21 ideas
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| Full Idea: The facts of geometry order themselves into a geometry, the facts of arithmetic into a theory of numbers, the facts of statics, electrodynamics into a theory of statics, electrodynamics, or the facts of the physics of gases into a theory of gases. | |
| From: David Hilbert (Axiomatic Thought [1918], [03]) | |
| A reaction: This is the confident (I would say 'essentialist') view of axioms, which received a bit of a setback with Gödel's Theorems. I certainly agree that the world proposes an order to us - we don't just randomly invent one that suits us. |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| Full Idea: If a theory is to serve its purpose of orienting and ordering, it must first give us an overview of the independence and dependence of its propositions, and second give a guarantee of the consistency of all of the propositions. | |
| From: David Hilbert (Axiomatic Thought [1918], [09]) | |
| A reaction: Gödel's Second theorem showed that the theory can never prove its own consistency, which made the second Hilbert requirement more difficult. It is generally assumed that each of the axioms must be independent of the others. |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| Full Idea: It is necessary to study the essence of mathematical proof itself if one wishes to answer such questions as the one about decidability in a finite number of operations. | |
| From: David Hilbert (Axiomatic Thought [1918], [53]) |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| Full Idea: The linearity of the equation of the plane and of the orthogonal transformation of point-coordinates is completely adequate to produce the whole broad science of spatial Euclidean geometry purely by means of analysis. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This remark comes from the man who succeeded in producing modern axioms for geometry (in 1897), so he knows what he is talking about. We should not be wholly pessimistic about Hilbert's ambitious projects. He had to dig deeper than this idea... |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| Full Idea: The laws of calculation and the rules of integers suffice for the construction of number theory. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This is the confident Hilbert view that the whole system can be fully spelled out. Gödel made this optimism more difficult. |
| 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. |
| 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. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| Full Idea: By pushing ahead to ever deeper layers of axioms ...we also win ever-deeper insights into the essence of scientific thought itself, and become ever more conscious of the unity of our knowledge. | |
| From: David Hilbert (Axiomatic Thought [1918], [56]) | |
| A reaction: This is the less fashionable idea that scientific essentialism can also be applicable in the mathematic sciences, centring on the project of axiomatisation for logic, arithmetic, sets etc. |