Of gaps, gluts, and God's ability to change the past

Abstract

Can God change the past? The standard Aquinas line answers this question negatively: God cannot change the past since such an act implies a contradiction; thus is not within the purview of God's omnipotence. While the Aquinas line is well-known, there are other, non-standard solutions to this question. In this paper, I look into such answers. In particular, I explore those answers that employ the resources of gappy and glutty logics. I show how these solutions are motivated and how each offers an alternative conception of what it is for God to be omnipotent. Finally, I consider and reply to potential issues that may be raised against these non-standard answers.

Keywords:

• Aquinas
• classical logic
• gappy logics
• glutty logics
• paradox of omnipotence

Acknowledgments

A version of this paper was presented at the God, Time, and Change conference of the European Society for Philosophy of Religion held on September 3–5, 2022 at Oriel College, Oxford. My thanks to the organisers and participants for their useful feedback and suggestions. Special thanks to Zoltan Balazs, Pablo Dopico, Henry Fernando, Victoria Harrison, Jan Gresil Kahambing, Tim Mawson, and Carl-Johan Palmqvist. My thanks also to Abbas Ahsan, Dennis Bargamento, Jc Beall, Hazel T. Biana, Ben Blumson, Peter Eldridge-Smith, James Franklin, Brian Garrett, Alan Hajék, Yujin Nagasawa, L. Nathan Oaklander, Martin Pickup, Richard Swinburne, and the anonymous referees of this journal.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Compare the above argument with the more familiar paradox of the stone:

1. Either God can create a stone which God cannot lift or God cannot create such a stone.

2. If God can create a stone which God cannot lift, then God cannot do everything.

3. If God cannot create a stone which God cannot lift, then God cannot do everything.

4. Therefore God is not omnipotent.

Following Yujin (Nagasawa, 2008), the stone problem is classified as a Type A paradox, i.e. a paradox involving a purported incoherence of one of God's omni-properties, which, in this case, involves God's omnipotence. On the other hand, the puzzle that we are concerned with in this paper may be classified as a Type C paradox, i.e. a paradox which purports to show an inconsistency between God's omni-properties, viz. His omnipotence, and a contingent feature of the world, viz., the actual temporal facts of our world. Arguably, both the standard and non-standard solutions to the stone problem can be used as solutions to our current puzzle.

2 Admittedly, there are other logics – e.g. an intuitionistic logic – that might be classified as a logic of gaps. Compared to the logic presented above, these logics need not be three-valued nor must they subscribe to the gappy definition of logical consequence. For this paper, however, we will only focus on the logic of gaps as we have described it here.

3 Cotnoir (2018) offers an alternative presentation of a glutty semantics that relates to God's omnipotence.

4 Beall and Cotnoir (2017) use this insight to show that the limit sentence ‘God cannot create a stone that God cannot lift’ and its entailed sentence ‘Either God can create a stone that God cannot lift or God cannot create a stone that God cannot lift’ are both in the gap.

5 Cotnoir (2018) distinguishes between two sorts of glutty theorists (aka dialetheists). On the one hand, for light dialetheists, ‘creating a stone that God cannot lift’ is a property that God might or might not have – or a property that God has in some possible world. On the other hand, full-strength dialetheists would take such a property as something that God has or does not have in the actual world. That is, it is a contradictory property that God actually has. Whether one is a light or a full-strength dialetheists would not matter much, however, since the overall strategy of a glutty theorist is to show that the argument leading to the paradox of the stone is invalid.

6 Note that the following proof assumes the metaphysics of eternalism (aka the B-theory of time) – the philosophical view that the past, the present and the future are equally real, and that truths are relativised to times (or temporal segments). For a discussion of eternalism, see Sider (2005).

7 One may worry whether, in creating new timelines, God really changed the past. That is, in a world like B, it seems that God does not change some past fact p into $\mathrm{\neg }p$ since He only creates a new timeline where $\mathrm{\neg }p$ but does not change the fact that p still holds in the old timeline. To answer this worry, a theorist who endorses eternalism may reply that the whole issue about God's ability to change the past involves an analysis of the modal term ‘can’. This analysis may be done in terms of B-worlds. That God can bring about some p implies that a possible world where God brought about p.

8 See, however, a Curry-like paradox that Tedder and Badia (2018) raised and a reply to it by Joaquin (2022).

9 For example, see Cotnoir (2018)'s solution to this issue.

10 My thanks to Yujin Nagasawa for highlighting this issue.

11 The problem of evil is a problem for a glutty theist as well. Weber (2018) discusses a variant of the problem as a case against a glutty theist who holds that it is both true and false of God that He is both omnipotent and omnibenevolent.

12 As an anonymous referee pointed out, there are some other, perhaps more satisfactory, solutions to these puzzling religious doctrines that may be found in an even richer logic, e.g. a four-valued semantics based on the logic of first-degree entailment (FDE). Beall (2021) already used FDE as the base logic for his solution to the fundamental problem of Christology. It is indeed interesting to see how a four-valued logic may solve these doctrinal puzzles (e.g. Aquinas's puzzle) and I aim to explore this in a future work.