Timothy Williamson is a professor of logic at Oxford. He is a principal architect of necessitism, the claim that everything that exists necessarily exists. Ontology is necessary. Things could not have been otherwise. The universe could not have evolved differently.

Necessitism is opposed to the idea of contingency, which denies that necessarily everything that is something is necessarily something. Ontology is contingent. Things could have been otherwise. There is ontological chance in the universe.

Necessitism grows out of the introduction of modal logic into quantification theory by Ruth Barcan Marcus in 1947, in which she proved the necessity of identity.

Before Marcus, most philosophers limited the necessity of identity to self-identity. Since her work, David Wiggins in 1965 and Saul Kripke in 1971 have suggested there is no contingent identity.

Williamson reads Barcan Marcus as proving that everything is necessarily what it is, everything that exists necessarily exists.

Williamson writes her argument as

The logical arguments for the necessity and permanence of identity are straightforward, and widely accepted in at least some form. Suppose that x is identical with y. Therefore, by the indiscernibility of identicals, x is whatever y is. But y is necessarily identical with y. Therefore x is necessarily identical with y. By analogous reasoning, x is always identical with y. More strongly: necessarily always, if x is identical with y then necessarily always x is identical with y. Of course, we understand 'x' and 'y' here as variables whose values are simply things, not as standing for definite descriptions such as 'the winning number' that denote different things with respect to different circumstances.

(Modal Logic as Metaphysics, pp.25-26)

There is a serious flaw in the reasoning that "x is whatever y is. But y is necessarily identical with y. Therefore x is necessarily identical with y."

Both Wiggins and Kripke made this error. Better reasoning may start with "x has the same properties as y." Here we must analyze internal properties and external properties separately. There are objects with identical internal properties, notably quantum particles like electrons.

Numerically distinct objects cannot have identical extrinsic (external) information, the same relations to other objects in their neighborhood, e.g., the same positions in space and time, unless they are one and the same object. So if "x has the same properties as y" means x has the same intrinsic (internal) properties and the identical external relations, this is only because it is in the same position as y, and therefore is numerically one and the same object as x.

This obviously cannot be used to prove two physical objects are one and the same object. But we can say truthfully that two objects are relatively identical.

However, if x and y are abstract logical propositions, and "x has the same properties as y," then since y is necessarily self-identical with y, x also is necessarily self-identical, but with what exactly? Trivially, we can conclude logically, x is necessarily self-identical with x." But it is only in some non-trivial sense of relative identity, which we call "qua" - "in some respect," that we can claim "x has the same properties as y" means that x is necessarily self-identical with y."

Thus we have, for example, if the logical propositions x and y have identical properties qua propositional logic, they are necessarily identical propositions. This much is the case in the symbolic logic of Williamson, Marcus, Kripke, and Wiggins. For more, see our metaphysical analysis of identity.

So Barcan Marcus may be correct if she can be understood as talking about a universe of discourse described by first-order logic. As Rudolf Carnap proposed, the first-order object language can be analyzed for truth values of propositional functions in a second-order metalanguage.

Propositions that are perfectly substitutable in quantified modal logic contexts are necessarily identical. But there are no numerically distinct physical objects that are perfectly identical. Information philosophy shows that numerically distinct objects can have a relative identity if their intrinsic internal information is identical.

Information philosophy has established the existence of metaphysical possibility in two ways. The first is quantum mechanical indeterminacy. The second is the increasing information in the cosmological and biological universe. There can be no new information without possibilities, which depend on ontological chance.

Since information philosophy has shown that the increase in information in our universe is a product of chance events – without possibilities there can be no new information created – in our metaphysics, ontology is irreducibly contingent.

In a deterministic universe (one without contingency or possibility), the total information is a constant, there is but one possible future, the evolution of the universe is entirely present at all times.

This might fit well with Williamson's parallel interest in permanentism, which is a form of pre-determinism or pre-destination that fits well with some theological views.

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