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

On 8/26/02 10:15 PM, Sean Choi wrote:
 >On a more serious note, I forwarded this to David

Sean Choi was kind enough to call to my attention the fact that
Aaron Bradford has recently written an interesting reply to one
of my messages to this list, an argument from April '99 about
the apparent disagreement between Bahnsen and Frame over whether
TAs, properly construed, could be expressed "directly" or

My schedule is quite full at the moment, and this prevents me from
engaging for now in an extended dialogue on these issues.  The
purpose of the following notes, then, is to thank Aaron for the
courtesy of his detailed attention, and to offer a single dose of
guidance for the construction of a reply to objections such as the
one he raises.

The article in question is archived at

In that message, I argue broadly as follows:

[a] There are at least three distinct relevant senses of "indirect"
     (and at least three corresponding senses of "direct") in the
     discussion of TAs.
[b] Bahnsen and Frame sometimes equivocate among these senses when
     arguing about TAs.
[c] Frame doubts that TAs are truthfunctionally distinct from
     "direct arguments".
[d] Bahnsen affirms that TAs are truthfunctionally distinct from
     "direct arguments".
[e] Bahnsen takes himself to be rebutting Frame at this juncture.
[f] Frame is talking about the use of Transposition to emphasize
     non-negated statements in his premises.
[g] Bahnsen is talking about the preconditions of a statement's
     having any truthvalue at all.
[h :.] Since [f] differs from [g], Bahnsen's cloudy rebuttal floats
     past Frame's foggy assertion (from [a], [e], [f], and [g]).
[i] Nothing in Bahnsen's rebuttal demonstrates a truthfunctional
     difference between his characterization of TAs and Frame's
     characterization of TAs. (from [b], [c], [d], and my
     explicit illustration)
[j] Nothing in Van Til prohibits the use of Transposition to
     ensure a positive rhetorical emphasis.
[k :.] Therefore, Frame's right (though he states it awkwardly)
     that there's no logical impediment to positive formulations
     of Van Til's envisioned TA (from [h], [i], and [j]).

Kindly take note of the goal of my argument above, and notice
(as we go along) what Aaron chooses to rebut, below.

Aaron's message summarizes certain aspects of my argument, and
then offers a counterproposal.  Using the Cartesian puzzle as
a sample, Aaron writes:

 >    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.

As Aaron points out, this syllogism matches the structure of
the one I constructed on the basis of Bahnsen's remarks in the
passage I examined.

Now, Aaron asserts:

 >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'?*

Aaron grants that the syllogism would be rendered fallacious by
a denial of its second premise.  So Aaron's strategy is to rebut
me by arguing that a denial of premise 2 is non-viable.  First,
he wonders what a denial of 2' would mean.  In the case of the
Cartesian conundrum, I should think it would mean something like

      "I neither affirm nor doubt that I exist; I'm agnostic on
      the question of my own reality".

Granting a similar paraphrase, Aaron's strategy leads him to
assert that in the very act of claiming agnosticism regarding
one's own existence, one thereby takes a definite stand on that
very issue.  By citing performative inconsistency at this
juncture, Aaron thinks he "puts the objection back in business",
and proceeds to recommend for consideration a revised
formulation of my syllogism.  But consider Aaron's moves:

First, consider what permits the apologist to assume that the
very act of claiming agnosticism regarding one's existence
amounts to taking a definite stand on that very issue?  If the
antichristian is agnostic *in general* regarding whether or not
she exists, then she is likewise agnostic *in particular* about
whether specific acts of withholding (or affirming or denying)
entail existence. The antichristian (say, a committed Buddhist
of a certain flavor) would simply swallow the infinite regress
of appeals to uncertainty, since the antichristian here is *not*
overtly committed to the view that intentional acts are a
non-illusory index of actual existence.

To his credit, Aaron doesn't simply take for granted the frame
of reference in which allegations of performative inconsistency
make sense.  Aaron recognizes that some monists feel no need to
hang their hats on a peg of ontic individuality.  For that
reason, he presses his own argument and discovers its weak
underbelly: an infinite regress problem.  But then, Aaron's
"slamming hammer" which "puts the argument back in business"
ends up offering more crisis than resolution.

Here's how it goes:  Aaron proposes a reformulation of the
Transcendental Premise (TP) that takes into account this
prohibition of ontic agnosticism or skepticism.  Aaron writes:

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

Thus Aaron takes the TP

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

from my abstract of Bahnsen's remarks, and reworks it by adding
~(X or ~X).  By doing this, Aaron means to hedge out the option
of withholding.  In plainspeak, the TP I sketched amounted to
the claim that "Without God, you can neither affirm X nor deny
X"; in plainspeak, Aaron's revision amounts to the claim that
"Without God, you can neither affirm X, nor deny X, nor refuse
to take a stand on X".  In other words, Aaron goes meta by one
order of reference, so that the TP covers X (in affirmation or
denial) and also covers next-order attitudes toward X.

But Aaron then teases out a damaging strategic implication in
this revision.  As my *general* phrase "next-order attitudes"
suggests, trying to sublate the antichristian's stubborn
withholding about the ontic presuppositions of X will simply
move her to express stubborn withholding about *those* alleged
presuppositions, and in turn to express agnosticism regarding
each further layer of assertion on the part of the apologist,
ad nauseam.  As Aaron acknowledges:

 >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.

Aaron proposes a second illustration of his revision and then a
third, and again correctly infers that each case leads to infinite
regress (though he neglects to point out that this is an apologetic
*stalemate* relative to the grand claims of a "proponent of the

 >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'.
 >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*!!!"

Here, as above, the stubborn antichristian might simply assert
that he's not necessarily delivering meaning, but might instead
be phenomenalizing without the least bit of epi, like a geyser.
("I *could* be arguing in my spare time", per John Cleese.)

So then, in response to my formulation, Aaron offers an amendment
that turns out to lead to the neverending abyss.  What does he
see as the value of that maneuver?  Aaron explains:

 >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.

Well, that's the point at issue -- the article of faith as it
were -- in every apologetic encounter centered on an alleged TA.
The apologist asserts that the antichristian's every intentional
act gives evidence that the apologist's preferred ontic frame of
reference is actual and preconditional to all such acts.  The
antichristian, if she's on her toes, denies this.  And, as Aaron
has aptly pointed out, an antichristian not ready to propose an
alternate ontic frame of reference upon which to stand while
shaking her fist and professing preconditionality may nevertheless
lead the apologist after the white rabbit as it leaps into the
bottomless hole.

Therefore, Aaron's proposed revision of my formulation does not
establish a strength but rather underscores a weakness of the
alleged TA.  As I asserted long ago on this list, that proposed
avenue leads explicitly to a shouting match.

In any event, Aaron considers this reformulation valuable because
he thinks it better captures what Bahnsen meant in the passage I

 >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.

Bear in mind that my formulation under discussion is, as noted
above, an abstract of what Bahnsen said in the relevant context.
By way of review, let's pay careful attention to how Bahnsen goes
about clarifying the meaning of his attempt to differentiate
"indirect" arguments from deductive and inductive ones:

      1a. Bahnsen first describes the truthfunctional relationship
          between the premises and conclusion of a deductive argument.
         1b. Then he asks what happens when a relevant premise is negated.
            1c. He concludes that negating a relevant premise blocks the
                path to the conclusion.

      2a. Next, he describes the truthfunctional relationship between
          the premises and conclusion of an inductive argument
         2b. and asks what happens when a relevant premise is negated.
            2c. He concludes that negating a relevant premise leaves a
                bumpier path to the conclusion.

      3a. Finally, he skips the description of the truthfunctional
          relationship between premises and conclusion in an "indirect"
          argument, since that's what he's trying to uncover.
         3b. But Bahnsen asks what happens in a supposed TA when a
             relevant premise is negated.
            3c. He concludes that negating a relevant premise has no
                effect at all on the path to the conclusion.

Because of these different effects on the path to the conclusion (1c,
2c, 3c), Bahnsen infers that the relationship between the premises
and conclusion of an "indirect" argument (3a) must differ from those
that obtain in the previous two cases (1a, 2a).  But he does not
specify just what this new relationship is.  That omission is what
led to my analysis.

Aaron now asserts that I missed Bahnsen's point:

 >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.

But of course, I have often explained on the list that Bahnsen aimed
for something deep in his claims about transcendental preconditions,
and I've rebutted some who claimed otherwise.  Indeed, this is
exactly what I insisted on in the message Aaron's analyzing.  If we
simply leave the matter at the level of first order indicative logic,
with premises that simply have no influence on the truth of the
conclusion, then the concept of "presupposition" would be trivial.
As I then wrote:

          But Bahnsen surely is not proposing that the jointly
           affirmed propositions constituting Christian Theism
           are trivially true

I likewise wrote:
           what Bahnsen's language about premises and conclusions
           seems to suggest is: if X is a premise of the
           transcendental argument's conclusion, then so is ~X.
           And that language seems to require that the TA's
           conclusion follow from a conjunction of X and ~X.
           This, however, is surely not Bahnsen's meaning.

So then, contrary to Aaron's new assertion, I was at pains to take
into account the fact that Bahnsen's explanation referred (to
borrow Aaron's handful of phrases) to "something more basic or
epistemically prior", "possibility", "make sense", "be intelligible
to us", and "be meaningful".  But the key issue to raise here is
that each of these terms is exceptionally vague and Bahnsen renders
none of the explicit.  Taking for granted that Bahnsen must have
had *some* model in mind, given the boldness of his rhetoric, I
chose to try to identify his position despite the lack of rigor in
his explanations of TAG.  I didn't simply ignore the nuances and
miss the fleeting brushes with depth, as Aaron suggests.

Aaron writes:
 >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".

That's precisely the point I made in the message under discussion,
in which I even linked to a prior message that explained just *why
a focus on contradictory truthvalues is inadequate*.

 >It is the former that makes an argument "transcendental".

But the former (viz., "meaning", "intelligibility", etc.) is by
no means "clear and distinct" (to return to Descartes).

 >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.

Here, at last, we return to the amusing crux of Aaron's message.
Remember, I proposed a paraphrase of Bahnsen's TP:

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

Then Aaron counterproposed that we take into account at least one
layer) of the antichristian's likely, infinitely regressive reply:

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

So then, does calling explicit attention to the lurking infinite
regress *more fully express the intended meaning of Bahnsen's
vague language*?  Possibly so, though clearly it does so only by
way of pointing out a weakness rather than fortifying.  But the
really interesting thing is that *swapping Aaron's revision into
my earlier message does not affect my analysis of the Bahnsen/Frame 
disagreement at all*.  My point there, as outlined at the outset
of the present note, is that in the midst of multiple definitions
of "indirect" and "negative" Frame was talking about recasting a
syllogism with fewer negated statements when he referred to
"positive" formulations.  That this was my point is even obvious
in parts of my formalization that Aaron quotes. And it's pretty
obvious that Aaron's revision, like my initial illustration, can be
altered  la Frame (by transposition of the TP) into a "positive

Aaron's proposal (arbitrarily limited by him to one iteration of
the regress -- without explanation or treatment of the regress
problem he noted):

 >    If ~God, then ~(X or ~X or ~(X or ~X ))
 >    (X or ~X or ~(X or ~X ))
 >    :. God

Aaron's same proposal, JFramed:

 >    If (X or ~X or ~(X or ~X )), then God.
 >    (X or ~X or ~(X or ~X ))
 >    :. God

The joy of elementary logical equivalence.

That's what my essay in three acts demonstrated.  Unhappily, Aaron's
attempt to rebut that essay offered a new premise that has no effect
on the conclusion of my argument ;)  Instead, Aaron spent his energy
revising an abstract of some remarks by Bahnsen -- an abstract to
which I expressed very limited commitment in the first place, as I
then explained:

           a proper TA should be modal, but for simplicity I'll use
           "(X or ~X)" to interpret "<>X" -- "possibly X" -- on the
           simplistic assumption that possibility amounts to

I even called my formulation deliberately "simplistic", and used
it as such because I correctly anticipated that for deciding the
*semantic* issue between Bahnsen and Frame, that degree of
simplicity did no harm.  The complexity of the illustration was
sufficient to make the point.  Aaron has now kindly demonstrated
that complexifying the abstract indeed adds nothing, and even
subtracts from the appearance of cogency in Bahnsen's remarks.

In Christ,

David Byron

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