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

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5 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
7791 The simplest of the logics based on possible worlds is Lewis's S5 [Lewis,CI, by Girle]
     Full Idea: C.I.Lewis constructed five axiomatic systems of modal logic, and named them S1 to S5. It turns out that the simplest of the logics based on possible worlds is the same as Lewis's S5.
     From: report of C.I. Lewis (works [1935]) by Rod Girle - Modal Logics and Philosophy 2.1
     A reaction: Nathan Salmon ('Reference and Essence' 2nd ed) claims (on p.xvii) that "the correct modal logic is weaker than S5 and weaker even than S4". Which is the greater virtue, simplicity or weakness?
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
18844 You would cripple mathematics if you denied Excluded Middle [Hilbert]
     Full Idea: Taking the principle of Excluded Middle away from the mathematician would be the same, say, as prohibiting the astronomer from using the telescope or the boxer from using his fists.
     From: David Hilbert (The Foundations of Mathematics [1927], p.476), quoted by Ian Rumfitt - The Boundary Stones of Thought 9.4
     A reaction: [p.476 in Van Heijenoort]
10. Modality / A. Necessity / 2. Nature of Necessity
11002 Equating necessity with informal provability is the S4 conception of necessity [Lewis,CI, by Read]
     Full Idea: C.I.Lewis's S4 system develops a sense of necessity as 'provability' in some fairly informal sense.
     From: report of C.I. Lewis (works [1935]) by Stephen Read - Thinking About Logic Ch. 4
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.