Combining Texts

All the ideas for 'Remarks on the definition and nature of mathematics', 'Model Theory for Modal Logic I' and 'Epiphenomenal Qualia'

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7 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5

9560	S5 provides the correct logic for necessity in the broadly logical sense [Fine,K]
	Full Idea: S5 provides the correct logic for necessity in the broadly logical sense.
	From: Kit Fine (Model Theory for Modal Logic I [1978], 151), quoted by Charles Chihara - A Structural Account of Mathematics
	A reaction: I have no view on this, but I am prejudiced in favour of the idea that there is a correct logic for such things, whichever one it may be. Presumably the fact that S5 has no restrictions on accessibility makes it more comprehensive and 'metaphysical'.

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')

17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / c. Knowledge argument

7880	If a blind persons suddenly sees a kestrel, that doesn't make visual and theoretical kestrels different [Papineau on Jackson]
	Full Idea: An ornithological Mary might know everything theoretical about kestrels, but be blind from birth, then have her sight restored. She now knows "That bird eats mice", so visual kestrels must be ontologically distinct from theoretical ones.
	From: comment on Frank Jackson (Epiphenomenal Qualia [1982]) by David Papineau - Thinking about Consciousness 6.3
	A reaction: A nice reductio, and I think this pinpoints best what is wrong with the knowledge argument. Knowledge, and the means of acquiring it, are two distinct things. When I see x, I don't acquire knowledge of x, AND knowledge of my seeing x.

7378	No one bothers to imagine what it would really be like to have ALL the physical information [Dennett on Jackson]
	Full Idea: That Mary "has all the physical information" is not readily imaginable, so no one bothers. They just imagine she knows lots and lots - perhaps everything known today - but that is just a drop in the bucket.
	From: comment on Frank Jackson (Epiphenomenal Qualia [1982]) by Daniel C. Dennett - Consciousness Explained 12.5
	A reaction: I certainly don't see how we can rule out a priori the possibility that someone who really had all the physical knowledge might be able to infer the phenomenal properties of colour.

7377	Mary learns when she sees colour, so her complete physical information had missed something [Jackson]
	Full Idea: It seems obvious that Mary will learn something about the world when she is released from her black-and-white room; but then it is inescapable that her previous knowledge was incomplete; she had all the physical information, so there is more to have.
	From: Frank Jackson (Epiphenomenal Qualia [1982], §1)
	A reaction: This is Jackson's famous 'knowledge argument', which seems to me misconceived. Since I don't think phenomenal colours are properties of objects (Idea 5456), Mary learns more about herself, and about her means of acquiring knowledge.