20 ideas
| 10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
| Full Idea: It is often the case that the concern for rigor gets in the way of a true understanding of the phenomena to be explained. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) | |
| A reaction: This is a counter to Timothy Williamson's love affair with rigour in philosophy. It strikes me as the big current question for analytical philosophy - of whether the intense pursuit of 'rigour' will actually deliver the wisdom we all seek. |
| 5831 | The new view is that "water" is a name, and has no definition [Schwartz,SP] |
| Full Idea: Perhaps the modern view is best expressed as saying that "water" has no definition at all, at least in the traditional sense, and is a proper name of a specific substance. | |
| From: Stephen P. Schwartz (Intro to Naming,Necessity and Natural Kinds [1977], §III) | |
| A reaction: This assumes that proper names have no definitions, though I am not clear how we can grasp the name 'Aristotle' without some association of properties (human, for example) to go with it. We need a definition of 'definition'. |
| 10565 | There is no stage at which we can take all the sets to have been generated [Fine,K] |
| Full Idea: There is no stage at which we can take all the sets to have been generated, since the set of all those sets which have been generated at a given stage will itself give us something new. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
| Full Idea: We might combine the standard axioms of set theory with the standard axioms of mereology. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 5829 | We refer to Thales successfully by name, even if all descriptions of him are false [Schwartz,SP] |
| Full Idea: We can refer to Thales by using the name "Thales" even though perhaps the only description we can supply is false of him. | |
| From: Stephen P. Schwartz (Intro to Naming,Necessity and Natural Kinds [1977], §III) | |
| A reaction: It is not clear what we would be referring to if all of our descriptions (even 'Greek philosopher') were false. If an archaeologist finds just a scrap of stone with a name written on it, that is hardly a sufficient basis for successful reference. |
| 5830 | The traditional theory of names says some of the descriptions must be correct [Schwartz,SP] |
| Full Idea: The traditional theory of proper names entails that at least some combination of the things ordinarily believed of Aristotle are necessarily true of him. | |
| From: Stephen P. Schwartz (Intro to Naming,Necessity and Natural Kinds [1977], §III) | |
| A reaction: Searle endorses this traditional theory. Kripke and co. tried to dismiss it, but you can't. If all descriptions of Aristotle turned out to be false (it was actually the name of a Persian statue), our modern references would have been unsuccessful. |
| 10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
| Full Idea: We are tempted to ask of second-order quantifiers 'what are you quantifying over?', or 'when you say "for some F" then what is the F?', but these questions already presuppose that the quantifiers are first-order. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005]) |
| 10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
| Full Idea: In doing semantics we normally assign some appropriate entity to each predicate, but this is largely for technical convenience. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
| Full Idea: Because of Dedekind's definition of reals by cuts, there is a bizarre modern doctrine that there are many 1's - the natural number 1, the rational number 1, the real number 1, and even the complex number 1. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) | |
| A reaction: See Idea 10572. |
| 10575 | Why should a Dedekind cut correspond to a number? [Fine,K] |
| Full Idea: By what right can Dedekind suppose that there is a number corresponding to any pair of irrationals that constitute an irrational cut? | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
| Full Idea: What is the union of the singleton {0}, of zero, and the singleton {φ}, of the null set? Is it the one-element set {0}, or the two-element set {0, φ}? Unless the question of identity between 0 and φ is resolved, we cannot say. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
| Full Idea: Set-theoretic imperialists think that it must be possible to represent every mathematical object as a set. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
| Full Idea: Logicists traditionally claim that the theorems of mathematics can be derived by logical means from the relevant definitions of the terms, and that these theorems are epistemically innocent (knowable without Kantian intuition or empirical confirmation). | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
| Full Idea: It is natural to have a generative conception of abstracts (like the iterative conception of sets). The abstracts are formed at stages, with the abstracts formed at any given stage being the abstracts of those concepts of objects formed at prior stages. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) | |
| A reaction: See 10567 for Fine's later modification. This may not guarantee 'levels', but it implies some sort of conceptual priority between abstract entities. |
| 5826 | The intension of "lemon" is the conjunction of properties associated with it [Schwartz,SP] |
| Full Idea: The conjunction of properties associated with a term such as "lemon" is often called the intension of the term "lemon". | |
| From: Stephen P. Schwartz (Intro to Naming,Necessity and Natural Kinds [1977], §II) | |
| A reaction: The extension of "lemon" is the set of all lemons. At last, a clear explanation of the word 'intension'! The debate becomes clear - over whether the terms of a language are used in reference to ideas of properties (and substances?), or to external items. |
| 10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
| Full Idea: Abstraction-theoretic imperialists think that it must be possible to represent every mathematical object as a Fregean abstract. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
| Full Idea: I propose a unified theory which is a version of ZF or ZFC with urelements, where the urelements are taken to be the abstracts. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10567 | We can create objects from conditions, rather than from concepts [Fine,K] |
| Full Idea: Instead of viewing the abstracts (or sums) as being generated from objects, via the concepts from which they are defined, we can take them to be generated from conditions. The number of the universe ∞ is the number of self-identical objects. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) | |
| A reaction: The point is that no particular object is now required to make the abstraction. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |