78 ideas
| 18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
| Full Idea: There is surely no metaphysical basis for logic, but equally there is no logical basis for metaphysics, if that implies that we can settle the choice of logic in advance of settling any seriously contested metaphysical-cum-semantic issues. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7.5) | |
| A reaction: Is this aimed at Tim Williamson's book on treating modal logic as metaphysics? I agree with the general idea that logic won't deliver a metaphysics. I might want to defend a good metaphysics giving rise to a good logic. |
| 11832 | We learn a concept's relations by using it, without reducing it to anything [Wiggins] |
| Full Idea: We can achieve a lot by elucidations that put a concept to use without attempting to reduce it but, in using the concept, exhibit its connexions with other concepts that are established. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], Pr.3) | |
| A reaction: This seems to be the best line of defence for analytic philosophy, given the much-cited observation that no one has successful reduced any concept by pure analysis. |
| 18819 | The idea that there are unrecognised truths is basic to our concept of truth [Rumfitt] |
| Full Idea: The realist principle that a statement may be true even though no one is able to recognise its truth is so deeply embedded in our ordinary conception of truth that any account that flouts it is liable to engender confusion. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 5.1) |
| 18826 | 'True at a possibility' means necessarily true if what is said had obtained [Rumfitt] |
| Full Idea: A statement is 'true at a possibility' if, necessarily, things would have been as the statement (actually) says they are, had the possibility obtained. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 6.6) | |
| A reaction: This is deliberately vague about what a 'possibility' is, but it is intended to be more than a property instantiation, and less than a possible world. |
| 18803 | Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables [Rumfitt] |
| Full Idea: The classical semantics of natural language propositions says 1) valid arguments preserve truth, 2) no statement is both true and false, 3) each statement is either true or false, 4) the familiar truth tables. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1) |
| 18814 | 'Absolute necessity' would have to rest on S5 [Rumfitt] |
| Full Idea: If there is such a notion as 'absolute necessity', its logic is surely S5. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 3.3) | |
| A reaction: There are plenty of people (mainly in the strict empiricist tradition) who don't believe in 'absolute' necessity. |
| 18798 | It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt] |
| Full Idea: Although intuitionistic propositional and first-order logics are sub-systems of the corresponding classical systems, intuitionistic second-order logic affirms the negations of some classical theorems. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1) |
| 18799 | Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt] |
| Full Idea: Double Negation Elimination is a rule of inference which the classicist accepts without restriction, but which the intuitionist accepts only for decidable propositions. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1) | |
| A reaction: This cures me of my simplistic understanding that intuitionists just reject the rules about double negation. |
| 18830 | Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic [Rumfitt] |
| Full Idea: Many set theorists doubt if the Generalised Continuum Hypothesis must be either true or false; certainly, its bivalence is far from obvious. All the same, almost all set theorists use classical logic in their proofs. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7.2) | |
| A reaction: His point is that classical logic is usually taken to rest on bivalence. He offers the set theorists a helping hand, by defending classical logic without resorting to bivalence. |
| 18843 | The iterated conception of set requires continual increase in axiom strength [Rumfitt] |
| Full Idea: We are doomed to postulate an infinite sequence of successively stronger axiom systems as we try to spell out what is involved in iterating the power set operation 'as far as possible'. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 9.3) | |
| A reaction: [W.W. Tait is behind this idea] The problem with set theory, then, especially as a foundation of mathematics, is that it doesn't just expand, but has to keep reinventing itself. The 'large cardinal axioms' are what is referred to. |
| 18836 | A set may well not consist of its members; the empty set, for example, is a problem [Rumfitt] |
| Full Idea: There seem strong grounds for rejecting the thesis that a set consists of its members. For one thing, the empty set is a perpetual embarrassment for the thesis. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 8.4) | |
| A reaction: Rumfitt also says that if 'red' has an extension, then membership of that set must be vague. Extensional sets are precise because their objects are decided in advance, but intensional (or logical) sets, decided by a predicate, can be vague. |
| 18837 | A set can be determinate, because of its concept, and still have vague membership [Rumfitt] |
| Full Idea: Vagueness in respect of membership is consistent with determinacy of the set's identity, so long as a set's identity is taken to consist, not in its having such-and-such members, but in its being the extension of the concept A. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 8.4) | |
| A reaction: To be determinate, it must be presumed that there is some test which will decide what falls under the concept. The rule can say 'if it is vague, reject it' or 'if it is vague, accept it'. Without one of those, how could the set have a clear identity? |
| 18845 | If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt] |
| Full Idea: Someone who is sympathetic to the thesis that the totality of sets is not well-defined ought to concede that we have no reason to think that the Power Set Axiom is true. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 9.6) | |
| A reaction: The point is that it is only this Axiom which generates the vast and expanding totality. In principle it is hard, though, to see what is intrinsically wrong with the operation of taking the power set of a set. Hence 'limitation of size'? |
| 18815 | Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt] |
| Full Idea: On the conception of logic recommended here, logical laws are higher-order laws that can be applied to expand the range of any deductive principles. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 3.3) | |
| A reaction: You need the concept of a 'deductive principle' to get this going, but I take it that might be directly known, rather than derived from a law. |
| 18804 | The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt] |
| Full Idea: I think it is a strategic mistake to rest the case for classical logic on the Principle of Bivalence: the soundness of the classical logic rules is far more compelling than the truth of Bivalence. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1) | |
| A reaction: The 'rules' to which he is referring are those of 'natural deduction', which make very few assumptions, and are intended to be intuitively appealing. |
| 18805 | Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt] |
| Full Idea: There is not the slightest prospect of proving that the rules of classical logic are sound. ….All that the defender of classical logic can do is scrutinize particular attacks and try to repel them. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1) | |
| A reaction: This is the agenda for Rumfitt's book. |
| 18827 | If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt] |
| Full Idea: If we specify the senses of the connectives by way of the standard truth-tables, then we must justify classical logic only by appeal to the Principle of Bivalence. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7) | |
| A reaction: Rumfitt proposes to avoid the truth-tables, and hence not to rely on Bivalence for his support of classical logic. He accepts that Bivalence is doubtful, citing the undecidability of the Continuum Hypothesis as a problem instance. |
| 18813 | Logical consequence is a relation that can extended into further statements [Rumfitt] |
| Full Idea: Logical consequence, I argue, is distinguished from other implication relations by the fact that logical laws may be applied in extending any implication relation so that it applies among some complex statements involving logical connectives. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 3.3) | |
| A reaction: He offers implication in electronics as an example of a non-logical implication relation. This seems to indicate that logic must be monotonic, that consequence is transitive, and that the Cut Law always applies. |
| 18808 | Normal deduction presupposes the Cut Law [Rumfitt] |
| Full Idea: Our deductive practices seem to presuppose the Cut Law. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 2.3) | |
| A reaction: That is, if you don't believe that deductions can be transitive (and thus form a successful chain of implications), then you don't really believe in deduction. It remains a well known fact that you can live without the Cut Law. |
| 18840 | When faced with vague statements, Bivalence is not a compelling principle [Rumfitt] |
| Full Idea: I do not regard Bivalence, when applied to vague statements, as an intuitively compelling principle which we ought to try to preserve. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 8.7) | |
| A reaction: The point of Rumfitt's book is to defend classical logic despite failures of bivalence. He also cites undecidable concepts such as the Continuum Hypothesis. |
| 18802 | In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt] |
| Full Idea: There is no prospect whatever of giving the sense of a logical constant without using that very constant, and much else besides, in the metalinguistic principle that specifies that sense. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1) |
| 11863 | (λx)[Man x] means 'the property x has iff x is a man'. [Wiggins] |
| Full Idea: The Lambda Abstraction Operator: We can write (λx)[Man x], which may be read as 'the property that any x has just if x is a man'. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 4.2) | |
| A reaction: This technical device seems to be a commonplace in modern metaphysical discussions. I'm assuming it can be used to discuss properties without venturing into second-order logic. Presumably we could call the property here 'humanity'. |
| 18800 | Introduction rules give deduction conditions, and Elimination says what can be deduced [Rumfitt] |
| Full Idea: 'Introduction rules' state the conditions under which one may deduce a conclusion whose dominant logical operator is the connective. 'Elimination rules' state what may be deduced from some premises, where the major premise is dominated by the connective. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1) | |
| A reaction: So Introduction gives conditions for deduction, and Elimination says what can actually be deduced. If my magic wand can turn you into a frog (introduction), and so I turn you into a frog, how does that 'eliminate' the wand? |
| 18809 | Logical truths are just the assumption-free by-products of logical rules [Rumfitt] |
| Full Idea: Gentzen's way of formalising logic has accustomed people to the idea that logical truths are simply the by-products of logical rules, that arise when all the assumptions on which a conclusion rests have been discharged. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 2.5) | |
| A reaction: This is the key belief of those who favour the natural deduction account of logic. If you really believe in separate logic truths, then you can use them as axioms. |
| 18807 | Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt] |
| Full Idea: Monotonicity seems to mark the difference between cases in which a guarantee obtains and those where the premises merely provide inductive support for a conclusion. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 2.3) | |
| A reaction: Hence it is plausible to claim that 'non-monotonic logic' is a contradiction in terms. |
| 18842 | Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt] |
| Full Idea: Menzel proposes that an ordinal is something isomorphic well-ordered sets have in common, so while an ordinal can be represented as a set, it is not itself a set, but a 'property' of well-ordered sets. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 9.2) | |
| A reaction: [C.Menzel 1986] This is one of many manoeuvres available if you want to distance mathematics from set theory. |
| 18834 | Infinitesimals do not stand in a determinate order relation to zero [Rumfitt] |
| Full Idea: Infinitesimals do not stand in a determinate order relation to zero: we cannot say an infinitesimal is either less than zero, identical to zero, or greater than zero. ….Infinitesimals are so close to zero as to be theoretically indiscriminable from it. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7.4) |
| 18846 | Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt] |
| Full Idea: One of the motivations behind Cantor's and Dedekind's pioneering explorations in the field was the ambition to give real analysis a new foundation in set theory - and hence a foundation independent of geometry. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 9.6) | |
| A reaction: Rumfitt is inclined to think that the project has failed, although a weaker set theory than ZF might do the job (within limits). |
| 14746 | What exists can't depend on our conceptual scheme, and using all conceptual schemes is too liberal [Sider on Wiggins] |
| Full Idea: It would be incredible if what there is, rather than what we select for attention, depends on human activity and our conceptual scheme. One might expand to possible sortal concepts, rather than our language, but that amounts to four-dimensionalism. | |
| From: comment on David Wiggins (Sameness and Substance Renewed [2001]) by Theodore Sider - Four Dimensionalism 5.3 | |
| A reaction: [compression of a nice anti-Wiggins paragraph] He suggests that Wiggins is seeking an intermediate course (between narrow chauvinism about concepts, and excessive liberalism) in a discussion of natural kinds versus artifacts. |
| 11900 | We can accept criteria of distinctness and persistence, without making the counterfactual claims [Mackie,P on Wiggins] |
| Full Idea: We might agree with Wiggins's theory of individuation, but reject his thesis that a thing's principle of individuation (of distinctness and persistence) must be preserved in all counterfactual situations. | |
| From: comment on David Wiggins (Sameness and Substance Renewed [2001]) by Penelope Mackie - How Things Might Have Been 8.7 | |
| A reaction: I'm not even convinced that initial individuation consists of falling under a sortal, and I prefer to discuss the powers of the thing, rather than counterfactual facts about behaviour. |
| 11870 | Activity individuates natural things, functions do artefacts, and intentions do artworks [Wiggins] |
| Full Idea: What a principle of activity does completely for a natural thing, and the function does imperfectly for an ordinary artefact, the artist's conception of his own making of the work must do for the painting. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 4.12) | |
| A reaction: This nicely sums up Wiggins on individuation, and he seems to effectively elide individuation with essence. I certainly feel uneasy that a work of art needs a quite separate account from other artefacts. Surely it is just that we are fussier about them? |
| 11866 | The idea of 'thisness' is better expressed with designation/predication and particular/universal [Wiggins] |
| Full Idea: It is hard to think of anything true and significant that could not be said using the idea of thisness not better said while respectiving the distinctions designation/predication and particular/universal. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 4.7) | |
| A reaction: Politis calls 'thisness' the 'ultimate subject of predication', so it is covered in logic by the name for an object. But we need to understand objects, and not just refer to them, and I'm not sure that 'universals' advance our understanding. |
| 11896 | A sortal essence is a thing's principle of individuation [Wiggins, by Mackie,P] |
| Full Idea: Wiggins bases sortal essentialism on the notion that a thing's principle of individuation is essential to it. | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001]) by Penelope Mackie - How Things Might Have Been 7.1 | |
| A reaction: This idea has failed to make much impression on me. I seem to be the only person who doesn't understand the concept of 'individuation'. Please let me know exactly what it means. Type individuation is not individual individuation, I presume. |
| 15835 | Wiggins's sortal essentialism rests on a thing's principle of individuation [Wiggins, by Mackie,P] |
| Full Idea: Wiggins bases sortal essentialism on the notion that a thing's principle of individuation is essential to it. | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001]) by Penelope Mackie - How Things Might Have Been 7.1 | |
| A reaction: My problem with this is that individuation is a human activity, not an intrinsic feature of the entities in the external world. Entities presumably have a 'unity', but I'm not sure about a 'principle' that does that job, though Aristotle is sympathetic. |
| 11841 | The evening star is the same planet but not the same star as the morning star, since it is not a star [Wiggins] |
| Full Idea: The evening star is the same planet but not the same star as the morning star. For Venus is not a star. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.3) | |
| A reaction: This is a nice objection to the idea that identity is entirely a matter of falling under the same sortal category. |
| 10679 | 'Sortalism' says parts only compose a whole if it falls under a sort or kind [Wiggins, by Hossack] |
| Full Idea: 'Sortalism' endorses the view that some things have parts, but denies that every collection of things composes something. Whenever there is a particular, there must be a sort or kind to which it belongs. | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001]) by Keith Hossack - Plurals and Complexes 7 | |
| A reaction: What is the status of 'the first of its kind'? This seems to say that a token only has identity if it has type-identity. This sounds wildly wrong to me. I've made a 'thing' for you, but I haven't decided what it is yet. |
| 14363 | Identity a=b is only possible with some concept to give persistence and existence conditions [Wiggins, by Strawson,P] |
| Full Idea: Wiggins says an identity a=b stands no chance of being true unless there is some concept f under which a falls and under which b falls, which 'determines identity, persistence and existence conditions for members of its extension'. | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001]) by Peter F. Strawson - Review of 'Sameness and Substance' p.604 | |
| A reaction: This is the first clear statement I have met of Wiggins's central idea, upon which his sortal essentialism is built. Strawson's exposition adds that each thing necessarily falls under the 'highest' appropriate sortal ('dog', rather than 'terrier'). |
| 14364 | A thing is necessarily its highest sortal kind, which entails an essential constitution [Wiggins, by Strawson,P] |
| Full Idea: In Wiggins's theory, necessity carries over from the kind to constitution. If Toby is necessarily a dog and 'dog' is a natural kind term, then Toby necessarily has the constitution of a dog, the features of which make up the real essence of being a dog. | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001]) by Peter F. Strawson - Review of 'Sameness and Substance' p.605 | |
| A reaction: The essence will then presumably consist of all and only the characteristics which are shared by all dogs whatsoever. So how do you decide the borderline between wolf and dog? Why isn't a wolf a dog? |
| 11851 | Many predicates are purely generic, or pure determiners, rather than sortals [Wiggins] |
| Full Idea: There are countless predicates in English that have the appearance of sortal predicates but are purely generic (animal, machine, artefact), or are pure determinables for sortal determination (space-occupier, entity, substance). | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.6) | |
| A reaction: This is preparing the ground for a specification of a sortal which defines something essential as being the hallmark of identity. It is never quite clear to me whether Wiggins's case rests on a nominal or a real essence. |
| 11865 | The possibility of a property needs an essential sortal concept to conceive it [Wiggins] |
| Full Idea: A thing could have a property only if its having the property could be conceived, and that requires some sortal concept which adequately answers the Aristotelian question what the thing is. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 4.5) | |
| A reaction: [Algebra omitted!] The core idea of Wiggins's theory. It seems at first glance to be a revival of Aristotelian essentialism, but his view of that seems to merely involve falling into a category. He treats sortal concepts as Aristotle's 'primary being'. |
| 14744 | Objects can only coincide if they are of different kinds; trees can't coincide with other trees [Wiggins, by Sider] |
| Full Idea: Wiggins says that coincidence is possible only between objects of different kinds. Trees and cats coincide with aggregates of matter, but never trees with trees or cats with cats. | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001]) by Theodore Sider - Four Dimensionalism 5.3 | |
| A reaction: At first glance this sounds quite plausible, but I think this commitment to the priority of kinds produces huge confusion, given that we only derive our notions of kinds from inductions derived from individuals. Language perpetuates old inductions. |
| 11852 | Is the Pope's crown one crown, if it is made of many crowns? [Wiggins] |
| Full Idea: The Pope's crown is made of crowns. There is no definite answer, when the Pope is wearing his crown, to the question 'how many crowns does he have on his head?' | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.7) | |
| A reaction: A very nice example, in which the identity of the item seems clear enough, until you try to apply a sortal to it. I can't get excited about it, though, because calling it one 'crown' creates uncertainty, but calling it the 'Pope's crown' doesn't. |
| 11875 | Boundaries are not crucial to mountains, so they are determinate without a determinate extent [Wiggins] |
| Full Idea: It can be perfectly determinate which mountain x is without x's extent's being determinate. A mountain is not, after all, something essentially demarcated by its extent or boundary. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 6.5) | |
| A reaction: This endorses something I have always wanted to assert ('a vague boundary is still a boundary'), but with the interesting addition that one might think about vagueness in terms of what is essential to a thing. Hm.... |
| 18839 | An object that is not clearly red or orange can still be red-or-orange, which sweeps up problem cases [Rumfitt] |
| Full Idea: A borderline red-orange object satisfies the disjunctive predicate 'red or orange', even though it satisfies neither 'red' or 'orange'. When applied to adjacent bands of colour, the disjunction 'sweeps up' objects which are reddish-orange. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 8.5) | |
| A reaction: Rumfitt offers a formal principle in support of this. There may be a problem with 'adjacent'. Different colour systems will place different colours adjacent to red. In other examples the idea of 'adjacent' may make no sense. Rumfitt knows this! |
| 18838 | The extension of a colour is decided by a concept's place in a network of contraries [Rumfitt] |
| Full Idea: On Sainsbury's picture, a colour has an extension that it has by virtue of its place in a network of contrary colour classifications. Something is determined to be 'red' by being a colour incompatible with orange, yellow, green, blue, indigo and violet. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 8.5) | |
| A reaction: Along with Idea 18839, this gives quite a nice account of vagueness, by requiring a foil to the vague predicate, and using the disjunction of the predicate and its foil to handle anything caught in between them. |
| 14749 | Identity is an atemporal relation, but composition is relative to times [Wiggins, by Sider] |
| Full Idea: Wiggins points out that identity is an atemporal relation whereas composition, like parthood, holds only relative to times. | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001]) by Theodore Sider - Four Dimensionalism 5.3 | |
| A reaction: If David Cameron is identical to the Prime Minister, that doesn't seem to be atemporal. If x=7 in this problem, I can change x to something else in the next problem. x had better not be equal to 7 and to 9. |
| 11844 | If I destroy an item, I do not destroy each part of it [Wiggins] |
| Full Idea: If I repair or destroy an item, I do not repair or destroy each part of it (and since each part of a part is a part this would be difficult). | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.6) | |
| A reaction: This seems like a nice refutation of any attempt to claim that a thing is no more than the sum of its parts, but one could analyse the notion of 'destroy', and find it just meant introducing gaps between parts. |
| 11861 | We can forget about individual or particularized essences [Wiggins] |
| Full Idea: Let us be realistic, and forget about individual or particularized essences. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 4.2) | |
| A reaction: This is the rather weird position you reach if you follow Wiggins's 'modest' essentialism, deriving from a thing merely falling under a sortal, or into a category. What is a natural kind, if its members don't each have a shared essence? |
| 11871 | Essences are not explanations, but individuations [Wiggins] |
| Full Idea: Essences of natural things are not fancified vacuities parading themselves ...as the ultimate explanation of everything that happens in the world. They are natures whose possession is a precondition of their owners being divided from the rest of reality. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 5.2) | |
| A reaction: Thus Wiggins rejects the explanation account of essence, with an assertion of his own (highly implausible) view that essence is about individuation rather than about behaviour. Individuation strikes me as an entirely human activity, and not 'real'. |
| 11879 | Essentialism is best represented as a predicate-modifier: □(a exists → a is F) [Wiggins, by Mackie,P] |
| Full Idea: Wiggins's proposal of a predicate-modifier account is the best formal representation of essential statements. ...This simple version is perfectly adequate to represent the claim that a is essentially-F: □(a exists → a is F). | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001], Ch.4) by Penelope Mackie - How Things Might Have Been 1.2 | |
| A reaction: I suppose that is right. Having an essence is a feature of an entity, but it has to boil done to characteristics that define the entity, and which it must presumably always have. Could an entity ever lack its essence? |
| 11835 | The nominal essence is the idea behind a name used for sorting [Wiggins] |
| Full Idea: Things being ranked under Names into sorts only as they agree with certain abstract ideas, to which we have annexed the Names, the essence of each sort comes to nothing but that abstract idea which the sortal name stands for. This is the nominal Essence. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], III.iii.15) | |
| A reaction: He contrasts 'nominal essence' with 'real essence'. A key passage for David Wiggins. One shouldn't put too much emphasis on nominal essence, since it means that someone referred to as 'that idiot over there' (you, perhaps) is necessarily an idiot. |
| 11876 | It is easier to go from horses to horse-stages than from horse-stages to horses [Wiggins] |
| Full Idea: If horse-stages made sense at all, it would be easier to go from horses to horse-stages than to go from horse-stages to horses. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 6.9) | |
| A reaction: A nice remark, analogous to 'it is easier to break a vase than to mend it'. Going from horse-stages to horses is the classic difficulty for 'bundle theories' (of objects, or persons): what is it that unites the bundle? |
| 11858 | The question is not what gets the title 'Theseus' Ship', but what is identical with the original [Wiggins] |
| Full Idea: Let us remember that the title in question is not the title to the sobriquet 'Theseus' Ship'; it is the title to identity with Theseus' ship, a particular ship originating from the eighth century B.C. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 3.4) | |
| A reaction: There is an assumption here that identity is defined by origin. What is the origin of the identity of those huge football clubs that began under the name of some village team in 1875? What is the origin of 'England' as a single entity? |
| 11843 | Identity over a time and at a time aren't different concepts [Wiggins] |
| Full Idea: People often speak of identity over time and distinguish it from identity at a time. But identity is just identity. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.3) | |
| A reaction: I myself am guilty of such usage, but it doesn't imply a commitment to a multivocal concept. The epistemological issues (of explaining what it is now, and simply reidentifying it later) seem profoundly different. Hume only admits identity over time. |
| 11864 | Hesperus=Hesperus, and Phosphorus=Hesperus, so necessarily Phosphorus=Hesperus [Wiggins] |
| Full Idea: The simple proof (from Ruth Barcan Marcus) is: Hesperus is necessarily Hesperus, so if Phosphorus is Hesperus, then Phosphorus is necessarily Hesperus. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 4.3) | |
| A reaction: This is the famous idea which she noticed well before Kripke. The point is that the simple logic of the case bestows a necessity on the identity. We shouldn't be confused by the a posteriori and contingent nature of the discovery. |
| 11831 | The formal properties of identity are reflexivity and Leibniz's Law [Wiggins] |
| Full Idea: The formal properties of identity are the reflexivity of identity, and Leibniz's Law (if x is the same as y, then whatever is true of one is true of the other). | |
| From: David Wiggins (Sameness and Substance Renewed [2001], Pr.2) | |
| A reaction: Presumably transitivity will also apply, and, indeed, symmetry. He seems to mean something like the 'axiomatic formal properties'. |
| 14362 | Relative Identity is incompatible with the Indiscernibility of Identicals [Wiggins, by Strawson,P] |
| Full Idea: Wiggins argues that Geach's Relative Identity is incompatible with the formal properties of identity, which include, besides transitivity, symmetry and reflexivity, the complete community of properties defined by the Indiscernibility of Identicals. | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001]) by Peter F. Strawson - Review of 'Sameness and Substance' p.603 | |
| A reaction: The tricky part is that Wiggins then goes on to say that identity depends on sortals, which sounds very close to the Geach view. I find disentangling them tricky. See Idea 14363 for a helpful comment from Strawson. |
| 11838 | Relativity of Identity makes identity entirely depend on a category [Wiggins] |
| Full Idea: The thesis of Relativity of Identity (which I steadfastly oppose) ..suggests that it makes all the difference to keeping track of continuants through space and time which concept one subsumes something under. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 1.1) | |
| A reaction: [Geach I take to be the villain of this idea] The point is that identity is entirely relative to the sortal concept, where Wiggins wants to make identity a combination of the object itself and our concept of it (I think). |
| 11847 | To identify two items, we must have a common sort for them [Wiggins] |
| Full Idea: As a necessary condition of the truth of an identity claim, some common sort f will have to be found to which they each belong. That is the point at which the primary question of identity can come into focus. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.2) | |
| A reaction: This is the plainest English expression I can find of Wiggins's main thesis. He maintains this thesis, while adamantly denying the idea that identity consists entirely of falling under a concept. |
| 11839 | Do both 'same f as' and '=' support Leibniz's Law? [Wiggins] |
| Full Idea: Is Leibniz's Law as true for 'is the same as' as it is for '='? | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 1.2) | |
| A reaction: [By Leibniz's Law he means if they are the same, they support the same truths] |
| 11845 | Substitutivity, and hence most reasoning, needs Leibniz's Law [Wiggins] |
| Full Idea: Leibniz's Law underwrites the substitutivity of identity and this is a principle not long dispensable in any form of reasoning. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.7) | |
| A reaction: Thus the modern fashion of deriving our metaphysics from our logic. Presumably we can derive it from our epistemology too, or even from our intuitions, if we thought they were good enough as evidence. |
| 18816 | Metaphysical modalities respect the actual identities of things [Rumfitt] |
| Full Idea: The central characteristic mark of metaphysical necessity is that a metaphysical possibility respects the actual identities of things - in a capacious sense of 'thing'. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 3.4) | |
| A reaction: He contrast this with logical necessity, and concludes that some truths are metaphysically but not logically necessary, such as 'Hesperus is identical with Phosphorus'. Personally I like the idea of a 'necessity-maker', so that fits. |
| 18825 | S5 is the logic of logical necessity [Rumfitt] |
| Full Idea: I accept the widely held thesis that S5 is the logic of logical necessity. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 6.4 n16) | |
| A reaction: It seems plausible that S5 is also the logic of metaphysical necessity, but that does not make them the same thing. The two types of necessity have two different grounds. |
| 18824 | Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right [Rumfitt] |
| Full Idea: Some philosophers describe the colour scarlet as a determination of the determinable red; since the ways the world might be are naturally taken to be properties of the world, it helps to bear this analogy in mind. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 6.4) | |
| A reaction: This fits nicely with the disposition accounts of modality which I favour. Hence being 'coloured' is a real property of objects, even in the absence of the name of its specific colour. |
| 18828 | If two possibilities can't share a determiner, they are incompatible [Rumfitt] |
| Full Idea: Two possibilities are incompatible when no possibility determines both. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7.1) | |
| A reaction: This strikes me as just the right sort of language for building up a decent metaphysical picture of the world, which needs to incorporate possibilities as well as actualities. |
| 11869 | Possible worlds rest on the objects about which we have suppositions [Wiggins] |
| Full Idea: Worlds are the shadows of our suppositions and they take on their identity from these. Suppositions take on their identity from (inter alia) the objects they relate to. If they sever themselves from these objects, then they collapse. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 4.11) | |
| A reaction: Sounds good. My picture is of possibilities which are suggested by objecfs in the actual world, with extreme possibilities being at fifth-remove from actuality. Any worlds that go beyond natural possibility are just there for fun. |
| 18821 | Possibilities are like possible worlds, but not fully determinate or complete [Rumfitt] |
| Full Idea: Possibilities are things of the same general character as possible worlds, on one popular conception of the latter. They differ from worlds, though, in that they are not required to be fully determinate or complete. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 6) | |
| A reaction: A rather promising approach to such things, even though a possibility is fairly determinate at its core, but very vague at the edges. It is possible that the UK parliament might be located in Birmingham, for example. Is this world 'complete'? |
| 11850 | Not every story corresponds to a possible world [Wiggins] |
| Full Idea: It is perfectly notorious that not every story corresponds to a possible world. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.4) | |
| A reaction: Thus a fantasy castle might be decorated with 'beautiful circular squares', or be threatened by a lump of enriched uranium twenty feet in diameter. Wiggins is replying to the claim that a possible world represents a 'story'. |
| 18831 | Medieval logicians said understanding A also involved understanding not-A [Rumfitt] |
| Full Idea: Mediaeval logicians had a principle, 'Eadem est scientia oppositorum': in order to attain a clear conception of what it is for A to be the case, one needs to attain a conception of what it is for A not to be the case. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7.2) | |
| A reaction: Presumably 'understanding' has to be a fairly comprehensive grasp of the matter, so understanding the negation sounds like a reasonable requirement for the real thing. |
| 18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
| Full Idea: In English, the word 'evidence' behaves as a mass term: we speak of someone's having little evidence for an assertion, and of one thinker's having more evidence than another for a claim. One the other hand, we also speak of 'pieces' of evidence. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 5.2) | |
| A reaction: And having 'more' evidence does not mean having a larger number of pieces of evidence, so it really is like an accumulated mass. |
| 11848 | Asking 'what is it?' nicely points us to the persistence of a continuing entity [Wiggins] |
| Full Idea: The special effectiveness of the 'what is it?' question is that, in the case of continuants, it refers us back to our constantly exercised idea of the persistence and life-span of an entity. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.2) | |
| A reaction: Compare 'this is a human' with 'this is a member of a family noted for its longevity'. We can't simply answer 'what is it?' by tossing it into the nearest category. I say we need an individual essence for explanation, not just a sortal. |
| 11859 | The mind conceptualizes objects; yet objects impinge upon the mind [Wiggins] |
| Full Idea: The mind conceptualizes objects; yet objects impinge upon the mind. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 3.6) | |
| A reaction: I like this piece of simple common sense. I personally don't think you can reach first base in a sensible discussion if you don't face up to both sides of this idea (especially the second half, which many philosophers, especially of language, neglect). |
| 11836 | We can use 'concept' for the reference, and 'conception' for sense [Wiggins] |
| Full Idea: We can use the Fregean 'concept' on the level of reference and naming, and prefer the word 'conception' for the Kantian idea of the sense, or the information needed to understand the concept. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], Pr.5) | |
| A reaction: This is a nice suggestion, and at first blush I think it should be adopted. Sometimes philosophers regret adopting a terminology several hundred years after it has been agreed. |
| 18817 | We understand conditionals, but disagree over their truth-conditions [Rumfitt] |
| Full Idea: It is striking that our understanding of conditionals is not greatly impeded by widespread disagreement about their truth-conditions. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 4.2) | |
| A reaction: Compare 'if you dig there you might find gold' with 'if you dig there you will definitely find gold'. The second but not the first invites 'how do you know that?', implying truth. Two different ifs. |
| 14894 | Indexicals have a 'character' (the standing meaning), and a 'content' (truth-conditions for one context) [Kaplan, by Macià/Garcia-Carpentiro] |
| Full Idea: Kaplan distinguished two different semantic features of indexical expressions: a 'character' that captures the standing meaning of the expression, and a 'content' that consists of their truth-conditional contribution in particular contexts. | |
| From: report of David Kaplan (Demonstratives [1989]) by Macià/Garcia-Carpentiro - Introduction to 'Two-Dimensional Semantics' 1 | |
| A reaction: This seems so clearly right that there isn't much to dispute. You can't understand the word 'I' or 'now' if you don't understand both its general purpose, and what it is doing in a particular utterance. But will this generalise to other semantics? |
| 14700 | 'Content' gives the standard modal profile, and 'character' gives rules for a context [Kaplan, by Schroeter] |
| Full Idea: Kaplan sees two aspects of meaning, the 'content', reflecting a thing's modal profile, which is modelled by standard possible worlds semantics, and 'character', giving rules for different contexts. Proper names have constant character; indexicals vary. | |
| From: report of David Kaplan (Demonstratives [1989]) by Laura Schroeter - Two-Dimensional Semantics 1.1.1 | |
| A reaction: This gives rise to 2-D matrices for representing meaning, and the possible worlds are used twice, for evaluating meaning and then for evaluating context of use. I've always been struck by the two-dimensional semantics of passwords. |
| 18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt] |
| Full Idea: The truth-grounds of '¬A' are precisely those possibilities that are incompatible with any truth-ground of A. | |
| From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7.1) | |
| A reaction: This is Rumfitt's proposal for the semantics of 'not', based on the central idea of a possibility, rather than a possible world. The incompatibility tracks back to an absence of shared grounding. |
| 11860 | Lawlike propensities are enough to individuate natural kinds [Wiggins] |
| Full Idea: For all the purposes of identity and individuation of things that belong to natural kinds..., it is enough to have regard for the lawlike propensities of members of the kind. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 4.1) | |
| A reaction: This may have got things in reverse, since it is hard to see how you could pick out any laws if you didn't assume the existence of natural kinds which were causing the regularities in the behaviour. |