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.


Cornell Anthony said...

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?

Alexander R Pruss said...

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