Please join me as I share highlights from Augustine’s Confessions. You can find the whole series @spaciously_spaced on Instagram.
Special thanks to the GMU chapter of Ratio Christi for allowing me to present on this topic at a recent meeting. I would like to apologize for not being able to adequately address the question regarding Plantinga’s argument against metaphysical naturalism. I have updated my comments below to include a brief summation. I will readily acknowledge that I still find myself trying to grasp all of its intricacies. I want to especially thank Marcel for his insightful feedback regarding Spiegel’s argument. I have incorporated the idea of UGN briefly in my summation.
What explains the practice of making inductive inferences? Why do we seem inclined to think that the future will resemble the past? Is this simply the result of conditioning; something baked into us through the repetition of daily experience? Or, is it something hardwired into us, an essential part of our cognitive makeup? The distinction here is significant. On the one side is David Hume’s position which represents an authentically empiricist perspective. For Hume, beliefs based upon inductive reasoning are without any rational justification and calls into question the foundation of scientific knowledge. If he is correct in his thinking, then the so-called problem of induction may well prove to be far more problematic for the Christian than it is for the scientist. On the other side, is the position being put forth in this paper. I wish to argue that inductive reasoning, far from being the product of nurture, is more properly conceived as the product of nature. I will begin by exploring what has come to be known as the problem of induction, arguing that Hume is not so much stating a problem as he is making a demonstration regarding the limitations of reason. It is in this section that I will delineate the larger implications of Hume’s thinking for the theist. I will then discuss what has come to be known as the principle of induction. Far from weakening the ability of reason, I contend that Hume’s demonstration actually points to a priori powers of reason. Finally, I will attempt to account for the production of inductive reasoning. How are we to explain the emergence of this phenomenon? Ultimately, I will contend that inductive reasoning provides a compelling demonstration of theistic design.
The Problem of Induction
Antony Flew defines induction as “a method of reasoning by which a general law or principle is inferred from observed particular instances.” We use it all the time in our day to day life. Anytime we make a general conclusion based upon limited observation, we are reasoning inductively. If I conclude that all women from El Paso are beautiful, solely based on having met a few dozen women who were born in that city, then I have drawn an inductive conclusion. Perhaps, more commonly, we all believe the sun will rise tomorrow and do so on the basis that we have seen it rise every morning of our lives. But induction transcends these mundane beliefs. Indeed, science itself, despite efforts to demonstrate otherwise, relies heavily upon induction. Flew underscores this long tradition of inductive reasoning in science by pointing to Newton’s rules of reasoning, as delineated in the preface to Book III of his Philosophiæ Naturalis Principia Mathematica.
The third rule runs: ‘The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.’ The fourth, which ‘we must follow, that the argument of induction may not be evaded by arbitrary hypotheses’, states: ‘In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true … till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.’
Whereas deductive reasoning provides certainty (starting with true premises leads one to a true conclusion), inductive reasoning does not. But the problem with induction is not simply the lack of certainty that it provides (most would agree that this really is not problematic at all), but rather that it seems to admit no justification whatsoever.
David Hume famously argued that while we certainly use induction all the time, when asked to justify it, we cannot. Take for instance the aforementioned belief that the sun will rise tomorrow. What justifies our believing this? Hume tells us that the belief is based upon an assumption commonly referred to as the uniformity of nature (UN). Simply put, it is the assumption that the future will resemble the past. As Samir Okasha states, it is “the assumption that objects we haven’t examined will be similar, in relevant respects, to objects of the same sort that we have examined.” But as Hume points out, this assumption is not necessarily true. One could easily conceive of a universe where the uniformity of nature does not hold.
The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality. That the sun will not rise tomorrow is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise.
But if UN is not logically true, can we at least provide empirical evidence to demonstrate its truth? Hume says that any attempt to do so descends into circular reasoning. If we argue that UN is true because it has always held true in the past, then we have simply used UN to prove UN and are guilty of begging the question. There are therefore no rational or empirical grounds upon which to justify inductively held beliefs. According to Okasha, “Hume concludes that our confidence in induction is just blind faith.” This is what is traditionally known as the problem of induction.
In response to Hume, some have turned to probability as a means of justifying inductive reasoning. If the premises of an inductive argument cannot guarantee the truth of its conclusion, at the very least they make it more likely than not. Bertrand Russell states,
It must be conceded, to begin with, that the fact that two things have been found often together and never apart does not, by itself, suffice to prove demonstratively that they will be found together in the next case we examine. The most we can hope is that the oftener things are found together, the more probable it becomes that they will be found together another time, and that, if they have been found together often enough, the probability will amount almost to certainty. It can never quite reach certainty, because we know that in spite of frequent repetitions there sometimes is a failure at the last, as in the case of the chicken whose neck is wrung. Thus probability is all we ought to seek.
Of course, an inductive argument’s probability is relative to the truth of the premises and whether it is based upon our total relevant knowledge. The upshot is that while scientific knowledge is not certain, we are justified in holding inductively formed beliefs on the basis that they are highly probable.
The problem with this line of reasoning is that it relies upon induction. To say that something is highly probable, is to say that a very high proportion of occurrences follow a particular pattern. Hume tells us in his Treatise on Human Nature that “probability is founded on the presumption of a resemblance betwixt those objects, of which we have had experience, and those, of which we have had none.” In other words, probability presupposes UN; and thus, also falls prey to circular reasoning. Hume continues,
I will go farther, and assert, that he could not so much as prove by any probable arguments, that the future must be conformable to the past. All probable arguments are built on the supposition, that there is this conformity betwixt the future and the past, and therefore can never prove it.
The question is whether this leaves us in a state of total skepticism. Has Hume effectively undermined our ability to justify any scientifically obtained knowledge? There is much debate as to whether Hume embraced this radical conclusion. In reviewing the many interpretations, Alexander Rosenberg concludes that Hume did not reject inductive reasoning. Instead, he confidently asserts that Hume considered it to be an inevitability for humans and essential to the scientific enterprise. Hume himself states, “. . . none but a fool or madman will ever pretend to dispute the authority of experience, or to reject that great guide of human life . . .” Or, as Alvin Plantinga states, “it is the person who does not reason inductively who requires therapy.” So then, if Hume was not advocating a form of Pyrrhonean skepticism, what exactly was his point?
Many philosophers would agree with Rosenberg that Hume was never suggesting that we abandon inductive reasoning. In separate works, both Antony Flew and A. J. Ayer argue that Hume should not be read as presenting a problem or difficulty. Instead, he was simply demonstrating the limitations of reason. We can see this clearly in Hume’s own words.
. . . in all reasonings from experience, there is a step taken by the mind, which is not supported by any argument or process of the understanding; there is no danger, that these reasonings, on which almost all knowledge depends, will ever be affected by such a discovery. If the mind be not engaged by argument to make this step, it must be induced by some other principle of equal weight and authority; and that principle will preserve its influence as long as human nature remains the same.
For Hume, that principle is custom or habit. Ayer points us to the Treatise on Human Nature where Hume states,
. . . that all our reasonings concerning matters of fact are deriv’d from nothing but custom: and that belief is more properly an act of the sensitive, than of the cogitative part of our natures.
By sheer repetition of experience, the mind begins to naturally and automatically make the inductive step. It is not reason or universally intuited principles that serve as “the great guide to human life,” but rather custom built upon experience. Just as a dog expects to be fed by her master whenever he comes home from work, so also humans form inductive beliefs on the basis of instinct. When something happens often enough, we form the expectation that it will happen again.
Custom, then, is the great guide of human life. It is that principle alone, which renders our experience useful to us, and makes us expect, for the future, a similar train of events with those which have appeared in the past.
As we will see later, Hume’s point is not terribly challenging for the scientist. However, for the Christian it has potential to be highly problematic. By relegating inductive reasoning to habit, Hume believed he had demonstrated a fundamental weakness of our cognitive faculties. According to Hume,
. . . we cannot give a satisfactory reason, why we believe after a thousand experiments, that a stone will fall, or a fire burn; can we ever satisfy ourselves concerning any determination, which we may form, with regard to the origin of worlds, and the situation of nature, from, and to eternity?
Because the natural powers of the human mind are so limited, as a matter of practice we should refrain from metaphysical speculation. Or as Hume more eloquently puts it, we should limit “our enquiries to such subjects as are best adapted to the narrow capacity of human understanding.” If we can’t even justify induction, how can we possibly justify anything beyond our own immediate experience? Rather than advocating complete skepticism, Hume is simply espousing a naturalistic, mitigated version which rejects knowledge claims that go beyond immediate experience. Hume continues,
It seems to me, that the only objects of the abstract sciences or of demonstration are quantity and number, and that all attempts to extend this more perfect species of knowledge beyond these bounds are mere sophistry and illusion.
According to Flew, Hume’s point is that it is impossible to postulate “any universal proposition from any evidence which can be provided by experience.” While philosophers of science have wrestled with the implications of Hume’s thought for generations, all the scientist needed to do to free herself from the problem of induction was to abandon any universal or metaphysical conclusions. So, in essence, the problem of induction provides atheists like Hume, Flew, Ayer and Russell a key premise in the argument for scientific naturalism: we cannot and should not draw conclusions that transcend the very grounds upon which those conclusions are based.
The Principle of Induction
In formulating a response to this challenge, the Christian can look to what has come to be known as the principle of induction. It is important to note that Hume himself seems to speak of induction in terms of being a principle, as evidenced by the quotes above. Many philosophers have picked up on this, taking Hume’s intimations much farther. For example, Flew believes induction should be viewed as a rule guiding how we reason.
. . . the much talked about Principle of Induction should be construed: not as the wonder premise missing from Hume’s failed syllogism; but rather as a fundamental and primary rule of procedure for argument from experience.
While the principle of induction doesn’t prove that something is necessarily true, as with logical principles, it does prove that something is probably true. But Russell goes much farther than Flew, making an interesting connection between the principle of induction and the logical principles of thought.
In addition to the logical principles which enable us to prove from a given premise that something is certainly true, there are other logical principles which enable us to prove, from a given premise, that there is a greater or less probability that something is true. An example of such principles—perhaps the most important example is the inductive principle . . .
The logical principles of thought to which Russell alludes, are known a priori; they are self-evident laws that govern all reasoning. Can we say the same for the principle of induction? Or is it more appropriate to think of it as an ad hoc principle, which seems more in keeping with what Hume is saying? Consider what makes a principle of reason a priori. When we think of the logical laws of thought pertaining to contradiction and identity, we can say that they are properly basic. Their truth is prima facie; we accept them without the need of supporting argumentation. In fact, they are incapable of being supported by argumentation. As Russell points out, “logical principles are known to us, and cannot be themselves proved by experience, since all proof presupposes them.” Is this also the case with the principle of induction? Some of the most well-known commentators on Hume would seem to think so. Ayer asserts that there is no question that the principle of induction is universally assumed by all humans. In fact, he specifically connects it with the entire corpus of principles of logic, including causality, saying that, “They cannot be proved . . . nature is so constituted that we cannot avoid accepting them.” Returning to Flew, he adds:
it would be absurd to dismiss as irrational or non-rational all appeals to experience as a guide for our expectations, on the grounds that no further reason could be offered for such appeals beyond the ultimate reason that just this is a large part of what it is to be a rational man.
Perhaps Russell gives us our most forceful statements regarding the nature of the principle of induction. He begins by stating that “. . . the principle of induction . . . is itself not capable of being proved by experience, and yet is unhesitatingly believed by everyone, at least in all its concrete applications. In these characteristics the principle of induction does not stand alone.” He is, of course, speaking of the other laws of thought, such as identity, contradiction and excluded middle, all of which are self-evident and fundamental to all thinking. But is it proper to think of the principle of induction in this same way? It is if we think of it in terms that Alvin Plantinga proposes. “A self-evident proposition is such that a properly functioning (mature) human being can’t grasp it without believing it.” Certainly, this would seem to be the case with the principle of induction, which cannot be proven without assuming its truth. This is why Russell accepts it as a priori, and has no trouble connecting it with the logical principles of thought. Experience cannot confirm or confute these principles, and yet they all seem to be firmly rooted in our rational nature. Of course, if we are to conceive of the principle of induction as an a priori truth, then we have moved beyond the traditional understanding of the concept. Plantinga asserts that we should view a priori beliefs as displaying “the same defeasibility structure displayed by perceptual beliefs, inductive beliefs, and so on.” More specifically,
But it doesn’t follow that what has a priori intuitive warrant is indefeasible, or infallible, or rationally unrevisable or indubitable, or anything of that Cartesian sort. Nor does it even follow that beliefs formed a priori are independent of experience in that they can’t be corrected or defeated by beliefs from other sources—testimony, for example. It may be, of course, that the very highest degrees of warrant are occupied only by a priori beliefs . . .
Therefore, it is entirely reasonable to view a priori warrant as coming in degrees with some a priori principles being more certain than others. In this way, the logical principles of thought have a different kind of a priori warrant than the principle of induction. Russell refers to this as non-logical a priori knowledge.
This does not mean that Russell is advocating rationalism or that to accept what he is arguing is somehow to abandon empiricism. While empiricism maintains that all knowledge is derived from experience, being an empiricist does not preclude one from acknowledging that there exist certain aspects of our knowledge (such as the principles of thought) which are logically independent of experience. Russell is careful to distinguish that knowledge of these principles is not innate as a pure rationalist would maintain. However, while experience cannot prove them, it most certainly makes their existence known. “Even that part of our knowledge which is logically independent of experience (in the sense that experience cannot prove it) is yet elicited and caused by experience.” We might say that the distinction he is making is between cognitive content and cognitive capacity. We are not born into this world pre-loaded with knowledge (cognitive content). However, we are born into this world pre-loaded with principles of reasoning (cognitive capacity), that make possible the accumulation of knowledge. Russell concludes,
Thus, while admitting that all knowledge is elicited and caused by experience, we shall nevertheless hold that some knowledge is a priori, in the sense that the experience which makes us think of it does not suffice to prove it, but merely so directs our attention that we see its truth without requiring any proof from experience.
While I agree with Russell’s assessment, I am not convinced that it is a proper interpretation of Hume.
Hume would say that the principle of induction is something conditioned within us entirely based upon our experience. He would deny any overarching universal principle of reason, or laws which are hardwired, or pre-loaded into our cognitive structure. For Hume, the principle of induction strictly refers to custom itself, which produces ad hoc guides which have wrongly come to be construed as innate and a priori. In this regard, he is a true empiricist. However, I don’t think Russell is wrong in extrapolating something more on the basis of what Hume has demonstrated. Even if Hume is correct that we only come to form beliefs about causality and the uniformity of nature after having been exposed to repeated experience, he still must account for why it is that human nature is prone to consistently and uniformly form these beliefs. Is it logically necessary that we form these beliefs? If, as Hume suggests, we can easily conceive of a universe where nature is not uniform, then it is also just as easy for us to conceive of a universe where nature is uniform, and yet individuals fail to form beliefs about the uniformity of nature. Hume uses the first case to demonstrate that inductive beliefs are not logically necessary, but rather formed upon the basis of custom. But what about the second case? How would he address that? He doesn’t. His entire argument presupposes a necessary connection between repeated experience and the formation of certain beliefs about repeated experience. Hume assumes that this happens, but he never explains why it does. Hume’s own argument reveals a blind spot which seems to have been properly identified by Russell. The great guide to life is not custom or habit, but rather a priori principles of reasoning, such as the principle of induction, which govern all thought and the formation of knowledge.
Let us briefly consider a scenario that illustrates this point with greater clarity. Early in Hume’s Enquiry Concerning Human Understanding he considers a thought experiment which has come to be known as the missing shade of blue.
Suppose, therefore, a person to have enjoyed his sight for thirty years, and to have become perfectly acquainted with colours of all kinds, except one particular shade of blue, for instance, which it never has been his fortune to meet with. Let all the different shades of that colour, except that single one, be placed before him, descending gradually from the deepest to the lightest; it is plain, that he will perceive a blank, where that shade is wanting, and will be sensible, that there is a greater distance in that place between the contiguous colours than in any other. Now I ask, whether it be possible for him, from his own imagination, to supply this deficiency, and raise up to himself the idea of that particular shade, though it had never been conveyed to him by his senses?
Hume readily acknowledges that it is universally accepted that the man will indeed be able mentally conjure up the missing shade of blue, without ever having experienced it. Of course, this contradicts his maxim that it is impossible for ideas to arise apart from experience, also a point which Hume readily acknowledges. So, how does Hume explain this phenomenon? He doesn’t. Hume simply dismisses it as an anomaly. “[T]his instance is so singular, that it is scarcely worth our observing, and does not merit, that for it alone we should alter our general maxim.” But I’m not so sure it is as singular as Hume suggests. Perhaps, the missing shade of blue reveals the fundamental problem with Hume’s entire argument about induction and causality. Hume fails to acknowledge the possibility that the man’s ability to envision the missing shade of blue is due to an innate cognitive power of abstraction, by which the missing shade is produced by comparing and contrasting all other known shades. Likewise, he also fails to acknowledge the possibility that our ability to reason inductively is due to an innate cognitive capacity to make connections between repeated events. One can admit innate cognitive capacity (the power of abstraction and the ability to make causal connections) without admitting to innate cognitive content (that we have prior knowledge of the missing shades universal essence or that we have pre-loaded knowledge of the uniformity of nature).
Of course, even though Hume doesn’t overtly make this distinction, he certainly speaks in terms that lend themselves to drawing these conclusions. He readily acknowledges that there is something essential within the operations of the mind that leads us to make causal connections and inductive inferences. Ultimately, it is unexplainable to him, and he is unwilling to chalk it up to anything more than instinct.
As nature has taught us the use of our limbs, without giving us the knowledge of the muscles and nerves, by which they are actuated; so has she implanted in us an instinct, which carries forward the thought in a correspondent course to that which she has established among external objects; though we are ignorant of those powers and forces, on which this regular course and succession of objects totally depends.
But this is really not so far from where we wish to go in this discussion. If Humean scholar Robert Fogelin can say of Hume’s argument that “we are naturally determined – hardwired, as it were – to form certain beliefs in certain circumstances,” then why can’t we wonder if this power is an essential part of cognition? And if it is, why can’t we ask what accounts for that ability?
The Production of Inductive Reasoning
It is not difficult to imagine why Hume avoids this discussion. Once we acknowledge that we have this innate cognitive ability to reason inductively, it invites the question as to its origin. How do we account for the production of this cognitive capacity? Plantinga states that inductive reasoning is warranted on the basis that “that is how a properly functioning human being forms beliefs . . .” In other words, part of the design plan of humanity is the ability to form nondeductive beliefs about the future based upon past observations. This ability to recognize uniformity in nature, and form beliefs and predictions about the future, is an essential part of human nature. Plantinga turns to Thomas Reid, from whom he draws heavily, to make this point.
. . . the principle is necessary for us before we are able to discover it by reasoning, and therefore is made a part of our constitution, and produces its effects before the use of reason.”
Reid argues that this truth is demonstrated by looking at the natural practice of children, who clearly utilize the principle long before they can confirm it rationally. Inductive reasoning comes to us naturally. Additionally, Plantinga acknowledges that it is not a principle that can be confirmed noncircularly.
. . . suppose I do note that when what was future came to pass, it resembled what was past: that is to note no more than that past futures have resembled past pasts. It is only by employing the very principle (or habit) in question, however, that I can see this as confirming that future futures will resemble past futures. So I can’t noncircularly confirm Reid’s principle.
But Plantinga argues that this isn’t problematic, as there are many principles that we accept in a properly basic way. If this is not problematic for the laws of reason, then why should it be problematic for the principle of induction?
For Plantinga, what we see operating in human reasoning suggests “intentional design on the part of a conscious agent, one who takes thought and aims to accomplish a purpose.” In fact, he takes the formation of this idea itself to be properly basic. It seems we have an inclination to consider as designed any natural organism which displays purpose and proper function. Our epistemic structure and powers, including the ability to form inductive inferences and grasp the laws of reason, represent a significantly high degree of purpose. Given this, it seems only natural to think of our cognitive capabilities as functioning according to a design plan. “If you think there is no naturalistic analysis of these notions, what you have is a powerful argument against naturalism. Given the plausible alternatives, what you have, more specifically, is a powerful theistic argument.”
Plantinga’s overall argument against metaphysical naturalism‘ s inability to account for design is both complex and compelling. As such, it is beyond the scope of this paper. Speaking in evolutionary terms, Plantinga argues that since metaphysical naturalism tends to be skeptical of beliefs, with some even discounting them as legitimate causes of action, then reliable cognition is not necessarily more fitness-enhancing than that of an unreliable sort. If this is the case, then truth is irrelevant and the naturalist cannot argue that extensive false beliefs would lead to maladaptive behavior, which in turn would not be favored by natural selection. Plantinga concludes that the probability of metaphysical naturalism plus evolution generating reliable cognition aimed at the production of true beliefs is either very low, or inscrutable.
James Spiegel provides a more overt argument for theism, specifically built upon the regularities we find in nature. Drawing upon George Berkeley’s language metaphor in his 1732 apologetic Alciphron, Spiegel attempts to formulate a Berkeleyian approach to the problem of induction. In this polemic, Berkeley argues that we can infer the existence of God from signs in the world. Spiegel points us to the words of Euphranor, Berkeley’s spokesperson in Alciphron.
Though I cannot with eyes of flesh behold the invisible God, yet I do in the strictest sense behold and perceive by all my senses such signs and tokens, such effects and operations, as suggest, indicate and demonstrate an invisible God, as certainly, and with the same evidence, at least, as any other signs perceived by sense do suggest to me the existence of your soul, spirit, or thinking principle . . .”
Just as we infer the existence of other minds (an invisible, rational cause) from the outward signs displayed by others (specifically language), we can infer the existence of an invisible, universal agent speaking through the workings of nature. “Like human language, the language of nature has a syntax, which we call the laws of nature.” Again, pointing to Berkeley’s own words:
The phenomena of nature, which strike on the senses and are understood by the mind, form not only a magnificent spectacle but also a most coherent, entertaining, and instructive . . . language or discourse.
Spiegel’s point is that along with the logical laws of thought (which Berkeley would have considered part of the language of nature), we can include the principle of induction. All of these principles together make up the syntax of nature, functioning very much like human language. Much like Plantinga’s argument above, this leads us quite naturally to think of this syntax in terms of being designed by an intelligent being. But whereas Plantinga locates his argument in the design plan evidenced by our cognitive faculties functioning properly, Speigel’s Berkeleyian approach is more focused outward, on the regularities found in nature. There are three steps in his argument.
- We begin with the observation that there are regularities in nature that help sustain and prosper life. Because these regularities have obtained universally and without exception (given certain qualifications), humanity has not only been able to survive, we have flourished. Since these regularities are fundamental to scientific discovery, we have been able to make astounding advances in science and technology. This has led to even greater benefits for humanity. In fact, these regularities are what have allowed us to discover more and more of the syntax of nature (its laws and principles).
- We next move to the conclusion that these regularities, benefits and syntax (laws of nature) are the result of an intelligent, purposeful and powerful mind which has designed the universe for our benefit.
- We conclude by maintaining that since this God is so obviously benevolent, we can trust that he will continue to maintain these regularities, benefits and laws. In other words, we can have complete confidence in the uniformity of nature that the future will continue to resemble the past.
We might add that while it is not logically necessary that nature remain uniform, Hume is correct that we can conceive of a universe where it doesn’t hold; it certainly seems logically necessary in a universe where God exists. It would be contradictory to God’s benevolent nature if he allowed the uniformity of nature to cease. In conclusion, Spiegel summarizes his argument.
In short, 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.
While Spiegel’s and Plantinga’s approaches clearly differ, they do share two common points. First, they point to design as evidence of divine intelligence and purpose standing behind the workings of the universe. Second, they both maintain the inability of metaphysical naturalism to properly account for the design found in nature. Spiegel states,
When it comes to the basic principle that nature is uniform, the scientist, whether or not she believes in the supernatural, exercises faith, precisely because no empirical evidence sufficient to justify this belief can be provided.
If you are dead certain naturalism is true, you will have to accept the cost, not only of rejecting this account of warrant, but of rejecting the very idea of proper function. A high price, no doubt—but no more than what a serious naturalism exacts.
Ultimately, it is their differences that leads me to favor Plantinga’s approach. On the one hand, Plantinga is justifying inductive reasoning on the grounds that it represents a properly basic belief, which in turn points to intentional design on the part of a conscious agent. Spiegel seems to approach the matter from the completely opposite direction, using the existence of a benevolent God to justify inductive reasoning and our continued belief in the uniformity of nature. The problem with this is that Spiegel opens himself up to Hume’s familiar charge of circular reasoning. He has essentially used the uniformity of God’s nature, or UGN, to justify our belief in UN. Spiegel’s Berkeleyian approach now has to address questions about the uniformity and benevolence of God’s nature. Specifically, how do we know that God’s past benevolence will continue into the future? Additionally, if we are going to argue that a failure of the uniformity of nature would be irreconcilable with the benevolent nature of God, then by the same logic we could reason that the existence of evil is irreconcilable as well. As theists, we know that the existence of evil is not incompatible with the existence of God. So, why should we suppose that the existence of dis-uniformity would? Because he doesn’t invoke the existence of God to justify inductive reasoning, Plantinga’s simplicity is to be preferred.
I began this paper by stating that the problem of induction was possibly a more troubling idea for the Christian than it ever was for the scientist – at least this has been the claim of scientific and metaphysical naturalists alike. My hope is that by facing the problem head on and seeing it for what it is, we have actually reversed that claim and demonstrated that it is more problematic for the atheist. Inductive reasoning provides a compelling premise in our overall argument for an intelligently designed universe.
 This paper will limit its focus to what has come to be called the old riddle of induction. The new riddle of induction, which deals with the question of what makes a property projectible, is not pertinent to my overall purpose of using inductive reasoning to point to the existence of God.
 Antony Flew, A Dictionary of Philosophy (Oxford: Oxford University Press, 1979), 171.
 I’m thinking here of Popper’s attempt to account for scientific knowledge on non-inductive grounds. Popper accepted Hume’s idea that inductive reasoning was completely without justification and maintained that scientists need only use deductive inferences. While it is not possible to prove a scientific theory true on the basis of limited observation (by induction), it is possible to prove a scientific theory false (by deduction).
 Antony Flew, Hume’s Philosophy of Belief: A Study of His First Inquiry (New York: Routledge Press, 2013), 80. Newton’s work was published in 1687, a few decades before the birth of Hume. His comments are quite sophisticated, anticipating some of the later discussion among philosophers of science wrestling with Hume’s writings on induction.
 Samir Okasha, Philosophy of Science: A Very Short Introduction (Oxford: Oxford University Press, 2002), 24.
 David Hume, An Enquiry Concerning Human Understanding, ed. Peter Millican (Oxford: Oxford University Press, 2007), 18.
 Okasha, Philosophy of Science, 27.
 Bertrand Russell, The Problems of Philosophy (Overland Park, KS: Digireads.com Press, 2011), 44-45, Kindle.
 Richard Swinburne, introduction to The Justification of Induction, ed. Richard Swinburne (Oxford: Oxford University Press, 1974), 6-7. Total relevant knowledge would include anything that might affect the probability of the conclusion. While “all swans are white” is a common example of inductive reasoning, it actually represents a bad inductive conclusion. Given what was known prior to Captain Cook’s discovery of black swans, an induction based upon species coloration had a high probability of error. Even at that time it was general knowledge that in multiple species of animals, color is a common variable characteristic.
 Robert J. Fogelin, “Hume’s Scepticism” in The Cambridge Companion to Hume, ed. David Fate Norton (Cambridge: Cambridge University Press, 1993), 95.
 Hume, Enquiry, 138.
 Alexander Rosenberg, “Hume and the Philosophy of Science,” in The Cambridge Companion to Hume, ed. David Fate Norton (Cambridge: Cambridge University Press, 1993), 77.
 Hume, Enquiry, 26.
 Alvin Plantinga, Warrant and Proper Function (Oxford: Oxford University Press, 1993), 126.
 A. J. Ayer, Hume: A Very Short Introduction (Oxford: Oxford University Press, 2000), 91; Flew, Hume’s Philosophy of Belief, 70, 88. The argument that follows is largely built upon the common flow of Flew and Ayer’s arguments. I will admit that I am clearly using observations by Flew, Ayer, and Russell (a bit later) in a manner that they would likely find unacceptable. However, my point is that even in the writings of some of the most well-known atheists, we can find elements that both undermine Hume’s thesis and, when properly understood, set us on a path to find evidence of theistic design in nature.
 Hume, Enquiry, 30.
 Ayer, Hume, 86
 Hume, Enquiry, 32.
 Ibid., 118.
 Rosenberg, “Hume and the Philosophy of Science,” 76.
 Hume, Enquiry, 118
 Flew, Hume’s Philosophy of Belief, 71.
 For example, logical positivism has its roots in Hume’s empiricism. It is easy to see Ayer’s verification principle as a natural outgrowth of Hume’s argument regarding inductive reasoning.
 Ibid., 88. It seems that Flew has included a subtle critique of his colleague Russell, who put the principle of induction forth to serve as the hidden premise in every inductive argument. In this way, Russell seemed to be attempting to make inductive reasoning logically conclusive, by converting it to a deduction.
 Russell, Problems, 50-51.
 Ibid., 51.
 Ayer, Hume, 87
 Flew, Hume’s Philosophy of Belief, 79.
 Russell, Problems, 48.
 Plantinga, Warrant, 108.
 Ibid., 112.
 Ibid., 111-112.
 Russell, Problems, 53.
 Ibid., 51.
 Ibid., 52. Russell’s argument that we must accept the principle of induction a priori or embrace total skepticism is not without contention. Russell states that “we must either accept the inductive principle on the ground of its intrinsic evidence or forgo all justification of our expectations about the future (56).” Paul Edwards argued that it was not necessary to embrace a non-empirical principle, arguing instead that we can provide justification for induction without begging the question. See Paul Edwards, “Russell’s Doubts About Induction,” in The Justification of Induction, ed. Richard Swinburne (Oxford: Oxford University Press, 1974), 19-25.
 Hume, Enquiry, 14.
 Ibid., 40.
 Fogelin, Hume’s Scepticism, 112.
 Plantinga, Warrant, 136.
 Ibid., 122.
 Ibid., 123.
 Ibid., 126.
 Ibid., 195.
 A case he makes in Warranted Christian Belief.
 Ibid., 214. Plantinga considers this to be a version of Thomas Aquinas’s Fifth Way, and at this point quotes Aquinas at length: “The fifth way is taken from the governance of the world. We see that things which lack knowledge, such as natural bodies, act for an end, and this is evident from their acting always, or nearly always, in the same way, so as to obtain the best result. Hence it is plain that they achieve their end, not fortuitously, but designedly. Now whatever lacks knowledge cannot move towards an end, unless it be directed by some being endowed with knowledge and intelligence; as the arrow is directed by the archer. Therefore some intelligent being exists by whom all natural things are directed to their end; and this being we call God.” As part of his overall argument, Plantinga agrees with the claim of Richard Dawkins that evolution is a “blind watchmaker,” arguing that evolution cannot produce design without the assistance of a divine watch-maker.
 He is constructing an argument based upon how he believes Berkeley would have responded to Hume. Even though Berkeley was alive at the time Hume first published his thoughts on induction, he never specifically addresses it in his writings.
 James Spiegel, “A Berkeleyan Approach to the Problem of Induction,” Science & Christian Belief 10, no. 1 (April 1998): 77
 Ibid., 78.
 Ibid. Here he is quoting from Siris.
 Spiegel, 79.
 Ibid., 80.
 Planting, Warrant, 213. He follows this up rather nicely by asserting, “the way to be a naturalist in epistemology, is to be a supernaturalist in ontology.”