Combining Texts

All the ideas for 'The Roots of Reference', 'Empty Names' and 'Remarks on the definition and nature of mathematics'

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9 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.

5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names

18935	Semantic theory should specify when an act of naming is successful [Sawyer]
	Full Idea: A semantic theory of names should deliver a specification of the conditions under which a name names an individual, and hence a specification of the conditions under which a name is empty.
	From: Sarah Sawyer (Empty Names [2012], 1)
	A reaction: Naming can be private, like naming my car 'Bertrand', but never tell anyone. I like Plato's remark that names are 'tools'. Do we specify conditions for successful spanner-usage? The first step must be individuation, preparatory to naming.

5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential

18945	Millians say a name just means its object [Sawyer]
	Full Idea: The Millian view of direct reference says that the meaning of a name is the object named.
	From: Sarah Sawyer (Empty Names [2012], 4)
	A reaction: Any theory that says meaning somehow is features of the physical world strikes me as totally misguided. Napoleon is a man, so he can't be part of a sentence. He delegates that job to words (such as 'Napoleon').

5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names

18934	Sentences with empty names can be understood, be co-referential, and even be true [Sawyer]
	Full Idea: Some empty names sentences can be understood, so appear to be meaningful ('Pegasus was sired by Poseidon'), ...some appear to be co-referential ('Santa Claus'/'Father Christmas'), and some appear to be straightforwardly true ('Pegasus doesn't exist').
	From: Sarah Sawyer (Empty Names [2012], 1)
	A reaction: Hang on to this, when the logicians arrive and start telling you that your talk of empty names is vacuous, because there is no object in the 'domain' to which a predicate can be attached. Meaning, reference and truth are the issues around empty names.

18938	Frege's compositional account of truth-vaues makes 'Pegasus doesn't exist' neither true nor false [Sawyer]
	Full Idea: In Frege's account sentences such as 'Pegasus does not exist' will be neither true nor false, since the truth-value of a sentence is its referent, and the referent of a complex expression is determined by the referent of its parts.
	From: Sarah Sawyer (Empty Names [2012], 2)
	A reaction: We can keep the idea of 'sense', which is very useful for dealing with empty names, but tweak his account of truth-values to evade this problem. I'm thinking that meaning is compositional, but truth-value isn't.

5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions

18947	Definites descriptions don't solve the empty names problem, because the properties may not exist [Sawyer]
	Full Idea: If it were possible for a definite description to be empty - not in the sense of there being no object that satisfies it, but of there being no set of properties it refers to - the problem of empty names would not have been solved.
	From: Sarah Sawyer (Empty Names [2012], 5)
	A reaction: Swoyer is thinking of properties like 'is a unicorn', which are clearly just as vulnerable to being empty as 'the unicorn' was. It seems unlikely that 'horse', 'white' and 'horn' would be empty.

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')

8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived

14296	Dispositions are physical states of mechanism; when known, these replace the old disposition term [Quine]
	Full Idea: Each disposition, in my view, is a physical state or mechanism. ...In some cases nowadays we understand the physical details and set them forth explicitly in terms of the arrangement and interaction of small bodies. This replaces the old disposition.
	From: Willard Quine (The Roots of Reference [1990], p.11), quoted by Stephen Mumford - Dispositions 01.3
	A reaction: A challenge to the dispositions and powers view of nature, one which rests on the 'categorical' structural properties, rather than the 'hypothetical' dispositions. But can we define a mechanism without mentioning its powers?