Combining Texts

All the ideas for 'works', 'Defending the Axioms' and 'works'

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19 ideas

1. Philosophy / A. Wisdom / 2. Wise People
15833 Tell cleverness from answers, but wisdom from questions [Mahfouz]
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 / j. Axiom of Choice IX
17610 The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [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]
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
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 / K. Features of Logics / 1. Axiomatisation
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
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]