What theists get “wrong” about ‘necessary beings’….

When a theist posits a “necessary being” they are posting a “being” (meaning an <object> that exists, and which must exist in all possible worlds). A necessary being can be anything from a metaphysical deity to quantum fluctuations, however theists posit this being as an <object> that has intensional states (meaning a mental disposition towards or about something). By doing so they are essentially claiming God is a mind that must exist in all possible worlds.

The “mistake” I see theists often make, and even some atheists make as well when evaluating the theist’s claim, is when they argue de dicto modality but try to smuggle in de re modality.

Allow me to explain:

The word “necessary” in an alethic modality in modal logic there are two ways to look at the modal scope of the modal operator:

De dicto:
□Ǝ A(X) ; x: X or “It is necessary that there exists x for all of X, or it is necessary that x exists in all possible worlds”

De re
Ǝ□ A(X)) ; x : X or “There exists x that necessarily for all of X, or there exists x that necessarily exists in all possible worlds”

While to some there may not be a substantial difference, there is significant difference in what is being posited by the theist. In the de dicto case, if x is a necessary being with the label of “God”, then they are saying God exists in all possible worlds, and can not fail to exist in any possible world. In the de dicto case the theist is specifically speaking about the proposition “God exists in all possible words” is true.

This type of modal argument is perfectly fine to posit arguendo for a theist to do. It would be no different than a scientist arguing quantum fluctuations must exist as a fundamental part of reality, and in all realities.

The issue is when they try to argue the de re modality. The de re modality is much more restrictive in scope and refers to the<object>, aka the “necessary being” they are referring to as God. Here, the theist is arguing that God must exist by metaphysical necessity. This claim is a much stronger claim than de dicto of positing a necessary God that exists in all possible words.

A simple analogy would be:

  1. The Law of Excluded middle (LEM) is a canonical law of logic that must be true in all possible words. vs
  2. It must be the case that LEM is true in all possible worlds.

In (1) we have a system of logic where in that system LEM is true in all possible world, but we can formulate logics that do not have the LEM axiom (called truth-gap logic). But with (2) it would mean we can not have a logical system that doesn’t have LEM, since the modal scope operator makes it necessary as in can not be any other way.

Atheists and theists both need be careful not to confuse these two very different claims as most theologians who understand the modality here will merely posit God by de dicto modality, while the more fundamentalist theist will assert de re modality. I argue positing de dicto is more stipulative and arguendo, while de re is making a very strong claim that requires a significant justification I don’t think theists can meet…and if they ever did, perhaps then I would consider believing in God.

Note: This is not a formal argument, and I’m shooting from the hip here off the top of my head from something that came up today in this group when someone brought up “necessity”.
Author: Steve McRae