15 ideas
| 13430 | Infinity: there is an infinity of distinguishable individuals [Ramsey] |
| Full Idea: The Axiom of Infinity means that there are an infinity of distinguishable individuals, which is an empirical proposition. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], §5) | |
| A reaction: The Axiom sounds absurd, as a part of a logical system, but Ramsey ends up defending it. Logical tautologies, which seem to be obviously true, are rendered absurd if they don't refer to any objects, and some of them refer to infinities of objects. |
| 13428 | Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey] |
| Full Idea: The Axiom of Reducibility asserted that to every non-elementary function there is an equivalent elementary function [note: two functions are equivalent when the same arguments render them both true or both false]. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], §2) | |
| A reaction: Ramsey in the business of showing that this axiom from Russell and Whitehead is not needed. He says that the axiom seems to be needed for induction and for Dedekind cuts. Since the cuts rest on it, and it is weak, Ramsey says it must go. |
| 13427 | Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey] |
| Full Idea: In 'a = b' either 'a' and 'b' are names of the same thing, in which case the proposition says nothing, or of different things, in which case it is absurd. In neither case is it an assertion of a fact; it only asserts when a or b are descriptions. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], §1) | |
| A reaction: This is essentially Frege's problem with Hesperus and Phosphorus. How can identities be informative? So 2+2=4 is extensionally vacuous, but informative because they are different descriptions. |
| 13334 | Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey] |
| Full Idea: Group A consists of contradictions which would occur in a logical or mathematical system, involving terms such as class or number. Group B contradictions are not purely logical, and contain some reference to thought, language or symbolism. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], p.171), quoted by Graham Priest - The Structure of Paradoxes of Self-Reference 1 | |
| A reaction: This has become the orthodox division of all paradoxes, but the division is challenged by Priest (Idea 13373). He suggests that we now realise (post-Tarski?) that language is more involved in logic and mathematics than we thought. |
| 13426 | Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey] |
| Full Idea: The formalists neglected the content altogether and made mathematics meaningless, but the logicians neglected the form and made mathematics consist of any true generalisations; only by taking account of both sides can we obtain an adequate theory. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], §1) | |
| A reaction: He says mathematics is 'tautological generalizations'. It is a criticism of modern structuralism that it overemphasises form, and fails to pay attention to the meaning of the concepts which stand at the 'nodes' of the structure. |
| 13425 | Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey] |
| Full Idea: The hopelessly inadequate formalist theory is, to some extent, the result of considering only the propositions of mathematics and neglecting the analysis of its concepts. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], §1) | |
| A reaction: You'll have to read Ramsey to see how this thought pans out, but it at least gives a pointer to how to go about addressing the question. |
| 22328 | I just confront the evidence, and let it act on me [Ramsey] |
| Full Idea: I can but put the evidence before me, and let it act on my mind. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], p.202), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 70 'Deg' | |
| A reaction: Potter calls this observation 'downbeat', but I am an enthusiastic fan. It is roughly my view of both concept formation and of knowledge. You soak up the world, and respond appropriately. The trick is in the selection of evidence to confront. |
| 22325 | A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey] |
| Full Idea: I have always said that a belief was knowledge if it was 1) true, ii) certain, iii) obtained by a reliable process. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], p.258), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 66 'Rel' | |
| A reaction: Not sure why it has to be 'certain' as well as 'true'. It seems that 'true' is objective, and 'certain' subjective. I think I know lots of things of which I am not fully certain. Reliabilism long preceded Alvin Goldman. |
| 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. |
| 22489 | 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot] |
| Full Idea: Geach puts 'good' in the class of attributive adjectives, such as 'large' and 'small', contrasting such adjectives with 'predicative' adjectives such as 'red'. | |
| From: report of Peter Geach (Good and Evil [1956]) by Philippa Foot - Natural Goodness Intro | |
| A reaction: [In Analysis 17, and 'Theories of Ethics' ed Foot] Thus any object can simply be red, but something can only be large or small 'for a rat' or 'for a car'. Hence nothing is just good, but always a good so-and-so. This is Aristotelian, and Foot loves it. |