Martin Glazier and Stephan Krämer – “The Logic of Contingent Actuality”

In this post, Martin Glazier and Stephan Krämer discuss the article they recently published in Ergo. The full-length version of their article can be found here.

The word “actually” can be used in many ways. One prominent use is to compare the way things actually are with the way they could have been or must be. For example, we may say that the weather could have been nicer than it actually is or that the chemical formula of any substance must be what it actually is. The orthodox view of this notion of actuality accepts the thesis of

actuality necessitism: for all p, if actually p, then it is necessary that actually p.

For example, since it is actually the case that Trump is president, the necessitist will take it to be necessary that he is actually president.

Although this view is widespread, there are reasons to reject it (Glazier forthcoming). One argument against it, which draws on Dorr and Goodman (2020), appeals to the idea that actuality – the collection of propositions that are actually true –  changes over time. Since actuality has been otherwise, it must be possible for it to be otherwise. So actuality necessitism is false.

In our paper “The Logic of Contingent Actuality”, we explore the logic that results if the assumption of necessitism is dropped. What principles govern necessity, possibility, and actuality, once we allow what is actually true to be contingent?

We do not think that under contingentism just anything goes with respect to actuality. Not every proposition – nor even, perhaps, every possible proposition – could have been actually true. The contingency of actuality has limits, some of which are imposed by the very nature or essence of the notion of actuality. With an eye to these limits, we develop a number of axiomatic systems of modal logic with contingent actuality.

What sort of semantics characterizes these systems? Necessitist logics are typically characterized by a possible worlds semantics with a designated actual world. The statement “actually p” is taken to be true at a possible world just in case p is true at the designated world.

However, a semantics like this will not do for contingentist logics. Instead, our semantics appeals to an actuality function: a function which maps each possible world w to another possible world which serves as w’s actual world. (This world may, but need not be, w itself.) Different possible worlds may therefore have different actual worlds. The statement ‘actually p’ is taken to be true at a world w just in case p is true at w’s actual world, the world to which the actuality function maps w. We establish soundness and completeness results for our contingentist systems.

References

• Dorr, C. and J. Goodman. (2020). “Diamonds are forever”. Noûs 54(3): 632-65.
• Glazier, M. (forthcoming). “The contingency of actuality”. Ergo

Want more?

Read the full article at https://journals.publishing.umich.edu/ergo/article/id/5713/.