This is part seven in my series on science.Here are the other parts: Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, Part 9, Part 10, and Bibliography.

The problem of induction:

Let’s say that we observe a large number of objects with characteristic A, noting that all of them also possess characteristic B. It is natural for us to conclude that, in all probability, all objects with A also possess B — including those objects with A that have yet to be observed (or cannot be observed). The question Hume asked is, “What rational justification is there for making this inference?” In essence, what reason do we have to believe that our conclusions about observed instances may be extended (even with probability) to include unobserved instances? The same question is also framed in temporal terms: What reason do we have to think that we can draw reliable conclusions about future (unobserved) instances on the basis of past (observed) instances?

Responses:
1. The common sense inductive response
That usually comes like this “Because it has been proved to be true in the past.” The problem with this answer is that it begs the question. The reply itself takes the form of an inductive argument — reasoning about the future on the basis of the past — and it must presuppose the very thing it aims to establish: the inductive principle. It is guilty of circular reasoning. As Hume puts it:
“To say [the inference that the future will be like the past] is experimental [i.e., based on experience], is begging the question. For all inferences from experience suppose, as their foundation, that the future will resemble the past, and that similar powers will be conjoined with similar sensible qualities. 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. It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future; since all these arguments are founded on the supposition of that resemblance.”

3. The return of Karl Popper:

Popper actually concedes Hume’s position on the problem and the solution he offers is to a different problem (one that asks whether past experience can ever justify attributing a truth value {i.e., either ‘true’ or ‘false’} to a scientific theory). Popper argues that a scientific theory, involving predictions about future instances, can indeed be shown to be false, by present or past observations (about this, he was correct). His argument, here, provides no reason for thinking that scientific theories can be shown to be true (or even probably true), by present or past observations. Popper actually believes that no such reason can be given and leaves neither an answer to Hume nor an answer to whether empirically based theories are likely to be true.

4. Pragmatic defense of Reichenbach and Salmon:

Reichenbach and Salmon rejected inductive and deductive attempts and chose a different route. Reichenbach argues that it is more intelligent to ‘bet’ on inductive reasoning than on other alternative methods of reasoning from experience. If we use induction, then we have at least some chance of being right (that is, if it turns out that the inductive principle is true), and, on the other hand, if we choose to use some alternative method, then we have no chance of success (regardless of whether the inductive principle is true). That’s why we are justified in choosing induction.

The problem with this is that it is a pragmatic justification and not an epistemic justification. It may motivate us to reason inductively, but it gives us no indication of the actual likelihood of its success (that being whether or not the inductive principle is true). In this respect, it suffers from the same problem as Pascal’s Wager. It may offer motivation for believing in God, but it leaves us still not knowing if He actually exists. A solution to the problem of induction requires an epistemic justification for believing that induction is reliable.

5. P.F. Strawson (language response):

In the last century, many looked into the philosophy of language to answer the philosophical questions (logical atomist). Logical positivism was one of these schools of thought. Strawson thinks of the inductive skeptic as doubting whether relying on inductive procedures is “reasonable” (i.e. epistemically justified). Strawson argues that our very understanding and use of the word “reasonable” includes the idea of conformance with inductive standards, in the present context. For example, when we say that a scientific theory about a natural law is “reasonable,” we are saying, at least, that it draws general conclusions based on an appropriate number of observed instances. Therefore, his statement “induction is reasonable” is an analytic truth, and the inductive skeptic is confused in the same way as the one who asks, “Is the law legal?”

There is something wrong with Strawson’s explanation. He, in the same passage, concedes that the statement “induction will continue to be successful” is contingently true, if true at all. This is why the “inductive skeptic” is worried. This shows that the skeptic can always rephrase his doubts and, in so doing, avoid Strawson’s “immune” terms, like “reasonable” and “justified.”
Even if Strawson is right that our everyday usage of the word “reasonable” includes the idea of conformance to inductive standards, it is still inadequate. For example, suppose there was a community where wishful thinking was considered a respectable and reasonable way of coming to conclusions about the future. For that community, its own linguistic usage of the statement “wishful thinking is reasonable” would be analytically true, but we would be within our rights to question their usage of such epistemic methods. In the same way, Strawson’s claim that “‘induction is reasonable’ cannot be meaningfully denied” is compatible with Hume’s conclusions.

6. A Priori explanation by BonJour:

Laurence BonJour thinks that only an a priori justification for induction offers any possibility of a solution.

Very important to his scheme is that there is an objective regularity in the universe. This regularity is of the same sort presupposed by inductive inference. This can be justified, a priori, by taking it to offer the best explanation of the standard inductive evidence, which is of those orderly, observed instances employed in the premise of an inductive argument. He does, however, recognize that this claim “depends on the tenability of a non-Humean, metaphysically robust conception of objective regularity (or objective necessary connection),” which is to say that it presupposes a universe in which there are real and constant (or near-constant) causal relations between the objects within it.
While he acknowledges the difficulties of his view, he believes that there still is hope for it. He gives no indication as to how one might even begin to provide an a priori justification for such a significant metaphysical perspective, though, and that is a major problem for his view. It was arguably Hume’s doubts about whether we could know of any “metaphysically robust objective regularity” that kicked off BonJour’s inductive skepticism, in the first place. The justification of our belief in the kind of universe that makes inductive inference possible is the very crux of the problem of induction. We must conclude that his proposed route takes us, at best, only a fraction of the way to a possible explanation.
Dr. J. P. Moreland comments about this attempt “Other philosophers have attempted to “justify” induction by claiming that inductive inferences are simply what we mean by using ordinary English words like rational, evidence, and so on. In English we use the word evidence simply to mean inductive evidence. The word rational means the following: “Rational= A belief is rational if and only if it is formed according to rule R where R is simply inductive inference(i.e., If all observed A will be B, then probably the next A  will be B ).”
The main problem with the ordinary-language defense of induction is that rationality is a matter not of behaving according to some word in language, but of approaching beliefs in a way that is intrinsically justifiable in a normative sense. In other words, what one wants is really to be rational, to have beliefs one ought to have, not merely to behave according to what the English language users mean by the word rational. After all, English could have developed among irrational people.
Furthermore, the ordinary-language argument fails to answer the problem of induction for another reason. Suppose we introduce a new word into English as follows: “Brashional= A belief is brashional if and only if it is formed according to rule R1 where R1 is simply counterinductive inference(i.e., if all observed As have been B, then probably  the next A will not have been B ).”
Brashional is defined according to counterinduction, in which inductive inferences break down. Hume’s problem of induction can now be restated as follows: Why should we prefer to be rational instead of brashional? The ordinary-language argument does not seem to be able to answer this question.”

7. Coherentism explanation:

What is Coherentism? It is the belief that to have a justified belief or set of beliefs they must be coherent with other sets of beliefs. Coherentism is different from the Coherence theory of truth. Which just maintains that something is true if it is coherent. They wish to say they are completely justified in believing they have solved the problem of Induction by taking a different position on justification itself. As the belief that “Nature is uniform” would perfectly cohere in their set of beliefs. Since they maintain that justification is a matter of a relationship between beliefs they are right. The problem of induction is that it doesn’t solve the problem of induction. For the issue of induction is how does one account for the uniformity of nature. This doesn’t address the issue of why we have uniformity in this world instead of the opposite. It also has the problem that we may have systems that are coherent and reject the uniformity of nature. Both systems would be equally justified.

8. The Objectivist explanation:

The objectivist argues that the answer is in the Law of identity. They argue that nature is by definition uniform. That A=A, or Nature=Uniform. This followed by the maxim “Existence exists”. This position misses the point that the law of identity doesn’t tell you how an object exists. We also have to remember that things can be self-identical and yet not exist(leprechauns, unicorn, Santa). We may also note that existence doesn’t exist on a materialist and nominalist, but is rather a universal. That it is exemplified in existents. You can’t taste, see, touch, smell or hear existence. It also reduces to a tautology that “Nature=Nature”.

9. Tu quoque response:

This is where the objector admits the failure of secular philosophy and only can attack the Christian worldview. He or she attempts to show that the Christian says God violates natural laws, and, therefore, the Christian cannot account for induction either. Michael Martin tried this with “TANG.”

Dr. Michael Butler has said:
“The problem with this is the perspective on “violations of natural laws.” There are competing definitions of natural law in the philosophy of science. Is a natural law descriptive or prescriptive? We already deny natural laws; God needs not violate them. It, then, must be pointed out that we do not know all the laws of nature, to say they would be violated. They do not define miracles correctly, and that leaves their objection as a strawman. The critical question is “What is a miracle?”
Dr. Martin asserts that science and Christianity are incompatible. He argues that since science presupposes the uniformity of nature and Christian theology teaches that God can and does perform miracles (which Dr. Martin defines as violations of the uniformity of nature), then science is inconsistent with Christianity. But why is this so? Even granting his definition of a miracle, why does it follow that science becomes impossible if there is no absolute uniformity of nature? Dr. Martin does not tell us. I would guess that he would contend that scientists would have an insurmountable, epistemological problem. Scientists would never know whether to fix the cause of an event to natural laws or to divine intervention. However, this is simply not true. How does it follow that there is no way to distinguish between a miracle and an event that is in accordance with natural laws? Dr. Martin’s definition of miracles, moreover, is somewhat defective. Christian theology teaches that God providentially is in charge of all events; all events are under his direct control. There are, thus, no impersonal natural laws. Under Dr. Martin’s definition, all events are miraculous. The Christian view of miracles is that they are events God causes to come about in a different way from His regular pattern for directing events. Thus, when humans die they usually stay dead, but, in the case of Jesus, God raised Jesus up. In doing so, God did not violate a natural law, but, rather, He departed from His regular pattern of action. Dr. Martin then states, “science assumes that insofar as an event has an explanation at all, it has a scientific explanation-one that does not presuppose God.” All Dr. Martin is telling us here is his view of science, but this begs the whole question. Of course atheistic scientists assume this, but Christian scientists do not. This does nothing to advance Dr. Martin’s argument that miracles are incompatible with science.
Dr. Martin begs the question regarding miracles. As Dr. Bahnsen has written, “[unbelievers] often think that they are treating the miracle-claims of the Bible as independent evidence that the Christian worldview is irrationally unacceptable. Their reasoning is something like this: we already know miracles do not occur (‘How could anybody believe…’), and since Christianity claims that such impossible things did occur (e.g., virgin birth, resurrection), we can draw the conclusion that Christianity must be false. But that conclusion is not so much ‘drawn” as it is taken for granted from the very outset. The denial of the very possibility of miracles is not a piece of evidence for rejecting the Christian worldview, but simply a specific manifestation of that very rejection. Only if the Christian worldview happens to be false could the possibility of miracles be cogently precluded. According to Scripture’s account, God is the transcendent and almighty Creator of heaven and earth. Everything owes its very existence and character to His creative power and definition (Gen. 1; Neh. 9:6; Col. 1:16-17). He makes things the way they are and determines that they function as they do. ‘His understanding is infinite’ (Ps. 147:5). Moreover, God sovereignly governs every event that transpires, determining what, when, where, and how anything takes place-from the movement of the planets to the decrees of kings to the very hairs of our heads (Eph. 1:11). According to the Bible, He is omnipotent and in total control of the universe. Isaiah 40 celebrates in famous phraseology the creation, delineating, directing, providence, and power of Jehovah (vv. 12, 22-28). He has the freedom and control over the created order that the potter has over the clay (Rom. 9:21). As the Psalmist affirms, ‘Our God is in the heavens; He has done whatsoever He pleased’ (115:3). [8]It is on the atheist’s worldview that there is no basis to assume the uniformity of nature. The philosopher David Hume has taught us that to say the future will be like the past is to beg the question. [9]Since the uniformity of nature is an unjustified assumption on the atheist’s worldview, he has no basis upon which to engage in scientific activities. 10.That the uniformity of nature is compatible with the Christian worldview is easily proven (remember that this unity is not an absolute one). God, who is providentially in control of all events, has revealed to us that we can count on regularities in the natural world. The Bible teaches that God providentially causes the harvest to come in due season, for example. Because of this regularity, we can be assured that scientific endeavors will be fruitful. Thus, far from presupposing the falsity of Christianity, science would be impossible without the truth of the Christian worldview.”

“2. (a) Science does not presuppose any absolute uniformity of nature; indeed modern science allows for areas of randomness in the universe. (b) Miracles are not necessarily violations or exceptions to natural law; sometimes they even have natural explanations (e.g. Ex. 14:21, the “strong east wind”). (c) There is no scientific consensus that scientific explanations must never presuppose God. This supposition is entirely groundless. Of course, divine providence is not in itself a scientific explanation. But there is no scientific rule to the effect that proper scientific explanations may not, in turn, presuppose divine providence”
Dr. John Frame

One comes across a tomb entitled “The Tomb of the Philosophers.” They look at the door and find an inscription. It reads this:
“1 Corinthians 1:20
‘Where is the wise man? Where is the scribe? Where is the debater of this age? Has not God made foolish the wisdom of the world?'”