Ideas of Frank P. Ramsey, by Theme

[British, 1903 - 1930, Cambridge University. Exceptional philosopher who died very young]

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3. Truth / H. Deflationary Truth / 1. Redundant Truth
"It is true that x" means no more than x
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: there is an infinity of distinguishable individuals
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
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
5. Theory of Logic / L. Paradox / 1. Paradox
Contradictions are either purely logical or mathematical, or they involved thought and language
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
The 'simple theory of types' distinguishes levels among properties
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Formalists neglect content, but the logicists have focused on generalizations, and neglected form
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism is hopeless, because it focuses on propositions and ignores concepts
8. Modes of Existence / D. Universals / 1. Universals
The distinction between particulars and universals is a mistake made because of language
We could make universals collections of particulars, or particulars collections of their qualities
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Obviously 'Socrates is wise' and 'Socrates has wisdom' express the same fact
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
Ramsey's Test: believe the consequent if you believe the antecedent
'If' is the same as 'given that', so the degrees of belief should conform to probability theory
10. Modality / B. Possibility / 8. Conditionals / e. Supposition conditionals
Asking 'If p, will q?' when p is uncertain, then first add p hypothetically to your knowledge
11. Knowledge Aims / A. Knowledge / 3. Belief / c. Aim of beliefs
Beliefs are maps by which we steer
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Belief is knowledge if it is true, certain, and obtained by a reliable process
14. Science / C. Induction / 6. Bayes's Theorem
Ramsey gave axioms for an uncertain agent to decide their preferences
19. Language / B. Meaning / 7. Meaning by Role
Sentence meaning is given by the actions to which it would lead
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
Causal laws result from the simplest axioms of a complete deductive system
All knowledge needs systematizing, and the axioms would be the laws of nature