16 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. |
| 3654 | The pineal gland links soul to body, and unites the two symmetrical sides of the body [Descartes, by PG] |
| Full Idea: The soul is united with the body in just one place, a gland (the pineal) in the centre of the brain. It is placed so that its slightest movement will affect the passions, and it plays the essential role of uniting the two symmetrical sides of the body. | |
| From: report of René Descartes (The Passions of the Soul [1649], §31) by PG - Db (ideas) | |
| A reaction: See Idea 4862 for Spinoza's nice response to Descartes' proposal. If Descartes had followed brain research for the last four hundred years, at what point would he have wavered? If every single part of the brain seems to 'interact', dualism looks unlikely. |
| 23221 | The brain, and all the mental events within it, consists entirely of sensitive and rational matter [Cavendish] |
| Full Idea: Sensitive and rational matter …makes not only the Brain, but all Thoughts, Conceptions, Imaginations, Fancy, Understanding, Memory, Remembrance, and whatsoever motions are in the Head or Brain. | |
| From: Margaret Cavendish (Philosophical Letters [1664], p.185), quoted by Matthew Cobb - The Idea of the Brain 2 | |
| A reaction: Judging by the date of this, and that she is a Cavendish, the influence of Hobbes must be strong, which was brave in 1664. A very strong statement of reductive physicalism, making sure that nothing is left out. |
| 4015 | For Descartes passions are God-given preservers of the mind-body union [Descartes, by Taylor,C] |
| Full Idea: Descartes sees passions not as opinions, but as functional devices that the Creator has designed for us to help preserve the body-soul substantial union. | |
| From: report of René Descartes (The Passions of the Soul [1649]) by Charles Taylor - Sources of the Self §8 | |
| A reaction: I wonder what Descartes would have made of the theory of evolution? |
| 4313 | Are there a few primary passions (say, joy, sadness and desire)? [Descartes, by Cottingham] |
| Full Idea: Descartes says there are six primary passions (wonder, love, hatred, desire, joy and sadness); Spinoza says there are just three (joy, sadness and desire). | |
| From: report of René Descartes (The Passions of the Soul [1649]) by John Cottingham - The Rationalists p.172 | |
| A reaction: A dubious project. However, it is now agreed that there are a few (six?) basic universal facial expressions, to which these passions may correspond. |
| 23989 | There are six primitive passions: wonder, love, hatred, desire, joy and sadness [Descartes, by Goldie] |
| Full Idea: Descartes said there are six primitive passions, namely wonder, love, hatred, desire, joy and sadness. The others are either species of these, or composed of them. | |
| From: report of René Descartes (The Passions of the Soul [1649], 353) by Peter Goldie - The Emotions 4 'Evidence' | |
| A reaction: [not sure about ref] It's a nice touch to add 'wonder', which doesn't make it onto anyone else's list. |
| 20037 | Merely willing to walk leads to our walking [Descartes] |
| Full Idea: Our merely willing to walk has the consequence that our legs move and we walk. | |
| From: René Descartes (The Passions of the Soul [1649], 18), quoted by Rowland Stout - Action 1 'Volitionism' | |
| A reaction: Stout attributes this to Descartes' dualism, as if legs are separate from persons. Stout says the idea of a prior mental act is not usually now considered as part of an action, or even to exist at all. If the volition is intentional, there is a regress. |
| 16763 | We don't die because the soul departs; the soul departs because the organs cease functioning [Descartes] |
| Full Idea: We ought to hold, on the contrary, that the soul takes its leave when we die only because this heat ceases and the organs that bring about bodily movement decay. | |
| From: René Descartes (The Passions of the Soul [1649], I.5), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 24.5 | |
| A reaction: This sounds like a pretty major change in our concept of death, given that we all now agree with Descartes. |
| 4016 | Descartes makes strength of will the central virtue [Descartes, by Taylor,C] |
| Full Idea: Descartes makes strength of will the central virtue. | |
| From: report of René Descartes (The Passions of the Soul [1649]) by Charles Taylor - Sources of the Self §8 | |
| A reaction: Presumably strength of will can serve evil ends, so this is a bit confusing. |