Combining Texts

All the ideas for 'fragments/reports', 'On Euclidean Geometry' and 'Truth and Probability'

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5 ideas

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
16886 The truth of an axiom must be independently recognisable [Frege]
     Full Idea: It is part of the concept of an axiom that it can be recognised as true independently of other truths.
     From: Gottlob Frege (On Euclidean Geometry [1900], 183/168), quoted by Tyler Burge - Frege on Knowing the Foundations 4
     A reaction: Frege thinks the axioms of arithmetic all reside in logic.
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
13766 'If' is the same as 'given that', so the degrees of belief should conform to probability theory [Ramsey, by Ramsey]
     Full Idea: Ramsey suggested that 'if', 'given that' and 'on the supposition that' come to the same thing, and that the degrees of belief in the antecedent should then conform to probability theory.
     From: report of Frank P. Ramsey (Truth and Probability [1926]) by Frank P. Ramsey - Law and Causality B
     A reaction: [compressed]
14. Science / C. Induction / 6. Bayes's Theorem
19143 Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson]
     Full Idea: Ramsey gave an axiomatic treatment of preference in the face of uncertainty, when applied to a particular agent.
     From: report of Frank P. Ramsey (Truth and Probability [1926]) by Donald Davidson - Truth and Predication 2
     A reaction: This is evidently the beginnings of Bayesian decision theory.
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
     Full Idea: Archelaus was the first person to say that the universe is boundless.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]
     Full Idea: Archelaus wrote that life on Earth began in a primeval slime.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus
     A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea.