Combining Texts

All the ideas for 'On Motion', 'Pragmatism and Objective Truth' and 'Mathematics: Form and Function'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

6 ideas

3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth

19086	Does the pragmatic theory of meaning support objective truth, or make it impossible? [Macbeth]
	Full Idea: Peirce and Sellars takes Peirce's conception of meaning, on which pragmatism is founded, to support an adequate account of objective truth; James, Dewey and Rorty say it forecloses all possibility of such an account.
	From: Danielle Macbeth (Pragmatism and Objective Truth [2007], p.169)
	A reaction: Ah. Very helpful. I thought there was a pragmatic theory of truth, then began to think that it was just a denial of truth. I've long suspected that Peirce is wonderful, and James is not very good (on this topic).

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

18189	ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]
	Full Idea: We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC.
	From: Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics
	A reaction: Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30).

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic

19093	Greek mathematics is wholly sensory, where ours is wholly inferential [Macbeth]
	Full Idea: Ancient mathematical concepts were essentially sensory; they were not mathematical in our sense - that is, wholly constituted by their inferential potential.
	From: Danielle Macbeth (Pragmatism and Objective Truth [2007], p.187)
	A reaction: The latter view is Frege's, though I suppose it had been emerging for a couple of centuries before him. I like the Greek approach, and would love to see that reunited with the supposedly quite different modern view. (Keith Hossack is attempting it).

14. Science / B. Scientific Theories / 1. Scientific Theory

19091	Seeing reality mathematically makes it an object of thought, not of experience [Macbeth]
	Full Idea: As mathematically understood, the world is not an object of experience but instead an object of thought.
	From: Danielle Macbeth (Pragmatism and Objective Truth [2007], p.183)
	A reaction: Since I am keen on citing biology to show that science does not have to be mathematical, this nicely shows that there is something wrong with a science which places a large gap between itself and the world.

18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts

19088	For pragmatists a concept means its consequences [Macbeth]
	Full Idea: In the pragmatist view, the meaning of a concept is exhausted by its consequences.
	From: Danielle Macbeth (Pragmatism and Objective Truth [2007], p.173)
	A reaction: I'm unclear why the concept of a volcanic eruption only concerns its dire consequences, and is supposed to contain nothing of its causes. Pragmatists seem to be all future, and no past. Very American.

27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity

12709	Motion is not absolute, but consists in relation [Leibniz]
	Full Idea: In reality motion is not something absolute, but consists in relation.
	From: Gottfried Leibniz (On Motion [1677], A6.4.1968), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 3
	A reaction: It is often thought that motion being relative was invented by Einstein, but Leibniz wholeheartedly embraced 'Galilean relativity', and refused to even consider any absolute concept of motion. Acceleration is a bit trickier than velocity.