Just because a set of claims can't be proven inconsistent in van Inwagen's relative identity logic, it doesn't follow that such claims don't imply a contradiction, or that it is metaphysically possible that all the claims are true.
relative identity logic(as a formal logical framework)
A specialized system of logical rules that allows for a different way of thinking about whether two things are 'the same'—instead of treating identity as all-or-nothing, it permits things to be identical in some respects but not others.
van Inwagen(as a philosopher being cited as a necessitarian)
Peter van Inwagen is a contemporary American philosopher who studies questions about what exists, what it means to exist, and whether God must exist.
Vlastimil Vohánka (2013) argues that van Inwagen has done nothing to show the logical possibility of any Trinity theory. Just because a set of claims can’t be proven inconsistent in van Inwagen’s relative identity logic, it doesn’t follow that such claims don’t imply a contradiction, or that it is metaphysically possible that all the claims are true. At one point van Inwagen tells a short non-theological story whose claims, when translated into his relative identity logic, have the same forms as the Trinity propositions. The story, he argues, is clearly not self-contradictory; thus, he conclud...