Combining Texts

All the ideas for 'Letter to Hutcheson 1739', 'Mathematical Thought from Ancient to Modern Times' and 'The Foundations of Mathematics'

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13 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 / K. Features of Logics / 1. Axiomatisation
Axioms reveal the underlying assumptions, and reveal relationships between different areas [Kline]
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]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
Virtues and vices are like secondary qualities in perception, found in observers, not objects [Hume]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
All virtues benefit either the public, or the individual who possesses them [Hume]
26. Natural Theory / C. Causation / 3. Final causes
The idea of a final cause is very uncertain and unphilosophical [Hume]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
That events could be uncaused is absurd; I only say intuition and demonstration don't show this [Hume]