display all the ideas for this combination of philosophers
3 ideas
| 6409 | The 'simple theory of types' distinguishes levels among properties [Ramsey, by Grayling] |
| Full Idea: The idea that there should be something like a distinction of levels among properties is captured in Ramsey's 'simple theory of types'. | |
| From: report of Frank P. Ramsey (works [1928]) by A.C. Grayling - Russell | |
| A reaction: I merely report this, though it is not immediately obvious how anyone would decide which 'level' a type belonged on. |
| 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. |