Combining Texts

All the ideas for 'works (fragments)', 'Model Theory' and 'Investigations into Logical Deduction'

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15 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason

1813	All reasoning endlessly leads to further reasoning (Mode 12) [Agrippa, by Diog. Laertius]

1811	Proofs often presuppose the thing to be proved (Mode 15) [Agrippa, by Diog. Laertius]

1815	Reasoning needs arbitrary faith in preliminary hypotheses (Mode 14) [Agrippa, by Diog. Laertius]

1812	All discussion is full of uncertainty and contradiction (Mode 11) [Agrippa, by Diog. Laertius]

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 / H. Proof Systems / 4. Natural Deduction

13832

Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking]

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]

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma

8850	Agrippa's Trilemma: justification is infinite, or ends arbitrarily, or is circular [Agrippa, by Williams,M]

13. Knowledge Criteria / E. Relativism / 1. Relativism

1814	Everything is perceived in relation to another thing (Mode 13) [Agrippa, by Diog. Laertius]