4 ideas
15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
Full Idea: Von Neumann's Limitation of Size axiom is not self-evident, and he himself admitted that it seemed too strong. | |
From: comment on John von Neumann (An Axiomatization of Set Theory [1925]) by Shaughan Lavine - Understanding the Infinite VII.1 |
13672 | All the axioms for mathematics presuppose set theory [Neumann] |
Full Idea: There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory. | |
From: John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2 | |
A reaction: Von Neumann was doubting whether set theory could have axioms, and hence the whole project is doomed, and we face relativism about such things. His ally was Skolem in this. |
6649 | Chomsky now says concepts are basically innate, as well as syntax [Chomsky, by Lowe] |
Full Idea: Chomsky now contends that not only the syntax of natural language but also the concepts expressible in it have an innate basis. | |
From: report of Noam Chomsky (Chomsky on himself [1994]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.7 n25 | |
A reaction: This seems to follow Fodor, who has been mocked for implying that we have an innate idea of a screwdriver etc. Note that Chomsky says concepts have an innate 'basis'. This fits well with modern (cautious) rationalism, with which I am happy. |
20716 | False prophets will perform wonders to deceive even the elect [Mark] |
Full Idea: For false messiahs and false prophets will appear and perform signs and wonders to deceive, if possible, even the elect. | |
From: St Mark (02: Gospel of St Mark [c.66], 13:22), quoted by Brian Davies - Introduction to the Philosophy of Religion | |
A reaction: This casts a rather different light on the miracles of Jesus, since they were performed in a context in which even Jesus believed that lots of people (and not just the son of God) could perform miracles. Undermines any Argument from Miracles. |