5 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. |
7765 | The use of a sentence is its commitments and entitlements [Brandom, by Lycan] |
Full Idea: Brandom develops a particular conception of 'use', according to which a sentence's use is the set of commitments and entitlements associated with public utterance of that sentence. | |
From: report of Robert B. Brandom (Articulating Reasons: Intro to Inferentialism [2000]) by William Lycan - Philosophy of Language Ch.6 | |
A reaction: It immediately strikes me that a sentence could only have commitments and entitlements if it already had a meaning. However, the case of money shows how there might be nothing more to a thing's significance than its entitlements. |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |