25 ideas
| 16985 | Possible worlds allowed the application of set-theoretic models to modal logic [Kripke] |
| Full Idea: The main and the original motivation for the 'possible worlds analysis' - and the way it clarified modal logic - was that it enabled modal logic to be treated by the same set theoretic techniques of model theory used successfully in extensional logic. | |
| From: Saul A. Kripke (Naming and Necessity preface [1980], p.19 n18) | |
| A reaction: So they should be ascribed the same value that we attribute to classical model theory, whatever that is. |
| 16982 | A man has two names if the historical chains are different - even if they are the same! [Kripke] |
| Full Idea: Two totally distinct 'historical chains' that be sheer accident assign the same name to the same man should probably count as creating distinct names despite the identity of the referents. | |
| From: Saul A. Kripke (Naming and Necessity preface [1980], p.08 n9) | |
| A reaction: A nice puzzle for his own theory. 'What's you name?' 'Alice, and Alice!' |
| 17813 | Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP] |
| Full Idea: The Löwenheim-Skolem theorem tells us that any theory with a true interpretation has a model in the natural numbers. | |
| From: Nicholas P. White (What Numbers Are [1974], V) |
| 17812 | Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP] |
| Full Idea: Statements involving finite cardinalities can be made without treating numbers as objects at all, simply by using quantification and identity to define numerically definite quantifiers in the manner of Frege. | |
| From: Nicholas P. White (What Numbers Are [1974], IV) | |
| A reaction: [He adds Quine 1960:268 as a reference] |
| 17518 | Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers] |
| Full Idea: If we count the concept 'coin in this box', we could regard coin as the 'unit', while taking 'in this box' to limit the scope. Counting coins in two boxes would be not a difference in unit (kind of object), but in scope. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Counting') | |
| A reaction: This is a very nice alternative to the Fregean view of counting, depending totally on the concept, and rests more on a natural concept of object. I prefer Ayers. Compare 'count coins till I tell you to stop'. |
| 17516 | If counting needs a sortal, what of things which fall under two sortals? [Ayers] |
| Full Idea: If we accepted that counting objects always presupposes some sortal, it is surely clear that the class of objects to be counted could be designated by two sortals rather than one. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Realist' vii) | |
| A reaction: His nice example is an object which is both 'a single piece of wool' and a 'sweater', which had better not be counted twice. Wiggins struggles to argue that there is always one 'substance sortal' which predominates. |
| 17520 | Events do not have natural boundaries, and we have to set them [Ayers] |
| Full Idea: In order to know which event has been ostensively identified by a speaker, the auditor must know the limits intended by the speaker. ...Events do not have natural boundaries. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Concl') | |
| A reaction: He distinguishes events thus from natural objects, where the world, to a large extent, offers us the boundaries. Nice point. |
| 17519 | To express borderline cases of objects, you need the concept of an 'object' [Ayers] |
| Full Idea: The only explanation of the power to produce borderline examples like 'Is this hazelnut one object or two?' is the possession of the concept of an object. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Counting') |
| 17511 | Recognising continuity is separate from sortals, and must precede their use [Ayers] |
| Full Idea: The recognition of the fact of continuity is logically independent of the possession of sortal concepts, whereas the formation of sortal concepts is at least psychologically dependent upon the recognition of continuity. | |
| From: M.R. Ayers (Individuals without Sortals [1974], Intro) | |
| A reaction: I take this to be entirely correct. I might add that unity must also be recognised. |
| 17510 | Speakers need the very general category of a thing, if they are to think about it [Ayers] |
| Full Idea: If a speaker indicates something, then in order for others to catch his reference they must know, at some level of generality, what kind of thing is indicated. They must categorise it as event, object, or quality. Thinking about something needs that much. | |
| From: M.R. Ayers (Individuals without Sortals [1974], Intro) | |
| A reaction: Ayers defends the view that such general categories are required, but not the much narrower sortal terms defended by Geach and Wiggins. I'm with Ayers all the way. 'What the hell is that?' |
| 17522 | We use sortals to classify physical objects by the nature and origin of their unity [Ayers] |
| Full Idea: Sortals are the terms by which we intend to classify physical objects according to the nature and origin of their unity. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Concl') | |
| A reaction: This is as opposed to using sortals for the initial individuation. I take the perception of the unity to come first, so resemblance must be mentioned, though it can be an underlying (essentialist) resemblance. |
| 17515 | Seeing caterpillar and moth as the same needs continuity, not identity of sortal concepts [Ayers] |
| Full Idea: It is unnecessary to call moths 'caterpillars' or caterpillars 'moths' to see that they can be the same individual. It may be that our sortal concepts reflect our beliefs about continuity, but our beliefs about continuity need not reflect our sortals. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Realist' vi) | |
| A reaction: Something that metamorphosed through 15 different stages could hardly required 15 different sortals before we recognised the fact. Ayers is right. |
| 17517 | Could the same matter have more than one form or principle of unity? [Ayers] |
| Full Idea: The abstract question arises of whether the same matter could be subject to more than one principle of unity simultaneously, or unified by more than one 'form'. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Realist' vii) | |
| A reaction: He suggests that the unity of the sweater is destroyed by unravelling, and the unity of the thread by cutting. |
| 17513 | If there are two objects, then 'that marble, man-shaped object' is ambiguous [Ayers] |
| Full Idea: The statue is marble and man-shaped, but so is the piece of marble. So not only are the two objects in the same place, but two marble and man-shaped objects in the same place, so 'that marble, man-shaped object' must be ambiguous or indefinite. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Prob') | |
| A reaction: It strikes me as basic that it can't be a piece of marble if you subtract its shape, and it can't be a statue if you subtract its matter. To treat a statue as an object, separately from its matter, is absurd. |
| 17523 | Sortals basically apply to individuals [Ayers] |
| Full Idea: Sortals, in their primitive use, apply to the individual. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Concl') | |
| A reaction: If the sortal applies to the individual, any essence must pertain to that individual, and not to the class it has been placed in. |
| 17521 | You can't have the concept of a 'stage' if you lack the concept of an object [Ayers] |
| Full Idea: It would be impossible for anyone to have the concept of a stage who did not already possess the concept of a physical object. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Concl') |
| 17514 | Temporal 'parts' cannot be separated or rearranged [Ayers] |
| Full Idea: Temporally extended 'parts' are still mysteriously inseparable and not subject to rearrangement: a thing cannot be cut temporally in half. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Prob') | |
| A reaction: A nice warning to anyone accepting a glib analogy between spatial parts and temporal parts. |
| 16981 | With the necessity of self-identity plus Leibniz's Law, identity has to be an 'internal' relation [Kripke] |
| Full Idea: It is clear from (x)□(x=x) and Leibniz's Law that identity is an 'internal' relation: (x)(y)(x=y ⊃ □x=y). What pairs (w,y) could be counterexamples? Not pairs of distinct objects, …nor an object and itself. | |
| From: Saul A. Kripke (Naming and Necessity preface [1980], p.03) | |
| A reaction: I take 'internal' to mean that the necessity of identity is intrinsic to the item(s), and not imposed by some other force. |
| 17509 | Some say a 'covering concept' completes identity; others place the concept in the reference [Ayers] |
| Full Idea: Some hold that the 'covering concept' completes the incomplete concept of identity, determining the kind of sameness involved. Others strongly deny the identity itself is incomplete, and locate the covering concept within the necessary act of reference. | |
| From: M.R. Ayers (Individuals without Sortals [1974], Intro) | |
| A reaction: [a bit compressed; Geach is the first view, and Quine the second; Wiggins is somewhere between the two] |
| 17512 | If diachronic identities need covering concepts, why not synchronic identities too? [Ayers] |
| Full Idea: Why are covering concepts required for diachronic identities, when they must be supposed unnecessary for synchronic identities? | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Prob') |
| 4942 | The indiscernibility of identicals is as self-evident as the law of contradiction [Kripke] |
| Full Idea: It seems to me that the Leibnizian principle of the indiscernibility of identicals (not to be confused with the identity of indiscernibles) is as self-evident as the law of contradiction. | |
| From: Saul A. Kripke (Naming and Necessity preface [1980], p.03) | |
| A reaction: This seems obviously correct, as it says no more than that a thing has whatever properties it has. If a difference is discerned, either you have made a mistake, or it isn't identical. |
| 16984 | I don't think possible worlds reductively reveal the natures of modal operators etc. [Kripke] |
| Full Idea: I do not think of 'possible worlds' as providing a reductive analysis in any philosophically significant sense, that is, as uncovering the ultimate nature, from either an epistemological or a metaphysical view, of modal operators, propositions etc. | |
| From: Saul A. Kripke (Naming and Necessity preface [1980], p.19 n18) | |
| A reaction: I think this remark opens the door for Kit Fine's approach, of showing what modality is by specifying its sources. Possible worlds model the behaviour of modal inferences. |
| 9385 | The very act of designating of an object with properties gives knowledge of a contingent truth [Kripke] |
| Full Idea: If a speaker introduced a designator into a language by a ceremony, then in virtue of his very linguistic act, he would be in a position to say 'I know that Fa', but nevertheless 'Fa' would be a contingent truth (provided F is not an essential property). | |
| From: Saul A. Kripke (Naming and Necessity preface [1980], p.14) | |
| A reaction: If someone else does the designation, I seem to have contingent knowledge that the ceremony has taken place. You needn't experience the object, but you must experience the ceremony, even if you perform it. |
| 4943 | Instead of talking about possible worlds, we can always say "It is possible that.." [Kripke] |
| Full Idea: We should remind ourselves the 'possible worlds' terminology can always be replaced by modal talk, such as "It is possible that…" | |
| From: Saul A. Kripke (Naming and Necessity preface [1980], p.15) | |
| A reaction: Coming from an originator of the possible worlds idea, this is a useful reminder that we don't have to get too excited about the ontological commitments involved. It may be just a 'way to talk', and hence a tool, rather than a truth about reality. |
| 16983 | Probability with dice uses possible worlds, abstractions which fictionally simplify things [Kripke] |
| Full Idea: In studying probabilities with dice, we are introduced at a tender age to a set of 36 (miniature) possible worlds, if we (fictively) ignore everything except the two dice. …The possibilities are abstract states of the dice, not physical entities. | |
| From: Saul A. Kripke (Naming and Necessity preface [1980], p.16) | |
| A reaction: Interesting for the introduction by the great man of the words 'fictional' and 'abstract' into the discussion. He says elsewhere that he takes worlds to be less than real, but more than mere technical devices. |