The Logic of Counterpart Theory with Actuality

Adam Rigoni, Richmond H. Thomason
2012 Journal of Philosophical Logic  
Journal of Philosophical Logic, forthcoming. Final publication available at Abstract It has been claimed that counterpart theory cannot support a theory of actuality without rendering obviously invalid formulas valid or obviously valid formulas invalid. We argue that these claims are not based on logical flaws of counterpart theory itself, but point to the lack of appropriate devices in first-order logic for "remembering" the values of variables. We formulate a mildly
more » ... ic version of first-order logic with appropriate memory devices and show how to base a version of counterpart theory with actuality on this. This theory is, in special cases, equivalent to modal first-order logic with actuality, and apparently does not suffer from the logical flaws that have been mentioned in the literature.
doi:10.1007/s10992-012-9248-0 fatcat:kyau36tggrdu7pu7iznimsq4aa