universal quantifiers, ranging over an infinity of possible worlds. | |
| From: Barbara Vetter (Potentiality [2015], 1.1) | |
| A reaction: The problem seems to be that possible worlds offer a very useful and interesting 'model' of modality, but say nothing at all about its nature. Any more than a weather map will show you what weather is. |
| 19029 | It is necessary that p means that nothing has the potentiality for not-p [Vetter] |
| Full Idea: Necessities mark the limits of the potentialities that objects have. More precisely, it is necessary that p just in case nothing has, or had, or will have a potentiality to be such that not-p. | |
| From: Barbara Vetter (Potentiality [2015], 6.2) | |
| A reaction: [See Vetter's other ideas for her potentiality account of modality] If we wish to build a naturalistic account of modality (and if you don't want that then your untethered metaphysics will drift away in logical space) then this is the way to go. |
| 17959 | Metaphysical necessity is even more deeply empirical than Kripke has argued [Vetter] |
| Full Idea: We support the views of metaphysical modality on which metaphysical necessity is an even more deeply empirical matter than Kripke has argued. | |
| From: Barbara Vetter (Essence and Potentiality [2010], p.2) | |
| A reaction: [co-author E. Viebahn] This seems to pinpoint the spirit of scientific essentialism. She cites Bird and Shoemaker. If it is empirical, doesn't that make it a matter of epistemology, and hence further from absolute necessity? |
| 17955 | Possible worlds allow us to talk about degrees of possibility [Vetter] |
| Full Idea: The apparatus of possible worlds affords greater expressive power than mere talk of possibility and necessity. In particular, possible worlds talk allows us to introduce degrees of possibility. | |
| From: Barbara Vetter (Essence and Potentiality [2010], §3) | |
| A reaction: A nice feature, but I'm not sure that either the proportion of possible worlds or the closeness of possible worlds captures what we actually mean by a certain degree of possibility. There is 'accidental closeness', or absence of contingency. See Vetter. |
| 19028 | Possibilities are potentialities of actual things, but abstracted from their location [Vetter] |
| Full Idea: When we speak of possibility, we speak of potentiality in abstraction from its possessor; a possibility is a potentiality somewhere or other in the world, no matter where. | |
| From: Barbara Vetter (Potentiality [2015], 6.1) | |
| A reaction: I note that, as so often, this is psychological abstraction, which is usually sneered at by modern philosophers (e.g. Geach), and yet is employed all the time. This is Vetter's key thesis, which I like. |
| 19010 | All possibility is anchored in the potentiality of individual objects [Vetter] |
| Full Idea: Potentiality is, metaphorically speaking, possibility anchored in individual objects; I claim that all possibility is thus anchored in some individual object(s) or other. | |
| From: Barbara Vetter (Potentiality [2015], 1.1) | |
| A reaction: This will be fine for specific physical possibilities, but may become tricky for possibilities that are increasingly abstract, or universal, or idealised. I agree with the general approach. Anchor modality in reality (which is physical!). |
| 19013 | Possibility is a generalised abstraction from the potentiality of its bearer [Vetter] |
| Full Idea: We should think of possibility as potentiality in abstraction from its bearer. So 'it is possible that p' is defined as 'something has an iterated potentiality for it to be the case that p'. | |
| From: Barbara Vetter (Potentiality [2015], 1.4) | |
| A reaction: If possibilities are abstractions from potentialities, I am inclined the treat potentialities as abstractions from dispositions, and dispositions (and properties) as abstractions from powers. Powers are not abstractions - they are the reality. |
| 17957 | Maybe possibility is constituted by potentiality [Vetter] |
| Full Idea: We should look at the claim that possibility is constituted by potentiality. | |
| From: Barbara Vetter (Essence and Potentiality [2010], §4) | |
| A reaction: A problem that comes to mind is possibilities arising from coincidence. The whole of reality must be described, to capture all the possibilities for a particular thing. So potentialities of what? Nice thought, though. |
| 19025 | Potentialities may be too weak to count as 'dispositions' [Vetter] |
| Full Idea: Potentialities may get exercised despite having a degree that is too low for them to qualify as dispositions. | |
| From: Barbara Vetter (Potentiality [2015], 5.7.4) | |
| A reaction: The key reason why her book is called 'Potentialities', rather than 'Dispositions'. She still wants to offer a naturalistic picture which ties potentialities to individual objects, but I am wondering whether potentialities are too abstract for the job. |
| 19019 | Potentiality is the common genus of dispositions, abilities, and similar properties [Vetter] |
| Full Idea: Potentiality can now be recognised as the common genus of dispositions and such related properties as abilities. | |
| From: Barbara Vetter (Potentiality [2015], 4.1) | |
| A reaction: This is the reason why Vetter defends a metaphysics of modality based on potentialities, rather than on narrower concepts such as dispositions, powers or essences. She can evade the problems which those narrower concepts raise. |
| 19022 | Water has a potentiality to acquire a potentiality to break (by freezing) [Vetter] |
| Full Idea: Water has no potentiality to break. But water has a potentiality to be frozen and turn into ice, which does have a potentiality to break. So water has a potentiality to acquire a potentiality to break. | |
| From: Barbara Vetter (Potentiality [2015], 4.6) | |
| A reaction: Thus potentially has an 'iterated' character to it, and an appropriate modal logic for it will have to allow for those iterations. She suggests a version of System T modal logic. |
| 23705 | A potentiality may not be a disposition, but dispositions are strong potentialities [Vetter, by Friend/Kimpton-Nye] |
| Full Idea: Although not all potentialities are dispositions, Vetter claims that all dispositions are potentialities which are had to a sufficiently high degree. | |
| From: report of Barbara Vetter (Potentiality [2015]) by Friend/Kimpton-Nye - Dispositions and Powers 2.4.2 | |
| A reaction: This sounds plausible. A potentiality could be faint or negligible, but once it is a serious possibility it becomes a 'disposition'. ...I suppose. But if the meteor is probably going to hit my house, it doesn't mean it has a disposition to do so. |
| 19009 | Potentiality does the explaining in metaphysics; we don't explain it away or reduce it [Vetter] |
| Full Idea: This book is a plea for recognising potentiality as an explanans in the metaphysics of modality, rather than as something in need of explanation or reduction. | |
| From: Barbara Vetter (Potentiality [2015], 1.1) | |
| A reaction: Something has to do the explaining, and it is obviously much better to have some aspect of the real world do the job, rather than remote abstractions such as laws, possible worlds or Forms. Personally I like the potentiality of 'powers'. |
| 19027 | Potentiality logic is modal system T. Stronger systems collapse iterations, and necessitate potentials [Vetter] |
| Full Idea: The logic for potentiality corresponds to modal system T, the minimum for metaphysics. The S4 axiom ◊◊φ → ◊φ says iterated potentialities collapse, and the S5 ◊φ → □◊φ says potentialities can't be lost. | |
| From: Barbara Vetter (Potentiality [2015], 5.9) | |
| A reaction: [compressed] This seems persuasive. I nice example of modern analytic metaphysics, that you have to find a logic that suits your theory. N.Salmon defends system T for all of metaphysics, though most people favour S5. |
| 19031 | There are potentialities 'to ...', but possibilities are 'that ....'. [Vetter] |
| Full Idea: Potentialities are 'potentialities to ....', while possibilities are 'possibilities that ....'. | |
| From: Barbara Vetter (Potentiality [2015], 6.4) | |
| A reaction: This feels a bit like a stipulation, rather than a precise description of normal usage. That said, it is quite a nice distinction. It sounds as if an event follows a potentiality, and a state of affairs follows a possibility. Active and passive? |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| Full Idea: Not all sentences using 'if' are conditionals. Consider 'if you want a banana, there is one in the kitchen'. The rough test is that a conditional can be rewritten as 'that A implies that B'. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.6.4) |
| 17958 | The apparently metaphysically possible may only be epistemically possible [Vetter] |
| Full Idea: Some of what metaphysicians take to be metaphysically possible turns out to be only epistemically possible. | |
| From: Barbara Vetter (Essence and Potentiality [2010], §4) | |
| A reaction: A nice clear expression of the increasingly common view that conceivability may be a limited way to grasp possibility. |
| 17956 | Closeness of worlds should be determined by the intrinsic nature of relevant objects [Vetter] |
| Full Idea: The closeness of possible worlds should be determined by similarity in the intrinsic constitution of whatever object it is whose potentialities are at issue. | |
| From: Barbara Vetter (Essence and Potentiality [2010], §3) | |
| A reaction: Nice thought. This seems to be the essentialist approach to possible worlds, but it makes the natures of the objects more fundamental than the framework of the worlds. She demurs because there are also extrinsic potentialities. |
| 19011 | If worlds are sets of propositions, how do we know which propositions are genuinely possible? [Vetter] |
| Full Idea: If possible worlds are sets of propositions, we need some way to distinguish those sets of propositions that do from those that do not correspond to genuine possibilities. | |
| From: Barbara Vetter (Potentiality [2015], 1.2) | |
| A reaction: The idea of a 'genuine' possibility does not seem to play a role in the conceptual scheme of those who treat possibility entirely in terms of possible worlds. If possibility is primitive, or is a set of worlds, there can be no criterion for 'genuine'. |
| 19037 | Are there possible objects which nothing has ever had the potentiality to produce? [Vetter] |
| Full Idea: Is it not possible that there be objects with (natural) properties that no actual thing ever had the potentiality to have, to produce, or constitute? (Call such properties 'super-alien properties'). | |
| From: Barbara Vetter (Potentiality [2015], 7.5) | |
| A reaction: This is a problem for her potentiality account of possibility. Her solution is (roughly) to either deny the super-aliens, or have chains of iterated possibility which take this case back to actuality. That sounds OK to me. |
| 19018 | Explanations by disposition are more stable and reliable than those be external circumstances [Vetter] |
| Full Idea: Patterns of behaviour may be explained by circumstances external to the individual, but dispositional explanations, based on the instrinsic make-up of individuals are typically more reliable and stable. | |
| From: Barbara Vetter (Potentiality [2015], 3.5) | |
| A reaction: [compressed] This is very nice support for the view I have been defending. She doesn't deal in essences, and prefers 'potentialities' (as broader) to 'dispositions'. The point is to explain events by the natures of the ingredients. |
| 19020 | Grounding is a kind of explanation, suited to metaphysics [Vetter] |
| Full Idea: Grounding is a kind of explanation - and specifically, the kind of metaphysical explanation that metaphysicians are after. | |
| From: Barbara Vetter (Potentiality [2015], 4.5) | |
| A reaction: Depending on how you interpret 'grounding', it is plausible that it is the sort of explanation that physicists and economists are after as well. If the aim is to understand the structure of everything, the target is to know what grounds what. |
| 19039 | The view that laws are grounded in substance plus external necessity doesn't suit dispositionalism [Vetter] |
| Full Idea: The Armstrong/Tooley/Dretske view, which takes laws to be substantial but grounded in a relation of nomic necessitation external to the properties themselves, is not an attractive option for the dispositionalist. | |
| From: Barbara Vetter (Potentiality [2015], 7.8) | |
| A reaction: The point is that the dispositionalist sees laws as grounded in the properties. I prefer her other option, of dispositionalism plus a 'shallow' view of laws (which she attributes to Mumford). The laws are as Lewis says, but powers explain them. |
| 19038 | Dispositional essentialism allows laws to be different, but only if the supporting properties differ [Vetter] |
| Full Idea: Even on the dispositional essentialist view the world might have been governed by different laws, if those laws involved different properties. What is excluded is the possibility of different laws involving the same properties as our actual laws. | |
| From: Barbara Vetter (Potentiality [2015], 7.8) | |
| A reaction: Important. Critics of dispositional essentialism accuse it of promoting the idea that the laws of nature are necessary, a claim for which we obviously have no evidence. I prefer to say they are necessary given that 'stuff', rather than those properties. |
| 17993 | Laws are relations of kinds, quantities and qualities, supervening on the essences of a domain [Vetter] |
| 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: Barbara Vetter (Dispositional Essentialism and the Laws of Nature [2012], 9.3) | |
| A reaction: Hm. How small can the domain be? Can it embrace the multiverse? Supervenience is a rather weak relationship. How about 'are necessitated/entailed by'? Are the relationships supposed to do the explaining? I would have thought the natures did that. |
| 19026 | If time is symmetrical between past and future, why do they look so different? [Vetter] |
| Full Idea: Any defender of the symmetry of time will have to provide some explanation of the obstinate appearance that the future is very different from the past. | |
| From: Barbara Vetter (Potentiality [2015], 5.8) | |
| A reaction: Presumably you have to say that it is all there, but only one end of the time spectrum is revealed to us, namely the past. But how do we get this uniquely lopsided view? Being an ominiscient god is more obvious than being a lopsided human. |
| 19041 | Presentists explain cross-temporal relations using surrogate descriptions [Vetter] |
| Full Idea: Presentists usually deal with the lack of cross-temporal relations by the construction of a surrogate, by way of paraphrasing the objectionable relation ascriptions. 'I admire Socrates' becomes 'I admire the Socrates properties'. | |
| From: Barbara Vetter (Potentiality [2015], 7.9) | |
| A reaction: [compressed. The cites Markosian 2004:63] Why can't I just say 'I admire Socrates, who no longer exists'? The present includes tensed facts, and memories and evidence-based theories. Admiring is not a direct relation between objects. |
| 3029 | Stilpo said if Athena is a daughter of Zeus, then a statue is only the child of a sculptor, and so is not a god [Stilpo, by Diog. Laertius] |
| Full Idea: Stilpo asked a man whether Athena is the daughter of Zeus, and when he said yes, said,"But this statue of Athena by Phidias is the child of Phidias, so it is not a god." | |
| From: report of Stilpo (fragments/reports [c.330 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.10.5 |