22 ideas
| 10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
| Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.4) |
| 10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
| Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.2) |
| 10885 | Computer proofs don't provide explanations [Horsten] |
| Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.3) |
| 10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
| Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.3) |
| 15797 | All structures are dispositional, objects are dispositions sets, and events manifest dispositions [Fetzer] |
| Full Idea: I propose a dispositional ontology for the physical world, according to which a) every structural property is a dispositional one, b) a physical object is an ordered set of dispositions, and c) every event manifests a dispositional property of the world. | |
| From: J.H. Fetzer (A World of Dispositions [1977], Intro) | |
| A reaction: Mumford says this is consistent with ontology as a way of describing the world, rather than being facts about the world. I like Fetzer's sketch, which sounds to have a lot in common with 'process philosophy'. |
| 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'. |
| 15800 | All events and objects are dispositional, and hence all structural properties are dispositional [Fetzer] |
| Full Idea: Every atomic event in the world's history is a manifestation of some dispositional property of the world and every physical object is an instantiation of some set of dispositions; hence, every structural property is dispositional in kind. | |
| From: J.H. Fetzer (A World of Dispositions [1977], 5) | |
| A reaction: I quite like this drastic view, but there remains the intuition that there must always be something which has the disposition. That may be because I have not yet digested the lessons of modern physics. |
| 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. |
| 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. |
| 15798 | Kinds are arrangements of dispositions [Fetzer] |
| Full Idea: Kinds of things are specific arrangements of dispositions. | |
| From: J.H. Fetzer (A World of Dispositions [1977], 2) | |
| A reaction: A 'disposition' doesn't seem quite the right word for what is basic to the physical world, though Harré and Madden make a good case for the 'fields' of physic being understood in that way. I prefer 'power', though that doesn't solve anything. |
| 15799 | Lawlike sentences are general attributions of disposition to all members of some class [Fetzer] |
| Full Idea: Lawlike sentences are conceived as logically general dispositional statements attributing permanent dispositional properties to every member of a reference class. ...Their basic form is that of subjunctive generalizations. | |
| From: J.H. Fetzer (A World of Dispositions [1977], 3) | |
| A reaction: I much prefer talk of 'lawlike sentences' to talk of 'laws'. At least they imply that the true generalisations about nature are fairly fine-grained. Why not talk of 'generalisations' instead of 'laws'? Fetzer wants dispositions to explain everything. |