I am thoroughly interested in the Deductive Closure Principle (DCP). I have written on this from time to time, and am worried that much of philosophy is misguided because of it. Here is the principle formally: If S (some finite cognizer) believes P (some proposition), if P->Q (P entails some other proposition Q), then S knows P. Now, much has to be said about the entailment relation here—especially when it’s a matter of debate if Q really follows from P. Supposing, though, that we have really solid philosophical foundations for thinking that Q does necessarily (or logically, to be more humble) follow from P. In this case, says the DCP, whatever follows from P, if S knows P, S also knows. William Lane Craig  has used this notion without explicit reference which I think worth re-printing. To summarize (with added premises and my own paraphrase):
- If the Bible teaches that the soul exists (P), then (->) the soul exists (Q).
- (1) is true iff the Bible is true.
- The Bible is true. (His metaphysical system: natural theological arguments (in conjunction with reformed epistemology i.e., properly basic belief in God).
- If S is said to know Q in virtue of knowing P (since P->Q), the DCP must be correct.
- The DCP holds. (Variation in the strength of entailment is being put away here since it is almost undeniable that the Bible teaches that human beings have souls).
- Therefore, if the Bible is true, the soul exists. (1)-(5).
- The Bible is true (1).
- Therefore, the soul exists. (1)-(7).
While W.L. Craig acknowledges that there are independent philosophical grounds for affirming that the soul exists, the DCP is a way in which the extra work might be avoided? The two objections lurking are the following: (1) Wouldn’t this make the—if it happened—the discovery of there being “no soul” a strict refutation of Christianity? And (2) Isn’t this form of reasoning ad hoc since it simply rules out anything that any other view or system or account posits? Let me respond: (1*) At best, this would either suggest (i) that the entailment relation has to be given up i.e., go with Peter van Inwagen and think that Christianity and materialism are consistent or (ii) think that the Bible is not infallible nor, if one wants to preserve the legitimacy of the Bible, that the Bible has to be infallible if it is to be considered God’s word. At any rate, some give and take might be inevitable—but I suspect that this won’t be a problem since (i) the entailment relation is really strong here, (ii) the grounds for affirming the Bible are also very strong and (iii) all contemporary materialist accounts of human beings miserably fail. (2*) Sure, maybe it is ad hoc. But just because x is ad hoc does not make x false. Let us suppose that theism is true. Any postulated entity on theism that theism does not imply (nor is consistent with) can be rejected reasonably i.e., a possible world in which God does not exist (God necessarily exists in all possible worlds). So, this might “appear ad hoc”; however, even if it is—which is not clear—it does not falsify the claim in question.
So, there is something to be said here. At any rate, this is all I have to say.
 “Why should we believe we have a soul?” https://www.youtube.com/watch?v=2xu4jRSoLUk: Accessed Jan. 11/17.