Some Clarifications on an Argument Against the Bible Being a Fallible Collection of Infallible Books

In previous posts (HERE and HERE), I formulated the following argument against the Bible being a fallible collection of infallible books:

1. If a collection of books is fallible, then it can be the case that something that one of the books in the collection teaches is wrong (since at least one of the books could be fallible).
2. If a collection of books is a collection of infallible books, then all of the books in the collection are infallible.
3. If a book is infallible, then it cannot be the case that something it teaches is wrong.
4. Therefore, if a collection of books is a collection of infallible books, then all of the books in the collection are such that it cannot be the case that something that one of the books in the collection teaches is wrong (2, 3).
5. Therefore, if a collection of books is a collection of infallible books, then it is not the case that the collection of books is fallible (1, 4).
6. Assume for reductio that Sacred Scripture is a fallible collection of infallible books.
7. Then, Sacred Scripture is not a fallible collection of infallible books (5, 6).
8. Contradiction (6, 7). Therefore, Sacred Scripture is not a fallible collection of infallible books.

After recently receiving some friendly pushback on this argument in the form of private correspondence, I would like to clarify some of the fundamental principles and assumptions at play in the argument which were left implicit in previous presentations.

Probably the most significant clarification is that the modality I generally have in mind in this argument when I say that it can be the case that such-and-such is epistemic modality. In this regard, to say that something is epistemically possible, for instance, is to say that it could, for all I know, be the case. For example, for all I know, it could rain tomorrow. This kind of possibility is distinct from metaphysical possibility. A simple example will illustrate this distinction. Consider the Riemann hypothesis (perhaps the most famous unproven conjecture in mathematics). As a mathematical statement, the Riemann hypothesis is either (metaphysically) necessarily true or necessarily false. However, since it has yet to be proven, it may for all we know be true, and it may for all we know be false. Even if the hypothesis is necessarily true (metaphysically), it may be false for all we know. That is to say, it is epistemically possible that it is false even if it is metaphysically necessary that it is true. Another thing to make note of is that unlike metaphysical possibility, epistemic possibility is person-relative. Something could be epistemically possible for me that is not epistemically possible for you, and this is because I know things that you don't, and you know things that I don't.

With this clarification in mind, what the argument is really driving at is that, for someone who believes that the canon is fallible, it is epistemically possible for him that some of the books in the canon are not infallible and that therefore at least one of the books in the canon can teach error. At the same time, for someone who believes that the canon simply is a collection of infallible books (and therefore contains only infallible books), it is not epistemically possible for him that at least one of the books in the canon can teach error. But then it both is and isn't epistemically possible that at least one of the books in the canon can teach error, and this is a contradiction. Such a person, therefore, has an inconsistent set of beliefs.

Even if the canon is in fact correct and therefore contains only infallible books and hence it is metaphysically impossible that at least one of the books teaches error, it is still epistemically possible (from the epistemic perspective of someone who holds that the canon is only known fallibly) that at least one of the books in the collection teaches error. This is all that the argument needs to go through. For in believing that the canon is fallible, one is committed to saying that, for all he knows, one or more of the books in the canon can teach error. But in believing that in fact all of the books in the canon are infallible, one is committed to saying that, for all he knows, none of the books in the canon can teach error. Hence, to reiterate, such a person has an inconsistent set of beliefs.

I think that the foregoing reasoning presupposes the following three epistemological principles:

• BBK Principle: If S believes p, then S believes that he knows p.
• Normative Belief Closure (NBC): If S believes p and believes p → q, then S ought to believe q (i.e., S is rationally committed to q).
• Know-Might Principle (KMP): If S knows p, then 'it might be that ~p' (i.e., 'it is epistemically possible that ~p') is false for S.

A brief comment on each of these is in order. BBK, though contestable, is pretty plausible. The intuition behind it is that a genuine belief should carry with it some real conviction. NBC, although a sometimes-questionable news source, is a defensible principle. It is, I think, intuitive to think that if S believes some proposition p, then he is rationally committed to believing whatever he sees to follow from p so that he ought to believe whatever he sees to follow from p. One significant objection that might be lodged against this principle is that it seems strange to say that S ought to believe whatever he sees to follow from p unless he is justified in believing p. In response, I think it is plausible that unjustified beliefs still come with rational commitments. For example, even if my belief that pigs can fly is unjustified, I still arguably exhibit a rational failing if I refrain from also believing that some things can fly (the philosopher James Pryor gives a very similar example in his "What's Wrong with Moore's Argument?", pp. 364).

KMP needs to be understood in an appropriately nuanced way so as to be compatible with the idea that genuine knowledge can be fallible. In epistemology, this view is referred to as fallibilism, which is a very widely accepted position. KMP, though highly plausible in its own right, is apparently incompatible with the truth of concessive knowledge attributions (CKAs), which have the following general form: S knows p, but it might be (from S's perspective) that ~p. Notice that the person who believes that the Bible is a fallible collection of infallible books is plausibly interpreted as being committed to a CKA like the following: S knows that all of the books in the canon are infallible, but it might be (from S's perspective) that not all of the books in the canon are infallible. This is to say that while such a person might have knowledge that the canon is correct, he nevertheless does not have infallible knowledge that the canon is correct. Fallibilism entails that there can be true CKAs, but KMP apparently entails that there cannot be true CKAs. Hence (assuming we ought to be fallibilists), we seem to be in a bind.

Drawing from the work of the philosopher Charity Anderson (see her "Fallibilism and the Flexibility of Epistemic Modals"), an elegant solution to this problem is to simply relativize what is epistemically possible for S with respect to p to S's knowledge minus p itself. Then, assuming that this slightly restricted knowledge base does not logically entail p (but still provides strong evidence for p), we can say that relative to this knowledge base, it is epistemically possible for S that ~p, but that this knowledge base is still sufficient for S to know p in a fallible way. Let K–p denote S's knowledge minus p. Then, we can reformulate the general form of a CKA as follows: S knows p, but it might be (from the perspective of K–p) that ~p. In this way, KMP is compatible with the truth of various CKAs and hence is also compatible with fallibilism.

Let us now observe how these principles (BBK, NBC, and KMP) are used in the reasoning behind the argument under discussion. I take it that any Protestant who believes that the canon itself is fallible nevertheless believes that it is in fact correct and hence believes that it in fact contains only infallible books. Hence, let S be such a Protestant and p be the proposition that the canon contains only infallible books. Then, by BBK, S believes that he knows that the canon contains only infallible books. Now, from p, it follows (as a conceptual truth) that none of the books in the canon can teach error (where the can in this specific instance expresses metaphysical possibility). Call this entailed proposition q. Hence, we can state that p → q. Moreover, it is reasonable to assume that S knows that p → q (if he doesn't, he ought to!). Since S knows that p → q, he, a fortiori, also believes that p → q. Next, by NBC, S ought to believe q, i.e., S is rationally committed to q. Hence, assuming that S is at least to this extent rational, he will thereby believe q. By BBK, S then believes that he knows q. Then, by KMP, if S knows q, then ~q is not epistemically possible for him. Assuming that S is made aware of KMP and comes to accept it, he then, by NBC, ought to believe that ~q is not epistemically possible for him (since he believes that he knows q). So, assuming that S is at least to this extent rational, he will thereby believe that ~q is not epistemically possible for him, i.e., it is not epistemically possible for S that one or more of the books in the canon can teach error. However, S also believes that the canon is itself fallible such that even though S believes that the canon contains only infallible books, it is epistemically possible for him that the canon does not contain only infallible books. Now, a fallible book, of course, can teach error. Hence, S is thereby rationally committed to the belief that it is epistemically possible for S that one or more of the books in the canon can teach error, and assuming therefore that S is at least to this extent rational, he will thereby (by NBC) believe this.

Therefore, S is rationally committed to the belief that it both is and is not epistemically possible for S that at least one of the books in the canon can teach error. This contradiction demonstrates that S thereby has an inconsistent belief set and therefore cannot sensibly believe that the Bible is a fallible collection of infallible books (since it is this belief that led to the inconsistent belief set). Such a belief is, on analysis, epistemically incoherent.

If there is a flaw in this reasoning, I suspect it will involve the notion that the proposition that at least one of the books in the canon can teach error is not both epistemically possible and epistemically impossible in the same respect due to the possibility/impossibility claims being relative to subtly different knowledge bases. I'll have to think more about this in the future.