Friday, May 10, 2019

Closure views of modality

Logical-closure views of modality have this form:

  1. There is a collection C of special truths.

  2. A proposition is necessary if and only if it is provable from C.

For instance, C could be truths directly grounded in the essences of things.

By Goedel Second Incompleteness considerations like those here, we can show that the only way a view of modality like this could work is if C includes at least one truth that provably entails an undecidable statement of arithmetic.

This is not a problem if C includes all mathematical truths, as it does on Sider’s view.

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2 comments:

  1. Cornell AnthonyMay 22, 2019 at 12:00 AM

    A question about modality and modal realism

    Can there be a possible world where modal realism is true and potentialities can have a real causal relationship with actualities?

    ReplyDelete
  2. Alexander R PrussMay 22, 2019 at 8:15 AM

    I doubt it. But it's not a simple question.

    ReplyDelete