Combining Texts

All the ideas for 'Posthumous notes', 'Frege's Distinction of Sense and Reference' and 'Model Theory'

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11 ideas

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 / F. Referring in Logic / 1. Naming / b. Names as descriptive

9182	Ancient names like 'Obadiah' depend on tradition, not on where the name originated [Dummett]

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]

11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism

21971

Transcendental philosophy is the subject becoming the originator of unified reality [Kant]

19. Language / B. Reference / 3. Direct Reference / b. Causal reference

9181	The causal theory of reference can't distinguish just hearing a name from knowing its use [Dummett]