Contingently existing propositions

Abstract

I argue that propositions are contingent existents. Some propositions that in fact exist might not have existed and there might have been propositions that are distinct from every actually existing proposition. This is because some propositions are singular propositions, which are propositions containing ordinary objects as constituents, and so are ontologically dependent on the existence of those objects; had those objects not existed, then the singular propositions would not have existed. I provide both a philosophical and technical understanding of the contingent status of propositions.

Keywords::

• singular propositions
• necessity
• contingency
• existence

Notes

^1. In interpretations with varying domains, this choice carries the consequence that objects are in the extension of a predicate at a world where it does not exist, which seems problematic. The upside of this decision is that it does not require complications to the proof theory, which is why I adopt it here. A more semantically and metaphysically satisfying alternative is to assign, for each world w in W, the set of all identity pairs on D_w as the extension of =  relative to w, thus allowing the extension of identity to varying across worlds. This alternative requires a more complicated proof theory, which is why I opt for the first, simpler semantics for identity for the purposes of this essay. I show how to modify the identity rules for a sound and complete proof theory for a semantics in which the extension of =  relative to w is the set of all identity pairs on D_w in my ‘Things that might not have been’.

^2. This is to adopt a real-world, as opposed to a general, conception of validity, where a sentence Φ is a general validity just in case, for every interpretation I and every world w in W_I, Φ is true at w in I. There are sentences that are real-world validities that are not general validities, like the sentence AFa → Fa, which I discuss later in the text. While the choice between the two conceptions is contentious, see (Zalta 1988) and (Nelson and Zalta 2012) for a defense.

^3. Proof. Suppose, for purposes of reductio, that ▪Fa → ▪AFa is false in some interpretation I. Then, by the semantics of → , 1. ▪Fa is true in I and 2. ▪AFa is false in I. 1. ▪Fa is true in I just in case, for all worlds w in W_I, Fa is true at w, in which case, where o is the value of a in I, o is in the extension of F at w. 2. ▪AFa is false in I just in case, for some world w′ in W_I, AFa is false at w′, in which case Fa is false at w^*, in which case o is not in the extension of F at w^*. But w^* is a world in W_I and so, because what is true of w in 1 is true of every world in W_I, what is true of w in 1 is also true of w^*. So, by 1, o is in the extension of F at w^*. But then o is both in and not in the extension of F at w^*, which is a contradiction. So, there is no interpretation I in which ▪Fa → ▪AFa is false.

Additional information

Notes on contributors

Michael Nelson

Michael Nelson earned his PH.D. from Princeton University in 2002. After teaching for 3 years at Yale University, he moved to UC-Riverside in 2005, where he is currently an Associate Professor of Philosophy.