To begin, we should notice that Chris hasn't clearly articulated the reasoning behind his central objection that induction is unjustified on a secular view. In particular, even after six months of debate and blogging correspondence, he has never explained what his standards of justification are. I warned him about this deficiency back in November of 2010, writing that
there is a second possible interpretation of your criticism, which is that any non-deductive inference should be taken as invalid and therefore irrational. But if that's what you're saying, then I would simply reject whatever standard of rationality leads you to make that judgment. Non-deductive reasoning, e.g. inductive reasoning, is not irrational simply because it's not deductively valid---at least, not by my standard... But whatever you are using as a standard of rationality, I must insist that on my standard, there is at least one form of non-deductive reasoning which is perfectly rational: inductive reasoning. (source)
In our latest correspondence (which he has as yet declined to make public), I pressed the point:
I need you to explain, what are your standards of reasoning? What criteria do we use to distinguish good reasons from bad reasons? For me, my standards of reasoning cover inductive inferences directly. In other words, according to my standards, a cogent inductive argument IS a good reason to believe some conclusion! It seems to me that most people, including scientists and philosophers, use similar standards. But you apparently don't want to use a standard which directly grants inductive inferences as reasonable/rational/justified/etc. Well, okay. But then I have to ask, what DOES make for good reason, on your view?
For causes unknown to me, he has persistently declined to volunteer this rather essential information---and, to be sure, it is essential. He clearly intends to use different standards of rational justification than I do; but if he cannot articulate those standards, then how can he ever show that induction is "justified" by presupposing the existence of the God of Calvinism?
Indeed, his case for getting induction from Calvinism is extremely vague. Consider his remarks from our Skype debate in August 2010:
If God exists, then he created and hence caused us, our minds, and the world that we know with our minds, and the way that they all work. On this presupposition our conceptual scheme is automatically in touch with and corresponds to objects of experience with God as the connecting link. If we deny this view, then there's nothing to connect the [unintelligible] to God. But God is the connecting link between everything else. What is left is a loose and disjointed epistemology. There are, in this case, random objects of knowledge not connected together by God's creative, sovereign, fore-ordaining Word. There are not objects connected to the mind of man and his conceptual scheme. By definition, this world view cannot answer the skeptic, because it begins with a separation between the mind and objects in the world. Since God has not been brought into the picture at the start, we have what we might call an egocentric predicament. On the other hand, there is no egocentric predicament for the creationist. (source)
This is all I could find in his opening statement which resembled any kind of positive case for taking inductive inferences as justified. Since then, I have asked him to clarify his position, but thus far he has declined. This is unsurprising, considering the difficulty of his task. In fact, the alleged existence of God, whether Calvinist, Catholic or Muslim, simply does not help us along to finding appropriate standards of justification; given that induction is required to hold onto any conception of the external world (and even our private thoughts), it's easy to see that religious doctrines are likewise incapable of providing us the means of using a given standard to justify induction indirectly. The attempted solution which Chris presented in our debate falls into circularity, as I explained in our correspondence:
The problem with this position is that it already assumes induction. God's causal powers, as Hume pointed out in his famous essay, like all causal powers, consist only of our inferred or assumed regularities set in the context of other such inferred/assumed regularities. So, you can make all the assumptions or inferences you like, but they will only be rationally justified if they meet with some standard of rationality/justification. And since this is what we're after, an (unjustified) assumption that God has such causal powers, i.e. that the regularities you wish to infer already hold, isn't going to help us in the least. That's why I said you haven't been able to show any coherent and uniquely religious answer to induction. You're not adding anything relevant to the conversation when you talk about a creator-deity.
All Chris can do is to assume what we all assume---that induction is justified---and then, on top of that, assume that the God of Calvinism exists, that He created the universe and everything in it, that he inspired the 66-book Protestant Bible, that only his favorite strain of Calvinism properly interprets that Bible, etc. He's not giving us a novel way to deal with induction. Instead, he's only adding superfluous nonsense to what we already accept about induction!
In fact, we can generalize on this approach: Notice that inductive inferences are justified if and only if they meet with our standards of justification. If those standards are independent of the existence or nonexistence of God, then so too is the justification of induction. If on the other hand those standards depend on the existence or nonexistence of God, then we require from Chris an explanation of how his standards differ from non-Calvinist standards, and furthermore why we should be interested in using those standards. After all, how can we ever suppose that induction is justified on Chris's view if we don't know what his standards are? And even once we are able to identify them, why should we exchange our pre-existing non-Calvinist standards for his uniquely Calvinist standards? So far, he has declined to address either of those issues.
It's hard to anticipate what Chris might want to use as a standard for justification, but I suspect it must have something to do with the Protestant Bible. However, in order to make sense even just of the words on the pages---the very strokes of ink which make up the Hebrew, Greek and Aramaic characters---we need to have some kind of coherent conception of language already in place, and this requires induction. If we wish to make sense of the thoughts expressed by that language, for example the notion of Delilah having her lover's hair cut, we must first know what cutting and hair are, which is to say that we rely on the regularities of the world which make cutting hair possible. So, if Chris wants to use the Bible as a part of a standard of rationality or justification, he can only do so against the backdrop of some kind of uniformity of nature. In short, Chris would have the cart before the horse: induction is required in order to make sense of the Bible, not the other way around. If he wishes to use the Bible as part of his standards of justification, then it will only be on top of the inductive standards he must also use. Again, Chris would not be contributing anything relevant to the discussion of induction, or providing a uniquely Calvinist substitute for secular inductive standards; he would only be tacking on superfluous religious dogma to the inductive standards we already use.
Moreover, the Bible actually conflicts with the inductive standards we ordinarily use, as I informed Chris in our correspondence:
If you want to re-define the word "rational" in that way [such that accepting the Calvinist interpretation of the Bible is rational a priori by our standards of justification], then you are welcome to do so, though I will not follow you in your peculiar convention. The result, however, is a great inconsistency, unless you jettison some of the word's current meaning. In particular, induction compels us to accept truths which are plainly at odds with your form of Christianity, for example that the earth is billions of years old, and that we evolved from lower forms of life. Induction shows us that prayer is ineffective in curing disease, and that at least a few of the books of the New Testament were forged. (source)
Chris's defense against these charges consists of little more than claiming that they are merely unsupported assertions on my part. Yet clearly this is not the case. While it may be true that I have not personally marshaled all the evidence in favor of geologic time, biological evolution, the medical inefficacy of prayer, or the forgery of certain New Testament books, who can credibly deny that geologists, biologists, historians and other scientists have not done so in my absence? It seems an act of desperation to demand that I personally reproduce the arguments and experiments developed by these experts before we can accept their results. In the mean time, anyone familiar with these issues ought to know very well that the evidence points against the respective religious dogmas. These kinds of radical denials ought not even be taken seriously, a lesson we should have learned from our experience with Kent Hovind, Ken Ham and Kirk Cameron, among others. The only reasonable response available to Chris, it seems to me, is to acknowledge that the physical evidence really does point us away from his brand of Calvinism, but that we have other reasons to accept Calvinism which somehow trump that evidence. Unfortunately, this defense only works out if we can actually produce those reasons, which thus far he has not done, and which indeed it appears he cannot ever succeed in doing.
In contrast, secular standards of justification appear to me quite sufficient for accepting induction as rational. In the course of our debate and ensuing correspondence, I have addressed three particular concerns regarding inductive standards: First, we might ask, is it rational to choose to use induction? As I pointed out in the debate, however, we don't have a choice, here; we will use induction, whether or not we make a conscious choice to do so. This was the position of David Hume, and indeed Chris agreed with it at the time of our debate, even though he inexplicably thinks we need God to be able to agree. Second of our concerns is this: are individual inductive inferences rationally justified? Recall again that inductive inferences are justified if and only if they meet with our standards of rational justification. Along with philosopher Peter Strawson, I suggest that those standards deal directly with induction. In other words, a strong inductive case is part of what we mean by rational justification. To put it another way---and to borrow Strawson's analogy---asking whether or not inductive inferences are rationally justified is a bit like asking whether or not laws are legal. I furthermore suggest that Chris must use similar standards if he is to make sense of the world---even if he is to make sense of God---since induction is a prerequisite to that purpose. Third, and finally, we could inquire as to whether or not we have any motivation for using a standard of justification which permits inductive inferences. The answer to this question seems a resounding yes, since as I illustrated in great detail in our Skype debate, induction is absolutely required if we wish to develop any plans or strategies for predicting and controlling our experiences. So, if we want to be actors in the world, we ought to use inductive standards.
Although these three issues all regard induction in some way, they differ quite dramatically from one another, and accordingly demand differing responses. Chris, however, seems not to agree. He writes (emphasis original):
...the various answers that are being provided are not the same answer to the problem of induction. For example, an a priori solution to the problem of induction is not the same as a pragmatic solution to the problem of induction, however Ben has used both. This is not necessarily a problem insofar as the attempted answers are consistent with one another, but I am not sure Ben is even aware that he is offering multiple answers, and whether or not they are consistent with one another is debatable. (source)
Needless to say, I'm very much aware of the differences between my answers, and this all stems from the fact that there are different issues which demand our attention. Why, then, should Chris express surprise at my varying points? Perhaps he thinks we should only deal with one single issue, and ignore the others; but then on which issue does he want to focus our attention? He has not indicated to me anything which might suggest an answer to this. Alternatively, maybe he just doesn't appreciate the distinctions I've drawn. Yet if that is the case, then he seems to be in no position to disagree with my view, since one must first understand a view before one may sensibly oppose it. So, all this underscores the deficiencies in his own position. At best, Chris has neglected to offer uniquely Calvinist account of induction, while ignoring no less than two essential concerns regarding induction. At worst, he has conflated several of the distinct issues involved, causing him to adopt an ultimately incoherent position on induction and engage in a fundamentally unintelligible criticism of mine.
Whatever unspoken content his caginess has hidden from us, one fact stands out from our correspondence as abundantly clear: Calvinism is useless for helping us deal with induction. Chris is in exactly the same boat that we all are---that is, whether or not we realize it, we all use inductive standards of justification whenever we make sense of the otherwise disconnected experiences we have. Chris is not somehow exempt from this unavoidable human situation. Presuppositionalist Calvinists like to say that non-Calvinists "borrow" from the Calvinist world view, but ironically enough, in this case it is the Calvinist who is using independently secular standards without realizing it. The only difference between us is that, in addition to using those secular inductive standards, Chris has lumped in a host of arbitrary religious dogma along with them. If he thinks he can justify that dogma, he is welcome to continue to try to do so. However, he will make no progress towards that goal by invoking the circularity of using induction to make sense of Calvinist theology, then in turn claiming that Calvinist theology justifies inductive inferences. To the extent that the task depends on that circularity, Calvinism is thusly impotent for justifying itself.