Combining Texts

All the ideas for 'fragments/reports', 'The Foundations of Mathematics' and 'Infinitism solution to regress problem'

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14 ideas

2. Reason / A. Nature of Reason / 6. Coherence
Why should we prefer coherent beliefs? [Klein,P]
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 / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
Infinitism avoids a regress, circularity or arbitrariness, by saying warrant just increases [Klein,P]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / e. Pro-foundations
If justification is endless, no link in the chain is ultimately justified [Ginet on Klein,P]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
Reasons acquire warrant through being part of a lengthening series [Klein,P]
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]
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]