Combining Texts

All the ideas for 'Saundaranandakavya', 'Remarks on the definition and nature of mathematics' and 'Remarks on the Foundations of Mathematics'

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

---

8 ideas

1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy

7910	Pursue truth with the urgency of someone whose clothes are on fire [Ashvaghosha]
	Full Idea: As though your turban or your clothes were on fire, so with a sense of urgency should you apply your intellect to the comprehension of the truths.
	From: Ashvaghosha (Saundaranandakavya [c.50], XVI)
	A reaction: The best philosophers need no such urging. I retain a romantic view that we should be 'natural' in these things. See Plato's views in Idea 2153 and 1638. However, maybe I should be confronted with this quotation every morning when I awake.

3. Truth / H. Deflationary Truth / 1. Redundant Truth

11074	'It is true that this follows' means simply: this follows [Wittgenstein]
	Full Idea: The proposition: "It is true that this follows from that" means simply: this follows from that.
	From: Ludwig Wittgenstein (Remarks on the Foundations of Mathematics [1938], p.38), quoted by Robert Hanna - Rationality and Logic 6
	A reaction: Presumably this remark is simply expressing Wittgenstein's later agreement with the well-known view of Ramsey. Early Wittgenstein had endorsed a correspondence view of truth.

5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic

17807	To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
	Full Idea: In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command.
	From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist')
	A reaction: This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism.

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

17806	It is untenable that mathematics is general physical truths, because it needs infinity [Curry]
	Full Idea: According to realism, mathematical propositions express the most general properties of our physical environment. This is the primitive view of mathematics, yet on account of the essential role played by infinity in mathematics, it is untenable today.
	From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The problem')
	A reaction: I resist this view, because Curry's view seems to imply a mad metaphysics. Hilbert resisted the role of the infinite in essential mathematics. If the physical world includes its possibilities, that might do the job. Hellman on structuralism?

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

11073	Two and one making three has the necessity of logical inference [Wittgenstein]
	Full Idea: "But doesn't it follow with logical necessity that you get two when you add one to one, and three when you add one to two? and isn't this inexorability the same as that of logical inference? - Yes! it is the same.
	From: Ludwig Wittgenstein (Remarks on the Foundations of Mathematics [1938], p.38), quoted by Robert Hanna - Rationality and Logic 6
	A reaction: This need not be a full commitment to logicism - only to the fact that the inferential procedures in mathematics are the same as those of logic. Mathematics could still have further non-logical ingredients. Indeed, I think it probably does.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

17808	Saying mathematics is logic is merely replacing one undefined term by another [Curry]
	Full Idea: To say that mathematics is logic is merely to replace one undefined term by another.
	From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'Mathematics')

29. Religion / C. Spiritual Disciplines / 3. Buddhism

7909	The Eightfold Path concerns morality, wisdom, and tranquillity [Ashvaghosha]
	Full Idea: The Eightfold Path has three steps concerning morality - right speech, right bodily action, and right livelihood; three of wisdom - right views, right intentions, and right effort; and two of tranquillity - right mindfulness and right concentration.
	From: Ashvaghosha (Saundaranandakavya [c.50], XVI)
	A reaction: Most of this translates quite comfortably into the aspirations of western philosophy. For example, 'right effort' sounds like Kant's claim that only a good will is truly good (Idea 3710). The Buddhist division is interesting for action theory.

29. Religion / D. Religious Issues / 2. Immortality / d. Heaven

7908	At the end of a saint, he is not located in space, but just ceases to be disturbed [Ashvaghosha]
	Full Idea: When an accomplished saint comes to the end, he does not go anywhere down in the earth or up in the sky, nor into any of the directions of space, but because his defilements have become extinct he simply ceases to be disturbed.
	From: Ashvaghosha (Saundaranandakavya [c.50], XVI)
	A reaction: To 'cease to be disturbed' is the most attractive account of heaven I have encountered. It all sounds a bit dull though. I wonder, as usual, how they know all this stuff.