77 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. |
| 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? |
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| Full Idea: Second-order set theory is just like first-order set-theory, except that we use the version of Replacement with a universal second-order quantifier over functions from set to sets. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VII.4) |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| Full Idea: A member m of M is an 'upper bound' of a subset N of M if m is not less than any member of N. A member m of M is a 'least upper bound' of N if m is an upper bound of N such that if l is any other upper bound of N, then m is less than l. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) | |
| A reaction: [if you don't follow that, you'll have to keep rereading it till you do] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| Full Idea: Since combinatorial collections are enumerated, some multiplicities may be too large to be gathered into combinatorial collections. But the size of a multiplicity seems quite irrelevant to whether it forms a logical connection. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.2) |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| Full Idea: Many of those who are skeptical about the existence of infinite combinatorial collections would want to doubt or deny the Axiom of Choice. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.2) |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| Full Idea: The Power Set is just he codification of the fact that the collection of functions from a mathematical collection to a mathematical collection is itself a mathematical collection that can serve as a domain of mathematical study. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.1) |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| Full Idea: The Axiom of Replacement (of Skolem and Fraenkel) was remarkable for its universal acceptance, though it seemed to have no consequences except for the properties of the higher reaches of the Cantorian infinite. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], I) |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| Full Idea: The Axiom of Foundation (Zermelo 1930) says 'Every (descending) chain in which each element is a member of the previous one is of finite length'. ..This forbids circles of membership, or ungrounded sets. ..The iterative conception gives this centre stage. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.4) |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| Full Idea: Combinatorial collections (defined just by the members) obviously obey the Axiom of Choice, while it is at best dubious whether logical connections (defined by a rule) do. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.2) |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| Full Idea: The controversy was not about Choice per se, but about the correct notion of function - between advocates of taking mathematics to be about arbitrary functions and advocates of taking it to be about functions given by rules. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], I) |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| Full Idea: The Peano-Russell notion of class is the 'logical' notion, where each collection is associated with some kind of definition or rule that characterises the members of the collection. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.1) |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| Full Idea: The iterative conception of set was not so much as suggested, let alone advocated by anyone, until 1947. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], I) |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| Full Idea: The iterative conception of sets does not tell us how far to iterate, and so we must start with an Axiom of Infinity. It also presupposes the notion of 'transfinite iteration'. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.5) |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| Full Idea: The iterative conception does not provide a conception that unifies the axioms of set theory, ...and it has had very little impact on what theorems can be proved. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.5) | |
| A reaction: He says he would like to reject the iterative conception, but it may turn out that Foundation enables new proofs in mathematics (though it hasn't so far). |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| Full Idea: Limitation of Size has it that if a collection is the same size as a set, then it is a set. The Axiom of Replacement is characteristic of limitation of size. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.5) |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| Full Idea: A collection M is 'well-ordered' by a relation < if < linearly orders M with a least element, and every subset of M that has an upper bound not in it has an immediate successor. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| Full Idea: The distinctive feature of second-order logic is that it presupposes that, given a domain, there is a fact of the matter about what the relations on it are, so that the range of the second-order quantifiers is fixed as soon as the domain is fixed. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.3) | |
| A reaction: This sounds like a rather large assumption, which is open to challenge. I am not sure whether it was the basis of Quine's challenge to second-order logic. He seems to have disliked its vagueness, because it didn't stick with 'objects'. |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| Full Idea: The Law of Excluded Middle is (part of) the foundation of the mathematical practice of employing proofs by contradiction. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.1) | |
| A reaction: This applies in a lot of logic, as well as in mathematics. Come to think of it, it applies in Sudoku. |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| Full Idea: Mathematics is today thought of as the study of abstract structure, not the study of quantity. That point of view arose directly out of the development of the set-theoretic notion of abstract structure. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.2) | |
| A reaction: It sounds as if Structuralism, which is a controversial view in philosophy, is a fait accompli among mathematicians. |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| Full Idea: One reason to introduce the rational numbers is that it simplifes the theory of division, since every rational number is divisible by every nonzero rational number, while the analogous statement is false for the natural numbers. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.3) | |
| A reaction: That is, with rations every division operation has an answer. |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| Full Idea: The chief importance of the Continuum Hypothesis for Cantor (I believe) was that it would show that the real numbers form a set, and hence that they were encompassed by his theory. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.2) |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| Full Idea: The Cauchy convergence criterion for a sequence: the sequence S0,S1,... has a limit if |S(n+r) - S(n)| is less than any given quantity for every value of r and sufficiently large values of n. He proved this necessary, but not sufficient. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], 2.5) |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| Full Idea: Roughly speaking, the upper and lower parts of the Dedekind cut correspond to the commensurable ratios greater than and less than a given incommensurable ratio. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], II.6) | |
| A reaction: Thus there is the problem of whether the contents of the gap are one unique thing, or many. |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| Full Idea: Counting a set produces a well-ordering of it. Conversely, if one has a well-ordering of a set, one can count it by following the well-ordering. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) | |
| A reaction: Cantor didn't mean that you could literally count the set, only in principle. |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| Full Idea: The indiscernibility of indefinitely large sizes will be a critical part of the theory of indefinitely large sizes. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VIII.2) |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| Full Idea: My proposal is that the concept of the infinite began with an extrapolation from the experience of indefinitely large size. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VIII.2) | |
| A reaction: I think it might be better to talk of an 'abstraction' than an 'extrapolition', since the latter is just more of the same, which doesn't get you to concept. Lavine spends 100 pages working out his proposal. |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| Full Idea: The intuitionist endorse the actual finite, but only the potential infinite. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.2) |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| Full Idea: The symbol 'aleph-nought' denotes the cardinal number of the set of natural numbers. The symbol 'aleph-one' denotes the next larger cardinal number. 'Aleph-omega' denotes the omega-th cardinal number. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.3) |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| Full Idea: The ordinals are basic because the transfinite sets are those that can be counted, or (equivalently for Cantor), those that can be numbered by an ordinal or are well-ordered. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) | |
| A reaction: Lavine observes (p.55) that for Cantor 'countable' meant 'countable by God'! |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| Full Idea: The paradox of the largest ordinal (the 'Burali-Forti') is that the class of all ordinal numbers is apparently well-ordered, and so it has an ordinal number as order type, which must be the largest ordinal - but all ordinals can be increased by one. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.5) |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| Full Idea: The paradox of the largest cardinal ('Cantor's Paradox') says the diagonal argument shows there is no largest cardinal, but the class of all individuals (including the classes) must be the largest cardinal number. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.5) |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| Full Idea: Every theorem of mathematics has a counterpart with set theory - ...but that theory cannot serve as a basis for the notion of proof. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.3) |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| Full Idea: In modern mathematics virtually all work is only up to isomorphism and no one cares what the numbers or points and lines 'really are'. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.1) | |
| A reaction: At least that leaves the field open for philosophers, because we do care what things really are. So should everybody else, but there is no persuading some people. |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| Full Idea: Intuitionism in philosophy of mathematics rejects set-theoretic foundations. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.3 n33) |
| 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? |
| 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. |
| 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. |
| 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. |
| 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. |
| 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? |
| 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. |
| 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 |
| 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. |