Williamson’s Argument On Necessitism

In recent decades,the development of possible world semantics has been in the ascendant.The disputes caused by the definition of “possible world” and its ontological status issues are constantly increasing,and there is a growing trend.Nowadays,people’s views are still inconsistent.It is under this circumstance that Williamson put forward his own theory of necessitism,advocating the replacement of possible and realistic struggle with the opposition of contingency and necessity,in order to clarify various confused disputes.He put forward three famous arguments about necessitism: one is based on Bacon’s formula,the other is based on the limitation of existence,the third is based on the strong modal comprehension axiom,and the third is also his most important argument,which we call the core argument.The formation of Williamson’s necessitism theory is inevitably influenced by Leibniz.Leibniz put forward the proposition of possibility and necessity in the non-modal field.His "complete concept" and "possible world" theory played an early guiding role in Williamson’s establishment of his own theory of necessitism.Leibniz believes that there is no contingent attribute in an individual,and all attributes have been included in an individual entity beforehand.At the same time,Leibniz advocates that the possible world opposite to the real world is possible,and many possible worlds can be constructed by counterfactual assumptions.The core argument is the demonstration of necessitism based on high-order modal logic as background logic and strong modal comprehension axiom as premise.The formation of higher-order modal logic is of great significance,which broadens people’s theoretical horizons in a broader way.Modal comprehension axiom means that there exists an equivalent property for any formula.Williamson argues that inevitability has more advantages than contingency in higher-order modal logic.Williamson’s core argument is based on the strong modal comprehension axiom in higher-order modal logic.Williamson tried to prove the status of metaphysics through the validity of necessitism and realize the return from logic to metaphysics.To some extent,he has achieved this goal,but his core argument of inevitability is also problematic.It is still a long way to go for us to correctly understand Williamson’s necessitism argument and to explore more ways to realize the return of metaphysics.