18 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. |
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) |
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. |
2602 | What experience could prove 'If a=c and b=c then a=b'? [Descartes] |
Full Idea: Please tell me what the corporeal motion is that is capable of forming some common notion to the effect that 'things which are equal to a third thing are equal to each other'. | |
From: René Descartes (Comments on a Certain Broadsheet [1644], p.366) |
2600 | The mind's innate ideas are part of its capacity for thought [Descartes] |
Full Idea: I have never written or taken the view that the mind requires innate ideas which are something distinct from its own faculty of thinking. | |
From: René Descartes (Comments on a Certain Broadsheet [1644], p.365) |
2601 | Qualia must be innate, because physical motions do not contain them [Descartes] |
Full Idea: The ideas of pains, colours, sounds etc. must be all the more innate if, on the occasion of certain corporeal motions, our mind is to be capable of representing them to itself, for there is no similarity between these ideas and the corporeal motions. | |
From: René Descartes (Comments on a Certain Broadsheet [1644], p.365) | |
A reaction: Simple and brilliant! We know perfectly well that there is no redness zooming through the air from a tomato (or the air would be pink!). Redness occurs when the light arrives, so we add the redness, so it is innate. |
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. |
5994 | Is the cosmos open or closed, mechanical or teleological, alive or inanimate, and created or eternal? [Robinson,TM, by PG] |
Full Idea: The four major disputes in classical cosmology were whether the cosmos is 'open' or 'closed', whether it is explained mechanistically or teleologically, whether it is alive or mere matter, and whether or not it has a beginning. | |
From: report of T.M. Robinson (Classical Cosmology (frags) [1997]) by PG - Db (ideas) | |
A reaction: A nice summary. The standard modern view is closed, mechanistic, inanimate and non-eternal. But philosophers can ask deeper questions than physicists, and I say we are entitled to speculate when the evidence runs out. |