Geisler, Howe, and the Importance of Formal Logic

This past summer I read through Norman Geisler’s book, If God, Why Evil? and noticed that in it he appears to commit the formal fallacy of denying the antecedent. I won’t bother with rehashing the details of that now; you can read that short post here.

Some time after that post appeared Richard Howe (Professor Emeritus of Philosophy and Apologetics at Southern Evangelical Seminary) took the time to comment on my post and we were able to briefly chat about it at the national conference of Evangelical Philosophical Society in Atlanta last November. In his post Professor Howe notes “The critic [that’s me!] pointed out (I think correctly, taken in one way) that Geisler’s argument, when cast into predicate or quantificational logic this way, commits the fallacy of denying the antecedent.” I was glad to read this since I highly respect Geisler’s work and didn’t expect to see such a basic fallacy in one of his books. After publishing the post I half-expected to be informed that it was me that made such a basic mistake. But, it turns out, I was right. Well, kind of.

The Alleged Failure of Symbolization

According to Howe, the problem isn’t actually rooted in how Geisler casts the argument, but in my attempt to reconstruct the argument using the tools of predicate logic. This, Howe maintains, is problematic because it fails to capture the metaphysics that goes along with the argument. Here are two examples from Howe that he believes shows how symbolization cannot fully capture all of the metaphysics that goes along with an argument.

FAILURE ONE:
Taking advantage of how the excluded middle or certain other logical relationships overlook the metaphysical relationships can be the basis of many jokes. ‘The temperature is 93 degrees. The temperature will rise this afternoon. Therefore 93 degrees will rise this afternoon.’
I suppose that someone might find this funny1, but it gives me no pause about the power of symbolization. Instead, the joke simply trades on an equivocation of ‘is’ which can be easily remedied. The first statement employs an is of predication, whereas the second statement presupposes that an is of identity was used in that initial premise. Were this not intended as a joke, all one would need to do is point out that more clarity is needed before beginning to symbolize the statements. Doing so would avoid the confusion entirely. What, then, of the second alleged failure?

FAILURE TWO:
Many otherwise legitimate scientific arguments, for example, when reproduced into formal, truth-functional arguments commit the fallacy of affirming the consequent (like, ‘If the substance is acidic, then the blue litmus paper will turn red. The blue litmus paper turned red. Therefore, the substance is acidic.’)
Here too all that is needed is just a little more precision about what terms mean. The scientist who makes the mistake above is indeed making a mistake and could benefit from more philosophical precision. The reason we may be inclined to accept this statement is that we tend to recognize that what the scientist meant to say, even if she didn’t, is “Only if the substance is acidic, then the blue litmus paper will turn red.” There is an important difference between ‘if’ and ‘only if’ and recognizing that difference clears up the confusion quite easily. (In an earlier post I noted that this is the same confusion that led the theologian and Bible translator Paul Enns to fallaciously conclude from Genesis 2:17 that if Adam obeyed God’s command then he would not die.)

Howe’s Reconstruction of Geiser’s Argument

Howe believes that my using predicate logic to evaluate Geisler’s argument is what leads to the fallacy of denying the antecedent. He also believes that there is a way to fix Geisler’s argument that avoids the fallacy. (Before looking at Howe’s reconstruction, it’s worth noting that the problem isn’t due to my using predicate logic. Reconstructing Geisler’s argument as a categorical syllogism leads to the same end—an invalid argument.)

Howe’s reconstruction of Geisler’s argument is pretty straightforward.

Let’s use the same legend from my original post.

Tx: x is a thing

Cxy: x created y

e: evil

g: God

Initially I framed Geisler’s first premise, “God created all things” as a simple conditional.

(x)(Tx > Cgx)

Howe argues that this does not “adequately [capture] the metaphysics behind Geisler’s first premise.” Instead, “in its broader context, Geisler was not merely saying that God created all things but also that everything was created by God.” So, instead of simply representing the first premise of the argument as a conditional, required by Geisler’s broader metaphysical commitments, it should be represented bi-conditionally as:

(x)((Tx > Cgx) & (Cgx > Tx))

This we would read as “For any x, if x is a thing then God created x and if God created x, then x is a thing.” With this in place we can get to Geisler’s conclusion that God did not create evil. Howe then helpfully goes on to provide the full formal proof, but as we shall see, this actually shows us how the reconstruction of Geisler’s argument is really an entirely different argument.

Howe’s Proof

  1. (x)(Tx > Cgx) & (Cgx > Tx))                     (premise)
  2. (x)(Ex > ~Tx) Therefore (x)(Ex > ~Cgx)  (premise/conclusion)
  3. (Ta > Cga) & (Cga > Ta)                         (Universal instantiation)
  4. Ea > ~Ta                                                 (Universal instantiation)
From here we get the following a conditional proof.
  1. Ea                                                           (assumption)
  2. ~Ta                                                         (Modus ponens: 4, 5)
  3. Cga > Ta                                                (simplification: 3)
  4. ~Cga                                                      (Modus tollens: 7, 6)
And from this we can get our desired conclusion.
  1. Ea > ~Cga                                              (Conditional proof: 5-8)
  2. (x)(Ex > ~Cgx)                                         (Universal generalization: 9)
So what does all of this tell us? At least two things come to mind. First, Howe is right that the bi-conditional does allow one to validly deduce Geisler’s conclusion. There is no dispute about that. However, the second thing this argument tells us that it’s not exactly clear how this helps Geisler’s argument.

Recall that what Geisler states in his book is that God created all things, which Howe represents as (Ta > Cga). But if you look back through Howe’s formal proof above you’ll notice that this initial premise isn’t actually used to get to what was supposed to be Geisler’s conclusion. The presence of Geisler’s original premise is entirely superfluous in the proof for Geisler’s conclusion. It shows up in the initial premises of the argument, but when Howe simplifies (3) on line 7 it disappears and never returns. (If you look through the justification of each line, you’ll notice that Geisler’s original claim is never cited.)

It could just be me, but fixing an argument by never actually using the main premise of the original argument is a bit strange. It seems instead that instead of a reconstruction of Geisler’s argument we just have a new (valid) argument from Howe.

Furthermore, the second half of Howe’s bi-conditional doesn’t get any support in the text of Geisler’s book. So if the non-believer were to evaluate Geisler’s original argument, she would have no reason to cast his original premise as a bi-conditional.

This highlights precisely why symbolization is so important. Both Howe and I might read into Geisler’s argument various unstated metaphysical claims, but we can’t count on everyone to do that. We should take care that our arguments are precise in stating all that the needs to be stated in order to reach our conclusions. This allows everyone, believer and non-believer, the opportunity to evaluate the reasons we believe what we do.

Footnotes

  1. Rare is the case when a philosopher’s joke is considered to be funny by anyone besides philosophers! ↩︎