The Tortoise Is Unfair

I was asked about this video in which the justification for deductive reasoning is put in question. The person who asked me to comment on it mentioned that followers of Van Til's brand of apologetics had forwarded him the video. 

Now, it is unclear to me what the purpose of that could be. Do these persons reject deductive reasoning despite Jesus Himself using it (Matthew 22:23-33)? Or are they perhaps suggesting that circular reasoning is acceptable (if so, see here)? Or perhaps they intended to use parity of reasoning to compare the way in which inductive reasoning is justifiable to the way in which deductive reasoning is possible? In this last case, I think "counter induction" (mentioned by the presenter around the 8 minute mark) provides a relevant problem for inductive reasoning that does not appear for deductive reasoning (see below).

Of course, one point of the video seems to be to question whether there is a problem for deduction relevantly similar to the problem of induction. One point made can be summarized as follows: if one can't use inductive reasoning to circularly justify inductive reasoning, it would seem one can't use deductive reasoning to circularly justify deductive reasoning. 

Well, I agree with this. But around the 13 minute mark, the presenter mentions that a form of deductive reasoning he calls "modus morons" (affirming the consequent). Now, if "modus morons" is alleged to be a problem for the justifiability of modus ponens similar to how counter induction is a problem for the justifiability of induction, I think point made around minute 25 illustrates a relevant disanalogy: "modus morons" leads to the principle of explosion and trivialism. 

If anything is derivable on "modus morons," this just means "modus morons" is self-admittedly self-defeating, unjustified, etc. This is not the case for the principle of counter induction (even though it might be counter-intuitive). Why, then, should anyone entertain that "modus morons" could be "justified"? What would that mean? The presenter says towards the end of the video that he still thinks "modus morons" could be meaningful but fails to expand on whether he thinks meaningfulness is a sufficient condition for justification.

Likewise, if one who accepts inductive reasoning as "justified" goes on to say that conclusions of inductive arguments could be false, I have to wonder what sort of "justification" is being advocated. And this should be considered the central takeaway of the video: regarding the "justification" of anything (deduction or otherwise), one must define what he means for something to be "justified"! Whether or not this invokes a problem of the criterion, without clarity regarding the sort of justification one is after, it will remain unclear when exactly one is justified in believing a certain form of reasoning.

For example, is the sort of "justification" in which one is interested infallibilistic? If so, then as mentioned above, that would constitute a relevant distinction between inductive (fallibilistic) and deductive reasoning (infallibilistic) in terms of self-consistency: inductive reasoning does not always lead to true beliefs, so use of inductive reasoning to justify inductive reasoning does not necessarily lead to a true belief. By contrast, use of deductive reasoning does always lead to true beliefs if one's premises are true.

In turn, this leads us to ask what structure of justification one accepts: foundationalism, coherentism, infinitism, or positism? The presenter fails to mention that it just may be the case that deductive reasoning is itself [or legitimated by something which is itself] noninferentially, intrinsically, or foundationally justified.

Now, I say that less as a criticism of the presenter himself (since I'm sure he had his own reasons for the video) than I do as a criticism of those (perhaps certain Van Tilian apologists) who suggest deduction and induction are in the same justificatory boat. Nevertheless, I do wonder whether the presenter (since he styles himself as a skeptic, although to what extent is unclear) believes in epistemic neutrality, as if all positions are on equal epistemic footing and we are all capable of completely criterionless judgments. This would be silly.

Finally, I've read Lewis Carroll's tortoise story before (link). It is amusing, but it has never particularly bothered me. For starters, just because the tortoise doesn't accept the conclusion of a deductive argument doesn't mean Achilles is obliged to indulge him. If one presents a necessary truth and another rejects said truth, we can't compel that person to believe it. Our engagement may provide an occasion for the Holy Spirit to work, but how much effort one expends to persuade another who initially balks at truth is a matter of conscience, not obligation.

Supposing one rejects the reasoning in this post, for example, I might attempt a few further remarks to persuade him, but at some point, I will simply recognize that I am not dealing with a fair individual. The root of the problem in such people is ethical, not rational (Romans 1, cf. Hebrews 10:26, etc.). They may reason validly, but they reason in vain because they would rather avow false premises and rebelliously refuse to submit their consciences to the foundational truth of God's word than to admit that valid reasoning is impossible apart from a Christian worldview.