Combining Texts

All the ideas for 'Remarks on the definition and nature of mathematics', 'Adverbial Theory' and 'Wittgenstein'

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

---

5 ideas

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 / 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')

12. Knowledge Sources / B. Perception / 4. Sense Data / b. Nature of sense-data

2713	Are sense-data independent, with identity, substance and location? [Tye]
	Full Idea: Can sense-data exist unsensed? Can two persons experience numerically identical sense-data? Do sense-data have surfaces which are not sensed? What are sense-data made of? Are they located?
	From: Michael Tye (Adverbial Theory [1995], p.7)

15. Nature of Minds / A. Nature of Mind / 4. Other Minds / d. Other minds by analogy

7091	The argument from analogy is not a strong inference, since the other being might be an actor or a robot [Grayling]
	Full Idea: The argument from analogy is a weak one, because it does not logically guarantee the inference I draw to the other's inner states, for he might be dissimulating or acting, or may even be a cleverly contrived robot which feels nothing.
	From: A.C. Grayling (Wittgenstein [1988], Ch.3)
	A reaction: This gives the impression that for an argument to be strong it must logically guarantee its inference. It strikes me that analogy is a good reason for believing in other minds, but that is because I am looking for the best explanation, not logical proof.