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Truthfunctionality & TA's: Bahnsen vs. Byron - Frame




David Byron has written to the effect that Bahnsen "does not refute Frame's
revision of Van Til" with respect to "negative phrasing" on TA's.  Byron
critiques Bahnsen's claim that TA's are distinct from direct arguments, both
inductive and deductive (see http://www.baroquepotion.com/vantil/archive-Apr-1999/msg00020.html ) . Bahnsen held that TA's have a unique form based on truthfunctionality.  Byron's conclusion has strong implications.  I intend to defend Bahnsen's position against Bryon's critique.

Byron quotes Bahnsen to accurately depict Bahnsen's position (Byron quotes on and around pages 500-502 of his _Van Til's
Apologetic: Readings and Analysis_, (Phillipsburg: P&R, 1998).:

                But we realize even more clearly and definitively the 
    distinctiveness of transcendental arguments when we 
    contrast their logical character (that is, the 
    truth-functional relation of their conclusions to 
    their premises) with that of rational and empirical 
    arguments.

According to Bahnsen, in both deductive or inductive arguments, the truth value of every premises affects the conclusion.  Yet, with transcendental arguments, this is not the case.  In his words:

            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
            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.


Bryon formulizes Bahnsen's claim about transcendental arguments in the following way (the NEGATIVE is how Bahnsen would state it; the POSITIVE is how Frame would equate the same argument):

    NEGATIVE                                       POSITIVE
1.    If ~God, then ~(X or ~X)                  [ If (X or ~X), then God.
2.    (X or ~X).                                       [ (X or ~X).
3.    Therefore, God.                              [ Therefore, God.

Now Byron's argument is as follows:

It is clear that we cannot deny 1 and maintain 3, our conclusion.  This is rather obvious.  If the transcendental premise (TP) is false, then the argument is not sound.  Therefore, according to Bahnsen, the non-controversial premise (or granted premise) can be either true or false.  However, as David's example shows, we also cannot deny 2.  This procedure would result in affirming the consequent and "yields nothing worthwhile in the syllogism."  Indeed, it "renders it fallacious."  Therefore, there is *nothing* distinct about transcendental arguments with respect to truth-functionality.  And there is nothing gained by the "indirect" (left side) that isn't gained by the "direct" (right side).  Byron seems to have undermined Bahnsen's principle of demarcation for transcendental arguments (and Bahnsen's use of "indirect arguments").  Or has he????

Let's look at some paradigmatic examples of TA's:

[Cogito reformulated in an unsophisticated fashion -- it is granted that Descartes, indeed, no Cartesian made this argument, though Malebranche made an interesting and separate TA regarding ideas in God's mind!]

1.  I doubt that I exist
2.  A necessary precondition for the possibility of doubting my existence is that I exist
3.  I exist

Notice the structure of both David's argument and the reformulated Cogito.  In the former, the transcendental premise (TP) is #1, the granted premise is #2, and the conclusion is #3.  In the latter, the TP is #2, the granted premise is #1, and the conclusion is #3.  In Byron's example, God is the proposed necessary presupposition; in the reformulated Cogito, self-existence is the proposed necessary presupposition.  Now let's set up the reformulated Cogito ala Byron, but maintaining semantics rather than syntax:

1'.  If it is not the case that I exist, then it is not the case that (I doubt my existence OR it is not the case that I doubt my existence).
2'.  I doubt my existence OR it is not the case that I doubt my existence 
3'.  I exist.

Again, according to Byron, the truth value of the TP cannot be false while maintaining that the argument is sound.  This is obviously true.  The hammer slams when we deny 2'.  If we deny this, then it is a clear case again of affirming the consequent, which gives us nothing but a fallacious argument.  But what proposition would be expressed in denying 2'?  How would the TA proponent respond if I did what David suggests, and stated "I deny the proposition that *I doubt my existence OR it is not the case that I doubt my existence*"?  Clearly, the TA proponent would retort "But you couldn't deny 2' without presupposing that you exists (3'), for how could you deny 2' if you didn't exist?"  That is, in transcendental arguments, the possibility of the granted premise (regardless of truth value) requires the necessary presupposition, which is stated in the TP.  And the proponent of the TA would insist that 1' doesn't properly capture what is being asserted in 2 ( "A necessary presupposition for the possibility of").  In attempting to account for this possibility, therefore, 1 in David's formulation would be recast as:

    If ~God, then ~(X or ~X or ~(X or ~X ))

This would preclude the implications of denying his premise 2.  But following David's objection, one could further object and recast 2 from (X or ~X) to (X v ~X v ~(X v ~X )).  This of course, puts the objection back in business.  Yet, this would only force the TA proponent to account for this too in premise 1 as ~(X v ~X v ~(X v ~X ) v ~(X v ~X v ~(X v ~X ))).  And of course this can go on, ad infinitum.  Another example:

1.  The law of non-contradiction (LONC) is false
2.  A necessary precondition for the possibility of using false (as opposed to true!) is the LONC
3.  LONC is true

Byron formulation:

1' If it is not the case that the LONC is true, then it is not the case that (LONC is false OR it is not the case that the LONC is false)
2' LONC is true OR LONC is false
3' LONC is true

Now let's deny 2', "It is false that *LONC is true OR LONC is false*".  Clearly, this could not be made without presupposing LONC, for the very argument is illustrating that using 'false' and opposed to 'true' presupposes LONC.  Moreover, 1' could be expanded ad infinitum to include negations of 2'.

Again, but we'll jump right to the Byron formulation:

1.  If other people don't exist, then it is not the case that (language is meaningful OR it is not the case that language is meaningful)
2.  Language is meaningful OR it is not the case that language is meaningful
3.  Other people exist

Denying 2, "I say to you, it is not the case that *language is meaningful OR it is not the case that language is meaningful*!!!"  But, according to the TP, saying it presupposes meaning, which presupposes rules, which presupposes the existence of other people!!

Of course, we can include any transcendental argument to illustrate this point.  David's argument presupposes that in denying the "granted premise" (the premise that is not the transcendental premise), the opponent is not presupposing the proposed presupposition.  And of course, in his formulation, it is not.  However, what is wrong with his analysis, is that for *every* sound transcendental argument, this could not occur.  And of course, this is what Bahnsen was saying all along.  Therefore, it appears that his translation is suspect.  Moreover, Byron "fleshes out" the "possibility" claim in the TP as either possible truth conditions (X v ~X), but in every illustration Bahnsen gave on this point (that I am aware of, including the one Byron quotes), the "possibility" encompasses something more basic or epistemically prior.  In the above quote Byron uses, Bahnsen speaks of conditions which must be for the granted premise to make sense, be meaningful, or be intelligible to us.  This is clearly distinct and prior from considering "contradictory truth values".  It is the former that makes an argument "transcendental".  So then, finally, Frame's "negative phrasing" misses the point of Van Til's stress on "indirect" arguments, and Bahnsen's line of demarcation still stands.

Warm Regards,

Aaron Bradford











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