11 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) |
| 21750 | Science is sympathetic to truth as correspondence, since it depends on observation [Quine] |
| Full Idea: Science, thanks to its links with observation, retains some title to a correspondence theory of truth. | |
| From: Willard Quine (On the Nature of Moral Values [1978], p.63) | |
| A reaction: I would describe what he is affirming as a 'robust' theory of truth. An interesting aside, given his usual allegiance to disquotational, and even redundancy, accounts of truth. You can hardly rely on observations if you think they contain no truth. |
| 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) |
| 21748 | More careful inductions gradually lead to the hypothetico-deductive method [Quine] |
| Full Idea: Our inductions become increasingly explicit and deliberate, and in the fulness of time we even rise above induction, to the hypothetico-deductive method. | |
| From: Willard Quine (On the Nature of Moral Values [1978], p.57) | |
| A reaction: This seems to defer to Hempel's account of scientific theorising. I wander what exactly 'rising above' means? |
| 21749 | Altruistic values concern other persons, and ceremonial values concern practices [Quine] |
| Full Idea: Altruistic values attach to satisfactions of other persons, without regard to ulterior satisfactions accruing to oneself. Ceremonial values attach to practices of one's society, without regard to satisfactions accruing to oneself. | |
| From: Willard Quine (On the Nature of Moral Values [1978], p.58) | |
| A reaction: An interesting distinction, but probably as blurred and circular as (according to Quine) the analytic/synthetic distinction. |
| 21751 | Love seems to diminish with distance from oneself [Quine] |
| Full Idea: One cannot reasonably be called upon to love even one's neighbour quite as oneself. Is love to diminish inversely as the square of the distance? Is it to extend to other species than one's own? | |
| From: Willard Quine (On the Nature of Moral Values [1978], p.65) | |
| A reaction: Quine isn't actually saying that love is inherently egoistic, but that is the implication. The power of my love is at its most powerful when it is closest to home. |
| 9409 | Laws are the best axiomatization of the total history of world events or facts [Lewis, by Mumford] |
| Full Idea: The Mill-Ramsey-Lewis theory takes laws to be axioms (or theorems) of the best possible systematizations of the world's total history, where such a history is a history of events or facts. | |
| From: report of David Lewis (Psychophysical and theoretical identifications [1972]) by Stephen Mumford - Laws in Nature 1.3 |
| 9423 | If simplicity and strength are criteria for laws of nature, that introduces a subjective element [Mumford on Lewis] |
| Full Idea: Lewis's simplicity and strength criteria introduce an element of subjectivity into the laws, because the best system seems to be determined by what we take to be simple and strong in a system. | |
| From: comment on David Lewis (Psychophysical and theoretical identifications [1972]) by Stephen Mumford - Laws in Nature 3.5 | |
| A reaction: [Mumford cites Armstrong 1983:67 for this] |
| 9424 | A number of systematizations might tie as the best and most coherent system [Mumford on Lewis] |
| Full Idea: Since the best system view is a coherence theory, the possibility could not be ruled out that a number of different systematizations of the same history might be tied for first place as equally best. | |
| From: comment on David Lewis (Psychophysical and theoretical identifications [1972]) by Stephen Mumford - Laws in Nature 3.5 | |
| A reaction: [Mumord cites Armstrong 1983:70] Personally I am a fan of coherence theories, and this problem doesn't bother me. |