Combining Texts

All the ideas for 'Noneism or Allism?', 'works' and 'First-Order Logic'

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23 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]
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 / 1. Overview of Logic
10282 Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [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 / G. Quantification / 4. Substitutional Quantification
15533 We can quantify over fictions by quantifying for real over their names [Lewis]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
15534 We could quantify over impossible objects - as bundles of properties [Lewis]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10283 A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]
10284 There are three different standard presentations of semantics [Hodges,W]
10285 I |= φ means that the formula φ is true in the interpretation I [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
5. Theory of Logic / K. Features of Logics / 6. Compactness
10287 If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10286 A 'set' is a mathematically well-behaved class [Hodges,W]
7. Existence / A. Nature of Existence / 1. Nature of Existence
15532 'Allists' embrace the existence of all controversial entities; 'noneists' reject all but the obvious ones [Lewis]
7. Existence / A. Nature of Existence / 2. Types of Existence
15535 We can't accept a use of 'existence' that says only some of the things there are actually exist [Lewis]
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]