5 ideas
| 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. |
| 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? |
| 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') |
| 8130 | Qualities of experience are just representational aspects of experience ('Representationalism') [Harman, by Burge] |
| Full Idea: Harman defended what came to be known as 'representationalism' - the view that qualitative aspects of experience are nothing other than representational aspects. | |
| From: report of Gilbert Harman (The Intrinsic Quality of Experience [1990]) by Tyler Burge - Philosophy of Mind: 1950-2000 p.459 | |
| A reaction: Functionalists like Harman have a fairly intractable problem with the qualities of experience, and this may be clutching at straws. What does 'represent' mean? How is the representation achieved? Why that particular quale? |
| 11127 | If concepts just are mental representations, what of concepts we may never acquire? [Peacocke] |
| Full Idea: We might say that the concept just is the mental representation, ...but there are concepts that human beings may never acquire. ...But if concepts are individuated by their possession conditions this will not be a problem. | |
| From: Christopher Peacocke (Rationale and Maxims in Study of Concepts [2005], p.169), quoted by E Margolis/S Laurence - Concepts 1.3 | |
| A reaction: I'm not sure that I understand the notion of a concept we (or any other creature) may never acquire. They no more seem to exist than buildings that were never even designed. |