12 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. |
| 5049 | Intelligent pleasure is the perception of beauty, order and perfection [Leibniz] |
| Full Idea: An intelligent being's pleasure is simply the perception of beauty, order and perfection. | |
| From: Gottfried Leibniz (A Résumé of Metaphysics [1697], §18) | |
| A reaction: Leibniz seems to have inherited this from the Greeks, especially Pythagoras and Plato. Buried in Leibniz's remark I see the Christian fear of physical pleasure. He should have got out more. Must an intelligent being always be intelligent? |
| 10370 | Causal relata are individuated by coarse spacetime regions [Quine, by Schaffer,J] |
| Full Idea: Quine's view is that causal relata are individuated by spacetime regions, which is even less fine-grained than Davidson's account of events.... He says fine-grained events are poorly individuated and unfamiliar. | |
| From: report of Willard Quine (Events and Reification [1985]) by Jonathan Schaffer - The Metaphysics of Causation 1.2 | |
| A reaction: [Schaffer cites Davidson 1985 as accepting this view] This is a nice suggestion, if we are looking for a naturalistic account of causal relata. It makes a minimum ontological commitment (a Quine trait), and I would supplement it with active 'powers'. |
| 5048 | Perfection is simply quantity of reality [Leibniz] |
| Full Idea: Perfection is simply quantity of reality. | |
| From: Gottfried Leibniz (A Résumé of Metaphysics [1697], §11) | |
| A reaction: An interesting claim, but totally beyond my personal comprehension. I presume he inherited 'quantity of reality' from Plato, e.g. as you move up the Line from shadows to Forms you increase the degree of reality. I see 'real' as all-or-nothing. |
| 5050 | Evil serves a greater good, and pain is necessary for higher pleasure [Leibniz] |
| Full Idea: Evils themselves serve a greater good, and the fact that pains are found in minds is necessary if they are to reach greater pleasures. | |
| From: Gottfried Leibniz (A Résumé of Metaphysics [1697], §23) | |
| A reaction: How much pain is needed to qualify for the 'greater pleasures'? Some people receive an awful lot. I am not sure exactly how an evil can 'serve' a greater good. Is he recommending evil? |