8 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. |
| 18239 | What is contemplated must have a higher value than contemplation [Kant, by Korsgaard] |
| Full Idea: Kant objects that the world must have a final purpose in order to be worth contemplating, so contemplation cannot be that final purpose. | |
| From: report of Immanuel Kant (Critique of Judgement II: Teleological [1790]) by Christine M. Korsgaard - Aristotle and Kant on the Source of Value 8 'Arist and' | |
| A reaction: That is a very good objection. If we contemplate the ordered heavens, the ordering of the heavens seems to have a greater value than our contemplation of them. The reply is that the contemplation is the final purpose being contemplated! |
| 18238 | Only a good will can give man's being, and hence the world, a final purpose [Kant] |
| Full Idea: A good will is that whereby alone [man's] being can have an absolute worth and in reference to which the being of the world can have a final purpose. | |
| From: Immanuel Kant (Critique of Judgement II: Teleological [1790], C3 443), quoted by Christine M. Korsgaard - Aristotle and Kant on the Source of Value 8 'Kant' | |
| A reaction: I wish Kant gave a better account of what a 'good' will consists of. This is an awful burden to bear when you are making decisions. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 22053 | The Critique of Judgement aims for a principle that unities humanity and nature [Kant, by Bowie] |
| Full Idea: The Critique of Judgement aims to show how judgement functions 'according to the principle of the appropriateness of nature to our capacity for cognition'. It is meant to provide a principle of the unity of humankind and nature. | |
| From: report of Immanuel Kant (Critique of Judgement II: Teleological [1790]) by Andrew Bowie - German Philosophy: a very short introduction 1 | |
| A reaction: Hence this work is often overlooked as a key part of Kant's 'system'. At first he probably didn't realise he was creating a system. Kant set an agenda for the philosophy of the ensuing thirty years. |
| 18237 | Without men creation would be in vain, and without final purpose [Kant] |
| Full Idea: Without men the whole creation would be mere waste, in vain, and without final purpose. | |
| From: Immanuel Kant (Critique of Judgement II: Teleological [1790], C3 442), quoted by Christine M. Korsgaard - Aristotle and Kant on the Source of Value 8 'Kant' | |
| A reaction: The standard early twenty-first century response to that is 'get over it'! The remark shows how deep religion runs in Kant, despite his great caution about the existence of God. His notion of 'duty' is similarly religious. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |