13 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. |
| 18189 | ZFC could contain a contradiction, and it can never prove its own consistency [MacLane] |
| Full Idea: We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC. | |
| From: Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30). |
| 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!' |
| 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. |
| 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. |
| 20416 | By 1790 aestheticians were mainly trying to explain individual artistic genius [Kemp] |
| Full Idea: By 1790 the idea that a central task for the aesthetician was to explain or at least adequately to describe the phenomenon of the individual artistic genius had definitely taken hold. | |
| From: Gary Kemp (Croce and Collingwood [2012], Intro) | |
| A reaction: Hence when Kant and Hegel write about art, though are only really thinking of the greatest art (which might be in touch with the sublime or Spirit etc.). Nowadays I think we expect accounts of art to cover modest amateur efforts as well. |
| 20417 | Expression can be either necessary for art, or sufficient for art (or even both) [Kemp] |
| Full Idea: Seeing art as expression has two components: 1) if something is a work of art, then it is expressive, 2) if something is expressive, then it is a work of art. So expression can be necessary or sufficient for art. (or both, for Croce and Collingwood). | |
| From: Gary Kemp (Croce and Collingwood [2012], 1) | |
| A reaction: I take the idea that art 'expresses' the feelings of an artist to be false. Artists are more like actors. Nearly all art has some emotional impact, which is of major importance, but I don't think 'expression' is a very good word for that. |
| 20419 | We don't already know what to express, and then seek means of expressing it [Kemp] |
| Full Idea: One cannot really know, or be conscious of, what it is that one is going to express, and then set about expressing it; indeed if one is genuinely conscious of it then one has already expressed it. | |
| From: Gary Kemp (Croce and Collingwood [2012], 1) | |
| A reaction: That pretty conclusively demolishes the idea that art is expression. I picture Schubert composing at the piano: he doesn't feel an emotion, and then hunt for its expression on the keyboard; he seeks out expressive phrases by playing. |
| 20418 | The horror expressed in some works of art could equallly be expressed by other means [Kemp] |
| Full Idea: The horror or terror of Edvard Much's 'The Scream' could in principle be expressed by different paintings, or even by works of music. | |
| From: Gary Kemp (Croce and Collingwood [2012], 1) | |
| A reaction: A very good simple point against the idea that the point of art is expression. It leaves out the very specific nature of each work of art! |