Combining Texts

All the ideas for 'fragments/reports', 'Review of Tait 'Provenance of Pure Reason'' and 'Proof of an External World'

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5 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

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.

6. Mathematics / C. Sources of Mathematics / 8. Finitism

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?

7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems

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.

11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty

6349	I can prove a hand exists, by holding one up, pointing to it, and saying 'here is one hand' [Moore,GE]
	Full Idea: I can prove now that two human hands exist. How? By holding up my two hands, and saying, as I make a certain gesture with the right hand, 'Here is one hand', and adding, as I gesture with the left, 'and here is another'.
	From: G.E. Moore (Proof of an External World [1939], p.1)
	A reaction: The words need to be spoken, presumably, so that what he is doing fits into the linguistic conventions of what will normally be accepted as a proof. In fact, just holding the hand up seems enough. The proof begs the question of virtual reality.

21. Aesthetics / C. Artistic Issues / 7. Art and Morality

468	Musical performance can reveal a range of virtues [Damon of Ath.]
	Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice.
	From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where?