Combining Philosophers

All the ideas for Anaxarchus, Richard Jeffrey and Alonzo Church

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4 ideas

5. Theory of Logic / K. Features of Logics / 7. Decidability
18758 Validity is provable, but invalidity isn't, because the model is infinite [Church, by McGee]
     Full Idea: Church showed that logic has a proof procedure, but no decision procedure. If an argument is invalid, there is a model with true premises and false conclusion, but the model will typically be infinite, so there is no way to display it concretely.
     From: report of Alonzo Church (A Note on the entscheidungsproblem [1936]) by Vann McGee - Logical Consequence 5
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / b. Worlds as fictions
16285 A possible world can be seen as a complete and consistent novel [Jeffrey]
     Full Idea: A novel describes a possible world in as much detail as is possible without exceeding the resources of the agent's language. But if talk of possible worlds seems dangerously metaphysical, focus on the novels themselves, when complete and consistent.
     From: Richard Jeffrey (The Logic of Decision [1965], 12.8), quoted by David Lewis - On the Plurality of Worlds
     A reaction: Lewis seems to cite this remark from Jeffrey as the source of the idea that ersatz linguistic worlds are like novels. Why won't a novel with one tiny inconsistency count as a possible world? People seem to live in it.
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
3061 Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
     Full Idea: Anaxarchus said that he was not even sure that he knew nothing.
     From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1
14. Science / C. Induction / 6. Bayes's Theorem
19155 Instead of gambling, Jeffrey made the objects of Bayesian preference to be propositions [Jeffrey, by Davidson]
     Full Idea: Jeffrey produced a version of Bayesianism that made no direct use of gambling (as Ramsey had), but treats the objects of preference ...as propositions.
     From: report of Richard Jeffrey (The Logic of Decision [1965]) by Donald Davidson - Truth and Predication 3
     A reaction: I'm guessing that Jeffreys launched modern Bayesian theory with this idea. It suggest that one can consider degrees of truth, rather than mere winning or losing.