Metaphysics and Formal Logic, Again: A Rejoinder to W. Paul Franks

Professor Paul Franks has graciously responded to my post regarding an issue between us about the logic of a syllogism by Norman L. Geisler found in Geisler’s book If God, Why Evil? My post was in response to Professor Franks’ original post where Franks argues that Geisler’s syllogism, when rendered in a formal logical schema, commits the fallacy of denying the antecedent. (The reader should note that Professor Franks is not necessarily denying the truth of Geisler’s conclusion. He is only challenging the validity of Geisler’s argument for that conclusion.) In my post, I more or less married the essence of some emails and personal conversations between Professor Franks and me, together with some additional thinking on my part about the whole issue of the relationship of formal logical schematizations and philosophical arguments in general and Geisler’s argument in particular.

It is important for the reader of our exchange to know that our conversation is not about whether or to what extent God is implicated regarding the evil that is in the world. This, no doubt, is a very important topic, and one with which any Christian apologist would do well to become familiar. Regardless of whether there might be any differences between Professor Franks and me on exactly how the “problem of evil” (as this issue has come to be known in the literature) should be assailed, I do not think that there are any differences between us regarding God’s absolute goodness.

In the interest of careful analysis and in order to avoid fogging up the discussion by trying to say too many things at once, let me take Professor Franks’ points in order and comment on them. First, Franks deals with the issue (as he seemingly understands it) of the “alleged failure of symbolization.” He characterizes my understanding of the problem as arising from Franks’ “attempt to reconstruct [Geisler’s] argument using the tools of predicate logic.” Not quite; but I can understand why Franks might think this. More precisely, the problem is not merely trying to symbolize any given argument. Rather, the problem arises when the symbolization of an argument fails to capture the full meaning of the premises in the argument. It is not formalization (or schematization or symbolization) per se that necessarily causes the breakdown. Rather, it is when the contextual meaning of those premises is left out or understated. Now, I am in no way suggesting that Professor Franks has deliberately tried to monkey with Geisler’s meaning in order to construe Geisler’s argument so that it commits a logical fallacy. I have every reason to think that he would not do such a thing. Throughout he has tried to be scrupulously fair.

Franks next comments on several examples I gave where the form of an argument (while seemingly valid, at least prima facie) nevertheless leads to an absurd (or scandalously wrong) conclusion. My first example was a philosophical joke where a single term (the term ‘is’) is used equivocally in a prose argument. Franks then points out that while the argument “might be funny” it gives him “no pause about the power of symbolization.” But of course, the example was not given so as to give someone pause about the “power” of symbolization, but rather to give one pause (albeit in a rather light-hearted way) about the concomitant potential limitation (or subtle dangers) of symbolization. Symbolizing an argument can indeed be a powerful and useful way to analyze the validity of a formal argument. But it can also obscure or even to do violence to the meaning of the premises in an argument. Giving an example such as I did can serve as a useful example only because the point that the example was trying to highlight was easily seen in the example. But I fear that Professor Franks has been scandalized by the ease in which he was able to (correctly) point out that the ‘is’ in one sentence of the joke is an “is of predication” and the ‘is’ in another sentence of the joke is an “is of identity.” Thus, his conclusion is that “all one would need to do is point out that more clarity is needed before beginning to symbolize the statements.” Exactly. That is the very reason I gave the example in the first place. It would not do for one to merely symbolize the joke’s argument without regard to the “is of predication” and “is of identity” distinction. But whereas the thing that needed clarification is quite easy to identify in this joke (indeed, self-evident to a philosopher like Professor Franks), the clarification that is needed in Franks’ original symbolization of Geisler’s argument is (apparently) somewhat harder to identify. My point in my first response to Franks was that Franks was wrong in understanding Geisler’s first premise (“God created all things”) as a simple conditional statement. (I will leave aside whether something is lost when one treats a Categorical Proposition as a Truth-Functional (or, in his specific rendering, Quantificational) proposition. For this, I refer the reader to the Veatch texts I mentioned in my first response to Professor Franks.) I argued that, once one correctly symbolizes the meaning of Geisler’s first premise, then no fallacy occurs. In other words, I tried to do what Franks suggested one should do in encountering imprecise symbolization, viz., to “point out that more clarity is needed before beginning to symbolize the statements.” Now, it would have been quite fair for Franks to object to my characterization of Geisler’s first premise as a bi‑conditional. This he does not explicitly do. But it is only in raising that objection that Franks can defend his original contention that Geisler’s argument commits the fallacy of denying the antecedent.

Things gets more interesting when Franks comments on another example of mine of how certain common scientific arguments seemingly commit the fallacy of affirming the consequent when rendered into the formal symbolization of Truth-Functional logic. Taking an argument that a scientist might make which says “If the substance is acidic, then the blue litmus paper will turn red. The blue litmus paper turned red. Therefore, the substance is acidic” and symbolizing it, casting it as a formal argument, one can see that it commits the fallacy of affirming the consequent. Franks suggests that, when pointing out why (despite what seems to be a formal fallacy) we nevertheless “may be inclined to accept this statement” is because “we tend to recognize that what the scientist meant to say, even if she didn’t.” This gets quite close to the very point about which my article was dealing except that I made my point somewhat stronger in saying that, in fact, the better way to capture what Geisler meant was by means of the bi‑conditional, and, further, that rendering Geisler’s first premise as a simple conditional is what (strictly speaking) creates a fallacy where none exists. The reason we understand the scientist’s argument and refrain from charging the scientist with committing a formal fallacy is because the argument was not offered as a formal argument in the first place, even if it appears to be one by virtue of the grammar. (This, I should note, is also true of Geisler’s argument. It was not offered as a formal argument.) The distance between the nature of a given argument which is not offered as a formal argument and the nature of the same argument if it was offered as a formal argument, can compensate for any fallacies that might emerge in the formal schematization of the argument. The very act of rendering the nonformal argument into the contours and requirements of a formal schematization can create formal fallacies even when there is nothing illicit about the argument in its original offering. This, in summary, was my entire point of my first article in this exchange.

I celebrate Franks’ point that “there is an important difference between ‘if’ and ‘only if’ [i.e., the difference between “if p, then q” and “q only if p”] and recognizing that difference clears up the confusion quite easily” for I made the same point in my article (except instead I make my point about the difference between an “if” and an “if and only if”, i.e, the difference between “if p, then q” and “p if and only if q”). It seems to me that both of Franks’ observations and commentaries on my examples show that, as a matter of principle, he grants my position. The only difference might be in whether he would deny that Geisler’s first premise means something that can only be captured by a bi‑conditional. But, oddly, he never raises this as an objection.

Next, Professor Franks comments on how I reconstruct Geisler’s argument. Unfortunately, he misses the exact point I was trying to make. Franks says that I believe that his “using predicate logic to evaluate Geisler’s argument is what leads to the fallacy of denying the antecedent.” Not at all. This could not be what I believe since I, too, use predicate logic in my attempt to exonerate Geisler in his argument. So the “culprit” is not the predicate logic as such, but rather, the incorrect symbolization of that argument by Professor Franks (if, indeed, I am right in claiming that it is an incorrect symbolization). After examining my formal proof, he then observes that “as we shall see, this [full formal proof] actually shows us how the reconstruction of Geisler’s argument is really an entirely different argument.”

We are now at the hub of my entire article. Everything I argue (and the conclusion I arrive at) is predicated upon my claim that, given the context of what Geisler’s philosophy about God and creation is, the first premise in Geisler’s argument needs to be symbolized as a bi‑conditional if it is to do justice to the meaning that Geisler attaches to the terms in the premise. What should have happened, therefore, in Franks’ rebuttal to my article was to challenge my claim that Geisler’s first premise means what I claim the bi‑conditional says. This he does not do; at least, not explicitly. Instead, he does something else. Dr. Franks thinks my formal proof tells us (at least) two things. First, he acknowledges (in fact, he says that “there is no dispute”) that the bi‑conditional “does allow one to validly deduce Geisler’s conclusion” Second, he nevertheless maintains that “it’s not exactly clear how this helps Geisler’s argument.” My short answer is that it shows that Franks is wrong to claim that Geisler’s argument commits a formal fallacy. This is what my formal demonstration shows. In saying that I have demonstrated Geisler’s conclusion but have not helped Geisler’s argument, Franks means that, given a different argument (i.e., given an argument that Geisler did not make) then one can indeed formally prove Geisler’s conclusion. Franks is (in so many words) claiming that I have changed Geisler’s argument into another argument.

Now one might think, contrary to what I said earlier, that Franks does, in effect, dispute my claim that the meaning of Geisler’s first premise is better symbolized as a bi‑conditional. After all, is not the charge that Geisler’s first premise is not a bi‑conditional (which I maintain Franks should have argued in his rebuttal to me but did not explicitly do so) tantamount to saying that I have, by rendering it as a bi‑conditional, changed the argument (which Franks seemingly does argue)? This certainly would be so. But this is not exactly what Franks actually argues. Instead, he seems to think that, even given the bi‑conditional, because I simplified out the one conjunct of the bi‑conditional that does logically entail the conclusion, I have somehow changed Geisler’s argument. He thinks this because the one conjunct that I do simplify out in my formal proof, is (in Franks’ estimation) a different premise than Geisler’s first premise. Franks maintains that in doing so, something (viz, the other conjunct of the bi‑conditional) has “disappeared [from the formal proof] and never returns.” Further, he says “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. (emphasis in original). Continuing, he says “If you look through the justification of each line [of the formal demonstration], you’ll notice that Geisler’s original claim is never cited.” He seems to think that because one cannot formally deduce the conclusion from the other conjunct, that I have only been able to salvage Geisler argument because I used a premise Geisler never used (amounting to saying that I have changed Geisler’s argument). He says that it is “a bit strange” to fix an argument “by never actually using the main premise of the original argument.”

But I never did this, unless I was wrong to say that Geisler’s original premise was a bi‑conditional. If Franks objects and maintains that Geisler’s first premise should not be a bi‑conditional, he should have made an argument to that effect. Franks’ points would be relevant if and only if he did so. This has been my main point all along. I might be wrong in claiming this, but this does not seem to be (explicitly) Franks’ objection. If I am right that Geisler’s first premise is a bi‑conditional, then the conjunct I do use in my formal proof is Geisler’s first premise. But Franks never seems to take issue with my claim that, in fact, what Geisler means is only captured by the bi‑conditional. But if Geisler’s meaning in context is better symbolized by the bi‑conditional, then, since I can take one of the conjuncts of the bi‑conditional (which is itself a conditional) and prove by the laws of logical inference that the conclusion follows, then I have shown that there is no formal fallacy committed. To bring up the fact that I utilize only one of the conjuncts simplified out of the bi‑conditional (and not the other) to make my proof as if that constitutes something “disappearing” either is to misunderstand how the bi‑conditional can work in a formal proof or is to deny that the first premise should have been rendered as a bi‑conditional in the first place. The former seems untenable to ascribe to Professor Franks. He quite deftly has demonstrated his understanding of formal logic. But the latter seems to be missing from any of this argumentation.

In the last part of Franks article, he does get close to the issue of whether Geisler’s meaning is indeed a bi‑conditional when he asks whether “the second half of Howe’s bi‑conditional” has “any support in the text of Geisler’s book.” Whether it does or not is irrelevant. Franks seems to worry that both he and I “might read into Geisler’s argument various unstated metaphysical claims, but we can’t count on everyone to do that.” So? Would not one have to consider the background and context of any philosophical reading regardless of whether we choose to render it in formal symbolizations? (This is exactly the problem with which I dealt in my dissertation regarding how so many critics of Aquinas’s Five Ways misunderstand his arguments for God’s existence precisely because they fail to consider the philosophical context and background that informs the arguments.) Would not that responsibility be ever more important especially when we choose to render it into formal symbolizations? Not only could the formal symbolization of an argument fail to manifest the philosophical meanings of the premises, but it could very well mask them and create a false sense of confidence that one has adequately assessed the argument. Must, therefore Geisler (or anyone else) unpack all of the metaphysical assumptions that inform the various terms and claims? To be sure, this could be quite difficult and I do not suspect that this is what Franks is suggesting.

After all is said and done, am I being unreasonable to claim that, given some context, Geisler’s meaning is better symbolized by a bi‑conditional? What can I say in defending this claim? The challenge of trying to formally schematize a philosophical argument was brought home vividly to me in graduate school when my dissertation director required me to schematize Aquinas Second Way; his efficient causality argument for God’s existence. (I had tackled a similar task earlier in my graduate career with Avicenna’s argument for a single first principle.) The challenge was that, while the rather straightforward grammar (both in Latin and English) of Aquinas’s terms and premises might readily suggest specific formal symbolizations, the meaning of his premises could be easily lost without introducing so many symbols (having carefully defined each one) that the formal schema then becomes so unwieldy that it defeats the purpose of schematizing it in the first place. In some cases, one might find that it would just be easier to read Aquinas’s philosophical arguments in their original prose. But if a formal schematization is called for, then, when trying to keep the schematization to a manageable size, there was the danger of me (inaccurately) making Aquinas’s argument begin to look facile. I am not suggesting that it is never possible to formally capture the meaning of a given argument. But the task can be especially challenging when the argument is a philosophical one.

As for Geisler’s argument, the proposition “God created all things” is laden with metaphysical content. For example, because of what the term ‘created’ means vis‑à‑vis God (or, at least, because of what the term ‘created’ means vis‑à‑vis God in Geisler’s philosophy), it is incoherent to suggest that “nothing” could be a thing that God created. As such, to say that God created all things is also to say that if some word before us refers to something that is not itself a “thing” then that something is not created by God. For example, to talk about a contradiction (like, for example, an uncreated created thing) is to talk about something that is not a “thing.” It would be incoherent to suggest that God could create an uncreated thing. Further, to talk about a relationship (to use a different example) between two finite things (like “being to the left of”), though “real” in some sense of the term ‘real’, is not itself a “thing” (Plato notwithstanding) that God created. Following Augustine, Geisler maintains that evil is a privation in a thing. As with the contradiction or relation, a privation is not something that God creates. With this understanding of evil, it follows (from the definition of ‘created’) that evil is not created. What is more, in the context of Geisler’s philosophy and theology, to say that God created all things is to also mean (as I argued in my first article) that there is no thing that is, that God did not create. This amounts to saying that when Geisler says “God created all things” he can only mean both “If x is a thing, the God created x” and “If God created x, then x is a thing.”

Now the challenge is this. How must one symbolize the proposition “God created all things” so as to capture all this metaphysical content? I insist that to merely state it as an A (Universal Affirmative) Categorical Proposition or to convert this categorical form into Quantificational logic and render it as Professor Franks does by making the premise amount to (x) (Tx > Cgx) is to precisely understate the meaning of the premise itself. Once understated, it is no wonder that one can, by the formal rules of inference, show that the conclusion does not logically follow. One shows this (as Franks did) by pointing out that it commits the fallacy of denying the antecedent. But, to capture all the meaning laden in the premise “God created all things” one must do precisely what Dr. Franks himself suggests, to wit, “point out that more clarity is needed before beginning to symbolize the statements” since, as Dr. Franks goes on correctly to observe, “there is an important difference between ‘if’ and ‘only if’ and recognizing that difference clears up the confusion quite easily.” What goes for the difference-between-the-‘if’-and-the-‘only-if’ goose, goes for the difference-between-the-‘if’-and-the-‘if-and-only-if’ gander.


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