Combining Texts

All the ideas for 'Dthat', 'Remarks on the definition and nature of mathematics' and 'The Scope and Language of Science'

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7 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 / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
8463 Maths can be reduced to logic and set theory [Quine]
     Full Idea: Researches in the foundations of mathematics have made it clear that all of (interpreted) mathematics can be got down to logic and set theory, and the objects needed for mathematics can be got down to the category of classes (and classes of classes..).
     From: Willard Quine (The Scope and Language of Science [1954], §VI)
     A reaction: This I take to be a retreat from pure logicism, presumably influenced by Gödel. So can set theory be reduced to logic? Crispin Wright is the one the study.
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 / B. Properties / 1. Nature of Properties
8461 The category of objects incorporates the old distinction of substances and their modes [Quine]
     Full Idea: The category of objects embraces indiscriminately what would anciently have been distinguished as substances and as modes or states of substances.
     From: Willard Quine (The Scope and Language of Science [1954], §6)
     A reaction: This nicely captures Quine's elimination of properties, by presenting them as inseparable from their objects/substances. Armstrong calls this 'Ostrich Nominalism' (for refusing to address the universals problem) but Quineans are unshaken.
17. Mind and Body / E. Mind as Physical / 6. Conceptual Dualism
8462 A hallucination can, like an ague, be identified with its host; the ontology is physical, the idiom mental [Quine]
     Full Idea: A physical ontology has a place for states of mind. An inspiration or a hallucination can, like the fit of ague, be identified with its host for the duration. It leaves our mentalistic idioms fairly intact, but reconciles them with a physical ontology.
     From: Willard Quine (The Scope and Language of Science [1954], §VI)
     A reaction: Quine is employing the same strategy that he uses for substances and properties (Idea 8461): take the predication as basic, rather than reifying the thing being predicated. The ague analogy suggests that Quine is an incipient functionalist.
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.