9 ideas
| 13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
| Full Idea: The difficulties historically attributed to the axiom of choice are probably better ascribed to the law of excluded middle. | |
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2) | |
| A reaction: The law of excluded middle was a target for the intuitionists, so presumably the debate went off in that direction. |
| 13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |
| Full Idea: The finitist may have no conception of function, because functions are transfinite objects. | |
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §4) | |
| A reaction: He is offering a view of Tait's. Above my pay scale, but it sounds like a powerful objection to the finitist view. Maybe there is a finitist account of functions that could be given? |
| 13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
| Full Idea: If experience shows that some aspect of the physical world fails to instantiate a certain mathematical structure, one will modify the theory by sustituting a different structure, while the original structure doesn't lose its status as part of mathematics. | |
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2) | |
| A reaction: This seems to be a beautifully simple and powerful objection to the Quinean idea that mathematics somehow only gets its authority from physics. It looked like a daft view to begin with, of course. |
| 1554 | Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind] |
| Full Idea: Prodicus insists that contradiction is impossible, since if two people are contradicting each other, they cannot both be speaking of the same fact. Only the one who is speaking the truth is speaking of facts as they are; the other does not speak facts. | |
| From: report of Prodicus (fragments/reports [c.423 BCE]) by Didymus the Blind - Commentary on Ecclesiastes (frags) | |
| A reaction: cf. Kant's 100 thalers example |
| 21051 | Check your rationality by thinking of your opinion pronounced by the supreme court [Rawls] |
| Full Idea: To check whether we are following public reason we might ask: how would our argument strike us presented in the form of a supreme court opinion? | |
| From: John Rawls (Political Liberalism [1993], p.254), quoted by Michael J. Sandel - Justice: What's the right thing to do? 10 | |
| A reaction: A very nice practical implementation of Kantian universalisability. How would your opinion sound if it were written into a constitution? |
| 21119 | Power is only legitimate if it is reasonable for free equal citizens to endorse the constitution [Rawls] |
| Full Idea: Exercise of political power is fully proper only when it is exercised in accordance with a constitution the essentials of which all citizens as free and equal may reasonably be expected to endorse in light of principles and ideals acceptable to reason. | |
| From: John Rawls (Political Liberalism [1993], p.217), quoted by Andrew Shorten - Contemporary Political Theory 02 | |
| A reaction: This is not the actual endorsement of Rousseau, or the tacit endorsement of Locke (by living there), but adds a Kantian appeal to a rational consensus, on which rational people should converge. Very Enlightenment. 'Hypothetical consent'. |
| 1555 | People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus] |
| Full Idea: In the old days people regarded the sun, the moon, rivers, springs, and everything else which is helpful for life as gods, because we are helped by them, just as the Egyptians regard the Nile as a god. | |
| From: Prodicus (fragments/reports [c.423 BCE], B05), quoted by Sextus Empiricus - Against the Professors (six books) 9.18 |
| 1543 | He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus] |
| Full Idea: He says that the gods worshipped by men neither exist nor have knowledge, but that the ancients exalted crops and everything else which is useful for life. | |
| From: Prodicus (fragments/reports [c.423 BCE]), quoted by Anon (Herc) - fragments 1428 19.12 |
| 535 | The gods are just personified human benefits [Prodicus] |
| Full Idea: Things from which benefits to human life have been derived have come to be considered deities, such as Demeter and Dionysus. | |
| From: Prodicus (fragments/reports [c.423 BCE], B5), quoted by (who?) - where? |