Apologetics to the Glory of God

Bahnsen, Van Til, TAG and Deduction

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

2) P

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

2) ~P

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.




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8 responses to “Bahnsen, Van Til, TAG and Deduction”

  1. Paul Avatar

    I’ve already planned on addressing most of this in my upcoming posts. Patience is a virtue 🙂

    Two quick points:

    1. A TA takes some meaningful experience. What does it mean to negate an experience?

    TAG answers the skeptic, right? The TAGster asks the skeptic to give him some experience he takes to be intelligible and meaningful, say, brushing ones teeth.

    So, the TAGster inserts “My experience of brushing my teeth” into the “slot”. That’s your “P.”

    You then go on to say we can “negate P.” But what does it mean to “negate an experience?” Something like,

    [~] It is not the case that I have an experience of brushing my teeth.

    But I thought he said he had that experience? What this business about negating a premise means, is that if the transcendental analysis was sound *given that original experience*, then it’s still be sound even if you want to “take back” that experience. The TAGster will just ask for a new experience. “Oh, you you don’t have the experience of brushing your teeth? Didn’t like where that led, eh? Okay, so give my some experience you think is intelligible.” “The tree is huge.” “Okay, so your experience is of the tree. Really? You’re serious this time, right. No give backs, you really mean you have this experience . . .”

    TAG will still get to the same conclusion, because if you’ve demonstrated that God is the precondition of the intelligible experience of brushing your teeth you’ll have done it for any experience, that was just an *instance* of the transcendental conclusion that is God.

    I suggest your interpretation is a bad one. Indeed, I also gave an example of an deductive argument that negates the first premise and is still valid. We can see how this undercuts your understanding of “originally sound.” I suggest you’re confused regarding Bahnsen and logic.

    [2] The source is the TAG Nuclear Strength apologetic series, where Butler gives about three of the lectures. Also, Bahnsen was involved in his MA thesis and he knew Butler was claiming TAG had a deductive form, I see no indication Bahnsen ever disagreed.

  2. BK Avatar

    OK, as patience is a virtue, you will now have to wait until tomorrow for me to point out the problems with your analysis above. Have a good night’s sleep 😉

  3. […] I move on to part 3, I thought I’d respond to a response to some of my posts on the topic. Now, what about a TA? Consider the […]

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  4. […] wrote a post on whether or not TAG is a deductive argument here which Brian Knapp responded to here and then Paul wrote more here and here and […]

  5. RubeRad Avatar

    I’m neither a logician or the son of a logician (but I am a mathematician, so hopefully that’s close enough), but how about this:?

    Your definition of “P presupposes CT” = “is a necessary condition for the intelligibility of CT” causes equivocation between what P means in “P presupposes CT” and “P” or “~P”.

    It would make more sense if you defined:
    “P presupposes CT”
    = “CT is a necessary condition for either P to be true, or ~P to be true”
    = “CT is a necessary condition for P, and CT is a necessary condition for ~P”.

    But then, you’re left with:
    P1p: P–>C
    P1n: ~P–>C
    P2p: P
    P2n: ~P

    Then you can have either P1p,P2p ==> C, or you can have P1n,P2n ==> C (leaving the opponent the only option of P is not true, and ~P is not true, which leaves only undecidable statements (Go”del, “this statement is false”, etc.)) (Although this means that I have implicitly equated “intelligible” with “decidable”, but if you don’t like that, you’ll have to come up with a definition for “intelligible” that is simple enough to logick with)

    Insert P=”laws of logic exist” and C=”God exists”. Or P=”There is good in the world” and ~P=”There is evil in the world”.

    But then what are you left with? A transcendental argument simply breaks down into a slightly more complex argument is purely deductive.

  6. BK Avatar

    Paul – yes, TAG answers the skeptic, and yes, one of the ways it does that is to look at the preconditions of intelligibility for any given experience. However, ‘P’ is a proposition, and so what one would insert into the argument would be something like “It is the case that I am brushing my teeth”. The negation of that would be something like “It is not the case that I am brushing my teeth.” TAG argues that whether you want to affirm P *or* deny P (you don’t need to do both), you must presuppose Q (er … CT). That’s actually one of two ways to demonstrate Q (well, one of two flavors of the same way). It is the “dilemma method”.

    From the Transcendental Argument lecture series by Bahnsen and Butler, the actual statement of TAG is as follows:

    1) Take P
    2) Show that Q is the precondition for P

    Look up above at the quote I gave about where Bahnsen says the same thing:

    “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.”

    Actually, Bahnsen claims this is the form of a TA. That may or may not be the case in every case, but for the sake of discussion I am happy to understand him to say that this is the form of TAG.

    He then proceeds to explain two ways (or two variations of the same way) to demonstrate that Q is the precondition of P. First, the indirect method, where one negates Q and shows that the result is that P (something the opponent does not doubt) is no longer possible. The second is the dilemma method, where one shows that both P *and* ~P presuppose Q, but since either P or ~P, then obviously Q. This is all from the Transcendental Argument lecture series, and (because Bahnsen is so explicitly clear here) is the lens I use to interpret less clear comments of his, like page 501 of VTA.

    So, is my particular view of what Bahnsen means by “sound” in VTA correct? I am not certain. *shrug* I am, however, as certain as I can get that my interpretation of his view of TAG as expressed in the TA lecture series is correct. Did he change his view? Maybe. Was he inconsistent? Perhaps. What do you think? Do you think he changed his mind? Or do you think when he says “this is not a deductive argument” that he means “this is a deductive argument”? Or perhaps you think he means something else altogether.

    Of course, then there is the question “is TAG deductive?” I still contend it is not, but am doing to based on an appeal to Bahnsen as an expert *on TAG* and an expert *on Van Til*. That is, my understanding of what this thing called TAG just *is*, is based on what I have read and listened to from Bahnsen. So if you are of the opinion that TAG is *not* deductive, I would love to hear why (which should first include a statement of what you think TAG looks like).


  7. Paul Avatar


    If you negate the experience, that means you didn’t have it.

    [E] It is the case that I am brushing my teeth.

    [~E] It is not the case that I am brushing my teeth.

    [E] is an experience, [~E] isn’t. [~E] actually says nothing positive. But initially, Bahnsen had told the skeptic to give him some intelligible experience that he takes to be something solid, something he can make sense of. He says, “Brushing my teeth.” If he then goes back and negates the premise, he’s essentially taking back the experience he gave Bahnsen as an example of something he could make sense of on his worldview. TAG attempts shows that God is the precondition of intelligible *experience.*

    So, maybe by “negate the premise” means to put in a new experience, as in “Right not I am experiencing not brushing my teeth, I am experiencing something else.” And then Bahnsen will argue for the preconditions for saying *that*. Maybe, “How do you intelligibly differentiate whatever you are doing now from brushing your teeth,” etc.

    In any case, the claim you want to make here doesn’t get you to your conclusion. I showed on my blog that while you’ll still get to CT (granting the argument for a moment) from either P or ~P, the *argument* for each is a *different argument*. The argument from “brushing teeth” to “CT” is *different* from the argument from “not brushing teeth” to “CT.” They take and and use *different* premises. And so it’s not at all clear why one would be deductively valid and the other invalid. I can do the same thing with deductive arguments. I can get to some conclusion from P and ~P, the premises *it takes* to get there will be different, though. And both ways will be deductive.

    Next, you undermine your own point. You write:

    The second is the dilemma method, where one shows that both P *and* ~P presuppose Q, but since either P or ~P, then obviously Q

    But note your initial premise was

    *P* presupposes Q.

    But *now* you say it’s really,

    P *v* ~P presupposes Q

    So, what’s the problem not with having the second premise be *either* P *or* ~P? Your entire argument for why one version is valid but the other is invalid as been defeated by your own words!

    As for my reading of Bahnsen, I explained what meant at my blog, and I’d think that giving as much weight you do to his flow-of-consciousness lectures is a slender read the hang your entire argument on. I think it’s ridiculous to interpret him the way you have and I have looked at various permutations of your understanding of Bahnsen and all that you would need to do if your interpretation were right in order to establish that. When he said “this is not a deductive argument” I explained what he meant. He was being imprecise and when he makes the same argument in the book he calls it “a direct argument.” He used those words interchangeably. Moreover, I demonstrated that van Til meant something quite refined in his claim about “deductive method,” and it wasn’t how you guys were reading him.

    Anyway, at this point i think it’s sufficient that your entire argument for why it wasn’t deductive has been debunked by you because you admit you didn’t state the first premise correctly. If you had, the argument would have followed (assuming we even know the rules and truth functions for “presuppose,” which we don’t; however, you read it as a conditional, and so I went with that reading. On your understanding, TAG is not truth functional and it doesn’t *guarantee* the truth of the conclusion, which is an odd consequence for something claiming “the impossibility of the contrary.). Nevertheless, that’s now water under the bridge because your re-stated first premise doesn’t submit to the problem you claimed for it *in this post*. I would think that you can see this and admit it.

  8. […] when I pushed him to clarify, he writes this [Bahnsen] then proceeds to explain two ways (or two variations of the same way) to demonstrate […]

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