Combining Texts

All the ideas for 'fragments/reports', 'Explanatory Coherence' and 'The Foundations of Mathematics'

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16 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: there is an infinity of distinguishable individuals [Ramsey]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey]
5. Theory of Logic / L. Paradox / 1. Paradox
Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
I just confront the evidence, and let it act on me [Ramsey]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey]
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
1: Coherence is a symmetrical relation between two propositions [Thagard, by Smart]
2: An explanation must wholly cohere internally, and with the new fact [Thagard, by Smart]
3: If an analogous pair explain another analogous pair, then they all cohere [Thagard, by Smart]
4: For coherence, observation reports have a degree of intrinsic acceptability [Thagard, by Smart]
5: Contradictory propositions incohere [Thagard, by Smart]
6: A proposition's acceptability depends on its coherence with a system [Thagard, by Smart]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]