Abstract
In addressing the problem of the (in)compatibility of divine foreknowledge and human freedom, philosophers of religion encounter problems regarding the metaphysics and structure of time. Some models of temporal logic developed for completely independent reasons have proved especially appropriate for representing the temporal structure of the world as Molinism conceives it. In particular, some models of the Thin Red Line (\(\mathsf {TRL}\)) seem to imply that conditionals of freedom are true or false, as Molinists maintain. Noting the resemblance between Molinism and \(\mathsf {TRL}\) models, Restall (Molinism and the thin red line. In: Perszyk K (ed) Molinism: the contemporary debate, pp 227–239, 2011) has advanced some criticisms of Molinism that have also been leveled against \(\mathsf {TRL}\) models. In particular, Restall believes that the implication \(p \rightarrow \mathbf {HF}p\) is not true in \(\mathsf {TRL}\) models. Because Molinists must also accept that this implication is not true, this is a problem for them. We will show that Restall’s criticism is wide of the mark. Firstly, it will be demonstrated that in many open future models (not just \(\mathsf {TRL}\)) the implication \(p \rightarrow \mathbf {HF}p\) is invalid. Secondly, while it is possible to account for this implication, some modifications are required in respect of the branching time semantics. In proposing one such modification, we show that this new semantics can be adopted by advocates of the \(\mathsf {TRL}\) and, as a consequence, by Molinists as well. We conclude that the principle stated by Restall is either a problem for many open future models (not just for Molinists) or can be accounted for by these models and so is not a problem for Molinists either.
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Notes
Sometimes, the term “fatalism” is used in this context, invoking a distinction between logical and theological fatalism. We favor the term “determinism” because there is at least a sense in which fatalism is not equivalent to the idea that there is a unique future history. On this view, a certain state of the world is destined to occur, regardless of any choices made by agents. This implies a certain form of determinism (in that a certain fate is decided), but this does not impede the existence of alternatives—that is, of different possibilities that lead to the same final outcome. To formally capture this idea of fatalism, it is necessary to assume that the past is branching—in other words, that many histories can converge on a single instant.
Under the label “Aristotelism” we collect the positions according to which propositions regarding future contingents cannot be true. By “untrue” we mean that these propositions can be considered either false (Peircean semantics, cf. Prior 1967: 128–129 and, more recently, Todd 2016) or neither true nor false (supervalutionism, cf. Thomason 1970, 1984). For present purposes, these two alternatives can be treated on par because both suppose that there is no true future history that is privileged over the others.
We will use the term “Aristotelian” without adopting any stance about the historical question of Aristotle’s actual theory (on this issue, see Crivelli 2004: 198–226).
A libertarian agent is an agent that can perform (at least) a free action in the following sense: the agent determines the action and the agent could do otherwise.
The expression “Thin Red Line” was introduced by Belnap and Green (1994).
Recall that by “untrue” we mean either false or neither true nor false. As Todd (2016) points out, there are some analogies between the positions according to which the propositions concerning the future lack a truth value or are false and the respective positions of Strawson and Russell regarding which truth value, if any, to assign to a proposition such as “The actual king of France is bald”, expressed at a time when France is a republic. However, Schoubye and Rabern (2017) show that the standard arguments for Russell’s treatment of definite descriptions fail to apply to the treatment of the future operator.
The \(\mathsf {TRL}\) model presented here suffices for theological Ockhamism (see for instance Plantinga 1986). Theological Ockhamists are committed to the claim that God believed yesterday that a certain agent a will do \(\varphi \) tomorrow. Since God’s beliefs are infallible, it follows that it is true today that agent a will do \(\varphi \) tomorrow, even though a, being free, could have done otherwise. Therefore, although many different alternatives are open to a, one of these is privileged because it is the alternative that a will choose, and this is guaranteed by divine foreknowledge. One might believe that every account of divine foreknowledge must accept a \(\mathsf {TRL}\) model; indeed, if God is prescient and infallible, He already knows what agents will do in the future. Therefore, it must already be true that they will decide in certain ways rather than others. This seems to commit us to a \(\mathsf {TRL}\) model. However, this is not a necessary consequence if a timeless solution to the problem of divine foreknowledge and human freedom is accepted. In the timeless model, God is out of time, and it is therefore unnecessary to claim that God knew yesterday what agents would do tomorrow. This timeless solution is demonstrably compatible with the Aristotelian model of contingent futures (cf. De Florio and Frigerio 2015). In the next section, we will show that Molinists require a more demanding framework than the \(\mathsf {TRL}\) model presented here. This more demanding framework will be referred to as \(\mathsf {TRL+}\).
Actually, Belnap and Green consider sentences such as: “Ann will read a novel and she will not go to the party. It is, however, possible that she will go the party, and then later she will drink a beer”. In the text, we use counterfactuals in order to show the relevance of Belnap and Green’s objection for Molinism.
Before Øhrstrøm, a similar solution was proposed by McKim and Davis (1976).
The Molinist maintains that counterfactuals of freedom (CF) are eternally known by God. They are the objects of middle knowledge, in as much as it is intermediate between the knowledge of eternal and immutable truths and the knowledge of contingent truths. By knowing the eternal truths and the CFs concerning every possible agent before the creation of the world, God knows the best world to be created because, for every possible world, He has foreknowledge of how free agents will behave in that world and of the outcomes of their actions. Being perfectly good, God can therefore choose the best of all possible worlds. From the Molinist perspective, it is obviously crucial that the truth of CFs is compatible with human freedom. The thesis that there is no opposition between the truth of CFs and human freedom is perfectly characterized by \(\mathsf {TRL+}\), as for any choice made by an actual or possible agent, it is already true (before the choice) that the agent will freely choose in a certain way. For a complete introduction to Molinism, see Flint (1998). See also Craig (1991), chap. XIII.
Actually, the Molinist needs a more complex model constituted by many trees. There are as many trees as there are possible initial states of the world, but we can overlook this complication here because, for our purposes, the resulting model would not be conceptually richer than what we are discussing.
The operator \( \mathbf {H} \) is the dual of the operator \( \mathbf {P} \): \( \mathbf {H} \varphi \equiv \lnot \mathbf {P}\lnot \varphi \).
Thanks to an anonymous referee for emphasizing this point.
We want to thank an anonymous referee for the criticisms and suggestions about our formal framework.
Friends of a dynamic and realist metaphysics of time could construe the idea of perspective we are presenting in strong sense. However, our semantic allows also an indexical reading according to which the perspective indicates that instant we consider our ‘now’, without any metaphysical privilege.
Since in these cases \( (H_{t} \cap H_{t'}) \subseteq H_{t} \), the quantification over the intersection is superfluous and it would be sufficient to quantify over the histories in \( H_{t} \). However, we stick to this formalization for symmetry with the future case.
When \(\varphi \) does not hold in the future of every history of the intersection, we have, as before, two options: either we can state that \( \mathbf {F}\varphi \) is false (Peirceanism) or we can use supervalutations.
Recall that the moment of evaluation and the perspective must be connected. It might be reasonable to introduce further conditions on their relationship. For example, it seems to be reasonable that the perspective \( t' \) must belong to the \(\mathsf {TRL}\) of the point of evaluation t (i.e. \( t' \in \mathsf {TRL}(t) \)). It would be unnatural if the “present” were not on the \(\mathsf {TRL}\) of a past point of evaluation. This is especially true if the perspective is interpreted in a realist and dynamical sense, as a point that moves on the tree. In this case, if the principle is not accepted, some counterintuitive consequences follow. For example, it might be the case that it is true today that Ann will drink a beer tomorrow. Nevertheless, when time flows and tomorrow becomes the present time, it is false that Ann drinks a beer. However, we will put aside this matter here. Our aim is to show that the \(\mathsf {TRL+}\) model can validate the principle of retrogradation of truth and the relationships between the perspective and the moment of evaluation are orthogonal to this problem.
For similar operators, cf. Belnap et al. (2001, p. 161) and Wawer (2014, p. 371). Notice that we could also introduce the operator Unsettled, but it would not be the dual of \( \square \). The future of t is unsettled or contingent with respect to t iff there are some histories radiating from t in which it is true at a moment subsequent to t and some histories radiating from t in which it is false at a moment subsequent to t. Consequently, p is unsettled iff also \( \lnot p \) is.
The following interpretation of counterfactuals is inspired by Thomason and Gupta (1980).
For an introduction to counterfactuals of freedom, cf. Perszyk (2011).
So, we accept Lewis (1973)’s view that counterfactuals with true antecendents have a truth value, even though they are pragmatically infelicitous.
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Acknowledgements
Previous versions of this paper were presented and discussed at Prior’s Metaphysics of Time Conference held at the Aalborg University and at the International Workshop on Ockhamism held at L’Aquila University. We want to thank all the participants for comments, criticisms, and suggestions, in particular Patrick Blackburn, Per Hasle, Andrea Iacona, David Jakobsen, Peter Øhrstrøm, Sven Rosenkranz, Giuliano Torrengo. The authors gratefully thank an anonymous referee for constructive comments and recommendations, which definitely help to improve the quality of the paper. We are, of course, solely responsible for any errors.
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De Florio, C., Frigerio, A. The Thin Red Line, Molinism, and the Flow of Time. J of Log Lang and Inf 29, 307–329 (2020). https://doi.org/10.1007/s10849-019-09304-4
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DOI: https://doi.org/10.1007/s10849-019-09304-4