16 ideas
| 19336 | Wisdom involves the desire to achieve perfection [Leibniz] |
| Full Idea: The wiser one is, the more one is determined to do that which is most perfect. | |
| From: Gottfried Leibniz (On the Ultimate Origination of Things [1697], p.151) | |
| A reaction: Debatable. 'Perfectionism' is a well-known vice in many areas of life. Life is short, and the demands on us are many. Skilled shortcuts and compromises are one hallmark of genius, and presumably also of wisdom. |
| 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. |
| 7696 | Leibniz first asked 'why is there something rather than nothing?' [Leibniz, by Jacquette] |
| Full Idea: The historical honour of having first raised the question "Why is there something rather than nothing?" belongs to Leibniz. | |
| From: report of Gottfried Leibniz (On the Ultimate Origination of Things [1697]) by Dale Jacquette - Ontology Ch.3 | |
| A reaction: I presume that people before Leibniz may well have had the thought, but not bothered to even articulate it, because there seemed nothing to say by way of answer, other than some reference to the inscrutable will of God. |
| 19341 | There must be a straining towards existence in the essence of all possible things [Leibniz] |
| Full Idea: Since something rather than nothing exists, there is a certain urge for existence, or (so to speak) a straining toward existence in possible things or in possibility or essence itself; in a word, essence in and of itself strives for existence. | |
| From: Gottfried Leibniz (On the Ultimate Origination of Things [1697], p.150) | |
| A reaction: Thus 'essence precedes existence'. Not sure I understand this, but at least it places an active power at the root of everything (though Leibniz probably sees that as divine). The Big Bang triggered by a 'quantum fluctuation'? |
| 19428 | Because something does exist, there must be a drive in possible things towards existence [Leibniz] |
| Full Idea: From the very fact that something exists rather than nothing, we recognise that there is in possible things, that is, in the very possibility or essence, a certain exigent need of existence, and, so to speak, some claim to existence. | |
| From: Gottfried Leibniz (On the Ultimate Origination of Things [1697], p.347) | |
| A reaction: I love the fact that Leibniz tried to explain why there is something rather than nothing. Bede Rundle and Dale Jacquette are similar heroes. As Leibniz tells us, contradictions have no claim to existence, but non-contradictions do. |
| 5047 | The world is physically necessary, as its contrary would imply imperfection or moral absurdity [Leibniz] |
| Full Idea: Although the world is not metaphysically necessary, such that its contrary would imply a contradiction or logical absurdity, it is necessary physically, that is, determined in such a way that its contrary would imply imperfection or moral absurdity. | |
| From: Gottfried Leibniz (On the Ultimate Origination of Things [1697], p.139) | |
| A reaction: How does Leibniz know things like this? The distinction between 'metaphysical' necessity and 'natural' (what he calls 'physical') necessity is a key idea. But natural necessity is controversial. See 'Essentialism'. |
| 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. |
| 19343 | We follow the practical rule which always seeks maximum effect for minimum cost [Leibniz] |
| Full Idea: In practical affairs one always follows the decision rule in accordance with which one ought to seek the maximum or the minimum: namely, one prefers the maximum effect at the minimum cost, so to speak. | |
| From: Gottfried Leibniz (On the Ultimate Origination of Things [1697], p.150) | |
| A reaction: Animals probably do that too, and even water sort of obeys the rule when it runs downhill. |
| 19429 | The principle of determination in things obtains the greatest effect with the least effort [Leibniz] |
| Full Idea: There is always in things a principle of determination which is based on consideration of maximum and minimum, such that the greatest effect is obtained with the least, so to speak, expenditure. | |
| From: Gottfried Leibniz (On the Ultimate Origination of Things [1697], p.347) | |
| A reaction: This is obvious in human endeavours. Leibniz applied it to physics, producing a principle that shortest paths are always employed. It has a different formal name in modern physics, I think. He says if you make an unrestricted triangle, it is equilateral. |
| 15877 | The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré] |
| Full Idea: In Poincaré's view, we try to construct a language within which the brute facts of experience are expressed as comprehensively and as elegantly as possible. The job of science is the forging of a language precisely suited to that purpose. | |
| From: report of Henri Poincaré (The Value of Science [1906], Pt III) by Rom Harré - Laws of Nature 2 | |
| A reaction: I'm often struck by how obscure and difficult our accounts of self-evident facts can be. Chairs are easy, and the metaphysics of chairs is hideous. Why is that? I'm a robust realist, but I like Poincaré's idea. He permits facts. |