Introduction
In his book C.S. Lewis's Dangerous Idea: In Defense of the Argument from Reason, Victor Reppert lists nine presuppositions of rational inference.
1. States of mind have a relation to the world we call intentionality, or about-ness.
2. Thoughts and beliefs can be either true or false.
3. Human beings can be in the condition of accepting, rejecting or suspending belief about propositions.
4. Logical laws exist.
5. Human beings are capable of apprehending logical laws.
6. The state of accepting the truth of a proposition plays a crucial causal role in the production of other beliefs, and the propositional content of mental states is relevant to the playing of this causal role.
7. The apprehension of logical laws plays a causal role in the acceptance of the conclusion of the argument as true.
8. The same individual entertains thoughts of the premises and then draws the conclusion.
9. Our processes of reasoning provide us with a systematically reliable way of understanding the world around us.[1]
Commenting on this list of presuppositions, Reppert writes, "It seems to me that all of these elements of reasoning are prima facie difficult to fit within the framework of philosophical naturalism."[2] Here I want to quickly sketch how I would assess one of Reppert's supporting arguments for that claim.
The Argument from the Psychological Relevance of Logical Laws
Reppert offers an argument he calls the "Argument from the Psychological Relevance of Logical Laws" (hereafter, the "Argument from Logical Laws"). He formulates it as follows.
1. If naturalism is true, then logical laws either do not exist or are irrelevant to the formation of beliefs.2. But logical laws are relevant to the formation of beliefs. (Implied by the existence of rational inference.)3. Therefore, naturalism is false.[3]
In order to assess this argument, I will do three things. First, I will offer a summary of what I take Reppert to mean by the expression "logical laws." Second, I will refer to a map of the philosophical terrain regarding the metaphysical nature of logical laws. Third, I will critically assess the argument's major premise, premise (1).
Logical Laws
By the expression, the "laws of logic" or "logical laws," I take Reppert to be referring to, at the very least, the following.
- The Law of Identity: P is P.
- The Law of Noncontradiction: P is not not-P.
- The Law of the Excluded Middle: Either P or not-P.
We may make four observations about each of these laws. First, each law is a sentence. Second, each law is a proposition, i.e., the kind of sentence which is capable of being either true or false. Third, each law is true. Fourth, each law is necessarily true, i.e., the kind of proposition which is true in every possible world.
The Metaphysical Nature of Logical Laws
In a recent pair of books, William Lane Craig has provided a useful service to the philosophical community by creating a map of the philosophical terrain with regard to one particular type of abstract objects, namely, mathematical objects. This map or diagram is shown below.
Source: William Lane Craig, “God and Abstract Objects” Philosophia Christi 17 (2015): 269-76.
I believe that we can apply Craig's work on mathematical objects to other types of (proposed) abstract objects, including propositions, and so I'm going to ask the reader to mentally replace the word "Mathematical" with "Propositional" when they read the above diagram.
Although I won't defend my views here, I believe that formalism, psychologism, arealism, and conventionalism are so utterly implausible as to be non-starters. Thus, either propositional objects exist (and so one of the remaining realist options is true) or they do not exist (and so one of the anti-realist options is true). I also happen to reject anti-realism, but I think at least one anti-realist option, fictionalism, is plausible. Again, I will not defend that position here. Instead, in what follows I will assume that realism about propositional objects is true. Let us now turn to a critical assessment of the Argument from Logical Laws.
A Critical Assessment of the Argument from Logical Laws
For the reader's convenience, here is premise 1.
1. If naturalism is true, then logical laws either do not exist or are irrelevant to the formation of beliefs.
Thus, premise 1 represents a dilemma for naturalism. Either logical laws do not exist or logical laws do exist, but are irrelevant to the formation of beliefs. In either case, given naturalists' commitment to rational inference, naturalists seem to have a major problem on their hands.
Or do they? Consider the first option.
1a. If naturalism is true, then logical laws do not exist.
Why think 1a? Reppert writes:
Even if turns out that a naturalistic worldview can account for causation in terms of mental content, a further problem can be brought forward. Rational inference involves the employment of the laws of logic. These laws are not physical laws. Indeed they pertain across possible worlds, including worlds with no physical objects whatsoever. So while the laws of physics denote the powers and liabilities of things in the physical world, the laws of logic tell us what must be true in any universe whatsoever. Even in possible worlds with no law of gravity, the law of noncontradiction still holds. If one accepts the laws of logic, as one must if one claims to have rationally inferred one belief from another belief, then one must accept some nonphysical, nonspatial, and nontemporal reality--at least something along the lines of the Platonic forms.[4]
The view Reppert describes and rejects above is formalism about propositional objects. As someone who rejects formalism, psychologism, arealism, and conventionalism, I believe that Reppert has the start of a potentially successful argument against materialist versions of naturalism (hereafter, "materialism").[5] But what about non-materialist versions of naturalism, i.e., those versions which are logically consistent with Platonism? Consider, for example, "source physicalism," the view that the physical exists and, if the mental exists, the physical caused the mental to exist. Source physicalism says precisely nothing about whether abstract objects exist, including propositional objects. So far as I can see, Reppert offers no reason whatsoever to believe that if Platonistic naturalism is true, then logical laws do not exist. Charitably interpreted, this is where I take the second horn of Reppert's dilemma to come into play.
Here's the second horn of the dilemma suggested by premise 1.
1b. If naturalism is true, then logical laws are irrelevant to the formation of beliefs.
As I read him, Reppert seems to think that 1b takes care of Platonistic naturalism. The idea seems to be as follows. It isn't enough for the Platonistic naturalist to appeal to abstract propositional objects to account for the mere existence of logical laws; rather, the Platonistic naturalist must also show that abstract propositional objects play a causal role in the formation of beliefs. But that is a contradiction in terms: by definition, abstract objects (if they exist) cannot cause anything and so abstract objects cannot partially or fully cause beliefs. That this is Reppert's argument is supported by the following passage.
Further, some have suggested that the existence of abstract entities, while perhaps not consistent with strict physicalism, can resolve the naturalist's problem. The idea is that in addition to physical states there can exist, consistent with naturalism, abstract entities such as propositions, states of affairs and so forth that do not have any particular spatial or temporal location and that exercise no causal power. Nevertheless, when one has a belief, one believes a proposition to be true. But even if we grant that these abstract states are consistent with naturalism, I fail to see that this can possibly help the naturalist account for reasoning. Whatever the abstract state is, that state must in some way be capable of affecting the way beliefs in the world of space-time are produced and sustained. And if physics is a closed system, then it seems impossible for abstract entities, even if they exist, to make any difference in how beliefs are caused. So I see no escape along these lines for the naturalist.[6]
Notice that, although Reppert's "even if" phrasing suggests that the logical consistency of naturalism with Platonism is in doubt, he provides absolutely no reason at all to think otherwise. But what, then, becomes of 1b? I'm inclined not only to endorse 1b, but to endorse a much broader version.
1c. If realism about propositional objects is true, then logical laws are irrelevant to the formation of beliefs.
Again, I refer the reader to the diagram shown earlier. At this point, we are assuming that some form of realism about propositional objects is true; furthermore, we are assuming that the only plausible versions of realism are absolute creationism or Platonism. Neither of these options entail that the existence of abstract propositional objects are relevant to the formation of beliefs. The upshot is that the truth or falsity of naturalism or theism is irrelevant to whether logical laws are irrelevant to the formation of beliefs.
This leads us to the argument's second premise.
2. But logical laws are relevant to the formation of beliefs. (Implied by the existence of rational inference.)
Reppert provides very little supporting argument in support of 2. He writes:
It is further supposed that we know these [logical] laws. But the only acceptable physicalist analysis of knowledge would have to be some kind of causal interaction between the brain and the objects of knowledge. But if we know or have insight into the laws of logic, we must be in some kind of physical relationship to the laws of logic. This is quite impossible if the laws of logic are, as I have contended, nonphysical, nonspatial and nontemporal.[7]
I am inclined to agree with everything Reppert writes in the above passage, but it provides no reason whatsoever to believe theism over naturalism. As we saw earlier with 1c, abstract propositional objects are irrelevant to the formation of beliefs, full stop. Theism makes no difference here. To see this, assume both that theism and Platonism are true. Reppert doesn't use these words, but he seems to think that if theism is true, dualism is very likely true and dualism avoids the inherent difficulty in physicalism with accounting for knowledge of non-physical objects. He seems to forget his own thesis, however. His thesis entails not just that formalism is false (and so propositional objects are not concrete physical objects) but also that psychologism is false (and so propositional objects are not concrete mental objects in human minds) and divine conceptualism is false (and so propositional objects are not concrete mental objects in God's mind). If propositional objects really are abstract objects, as Reppert claims, then the truth or falsity of dualism is irrelevant to the ability of concrete objects (humans) to stand in causal relations (have knowledge of) abstract objects (including abstract propositional objects). While not a so-called 'God of the gaps' argument, the Argument from Logical Laws does share one thing common with such arguments, namely that both God of the gaps arguments and the Argument from Logical Laws attempt to identify one or more problems with a naturalistic explanation without so much as even an attempt to demonstrate that theism does provide an explanation.
How, then, should we assess the plausibility of propositional objects on theism? Here I want to consider three realist options: Platonism, absolute creationism, and divine conceptualism.
Theism and Platonism
I want to begin by comparing mere theism (hereafter, "theism") with a specific version of theism I will call "anti-Platonist theism." By "theism," I mean the view that there exists an all-powerful, all-knowing, morally perfect being ("God") who created the physical world and is worthy of worship. So defined, theism says nothing about whether Platonism is true. We can compare two versions of theism: "Platonist theism" and "anti-Platonist theism." Platonist theism and anti-Platonist theism are theism conjoined with the affirmation or negation, respectively, of the proposition, "abstract objects exist."
While theism is logically consistent with Platonism, many Christian theists have affirmed anti-Platonist theism. These Christians have tended to subscribe to the theological doctrine of divine aseity, according to which everything distinct from God (and which is creatable by God) depends on God’s creative activity for its existing. Belief in that doctrine, combined with the auxiliary belief that aseity applies to things distinct from God which are uncreatable, motivates anti-Platonist theism. If anti-Platonist theists are correct, then the Argument from Logical Laws does not even get off the ground because there are no abstract propositional objects.
To avoid any misunderstandings, I do not have a settled view on what I consider to be an "in-house" debate between Christian theologians and philosophers about the scope of divine aseity. I mention this sectarian debate solely to highlight an issue which Reppert needs to address if he wishes to provide a complete defense of Christian theism, using his argument for theism from logical laws for support.
Theism and Absolute Creationism
In order to avoid the theological undesirability of Platonism, some (many?) theists have looked for refuge in "absolute creationism," the position that abstract objects exist but were somehow created by God. There are two problems with this view, however. First, absolute creationism seems to be metaphysically impossible. By definition, abstract objects cannot stand in causal relations. But creation is a type of causation, so the proposition, "God created abstract objects," is identical with the proposition, "God caused to exist things which cannot be caused to exist," which is self-contradictory. Second, absolute creationism is inconsistent with the timeless nature of abstract objects. To see this, recall that abstract objects are not only defined to be nonspatial but also nontemporal or timeless. To say that God created abstract objects, however, implies that abstract objects began to exist. To say that abstract objects began to exist seems to deny that abstract objects are timeless, which is tantamount to denying abstract objects altogether. Thus, absolute creationism seems to be logically incoherent.
Theism and Conceptualism
This leaves what I consider to be the most promising route for anti-Platonist theists who wish to affirm realism about mathematical objects, propositional objects, and the like. According to conceptualism about such objects, they exist as ideas in God's mind. Thus, conceptualism provides a way for the theist to simultaneously affirm realism and the dependence of such objects on God. Once again, however, I see two problems with this view. First, making propositional objects dependent upon God comes at a cost: the denial of their abstractness. Thus, conceptualism is logically inconsistent with Reppert's belief that logical laws are abstract. Second, at best, conceptualism seems only able to offer a partial explanation for propositional objects, namely, true propositions. Divine conceptualism, by itself, does not seem to have a good explanation for false propositions. The theistic conceptualist may account for false propositions by positing that God is able to think false propositions without believing false propositions. The problem, however, as Craig explains, is that that move in turn requires the conceptualist to posit "that God be constantly entertaining actual thoughts corresponding to every proposition and every state of affairs."[8] As Graham Oppy points out, that "threatens to lead to the attribution of God of inappropriate thoughts bawdy thoughts, banal thoughts, malicious thoughts, silly thoughts, and so forth."[9] Craig concludes, accordingly, that by positing God constantly has detestable thoughts, conceptualism undermines the holiness of God.[10]
Conclusion
Reppert's Argument from Logical Laws is an argument for theism which differs from other arguments in natural theology in interesting ways. Nevertheless, his defense of that argument is incomplete. First, Reppert's supporting argument for realism is incomplete. While Reppert provides an argument against conventionalism, he does not consider and refute all other alternatives to realism about logical laws. Second, even if abstract propositional objects were relevant to the formation of beliefs, theism would have no advantage over naturalism. Neither theistic Platonism nor absolute creationism entail that abstract propositional objects are relevant to the formation of beliefs. Finally, third, abstract propositional objects, if they exist, are irrelevant to the formation of beliefs. Even if I am right about all of this, however, it may be the case that Reppert's other arguments from reason succeed. All I have argued is that one of his arguments, the Argument from Logical Laws, fails.
Notes
[1] Victor Reppert. C. S. Lewis's Dangerous Idea: In Defense of the Argument from Reason (2003, Kindle Edition), Kindle Locations 687-692.
[2] Reppert 2003, Kindle Locations 692-693.
[3] Reppert 2003, Kindle Locations 783-784.
[4] Reppert 2003, Kindle Locations 766-770.
[5] I say "start" because Reppert's comments, as they stand, are at best an incomplete defense of realism about propositional objects. A complete defense of Reppert's argument would need to include a refutation of fictionalism, as well as other anti-realist positions. In what follows, however, I will assume (merely for the sake of argument) that fictionalism is false and, more broadly, that realism is true.
[6] Reppert 2003, Kindle Locations 482-488.
[7] Reppert 2003, Kindle Locations 770-773.
[8] William Lane Craig, God Over All: Divine Aseity and the Challenge of Platonism (Oxford University Press, 2016), 85.
[9] Graham Oppy, ‘Response to Greg Welty’, in Beyond the Control of God? (ed. Paul M. Gould Bloomsbury, 2014), 105.
[10] Craig 2016, 86.
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