21 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. |
| 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. |
| 20400 | Intentions either succeed or fail, so external evidence for them is always irrelevant [Wimsatt/Beardsley, by Davies,S] |
| Full Idea: Wimsatt and Beardsley claimed that either the intention succeeded, so one does not need to look outside the work for its meaning, or the intention failed, so external evidence does not help. | |
| From: report of W Wimsatt/W Beardsley (The Intentional Fallacy [1946]) by Stephen Davies - The Philosophy of Art (2nd ed) 5.3 | |
| A reaction: Actually, the external evidence may tell you much more clearly and accurately what the intention was than the work itself does. The best example may be the title of the work, which is presumably outside the work. |
| 7266 | The author's intentions are irrelevant to the judgement of a work's success [Wimsatt/Beardsley] |
| Full Idea: The design or intention of the author is neither available nor desirable as a standard for judging the success of a work of literary art. | |
| From: W Wimsatt/W Beardsley (The Intentional Fallacy [1946], §I) | |
| A reaction: This famous proposal may have been misunderstood. Note that it is a comment about judging the work, not about understanding it. The idea allows for a work being much more successful than the author's humble intentions (e.g. Pepys). |
| 7267 | Poetry, unlike messages, can be successful without communicating intentions [Wimsatt/Beardsley] |
| Full Idea: Poetry differs from practical messages, which are successful if and only if we correctly infer the intention. | |
| From: W Wimsatt/W Beardsley (The Intentional Fallacy [1946], §I) | |
| A reaction: I am not convinced by this claim. It is plausible that a work does much more than it intends (Astaire said he danced "to make a buck"), but it is rather odd to rate very highly a work of which you have missed the point. |
| 7268 | The thoughts of a poem should be imputed to the dramatic speaker, and hardly at all to the poet [Wimsatt/Beardsley] |
| Full Idea: We ought to impute the thoughts and attitudes of the poem immediately to the dramatic speaker, and if to the author at all, only by an act of biographical inference. | |
| From: W Wimsatt/W Beardsley (The Intentional Fallacy [1946], §I) | |
| A reaction: Wrong. If in Browning's "My Last Duchess" (say), we only inferred the mind of the speaker (and his Duchess), and took no interest in Browning's view of things, we would miss the point. We might end up respecting the Duke, which would be daft. |
| 7269 | The intentional fallacy is a romantic one [Wimsatt/Beardsley] |
| Full Idea: The intentional fallacy is a romantic one. | |
| From: W Wimsatt/W Beardsley (The Intentional Fallacy [1946], §II) | |
| A reaction: Wrong. Even with those most famous of anonymous artists, the architects and carvers of medieval cathedrals, without some discernment of the purpose you won't get it. The Taj Mahal is a love letter, not a potential ice cream parlour. |
| 7271 | Biography can reveal meanings and dramatic character, as well as possible intentions [Wimsatt/Beardsley] |
| Full Idea: The use of biographical evidence need not involve intentionalism, because while it may be evidence of what the author intended, it may also be evidence of the meaning of his words and the dramatic character of his utterance. | |
| From: W Wimsatt/W Beardsley (The Intentional Fallacy [1946], §IV) | |
| A reaction: I am very keen to penetrate the author's intentions, but I have always be doubtful about the use of biography as a means to achieve this. Most of the effort to infer intentions must come from a study of the work itself, not introductions, letters etc. |
| 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. |