# Proof that if an inference holds in propositional logic, then the inference holds in supervaluationism I am currently trying to work on problem 8, but I'm not sure exactly how to start it.

I was thinking of starting it by trying to prove that phi is indeed PL valid. I would have to show how that is connected to superevalution.

I was also thinking of incorporating this:

For any trivalent interpretation I, SVI(phi)=1 I(p)=1 For any precisification C of I, Vc (phi)=1 Therefore Vc(phi)=1

I can also repreat this with indeterminant as well. I wasn't sure if I would need to prove that phi is PL valid first before proving superevaluation.

• It would help to know which book you're using. You may also want to repeat the relevant definitions of superevaluation interpretations and precisification. – lemontree Feb 19 at 9:20
• BTW, you are not supposed to prove that phi is valid, but that phi logically follows from a set of premises Gamma. – lemontree Feb 19 at 9:22
• The book is "Logic for Philosophy" by Theodore Sider – Fiona717 Feb 19 at 15:36
• Supervaluation is defined: SVI(phi) = 1 if for all C, precicify I, Vc(phi)=1; =0 if for all c, precisify I, Vc(phi)=0, =# if otherwise – Fiona717 Feb 19 at 15:47
• What are the Cs supposed to represent? Classical models? What is the definition. of 'precisify I'? – sequitur Feb 20 at 17:04