Combining Texts

All the ideas for 'works (all lost)', 'works' and 'Model Theory'

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19 ideas

1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
21489 Super-ordinate disciplines give laws or principles; subordinate disciplines give concrete cases [Peirce, by Atkin]
2. Reason / D. Definition / 7. Contextual Definition
10476 The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
19095 Pragmatic 'truth' is a term to cover the many varied aims of enquiry [Peirce, by Misak]
19097 Peirce did not think a belief was true if it was useful [Peirce, by Misak]
21494 If truth is the end of enquiry, what if it never ends, or ends prematurely? [Atkin on Peirce]
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 / C. Ontology of Logic / 3. If-Thenism
21493 Pure mathematics deals only with hypotheses, of which the reality does not matter [Peirce]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
19102 Bivalence is a regulative assumption of enquiry - not a law of logic [Peirce, by Misak]
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 / 3. Reality
10352 The real is the idea in which the community ultimately settles down [Peirce]
8. Modes of Existence / A. Relations / 1. Nature of Relations
13498 Peirce and others began the mapping out of relations [Peirce, by Hart,WD]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / d. Dispositions as occurrent
21491 Peirce's later realism about possibilities and generalities went beyond logical positivism [Peirce, by Atkin]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
16376 The possible can only be general, and the force of actuality is needed to produce a particular [Peirce]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
19107 Inquiry is not standing on bedrock facts, but standing in hope on a shifting bog [Peirce]