Combining Texts

All the ideas for 'fragments/reports', 'Believing the Axioms I' and 'works'

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24 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]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
13011 New axioms are being sought, to determine the size of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13014 Extensional sets are clearer, simpler, unique and expressive [Maddy]
13013 The Axiom of Extensionality seems to be analytic [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13021 The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy]
13022 Infinite sets are essential for giving an account of the real numbers [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13023 The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13024 Efforts to prove the Axiom of Choice have failed [Maddy]
13025 Modern views say the Choice set exists, even if it can't be constructed [Maddy]
13026 A large array of theorems depend on the Axiom of Choice [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
13019 The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13018 Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
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]
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]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]