Combining Texts

All the ideas for 'Dthat', 'Remarks on the definition and nature of mathematics' and 'Geometrical Method and Metaphysics'

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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')

14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations

19398	Minds are best explained by their ends, and bodies by efficient causes [Leibniz]
	Full Idea: Whatever concerns reasonable substances (the minds of men) is more naturally explained by the consideration of ends, whereas other substances (bodies) are better explained by efficient causes.
	From: Gottfried Leibniz (Geometrical Method and Metaphysics [1712], p.89)
	A reaction: That is, I take it, that the type of causal explanation considered most appropriate is the one that leads to the greatest understanding. So there is no absolute or correct answer as to which type of causation is the more important.

19. Language / B. Reference / 3. Direct Reference / b. Causal reference

14080	Are causal descriptions part of the causal theory of reference, or are they just metasemantic? [Kaplan, by Schaffer,J]
	Full Idea: Kaplan notes that the causal theory of reference can be understood in two quite different ways, as part of the semantics (involving descriptions of causal processes), or as metasemantics, explaining why a term has the referent it does.
	From: report of David Kaplan (Dthat [1970]) by Jonathan Schaffer - Deflationary Metaontology of Thomasson 1
	A reaction: [Kaplan 'Afterthought' 1989] The theory tends to be labelled as 'direct' rather than as 'causal' these days, but causal chains are still at the heart of the story (even if more diffused socially). Nice question. Kaplan takes the meta- version as orthodox.