The past few days have seen a flurry of activity over at Aporetic Christianity on a variety of topics. The most recent has been a discussion as to whether TAG is deductive or not. Up until now I have replied to PM (Paul Manata) through comments, but I feel the need to stretch out a bit here, and so I will reply via a post rather than in comments. I hope PM doesn’t mind the change of venue.
After reading and responding to PM’s latest post there are two issues that I would like to lay out clearly here. First, did Bahnsen and Van Til believe TAG is deductive. Second, is TAG deductive?
Both PM and I agree that the truth of the second is not dependent upon the truth of the first (that is, Bahnsen and Van Til could both claim TAG is not deductive, when in fact it is, and vice versa). However, since Bahnsen and Van Til are the champions of TAG so to speak, I believe it is relevant to continue to invest time in addressing the first point.
What did Bahnsen and Van Til Think?
PM implied rather heavily that Bahnsen and Van Til thought TAG was deductive. I replied with some rather clear comments from Bahnsen and Van Til that either imply they believe there is a distinction, or explicitly declare that there is. In addition, Chris has written a number of posts on this topic here on CH, where he argues not only for Bahnsen’s position (because the context of the post demanded it), but also argues directly about the distinction between a TA and a deductive argument.
On a side note (to address one of PM’s comments) please note that just because one borrows an argument from someone (say Bahnsen, for example), does not mean one is appealing to that person as an authority. Chris does this in his post linked above, and PM seems to take issue with it. Regardless, it only means that person has made an argument that you feel is concise and well written, and that it makes sense to share that argument. I could appeal to PM’s argument against TAG as deductive, for instance, without appealing to Paul himself as an authority on logic, or philosophy, or TAs (Transcendental Arguments).
So, what are the quotes I shared? Well, for now I choose to share just one from Bahnsen, as I would like to keep this post from growing too large, and because (after all) Bahnsen is an expert on Van Til. Posting arguments from both sources seems redundant.
“Take P, show that Q is the precondition of P. That’s the argument. Now I’m gonna say more about it, but just make sure you understand that that’s how simple it is. Take anything – ‘P’, and then show that ‘Q’ is the precondition of ‘P’. I am not arguing, take ‘P’ and then deductively conclude ‘Q’. Nor am I saying, take ‘P’ and a lot of things analogous to ‘P’, and inductively say very generally ‘Q’. This is not a deductive argument. This is not an inductive argument. This is an argument that says what has to be true, what is the precondition, for ‘P’.” (Transcendental Arguments, Part 12 [GB1824], starting at 1:04:06) [emphasis mine]
I am a very perplexed at this point as to how PM reads Bahnsen saying “[TAG] is not a deductive argument” as saying that Bahnsen means TAG is a deductive argument. Granted, PM does offer reasons elsewhere that do have some bearing on the matter (such as Bahnsen not ‘correcting’ Butler when Butler purportedly casts TAG as deductive), but as PM has explained elsewhere, Bahnsen (like all of us) has made mistakes in the past. Regardless, nothing PM has offered is as explicit as the statement Bahnsen makes above . How else should we read Bahnsen saying “[TAG] is not a deductive argument” than to mean that Bahnsen believes TAG is not a deductive argument? It seems rather clear what he means, does it not?
Another relevant question is this – what exactly did Bahnsen mean when he said “This is not a deductive argument”? Since this is such an explicit statement, no matter what other theories PM has to offer, none will be found compelling if he cannot tell us what Bahnsen meant when he penned this statement.
Is TAG Deductive?
First, to answer an earlier question of PM’s, a “sound” argument is an argument with true premises and a valid form. We think of that mostly in reference to deduction, where a sound argument guarantees a certain conclusion.
1) All men are mortal
2) Socrates is a man
3) Therefore, Socrates is mortal
This is a standard, deductive argument. It is sound if and only if the form is (deductively) valid, and if the premises are true. If we assume (as most would) that the premises are true, then we would claim this is a sound argument, because the form is deductively valid (that is, it follows modus ponens). Now, what about a TA? Consider the following:
1) P presupposes CT
3) Therefore, CT
At first blush, this looks eerily like a deductive argument, does it not? In fact, we would even say that this argument is sound, just as the example of deduction above, because the premises are true, and the form is valid. But this is where things are different with a TA.
1) P presupposes CT
c) Therefore, CT
This construction makes most people want to scream “non-sequitur” out loud! In addition, I would not say that this argument is sound. Why? Because not all the premises are true, and an argument must have true premises to be termed “sound”. However – even though this argument is not sound, the conclusion still follows. Why? Because of the meaning of the word “presupposes”.
If P presupposes CT, then CT is a necessary precondition for the intelligibility of P. Whether we affirm or we deny P, CT must still be the case in order to make our affirmation or denial intelligible. So, while the former argument “works” as a deductive argument, it really isn’t one, because of the word “presuppose”, and we can see this because the second iteration yields the same conclusion.
PM’s Original Analysis
In conclusion, I would like to go back to the original post that started all of this, and try to make some sense out of what Bahnsen meant when he used the term “sound”. This is important, as PM’s analysis of this statement seems to be driving his conclusion that Bahnsen thought TAG is deductive.
PM starts his post with the following comment:
It was presented that way by Butler in Bahnsen’s presence, and Bahnsen never said anything. And it surely appears that it is, since the proponents who deny that TAG is deductive would nevertheless admit that if the premises of the argument were true,then the conclusion must be true. This is a deductive argument.
I don’t really know what to say about PM’s claim that Butler presented TAG as deductive in the presence of Bahnsen, and Bahnsen did not correct him. I guess I would need to hear the actual conversation (or see a transcript of it) in order to evaluate this. I would ask PM to cite this conversation, if possible.
Next, what about the comment that the proponents of TAG as non-deductive would admit that if the premises were true, then the conclusion must be true? He’s right -we would agree with this, but not because the argument is deductive. This is a feature of a TA as well as a deductive argument. The difference is that a TA doesn’t require the non-TP (non-Transcendental Premise) to be true, in order to yield a necessary conclusion. Why? Once again, because of the meaning of the word “presuppose” (see above).
Let’s now take a look at the quote from Bahnsen that seems to be driving PM to conclude what he does, especially because Bahnsen uses the word “sound”:
“To put it simply, in the case of ‘direct’ arguments (whether rational or empirical), the negation of one of their premises changes the truth or reliability of their conclusion. But this is not true of transcendental arguments, and that sets them off from the other kinds of proof or analysis. A transcendental argument begins with any item of experience or belief whatsoever and proceeds, by critical analysis, to ask what conditions (or what other beliefs) would need to be true in order for that original experience or belief to make sense, be meaningful, or be intelligible to us. Now then, if we should go back and negate the statement of that original belief (or consider a contrary experience), the transcendental analysis (if originally cogent or sound) would nevertheless reach the very same conclusion.” (Bahnsen, Van Til’s Apologetic, 501-502.)
Please note my emphasis of the word “originally” here – I think it is crucial to understanding what Bahnsen is saying. PM believes that Bahnsen’s use of the word “sound” here implies deduction – I disagree. I believe Bahnsen’s use of the word implies “an argument with true premises and a valid form.” That is, a TA can be either sound or not, but either way the conclusion follows – due to the “heavy lifting” done in the TP.
I believe that Bahnsen is essentially saying that if the argument is “sound” (true premises and valid form) in its original iteration, then it doesn’t matter if we deny the second premise – we will reach the very same conclusion. His use of the word “originally” is important to show that he is referring to a TA presented with both premises being affirmed (as in my first example above). If that argument is “cogent or sound”, then it doesn’t matter if we deny the second premise – we will still get the same result. Whereas, if that argument is not “cogent or sound”, then there is no guarantee that the conclusion will follow.
Next, PM makes the following comment regarding how a TAGger might respond to a sample deductive argument:
If they respond, but one of them isn’t sound, and a transcendental argument is still sound if you negate a premise. Then that’s confused. Soundness means valid argument with all true premises. It’s a deductive category in the first place. But if you negate a true premise, even in a transcendental argument, then it isn’t “sound” anymore. It’s a false premise.
We would agree that if you negate a true premise, even in a TA, then it isn’t “sound” anymore (at least not deductively sound). However, we would argue that the conclusion still necessarily follows, (again, due entirely to the meaning of the word “presupposes” in the first premise.)
In conclusion, I think it is helpful to state that much confusion between TAs and deductive arguments arise out of the way they appear (in the former form above) looking just like a deductive argument. Stating a TA in its “positive” form, without also including the form where the second premise is negated, is ambiguous and misleading. In addition, the use of the word “presuppose” is also ambiguous and misleading (just like the use of the word “Transcendental” is), and so that helps to muddy the waters.
There is much more I could say at this point, but I will hold off for now, lest this post (and replies to it) become unwieldy.