God, Propositions, and Necessary Existence

“In the beginning God created the heavens and the earth” (Genesis 1:1). For centuries Christians have taken this Bible verse to teach the doctrine of creation ex nihilo. Before the creation of the world, there was only God: the eternal Father, Son, and Holy Spirit. When God freely decided to create, he created ex nihilo, out of nothing. But this classical Christian doctrine leads to some perilous conclusions when taken in conjunction with Alvin Plantinga’s assertion that propositions exist necessarily. In this paper, I will exposit this problem and attempt to show that there are good reasons to think that propositions exist contingently, and that Plantinga offers no convincing reasons to think they exist necessarily.

First, I will present Alvin Plantinga’s understanding of the nature of propositions and their necessary existence. Second, I will attempt to show that one cannot cogently bring together both a Plantingalian belief in the necessary existence of propositions and a classical Christian doctrine of God and creation. Third, I will elaborate a weakness of Plantinga’s argument for the necessary existence of propositions and further contend that propositions exist contingently. Finally, I will acknowledge some implications of the contingent existence of propositions.

A preliminary word must be said about the philosophical method I will implement in the following paper. I take it that the goal of Christian philosophy is the acquisition of wisdom about God, the world, and humanity. I also take it that an essential component of gaining wisdom is discovering truth, and that, by the grace of God, some of the most important truths have been given to man in the “rule of faith” revealed in the Scriptures and summarized in the statements of ecumenical Christianity.^[1] Furthermore, I take it that important truths have been revealed to man through his pre-theoretical intuitions, and that it is additionally important for Christian philosophers to make philosophical systemizations that are grounded in their intuitions. However, when the latter pair (our pre-theoretical intuitions and philosophical systemizations) come into conflict with the former pair (the Scriptures and ecumenism), the latter pair must be reoriented and sometimes jettisoned.

I will attempt in the following paper to examine Plantinga’s understanding of propositions with a high value for philosophical rigor and a deep devotion to the Scriptures and creeds of Christianity, but also with a strong conviction that these two paired elements of Christian philosophical investigation must be properly related. Our pre-philosophical seemings and philosophical speculations must be made subordinate to the authority of the Scriptures and their ecumenical interpretation. I think this is nothing more than to say that we Christians must philosophize by faith, and not by sight (cf. 2 Corinthians 5:7).[2]

 “Necessity” in Plantinga’s Construal of Propositions

Plantinga recognizes two different ways a proposition can be necessary: a proposition can be necessary with respect to its truth value, and a proposition can be necessary with respect to its exemplification of the property being existent.[3] The former has to do with modality de dicto (modality with respect to a proposition’s truth value), and the second has to do with modality de re (modality with respect to a thing’s exemplifying a property). Plantinga uses possible world semantics to further clarify the two different ways a proposition can be necessary. A possible world, according to Plantinga, is a possible maximal state of affairs, or a complete way that things could have been. We can then say that a proposition, p, is necessarily true if and only if p is true in every possible maximal state of affairs. Furthermore, a proposition, p, necessarily exists if and only if p exists in every possible maximal state of affairs. While in the former case the truth of p cannot fail to obtain in a possible world, in the latter case it is the proposition p that cannot fail to obtain in a possible world. While Plantinga does not think that all propositions are necessarily true—indeed, he thinks that some propositions are necessarily false and still others are contingently true—he does think that propositions necessarily instantiate the property being existent; he thinks all propositions exist in every possible world.

Plantinga believes that propositions have many distinctive characteristics besides necessary existence, two of which are particularly significant for our discussion: their status as primary bearers of truth (and falsity) and their abstract nature.[4] For propositions to be the bearers of truth and falsity means that propositions are those items that can be true or false; they are those entities that can receive and sustain a truth value. For propositions to be abstract means that propositions are not concrete entities; at the very least, they differ in some substantial ways from material items, like the furnishings of a bedroom. Plantinga seems to take the truth-value-bearing nature of propositions for granted, without any serious argumentation. He does present one argument for both their abstract nature and their necessary existence. This argument is meant to show that, “propositions…cannot be concrete objects of any sort—at any rate, they can’t be concrete objects that do not exist necessarily.”[5] He means to demonstrate that propositions exist necessarily by establishing that their non-existence implies a contradiction. His argument can be construed in the following way:

(1) Propositions do not exist.

(2) If propositions do not exist, then it is true that propositions do not exist.

(3) If propositions do not exist is true, then it exists.

Therefore,

(4) If propositions do not exist, then at least one proposition exists.

Since (1) is assumed for the sake of argument, (2) and (3) seem obviously true, and (1), (2) and (3) entail the contradiction (4), Plantinga concludes

(5) It is impossible for propositions not to exist (i.e., propositions necessarily exist).

Plantinga uses this argument for the necessary existence of propositions to prove that propositions cannot be contingent concrete objects (like human mental acts).[6]

The Proposition Problem

It seems that a Plantingalian belief in the necessary existence of propositions comes into conflict with some basic tenets of the Christian faith. Call this the Proposition Problem. Before we draw out the Proposition Problem in the form of a reductio, we must first make the ecumenical definition of creation ex nihilo more explicit. Put simply, the ecumenical doctrine of creation ex nihilo asserts that God freely created out of nothing. God created out of nothing because only God existed before he created, and God freely created because God had no compulsion to create beyond his own free choice.[7] As Colin E. Gunton points out, the Athanasian understanding of God and creation ratified at the first Council of Constantinople affirms on the basis of Genesis 1:1 that there is “an absolute ontological distinction between creator and creature” such that for any thing, that thing is either God or God’s creature.[8] Furthermore, while those at the first Council of Constantinople affirmed that God necessarily exists, they equally affirmed that the “creation is contingent.”[9] For our purposes, we can say that the ecumenical doctrine of creation ex nihilo implies

(6) Necessarily, something exists in every possible world if and only if it is numerically identical with God.

An initial problem herein is manifest: the conjunction of a Plantingalian belief in the necessary existence of propositions with the Christian doctrine of creation ex nihilo leads to a series of implications that come into crass conflict with a traditional Christian doctrine of God. Consider the following reductio:

(6) Necessarily, something exists in every possible world if and only if it is numerically identical with God (from the Christian doctrine of creation ex nihilo).

(7) 7 + 5 = 12 exists in every possible world (from the Plantingalian affirmation of the necessary existence of propositions).

Therefore,

(8) 7 + 5 = 12 is numerically identical with God.

The above argument shows that if 7 + 5 = 12 necessarily exists, and if the Christian doctrine of creation ex nihilo is true, then the proposition 7 + 5 = 12 is numerically identical with God. Given the Indiscernibility of Identicals (“a principle than which none sounder can be conceived”[10]), any property that God has, the proposition 7 + 5 = 12 has also, and vice versa. If (8) is true, not only would 7 + 5 = 12 be responsible for my redemption and worthy of worship, but God would also be a mathematical truth. This seems to me to be patently false. The Lord God is the Redeemer of Israel, not 7 + 5 = 12 or any other proposition for that matter. 7 + 5 = 12 is necessarily true, not God. Moreover, if all propositions exist necessarily in the way Plantinga claims, then we can replace 7 + 5 = 12 in (7) and (8) with any other proposition, including the contradiction p & ~p. If Plantinga is right, not only would God be a mathematical truth, he would also violate of the law of non-contradiction. It is clearly absurd, then, to numerically identify God with any proposition, and much more so to numerically identify God with propositions in general. If we know anything from Scripture and our commonsense intuitions, it is that God and propositions cannot be the same thing.[11]

Since creation ex nihilo—including its affirmation of (6)—is a vital ecumenical truth grounded in Scripture that underpins the Christian faith,[12] the only way to avoid the above reductio in an orthodox fashion is to deny that propositions exist necessarily. Propositions, therefore, do not exist in every possible world; (7) is false, and it would be false if we replaced “7 + 5 = 12” with any other proposition. But even if propositions do not exist in every possible world, they clearly exist in some possible worlds, and they certainly exist in this possible world—in the actual world.[13] Since propositions exist in some possible worlds but not all possible worlds, they exist contingently. We can borrow some Athanasian language and conclude that propositions are God’s creatures, distinct from him, freely brought into existence by God’s divine power. Or, in other words, propositions are created objects that exist contingently and are not numerically identical with God.

A Respondeo to Plantinga’s Argument for the Necessary Existence of Propositions

What about Plantinga’s argument that the possible non-existence of propositions implies a contradiction? There is a vital weakness in Plantinga’s argument that significantly reduces the force of his reasoning: (2) is false. If propositions do not exist, then it is neither true nor false that propositions do not exist. This retort at first might seem to violate the law of bivalence, which states that for any proposition, p, p is either true or false. Upon closer inspection, this response to Plantinga leaves bivalence intact. In the words of Toner: “Certainly we insist on bivalence for propositions that exist. But if there is no proposition there at all, why scruple at denying ‘it’ a truth value?”^[14] Surely, if p exists it must be either true or false—but surely it is not the case that p must be either true or false if p does not exist.

It seems that Plantinga’s argument for the necessary existence of propositions is a subtle case of question-begging. This can be seen by further examining Plantinga’s position on actualism and the de dicto/de re modal distinction. Plantinga is a champion of serious actualism: “the view that necessarily no object has a property in a world in which it does not exist.”[15] Plantinga has also argued that “modality de dicto [is] a special case of modality de re”; this is because truth and falsity are properties of propositions.[16] Plantinga’s own work in the metaphysics of modality implies that non-existent propositions cannot be either true or false because non-existent objects cannot have properties, and truth and falsity are properties of propositions. The consequent of (2) is not entailed by the antecedent; it denies the antecedent. By asserting (2) Plantinga has merely assumed that propositions exist in every possible world, instead of proved it.

There is a possibility that I have misconstrued Plantinga’s argument for the necessary existence of propositions. Instead of a formal argument intended to establish that the possible non-existence of propositions implies a contradiction, Plantinga may intend to point out that it is counterintuitive to affirm that propositions could not exist. On this interpretation, Plantinga is arguing that it seems wrong to affirm that it is possible for propositions not to exist. If this is indeed the proper representation of Plantinga’s argument, then the easy response to Plantinga is that we do not share his intuition, and, furthermore, that what seems true to him by intuition comes into frightful conflict with the Christian doctrine of God and creation. We are safe to conclude, therefore, that neither reading of Plantinga’s argument for the necessary existence of propositions causes problems for Christians who wish to affirm that propositions are created, contingent entities.

Three Implications of the Contingent Existence of Propositions

There are a series of implications for many of the philosophical disciplines that result if propositions are created, contingently existent realities. Take philosophy of religion, for example. If propositions did not exist before God created, then it was not true that God exists before he created. This implication for philosophy of religion is not as radical as one might initially expect. Technically we can truly affirm that God existed before he created now that propositions have been created by God, even though no truth-value bearers (i.e., propositions) existed that corresponded to God’s existent reality before he created. Sure, if propositions did not exist before God created, then before God created it was not true that God exists—but neither was it false. This seems to be no serious issue, however. The basic content of the Christian doctrine of God still remains, even if we must change its articulation when speaking philosophically.[17]

Another implication for philosophy of religion stemming from the created and contingent existence of propositions is in regard to the nature of God’s knowledge. Theology proper typically calls God’s self-knowledge his necessary knowledge.[18] God’s self-knowledge is necessary because God exists necessarily, and he has his self-knowledge essentially; in every possible world in which God exists he knows himself, and since God exists in every possible world, he knows himself in every possible world. However, if propositions do not necessarily exist, then it follows that God’s necessary knowledge is not necessarily propositional. God did not know himself propositionally before he created, and he never would have if he did not create. Moreover, if God is immutable (as I think he is) such that his self-knowledge is the same in nature across every possible world, then his self-knowledge is essentially non-propositional. We might be tempted to think that it limits or reduces the dignity of God’s intellect for him to lack propositional self-knowledge. But that would be the case only if propositional self-knowledge is required for intellectual dignity, and there is no obvious reason to think that it is. In fact, since God is essentially supremely glorious (cf. Romans 11:36), if he lacked propositional self-knowledge, we should conclude that propositional self-knowledge is not required for intellectual dignity.

Finally, I would like to note an entailment of the contingent existence of propositions for modal logic. If all propositions exist contingently, including necessarily true propositions, then it is not true that whatever is necessary is necessarily necessary; in other words, the formal modal logic systems S4 and S5 are incorrect. Necessarily true propositions are not true in every possible world; they are only true in those possible worlds in which they exist. Many metaphysicians might follow Plantinga[19] by finding this implication the most startling, and it may indeed be. A number of advances in metaphysics and other disciplines have been made by philosophers implementing modal logics and possible worlds semantics that depend on S4 and S5 models. Nonetheless, it seems to me better to piously deny S4 and S5 (and be satisfied with the weaker modal system T), than to deny creation ex nihilo or embrace the absurdity of (8). Whatever S4 and S5 appear to add to our understanding of modality and other philosophical matters, they are misguided. The Christian must accept philosophic godliness over modal ingenuity.[20]

Conclusion

In this paper I have exposited Plantinga’s understanding of propositions. What I have found is that Plantinga’s affirmation of the necessary existence of propositions does not jibe well with an orthodox Christian conception of God and creation. The result is that we must deny that propositions necessarily exist—lest we confuse them with God—and instead affirm that they exist contingently as created entities. To assert that propositions exist contingently does require that a slew of changes be made to commonly held positions on philosophical and modal matters, but all of these changes seem to me quite worth the reward of an orthodox and pious conception of God and creation.

Notes

[1] Thomas F. Torrance, The Trinitarian Faith (New York: T&T Clark, 2006), 34–46.

[2] The point of this paragraph is not that Christian philosophers must deny some truths in favor of others, but rather that we should have an incomparably larger sum of trust in Scripture and its ecumenical interpretation than in our intuitive seemings (cf. Romans 1:18; 1 Corinthians 2:2; Galatians 1:6-10; Colossians 2:2–3, 2:8; 1 Peter 1:10–11).

[3] Plantinga’s understanding of propositions and modality can be found in his book, The Nature of Necessity (New York: Oxford University Press, 1979), and summarized by one of his followers in Kenneth Konyndyk, Introductory Modal Logic (Notre Dame, Indiana: University of Notre Dame Press, 1986).

[4] Alvin Plantinga, “Why Proposition Cannot Be Concrete,” in Essays in the Metaphysics of Modality, ed. Matthew Davidson (New York: Oxford University Press, 2003), 229. This article originally appeared in Warrant and Proper Function (Oxford: Oxford University Press, 1993), 117–120.

[5] Plantinga, “Propositions,” 229. Emphasis in original.

[6] See ibid., 229–233. See also Patrick Toner, “Contingently Existing Propositions?,” Philosophical Studies 129 (2006), 422–423 for a nice summary of Plantinga’s argument.

[7] See Torrance, Trinitarian Faith, 76–109. See also Colin E. Gunton, The Triune Creator: A Historical and Systematic Study (Grand Rapids: Eerdmans Publishing Company, 1998), 65-96 and Robert Letham, The Holy Trinity (Phillipsburg: P&R, 2004), 425–457. This is the understanding of creation ex nihilo first ratified by the Constantinopolitan theologians, although the idea of creation ex nihilo has its roots in the intertestamental period (Torrance, Trinitarian Faith, 95–98). The Reformational theologians continued the Constantinopolitan theological tradition by adopting this ecumenical understanding of creation ex nihilo (See Herman Bavinck, God and Creation [vol. 2 of Reformed Dogmatics; 4 vols.; ed. John Bolt; trans. John Vriend; Grand Rapids: Baker Academic, 2008], 416–420 and John Murray, “Calvin’s Doctrine of Creation,” Westminster Theological Journal 17, no. 1 [1954]: 21–430). Not only does creation ex nihilo (as defined above) have unprecedented historical impetus, there is good reason to believe it is at the heart of ecumenical Christianity. As Torrance has shown in his magisterial presentation of patristic theology, creation ex nihilo (again, as defined above) is a central article of the ecumenical “rule of faith” (Torrance, Trinitarian Faith, 96).

[8] Gunton, Creator, 67.

[9] Ibid. It is worth emphasizing at this point that, according to Gunton and Torrance, the Constantinopolitan theologians not only taught that created things are ontologically dependent on God, but also that since all created things owe their origin to God’s free will, created objects do not necessarily exist.

[10] Alvin Plantinga, “Transworld Identity or Worldbound Individuals?,” in Essays in the Metaphysics of Modality, ed. Matthew Davidson (New York: Oxford University Press, 2003), 75. This article originally appeared in Logic and Ontology, ed. Milton Munitz (New York: New York University Press, 1973), 193–212.

[11] I am inclined to think that a similar reductio could be run if we replaced “7 + 5 = 12” with any abstracta Plantinga thinks is necessary, whether it be “numbers, properties, pure sets” or “states of affairs” (Alvin Plantinga, “Actualism and Possible Worlds,” in Essays in the Metaphysics of Modality, ed. Matthew Davidson [New York: Oxford University Press, 2003], 110. This article originally appeared in Theoria 42 [1976]: 139–160).

[12] Torrance, Trinitarian Faith, 96.

[13] Propositions clearly exist in this possible world for no less a reason than that this sentence itself expresses a proposition; namely, that propositions clearly exist in this possible world.

[14] Toner, “Contingently Existing Propositions?,” 423.

[15] Alvin Plantinga, “On Existentialism,” in Essays in the Metaphysics of Modality, ed. Matthew Davidson (New York: Oxford University Press, 2003), 167. This article originally appeared in Philosophical Studies 44 (1983): 1–20.

[16] Plantinga, “Actualism,” 110.

[17] What I have suggested in this paragraph in regard to the proposition God exists can be generalized to be true of any necessarily true proposition about God.

[18] See Richard A. Muller, The Divine Essence and Attributes (vol. 3 of Post-Reformation Reformed Dogmatics: The Rise and Development of Reformed Orthodoxy, ca. 1520 to ca. 1725; 4 vols.; Grand Rapids: Baker Academic, 2003), 411–432.

[19] See Plantinga, “Propositions,” 230–231.

[20] See Torrance, Trinitarian Faith, 38.