23 ideas
| 15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
| Full Idea: The common feature of every designating term is that designation may change from state to state - thus it can be formalized by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3) | |
| A reaction: Specifying the objects sounds OK, but specifying states sounds rather tough. |
| 15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
| Full Idea: To first order modal logic (with quantification over objects) we can add a second kind of quantification, over intensions. An intensional object, or individual concept, will be modelled by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.3) |
| 15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
| Full Idea: Awareness logic enriched Hintikka's epistemic models with an awareness function, mapping each state to the set of formulas we are aware of at that state. This reflects some bound on the resources we can bring to bear. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) | |
| A reaction: [He cites Fagin and Halpern 1988 for this] |
| 15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
| Full Idea: In justification logics, the logics of knowledge are extended by making reasons explicit. A logic of proof terms was created, with a semantics. In this, mathematical truths are known for explicit reasons, and these provide a measure of complexity. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) |
| 11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
| Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics. | |
| From: Melvin Fitting (Intensional Logic [2007], §1) |
| 11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
| Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □. | |
| From: Melvin Fitting (Intensional Logic [2007], §3.3) | |
| A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic. |
| 12427 | All of mathematics is properties of the whole numbers [Kronecker] |
| Full Idea: All the results of significant mathematical research must ultimately be expressible in the simple forms of properties of whole numbers. | |
| From: Leopold Kronecker (works [1885], Vol 3/274), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 09.5 | |
| A reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date. Natural numbers have a special status, but not sufficient to support this claim. |
| 10091 | God made the integers, all the rest is the work of man [Kronecker] |
| Full Idea: God made the integers, all the rest is the work of man. | |
| From: Leopold Kronecker (works [1885]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Intro | |
| A reaction: This famous remark was first quoted in Kronecker's obituary. A response to Dedekind, it seems. See Idea 10090. Did he really mean that negative numbers were the work of God? We took a long time to spot them. |
| 17000 | We might fix identities for small particulars, but it is utopian to hope for such things [Kripke] |
| Full Idea: Maybe strict identity only applies to the particulars (the molecules) in a case of vague identity. …It seems, however, utopian to suppose that we will ever reach a level of ultimate, basic particulars for which identity relations are never vague. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 18) | |
| A reaction: I agree with this. Ladyman and Ross laugh at the unscientific picture found in dreams of 'simples'. |
| 11868 | A different piece of wood could have been used for that table; constitution isn't identity [Wiggins on Kripke] |
| Full Idea: Could the artificer not, when he made the table, have taken other pieces? Surely he could. [n37: I venture to think that Kripke's argument in note 56 for the necessity of constitution depends on treating constitution as if it were identity]. | |
| From: comment on Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 56) by David Wiggins - Sameness and Substance Renewed 4.11 | |
| A reaction: Suppose the craftsman completed the table, then changed a piece of wood in it for some reason. Has he now made a second table and destroyed the first one? Wiggins seems to be right. |
| 17044 | A relation can clearly be reflexive, and identity is the smallest reflexive relation [Kripke] |
| Full Idea: Some philosophers have thought that a relation, being essentially two-termed, cannot hold between a thing and itself. This position is plainly absurd ('he is his own worst enemy'). Identity is nothing but the smallest reflexive relation. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 50) | |
| A reaction: I have no idea what 'smallest' means here. I can't be 'to the left of myself', so not all of my relations can be reflexive. I just don't understand what it means to say something is 'identical with itself'. You've got the thing - what have you added? |
| 16999 | A vague identity may seem intransitive, and we might want to talk of 'counterparts' [Kripke] |
| Full Idea: When the identity relation is vague, it may seem intransitive; a claim of apparent identity may yield an apparent non-identity. Some sort of 'counterpart' notion may have some utility here. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 18) | |
| A reaction: He firmly rejects the full Lewis apparatus of counterparts. The idea would be that a river at different times had counterpart relations, not strict identity. I like the word 'same' for this situation. Most worldly 'identity' is intransitive. |
| 17058 | What many people consider merely physically necessary I consider completely necessary [Kripke] |
| Full Idea: My third lecture suggests that a good deal of what contemporary philosophy regards as mere physical necessity is actually necessary tout court. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], Add (g)) | |
| A reaction: He avoids the term 'metaphysically necessary', which most people would not use for this point. |
| 4970 | What is often held to be mere physical necessity is actually metaphysical necessity [Kripke] |
| Full Idea: My third lecture suggests that a good deal of what contemporary philosophy regards as mere physical necessity is actually necessary 'tout court'. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], Add (g)) | |
| A reaction: This huge claim rides in on the back of Kripke's very useful clarifications. It is the 'new essentialism', and seems to me untenable in this form. There is no answer to Hume's request for evidence of necessity. Why can't essences (and laws) change? |
| 17059 | Unicorns are vague, so no actual or possible creature could count as a unicorn [Kripke] |
| Full Idea: If the unicorn myth is supposed to be a particular species, with insufficient internal structure to determine it uniquely, then there is no actual or possible species of which we can say that it would have been the species of unicorns. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], Add (a)) | |
| A reaction: Dummett and Rumfitt discuss this proposal elsewhere. |
| 4950 | Possible worlds are useful in set theory, but can be very misleading elsewhere [Kripke] |
| Full Idea: The apparatus of possible worlds has (I hope) been very useful as far as the set-theoretic model-theory of quantified modal logic is concerned, but has encouraged philosophical pseudo-problems and misleading pictures. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 15) | |
| A reaction: This is presumably a swipe at David Lewis, who claims possible worlds are real. The fact that the originator of possible worlds sees them as unproblematic doesn't mean they are. Fine if they are a game, but if they assert truth, they need a metaphysics. |
| 15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
| Full Idea: Definite descriptions pick out different objects in different possible worlds quite naturally. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.4) | |
| A reaction: A definite description can pick out the same object in another possible world, or a very similar one, or an object which has almost nothing in common with the others. |
| 17003 | Kaplan's 'Dthat' is a useful operator for transforming a description into a rigid designation [Kripke] |
| Full Idea: It is useful to have an operator which transforms each description into a term which rigidly designates the object actually satisfying the description. David Kaplan has proposed such an operator and calls it 'Dthat'. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 22) |
| 9221 | The best known objection to counterparts is Kripke's, that Humphrey doesn't care if his counterpart wins [Kripke, by Sider] |
| Full Idea: The most famous objection to counterparts is Kripke's objection that Hubert Humphrey wouldn't care if he thought that his counterpart might have won the 1972 election. He wishes that he had won it. | |
| From: report of Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 12) by Theodore Sider - Reductive Theories of Modality 3.10 | |
| A reaction: Like Sider, I find this unconvincing. If there is a world in which I don't exist, but my very close counterpart does (say exactly me, but with a finger missing), I am likely to care more about such a person than about complete strangers. |
| 17052 | The a priori analytic truths involving fixing of reference are contingent [Kripke] |
| Full Idea: If statements whose a priori truth is known via the fixing of a reference are counted as analytic, then some analytic truths are contingent. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 63) |
| 4969 | I regard the mind-body problem as wide open, and extremely confusing [Kripke] |
| Full Idea: I regard the mind-body problem as wide open, and extremely confusing. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 77) | |
| A reaction: Kripke opposes reductive physicalism, but is NOT committed to dualism. He seems to be drawn to Davidson or Nagel (see his note 73). I think his discussion of contingent mind-brain identity is confused. |
| 4956 | A description may fix a reference even when it is not true of its object [Kripke] |
| Full Idea: In some cases an object may be identified, and the reference of a name fixed, using a description which may turn out to be false of its object. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 34) | |
| A reaction: This is clearly possible. Someone could be identified as 'the criminal' when they were actually innocent. Nevertheless, how do you remember which person was baptised 'Aristotle' if you don't hang on to a description, even a false one? |
| 17032 | Even if Gödel didn't produce his theorems, he's still called 'Gödel' [Kripke] |
| Full Idea: If a Gödelian fraud were exposed, Gödel would no longer be called 'the author of the incompleteness theorem', but he would still be called 'Gödel'. The description, therefore, does not abbreviate the name. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 37) | |
| A reaction: Clearly we can't make the description a necessary fact about Gödel, but that doesn't invalidate the idea that successful reference needs some description. E.g. Gödel is a person. |