Combining Texts

All the ideas for 'works', 'Building Blocks of Mathematical Logic' and 'Model Theory'

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11 ideas

1. Philosophy / G. Scientific Philosophy / 1. Aims of Science

6782	Realism is the only philosophy of science that doesn't make the success of science a miracle [Putnam]

2. Reason / D. Definition / 7. Contextual Definition

10476

The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]

5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic

10478

Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]

5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=

10477

|= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]

5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic

17699

Variables are auxiliary notions, and not part of the 'eternal' essence of logic [Schönfinkel]

5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction

10474

|= should be read as 'is a model for' or 'satisfies' [Hodges,W]

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models

10473

Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]

10475

A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]

10481

Models in model theory are structures, not sets of descriptions [Hodges,W]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

10480

First-order logic can't discriminate between one infinite cardinal and another [Hodges,W]

7. Existence / D. Theories of Reality / 4. Anti-realism

22181

Putnam says anti-realism is a bad explanation of accurate predictions [Putnam, by Okasha]