Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'Pragmatism in Retrospect' and 'Model Theory'

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15 ideas

2. Reason / D. Definition / 2. Aims of Definition
Definitions concern how we should speak, not how things are [Fine,K]
2. Reason / D. Definition / 7. Contextual Definition
The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
Peirce's theory offers anti-realist verificationism, but surely how things are is independent of us? [Horsten on Peirce]
Independent truth (if there is any) is the ultimate result of sufficient enquiry [Peirce]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
|= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
|= should be read as 'is a model for' or 'satisfies' [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
Models in model theory are structures, not sets of descriptions [Hodges,W]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
First-order logic can't discriminate between one infinite cardinal and another [Hodges,W]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
12. Knowledge Sources / D. Empiricism / 3. Pragmatism
Pragmatism is a way of establishing meanings, not a theory of metaphysics or a set of truths [Peirce]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]