A Proposed Solution to the Problem of Induction

Introduction

            On the standard conception of induction, it is a non-deductive type of inference whose premises could possibly be true and yet the inferred conclusion could be false. Yet, induction is something on which we rely in everyday life. For instance, if every one of my experiences of a solid yellow traffic light has been immediately followed by a red light, then I infer that my next experience with a solid yellow traffic light will be immediately followed by a red light (all else being equal, of course). Some philosophers have recognized, however, that despite induction’s crucial role in both everyday life and the scientific method, a problem of induction is posed that is a significant challenge to this form of reasoning. Samir Okasha summarizes the problem this way: “But what makes you so sure that it’s true? If someone asked you to justify your conviction, what would you say?”[1] I will consider this problem of induction, and then a proposed solution to this problem, from Steven Cowan and James Spiegel. I argue that this proposed solution is deficient, and propose a repaired version of their solution. Some potential objections to this repaired solution will be considered, and responses will be given. I argue that the Cowan-Spiegel solution to the problem of induction is deficient, but it can be salvaged using Alvin Plantinga’s Modal Ontological Argument (MOA).

The Problem of Induction

            The problem of induction finds its roots in modern philosophy with David Hume. Hume was concerned to establish the underlying reasoning behind cause and effect. He eventually came to the conclusion that experience provided us with the reason to expect specific cases of causation. For Hume, this naturally raised the question, “What is the foundation of all conclusions from experience?” His thesis was that experiential reasoning is not really reasoning at all.[2] Hume’s argument was that past experiences only allow us to say what happened in those particular cases and nothing more. He then proceeds to argue that induction can be based on either “demonstrative” reasoning (i.e., deductive reasoning), and “matters of fact,” which he takes to be, “evidently going in a circle, and taking that for granted, which is the very point in question.”[3] This is because these “matters of fact” are just probabilistic attempts to justify induction, and are hence inductive. For Hume, the result is the destruction of the rationality of induction, as he writes, “If there be any suspicion that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless, and can give rise to no inference or conclusion.”[4] While it is not the purpose of this paper to critique Hume directly, it is important to understand precisely what was claimed.

            The question of how induction is justified can be posed as a dilemma: either induction is justified deductively, or it is justified inductively. Inductive inference cannot be justified deductively. This is because deduction guarantees that if the premises are true, the conclusion will follow. Okasha notes the difference between induction and deduction when he writes, “It is easy to imagine a universe where nature is not uniform, but changes its course randomly from day to day.”[5]

            With respect to science’s use of induction, Del Ratzsch that there is no logical connection between data and inductive conclusions. He claims, “They [the data] do not dictate a particular theory as the proper one.”[6] (emphasis in original) Since deduction does dictate a particular conclusion from a validly structured argument and true premises, it thus follows that induction is not deductively justified.

            However, neither is induction justified inductively. It appears any attempt to do this would be circular. Richard DeWitt illustrates the problem with a simplified construction: What happens in nature today (the sun rising and other regularities) is mostly the same as yesterday; yesterday was much the same as the prior day, and so on and so forth from time immemorial. From that, we can gain a particular inference. Since in the past, the future was like the past, then in the future, the future will probably be like the past.[7] But notice that the inductive inference just is in use here, and thus appeal to induction to justify induction is hopelessly circular. DeWitt draws out this by writing, “The inference . . . depends on the assumption that its own conclusion is true.”[8]

            If induction cannot be justified deductively or inductively, then how can it be justified? One potential response is to insist that perhaps it can be justified via deduction after all. One may have noticed that a primary assumption of induction is called the Uniformity of Nature (UN) principle. UN states, “The future will probably be like the past in relevant ways.” A deductive argument for induction, then, may plausibly look like this:

1.     If in the past the future has been like the past in relevant ways, then in the future the future probably will be like the past in relevant ways (UN conditional).

2.     In the past, the future has been like the past.

3.     Therefore, in the future the future probably will be like the past in relevant ways.

In light of this argument, it does seem to be a deductive justification; the truth of the premises guarantees the truth of the conclusion. The problem, however, still remains. One might notice that the UN conditional requires induction to be justified in order to hold it as true, which raises the question all over again: How can one be justified in taking UN and induction to be true? There has been no shortage of answers, and one shall be considered next.

The Cowan-Spiegel Solution (CSS)

            Steven Cowan and James Spiegel offer a briefly discussed solution to the problem of induction (hereafter the solution shall be called CSS). Cowan and Spiegel distinguish between what they call Regularities in Nature (RN) and UN. RN is pretty straightforward: it describes the laws of nature. They imply that RN allows humans to survive, thrive, and do the vast majority of things that we do everyday. This is relatively uncontroversial. It is at this point they argue, “Regularities in nature are useful for human welfare and, thus, indirectly testify to the existence of a purposeful, intelligent and powerful mind at work behind the cosmic scene who seeks to benefit his creatures. That is, the laws of nature evidence the existence of a benevolent God.”[9]

            A crucial move is made at this point. CSS posits that since RN indirectly points to an omnibenevolent God, then we humans can trust that UN is true. This means that inductive inference is justified after all. “That is, we can trust that the future will resemble the past . . . [If we could not,] this would be inconsistent with the goodness of God and His love for His creatures.”[10] CSS certainly holds some intuitive plausibility; a benevolent God is plausibly a God of order, who would keep the natural order so that UN and induction are justified. But does it work? The next section attempts to answer that question.

CSS is Deficient as a Justification for UN

            CSS is not the only theistic solution to the problem of induction. Vern Poythress has kept his argument simple: God has created a world in which UN and induction are true; we are justified in accepting the Bible that testifies to this (implicit premise); therefore, God is the solution to the problem of induction. Lest anyone think Poythress ignores epistemology, he adds, “He [God] has made human beings in his image, so that our minds are in some ways in tune with his.”[11] Alvin Plantinga has argued that since we are made in God’s image, it follows that many of the things we value God does as well. As such, this would include simplicity (a consideration that interacts with induction crucially) and, plausibly, UN/induction.[12]

            Despite this, and despite the argument’s promise, CSS is deficient as a justification for UN. First, we must consider RN. We should note here that CSS argues that RN indirectly points to a benevolent God. While Cowan and Spiegel do not explain what it is to directly or indirectly point to something, it certainly appears as though an indirect inference is not a deductive inference. RN is consistent with a large number of hypotheses, including theism, deism, extraterrestrial design, etc. Any attempted justification of the RN-to-God move will be inductively based. Therefore, CSS is viciously circular. If CSS states that RN is really an application of UN, then the move will be circular. If RN is without UN, then the problem of induction remains a problem for the RN-to-God move.

            This can be seen in a “new” problem of induction. Imagine (as is true) the statement, “All observed emeralds are green,” is true, where every observed emerald has the property of being green. Now consider the statement, “All observed emeralds are grue,” where grue is the property of being green prior to 2020 and blue thereafter. The two statements are empirically equivalent; their inductive support is at precisely the same levels as one another.[13] So which do we choose? The analogous point to be made is that RN is completely consistent with any number of hypotheses, and it is only by appealing to inductive factors that one can justify the move to God. But that simply relies on UN, and hence induction remains unjustified. CSS requires induction in order to justify induction, and so it is defective as it stands.

A Proposed Solution: Plantinga’s Modal Ontological Argument (MOA)

            Even though CSS, as it stands, technically fails, there seems to be good reason to think that their second premise—that a benevolent God is justification for UN—is true. The only question is whether or not a good reason or argument can be given for God that does not itself rely on induction. Plantinga’s Modal Ontological Argument (MOA) provides just such an argument. The argument can be framed like this:

4.     There is a possible world in which maximal greatness is instantiated.

5.     Necessarily, a being is maximally great just in case it has maximal excellence in every world.

6.     Necessarily, a being has maximal excellence in every world just in case it has omniscience, omnipotence, and moral perfection in every world.

7.     If this being has maximal excellence in every world, then it has it in the actual world.

8.     If it has it in the actual world, then a maximally great being (MGB) exists.[14]

This argument is essentially arguing for a necessarily existent being; it is arguing for the MGB of Perfect Being Theology. In reality, the only real premise of MOA here is (4). This is because (5) and (6) are definitions (of what it means to be the MGB and what it means to be maximally excellent, respectively), and (7) and (8) are entailments of modal logic. In order to understand the MOA, one must understand the terms that Plantinga is using. Moreland and Craig summarize part of Plantinga’s argument as follows: “The argument assumes that the concept of God is possible . . . Plantinga conceives of God as a being that is ‘maximally excellent’ in every possible world.”[15]

            This concept of maximal excellence entails specific properties for that being in the world. Thus, Plantinga: “That is to say, a being B has maximal excellence in a world W only if B has omniscience, omnipotence, and moral perfection in W.”[16] At this point in the MOA, a being can be maximally excellent but only exist in one world, or a handful of worlds, or whatnot. So, if a being had these types of properties in more than one world, then in every world in which that being had these properties he would be maximally excellent. Now a being is maximally great, according to Moreland and Craig, just in case he possesses maximal excellence in every world (not to be confused with possessing maximal excellence in every possible world in which one exists—if this is even possible).[17]

            For these types of properties, Plantinga (and others) have commonly made reference to them as “great-making properties.” A great-making property is a property that it would be metaphysically better for some being to have than to lack. So, for example, the property of being a knower is a great-making property since, all things being equal, it is better for a being to have this property than to lack it. This is why, plausibly speaking, necessary existence (that is, existence in every possible world) is a great-making property.[18]

            But simply having these great-making properties (or these types of them) is not sufficient for maximal excellence. After all, I possess some of these great-making properties! Maximal excellence seems to require that one possess all of these great-making properties, not merely some of them. It seems to go further than this, however. There could be a being who possesses all of the great-making properties there are, but who nonetheless only has them to certain degrees. Perhaps the being is very powerful, but not omnipotent. Suppose the being knows a great deal, but is not omniscient, etc. This would not be a maximally excellent being. This is why we would say that a maximally excellent being would possess all of the great-making properties to the maximal degree possible.[19]

            As Plantinga notes, there are plausibly two ways to understand this conception of maximal excellence. First, a being that possesses all great-making properties to the maximal degree of which those properties admit. Second, a being that possesses all great-making properties to the maximal degree of which those properties admit in every possible world. These two claims do not necessarily amount to the same thing.[20] Plausibly, necessary existence is a great-making property (at least, it seems as though necessary existence would be a property it would be metaphysically better to have than to lack). If so, then it seems a being would only be maximally excellent if he met the aforementioned considerations, which include his existence in every possible world.

            Of course, this means that a maximally excellent being who possesses those properties in every possible world can be said to be the MGB. This also entails (7), the derived conclusion from implications of the premise and definition that MGB exists in the actual world. From (7) it follows that, obviously, MGB exists. The key insight of the MOA seems to be that if it is even possible for MGB to exist, then he does.[21] The question obviously remains: is (4) true? What reason do we have for thinking that MGB possibly exists?

            Plantinga, at least originally, did not see a good amount of hope for thinking this argument would be successful, in part because it could be rationally denied. He thought that because it is false that everyone who understands and thinks about the premise that MGB is possibly instantiated will believe it, it was not a successful example for natural theology (even though he did think it to be a sound argument).[22] A good solution to seeing whether or not MGB does possibly exist (and therefore exists in the actual world) is to appeal to our intuitions. “It might be said that the idea of a maximally great being is intuitively a coherent notion and, hence, possibly instantiated.”[23] If our intuitions are reliable guides to reality (as many think that they are), this is at least prima facie justification for thinking that MGB does possibly exist. As I have argued, if MGB possibly exists, then the MOA is successful, since MGB exists in the actual world. It is also vitally important to know that this omniscient, omnipotent, morally perfect being is identifiable with the Christian conception of God.

            If the MOA is successful, an argument can be formulated which provides necessary repairs to CSS for the problem of induction. While the MOA does provide an ontological basis for inductive-worlds to work, it also, and most crucially, provides the justification for taking induction to be rational. The difference is that something may exist (ontologically or metaphysically) and yet not be known or rationally held to exist. The argument for induction’s justification can be run as follows:

9.     If the MOA is successful, then there is a benevolent God.

10.  If there is a benevolent God, then there is justification for UN/induction.

11.  Therefore, if the MOA is successful, then there is justification for UN/induction.

12.  The MOA is successful.

13.  Therefore, there is justification for UN/induction.

(11) and (13) are entailed conclusions of (9-10) and (9-10, 12), respectively. (12) has been argued for in the previous section. Therefore, only (9) and (10) shall be defended in this section. In considering the idea that a successful MOA leads to a benevolent God, one must consider the idea, once again, of great-making properties. Plausibly, omnibenevolence (benevolence shown to all, as a minimum definition) is a property it is better for a being to have than to lack (possibly included under the idea of moral perfection).

            If this property of omnibenevolence is possessed by God, it is not one that is contingent or non-essential. Plantinga himself writes, though not in the context of the MOA directly, “Many of God’s properties—his omniscience and omnipotence, his goodness and love—are, as theists think of it, essential to him: he has them in every possible world in which he exists. . . . he has those properties in every possible world.”[24] (emphasis in original) If this is true, then it is not so much as possible that God is metaphysically conceivable without this property, which plausibly includes omnibenevolence as a sub-property of moral perfection. In any case, (9) should be only be regarded as false in cases where someone thinks the MOA is successful, and yet benevolence is not part of MGB’s properties.

            What about (10)? For a reminder, it states, “If there is a benevolent God, then there is justification for UN/induction.” Why would it follow from a benevolent God’s existence that UN, and hence, induction, is justified? It is here that CSS provides excellent insight. The argument is that if regularities were not present, then the results would be devastating for humanity. If gravity were not operative during some unpredictable times, or if the sun were not to rise tomorrow, or if any number of physical or natural laws were to cease operation (or operate radically outside of our predictive powers), humans would literally be unable to survive. Since a benevolent God would want humans to survive, there will be regularities and laws of nature. “Therefore,” Cowan and Spiegel conclude, “we can and should believe that the future will resemble the past, since a loving God rules the world.”[25] Essentially, if there is justification for the premises, then the justification is transferred to the conclusion as well, meaning that (10) is true, and UN/induction are justified.[26] There are certainly responses to this type of approach, and they will be discussed in the next section.

Objections

            Although the MOA appears to be successful, and although the MOA seems to result in CSS being effectively repaired, there are plenty of objections that have been lodged against the premises used. I shall consider only three types of objections, and afterward explain responses to these objections.

IBE does not rely on induction

            This first objection does not concern the MOA, with which the objector may happily agree. In fact, he may agree with the entire reformulation of CSS with the MOA as the initial start-up theistic argument. However, this objection is to the claim that CSS is deficient as a justification for UN. In effect, this objector might claim that the RN-to-God move is an inference to the best explanation (IBE), not a reliance upon induction or UN. This is an important claim, for it undercuts the motivation for repairing CSS in the first place. It argues that the question being asked is “What is the best explanation of regularities of nature?,” and has as its answer, “A benevolent God is the best explanation.” After comparing competing hypotheses, if any, the proponent of CSS can simply insist he has run the probability figures, and the benevolent God hypothesis comes out the winner. If this objection works, the entire point of the project is undercut.

Van Inwagen’s Epistemic Neutrality Objection (ENO)

            Philosopher Peter Van Inwagen objects, not to the solving of the problem of induction, nor to CSS, but rather to something else very much crucial to my proposed solution. Van Inwagen objects to the success of the MOA. That is, he believes there is something that has gone awry in the possibility premise. He writes, “The modal ontological argument . . . suffers from only one defect: there seems to be no a priori reason, or none accessible to the human intellect . . . to think that it is possible for there to be a necessarily existent being that has all perfections essentially.”[27]

            Van Inwagen does not simply proclaim this and therefore the reasoning behind the MOA is defeated. Rather, he argues for it by what I shall call the Epistemic Neutrality Objection (ENO). ENO relies on what it means for a proposition to be epistemically neutral with respect to some knower in some particular situation at a particular time. For Van Inwagen, some proposition is epistemically neutral for someone just in case the status of its affirmation and its denial are precisely the same.[28] From this epistemic neutrality, he seeks to combine it with a propositions’ being non-contingent (in the case that the proposition or its denial were to be a necessary truth) to develop a full account of ENO. The principle is as follows:

If a proposition p is non-contingent, and is known to be non-contingent by a certain person or certain population at a certain time, and if p is epistemically neutral for that person or population at that time, then the proposition that p is possibly true is also epistemically neutral for that person or population at that time.[29]

The force of all of this is revealed for Van Inwagen in that the idea that MGB is possibly instantiated must be epistemically neutral for any person for whom the proposition “There is MGB” is also epistemically neutral. Van Inwagen takes it to be the case that there is no a priori reason to think that proposition is not epistemically neutral. He also takes it that a posteriori reasons for God’s existence do not raise the probability with respect to these a priori arguments. Therefore, it follows that the proposition “MGB is possibly instantiated” is epistemically neutral.

The Incommensurability Objection

            The final objection is called the “incommensurability objection.” This idea is that God is considered to be the greatest possible being. It inherently seems to involve the concept of comparing one being’s metaphysical greatness with another. In fact, this can be called the “linear model.” This model postulates a kind of chain, where each being on a particular link occupies a space “greater than” or “lesser than” some other specific being on the chain (in some cases, as great as). This implies a universal value commensurability: “Every possible being is value commensurable.”[30] But this seems to be very suspect to the objector. How can one compare the respective values of a car and a hippo? Does this even make sense?[31] Because the very conception of God as the greatest possible being seems to rely on this universal value commensurability, and this principle makes no sense, the MOA cannot get off the ground.

Responses

Each of these objections has particular responses that can be made. The first objection was that the RN-to-God move made by CSS was based on IBE, and IBE does not need nor rely on induction or UN. It seems, however, that IBE either just is induction or relies on simplicity being a regular feature of reality, which is just UN. Consider how one can be justified in IBE. Suppose Jerry sees footprints leading up to his house in a straight line. IBE supports that, all else being equal, only one person walked up to Jerry’s door. But why think this? It seems that Jerry could say, “In all (or most) of my other experiences with footprints being formed in a straight line, only one person was walking (or that was the best explanation). Therefore, the best explanation is that only one person was walking.” However, this is clearly just inductive inference at work.

What if IBE just relies on simplicity? Suppose Jerry said instead, “The simplest theory is that there was only one person walking toward my house.” This will not succeed either. For we can just ask Jerry why he thinks simplicity will work here. Jerry’s justification will have to be something like the idea that simplicity is a feature of reality. However, it can then be asked how Jerry is justified in taking it to be the case that because these explanations have been relatively simple in the past, they will be in the future. Any justification Jerry offers will either be question-begging or a totally different justification than CSS. As such, the IBE objection seems to fail.

As to Van Inwagen, it seems as if, overall, one can accept his epistemic neutrality condition, and even its application into a broader principle of knowing that it is possible (though there may be concerns, they are not directly relevant to this response to Van Inwagen). Moreland and Craig also utilize the distinction between metaphysical possibility (i.e., that something is really possible) and epistemic possibility (i.e., for all we know, something is possible).[32] So it is not enough, in agreement with Van Inwagen, merely to say that for all one knows, MGB is possibly instantiated. This, in fact, would fall into ENO.

However, it seems that modal intuitions do in fact provide us with an a priori reason to think God’s existence is not epistemically neutral. Many people simply find themselves thinking there probably or possibly is a God, and it is based on this properly basic belief or modal intuition. Moreland and Craig write, “It might be said that the idea of a maximally great being is intuitively a coherent notion and, hence, possibly instantiated.”[33] Could it then be argued that the MOA only works for people who already believe? This is not quite clear. It seems that the MOA could work on those who find themselves believing God’s existence is coherent, and then upon an investigation of modal logic realizing that God must exist. In any case, ENO does not seem to work, given modal intuitions that cannot be dismissed without argument.

Finally, Yujin Nagasawa has offered what he has called the “Radial Model” for Anselmian theism. This grants the objector the idea that certain beings or things are not value commensurable. However, Nagasawa proposes the following: “God is the being than which no greater can be thought by virtue of occupying the top link in all local chains of being, each of which contains multiple non-divine beings.”[34] For Nagasawa, there is not a linear chain of beings all the way down, but rather a type of circle where God occupies the highest chain for any link down. Nagasawa shows that while not every non-divine being is value commensurable with every other non-divine being, it nevertheless makes sense to say that “an aardvark and a hedgehog are value commensurable.” But this implies that, “Every non-divine possible being is value commensurable with one or more other non-divine possible beings.”[35] If that is the case, then the incommensurability objection is also undercut.

Conclusion

            In this paper, I have explained the problem of induction as it relates to justification. Induction relies on UN, the idea that the future will be relevantly like the past. We saw that induction cannot be justified by deduction, induction, or by inference to the best explanation without being circular. Cowan and Spiegel argued that regularities in nature indirectly pointed to God, and that God would make the world so that inductive inferences would be generally successful. However, I argued Cowan and Spiegel reasoned in a circle, as regularities in nature that point to God depend on induction. I then offered the solution that the modal ontological argument of Alvin Plantinga can be used as a non-inductive a priori argument to repair Cowan and Spiegel’s solution. Finally, objections and responses were considered. Induction is epistemically justified for humans on the basis of God and his goodness.

BIBLIOGRAPHY

Cowan, Steven B. and James S. Spiegel. The Love of Wisdom. Nashville: B&H Publishing, 2009.

DeWitt, Richard. Worldviews: An Introduction to the History and Philosophy of Science. Malden MA: Blackwell, 2004.

Hume, David. “An Enquiry Concerning Human Understanding,” in Epistemology: Contemporary Readings, ed. Michael Heumer. New York: Routledge, 2002, 298-310.

Moreland, J.P. and William Lane Craig. Philosophical Foundations for a Christian Worldview. Downers Grove, IL: IVP Academic, 2003.

Nagasawa, Yujin. “Models of Anselmian Theism,” in Faith and Philosophy. 30, no. 1, (January 2013:), 3-25.

Okasha, Samir. Philosophy of Science: A Very Short Introduction. New York: Oxford, 2002.

Plantinga, Alvin. God, Freedom, and Evil. Grand Rapids, MI: William B. Eerdmans, 1974.

____________. Where the Conflict Really Lies. New York: Oxford, 2011.

Poythress, Vern. Logic: A God-Centered Approach to the Foundation of Western Thought. Wheaton, IL: Crossway, 2013.

Ratzsch, Del. Science & Its Limits. Downers Grove, IL: IVP, 2000.

Van Inwagen, Peter. “Three Versions of the Ontological Argument,” in Ontological Proofs Today, ed. Miroslaw Szatkowski. Piscataway, NJ: Transaction Books, 2012, 143-62.

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[1] Samir Okasha, Philosophy of Science: A Very Short Introduction (New York: Oxford, 2002), 20.

[2] David Hume, “An Enquiry Concerning Human Understanding,” in Epistemology: Contemporary Readings, ed. Michael Huemer (New York: Routledge, 2002), 302.

[3] Ibid., 303-04.

[4] Ibid., 305.

[5] Okasha, 25.

[6] Del Ratzsch, Science & Its Limits (Downers Grove, IL: IVP Academic, 2000), 19. While he was writing about the underdetermination problem, this does have application to induction directly.

[7] Richard DeWitt, Worldviews: An Introduction to the History and Philosophy of Science (Malden, MA: Blackwell, 2004), 60.

[8] Ibid.

[9] Steven B. Cowan and James S. Spiegel, The Love of Wisdom (Nashville: B&H Academic, 2009), 130.

[10] Ibid., 131.

[11] Vern Poythress, Logic: A God-Centered Approach to the Foundation of Western Thought (Wheaton, IL: Crossway, 2013), 53.

[12] Alvin Plantinga, Where the Conflict Really Lies (New York: Oxford, 2011), 299.

[13] DeWitt, 63.

[14] Alvin Plantinga, God, Freedom, and Evil (Grand Rapids, MI: William B. Eerdmans, 1974), 111.

[15] J.P. Moreland and William Lane Craig, Philosophical Foundations for a Christian Worldview (Downers Grove, IL: IVP Academic, 2003), 496. It is not clear that their re-formulation of the order of the MOA makes any difference; however it may make a dialectical difference, in that there may be some who find the very premise question begging because of what that modal claim entails.

[16] Plantinga, God, Freedom, and Evil, 108.

[17] Moreland and Craig, 496.

[18] Plantinga, God, Freedom, and Evil, 104-05.

[19] The “omni” attributes themselves, one might note, are just properties that do not admit of degrees: this is because they are the maximally degreed versions of particular great-making properties.

[20] Plantinga, God, Freedom, and Evil, 103.

[21] Moreland and Craig, 496-97.

[22] Plantinga, God, Freedom, and Evil, 112.

[23] Moreland and Craig, 497.

[24] Plantinga, Where the Conflict Really Lies, 300.

[25] Cowan and Spiegel, 131.

[26] Interestingly, on Plantinga’s internalist account of justification, and his thoughts on warrant in Warranted Christian Belief, it seems as though, if theistic solutions are the only ones for the justification for induction, unbelievers may acquire a defeater for their belief that induction is actually justified. It may be that, given their presupposition that induction is actually justified, induction can thus be utilized as a premise in a separate theistic argument.

[27] Peter Van Inwagen, “Three Versions of the Ontological Argument,” in Ontological Proofs Today, ed. Miroslaw Szatkowski (Piscataway, NJ: Transaction Books, 2012), 158.

[28] Ibid., 160. One might think this more or less describes agnosticism; perhaps there are important distinctions to be made (one being a state of belief, the other a state of propositions).

[29] Ibid.

[30] Yujin Nagasawa, “Models of Anselmian Theism,” in Faith and Philosophy, 30, no. 1 (January 2013:), 6.

[31] Ibid., 7.

[32] Moreland and Craig, 497.

[33] Ibid.

[34] Nagasawa, 14.

[35] Ibid. Nagasawa argues that a detailed analysis of what it means to be value commensurable will be something like the following: “For any non-divine possible being we can always conceive of another possible being that is genuinely slightly inferior or greater.” But this implies that, on the Anselmian conception, that every chain will have God and multiple non-divine beings in value commensurability.