Counting up arguments

Some time in the fall, Ted Poston asked me how I thought one should model the force of multiple arguments for the existence of God in a Bayesian setting. There are difficulties. For instance, when we discover a valid argument, what we are discovering is the necessary truth that if the premises are true, the consequent is as well. But necessary truths should have probability one. And it's hard to model learning things that have probability one. Moreover, the premises of the arguments are typically not something we are sure of. At the time, I suggested that we conditionalize on the contingent propositions reporting that the premises seem true. Poston ended up going with an urn model instead.

I want to try out another model for counting up the force of multiple arguments, one where we not worry about what is and what isn't necessary. I will develop the story with a toy model that has prior probabilities that make calculation easy, leaving it for future investigation to weaken my assumptions of prior independence and equiprobability.

So, suppose we're looking at decent (say: valid, non-question-begging) arguments for and against a conclusion q, and we find that there are m arguments for and n arguments against. How likely is q given this? Start the model by identifying in each argument the controversial premise. (If there is more than one, conjoin them.) Thus, we now have m+n controversial premises. Let's say that premises p₁,...,p_m support arguments for q and p_m+1,...,p_m+n support arguments for ~q.

Prior to the discovery of the arguments, in my model I will take the propositions p₁,...,p_m,p_m+1,...,p_m+n,q to be all independent, and, further, to each have probability 1/2.

I now model the discovery of the arguments as a discovery of material conditionals. Thus, we discover the m material conditionals p₁→q,...,p_m→q that favor q and the n material conditionals p_m+1→~q,...,p_m+n→~q that favor ~q. How do we model this discovery? We simply ignore all the messy details that the discoveries were at least in part a matter of discovering logical connections (though perhaps only in part; some of the premises beside the controversial premise might have been empirical). We simply conditionalize on the m+n discovered material conditionals.

What's the result? Well, we could use Bayes' Theorem, but that's just a tool for computing conditional probabilities, and sometimes other methods work better. We have m+n+1 "propositions of interest" (i.e., q and the p_i). Our prior probabilities assign equal chances to each of the 2^m+n+1 possible ways of assigning True or False to the propositions of interest. When we conditionalize on the material conditionals we rule out some combinations. For instance, if we assign True to p₁, we had better assign True to q as well, and we had better assign False to p_m+1,...,p_m+n, all on pain of contradiction.

We can say something about how many truth assignments remain after the conditionalizations:

1. Assign False to all the p_i and False to q: one combination
2. Assign False to all the p_i and True to q: one combination
3. Assign False to p₁,...,p_m and True to at least one of p_m+1,...,p_m+n and False to q: 2ⁿ−1 combinations
4. Assign True to at least one of p₁,...,p_m and False to all of p_m+1,...,p_m+n and True to q: 2^m−1 combinations.

All the combinations remain equally likely after conditionalizations. The final probability of q then is just the proportion of the combinations where q comes out true amongst all four types of combinations. Now, q comes out true in combinations of types (2) and (4). Thus, the final probability of q given the discovery D of the arguments is:

• P(q|D)=2^m/(2ⁿ+2^m).

Try some numbers. Say that we have 3 arguments in favor and 1 against. P(q|D)=2³/(2³+2¹)=8/10=0.8. With 4 arguments in favor and 1 against, P(q|D)=16/18=0.89 (for this, think of the theism-atheism debate as pitting the cosmological, design, religious experience and moral arguments against the argument from evil). If we have 10 arguments in favor and 2 against, then P(q|D)=1024/(1024+4)=0.996.

For a more realistic model, we will need to change our priors for the controversial premises so that they aren't all 1/2. Some of the controversial premises of the arguments will be fairly plausible and they will have priors higher than 1/2. Some may not be all that plausible and will have priors lower than 1/2. And maybe the conclusion q will have a prior other than 1/2. Furthermore, there may be mutual dependencies among the controversial premises over and beyond the dependencies induced by the fact that some of them imply q and others imply ~q (the latter dependencies are handled by our conditioning). All of this would require fiddling with the priors, and the simple "counting combinations" method of calculating the posterior P(q|D) will need to be replaced by a more careful calculation. Nonetheless, the principle will be the same.

Closure for knowledge

Here is a closure principle I don't know a counterexample to:

If you know that that s is the conclusion of a sound argument and (non-aberrantly) therefore believe that s, then you know that s.

The perils of intra-Christian apologetics

Here is a fascinating post by my colleague Frank Beckwith.  I can certainly theoretically see the danger, though I am not sure that as empirical matter of fact it's that common.  I suppose the danger is a species of the general thesis that arguing for p can convince one's interlocutor of ~p or of even worse things.

Proof

The folk seem to think that science can "prove" things. I used to think this just meant that they were confused about how science works. But there is a more charitable reading, which I got from a comment by Dan Johnson on prosblogion. Rather than taking the folk to be confused about how science works, we can take seriously the idea that meaning is a function of use, and take the folk to simply use the word "prove" differently from how philosophers do. The legal sense of "prove", as in "prove beyond reasonable doubt", seems to prove the point. :-) For if it is not otiose to specify that a proof is "beyond reasonable doubt", it must be possible to prove in a way that admits doubt! And hence a "proof", in the ordinary sense of the word, does not mean what philosophers and mathematicians mean by the word.

Another sound argument for the existence of God

1. (Premise) Many people know that God exists.
2. (Premise) If p is known, then p is true.
3. Therefore, God exists.

The argument is valid, and according to many strands of traditional theism, it is sound. But the argument sounds question-begging. The atheist will surely deny that (1) is true, unless "know" is used in the humorous sense of "She knows many thigs that aren't true".

On the other hand, if someone claimed that platypuses are reptiles, it would not be out of place to persuade her by telling her that biologists know that they are mammals. Yet if the move from (1) to (3) is question-begging, surely the move from:

4. Biologists know that platypuses are mammals

to:

5. Platypuses are mammals

would seem to be equally question-begging.

One option is to take the "know" in (4) as "claim to know". In that case, the argument from (4) to (5) is a non-deductive argument using the suppressed premises

6. Biologists are the relevant scientists to ask about platypuses' mammalian status

and

7. What the relevant scientists all claim to know is likely true.

The analogue in the case of (1)-(3) would then be to replace (2) with the premise:

8. What many people claim to know is likely true.

I actually think (8) is true. Of course, the "likely" here needs to be taken to mean "likely absent other evidence", just as in (7) (if one knows that all the biologists are in the pay of an organization that for tax purposes seeks to have platypus fur classified as mammalian fur, then that weakens the weight of the claim to knowledge). However, (8) is a pretty controversial principle of credulity. And I don't actually know that the argument from (4) to (5) uses a non-standard reading of "know".

Could there be a person who is rational in accepting (3) on the grounds of (1)? I think so. A person might rationally believe that there are persons of such an intellectual carefulness and honesty that when they claim to know, it is very likely that they do in fact know. One might then come to believe that there are many theists who claim to know theism to be true and who fall in this category. Thus, likely, (1) is true. And hence so is (3).

It's hard to come up with a sound argument that couldn't be rationally helpful, unless the conclusion is literally one of the premises.

Johnson's framework for theistic arguments

Occasionally, I've been offering theistic arguments that border on begging the question. Here, for instance, is one that's basically due to Kant, but transposed into an argument in a way that Kant would not approve of:

1. (Premise) We should be grateful for the wondrous universe.
2. (Premise) If something is not the product of agency, we should not be grateful for it.
3. Therefore, the wondrous universe is the product of agency.

The argument is indisputably valid.[note 1] Moreover, if theism is true, it is also sound, and I do take theism to be true. But soundness is, of course, not enough for a good argument. While premise (2) is pretty plausible (in the objective sense of "should"), it feels like premise (1) "begs the question".

Nonetheless, I think there could be something to (1)-(3). Dan Johnson, in the January 2009 issue of Faith and Philosophy has a fascinating little article on the ontological and cosmological arguments. He argues that a certain kind of circularity is not vicious. Suppose that I know p₁. I then infer p₂ from p₁ in such a way that I also know p₂. I then non-rationally (or irrationally) stop believing p₁, but as it happens, I continue to believe p₂. It will then often be the case that there will be a good argument from p₂ back to p₁ (perhaps given some auxiliary premises), and if I use that argument, I will be able to regain my knowledge of p₁. This is true even though there is a circularity: from p₁, to p₂, and back to p₁. Here is an uncontroversial example: I am told my hotel room is 314. I infer that my hotel room is the first three digits of pi. I then forget that my hotel room is 314, but continue to believe it is the first three digits of pi. I then infer that my hotel room is 314.

Johnson proposes that by the sensus divinitatis one may come to know that God exists (actually, throughout this, I can't remember if he talks of knowledge or justified belief). One may then infer from this various things, such as that possibly God exists. Then, one irrationally rejects the existence of God (it does not have to be a part of the theory that every rejection of the existence of God is irrational), but some of the things one inferred from that belief remain. And arguments like the S5 ontological argument then make it possible to recover the knowledge of the existence of God from the things that one had inferred from that belief. Johnson also applies this to the cosmological argument.

This same structure may be present in my Kantian argument. By the sensus divinitatis one comes to know that God exists (obviously this is not a Kantian idea!). One infers that the universe is such that we should be grateful for it. One then irrationally comes to be an atheist (again, there is need be no claim that every atheist is irrationally such), but one continues to believe that gratitude is an appropriate response to the universe. And if that belief is sufficiently deeply engrained, one can reason back from it to theism or at least to agency behind the universe.

Now let me move a little beyond the Johnson paper. I think it is not necessary for this structure that the initial knowledge of God's existence come from the sensus divinitatis. Any other way of having knowledge of God's existence will do—say, by argument or testimony. In fact, it is not even necessary for this structure that one oneself ever had the knowledge or even belief that God exists. Suppose, for instance, one's parents knew that God exists (in whatever way), and inferred from this that the universe is worthy of gratitude. They then instilled this belief in one, and did so in such a way as to be knowledge-transmitting. (Surely, value beliefs can be instilled in such a way.) But they did not instill the belief that God exists (maybe because they thought that the existence of God was something everybody should figure out for themselves). One then knows (1), and can infer (3).

This transmission can be mediated by the wider culture, too. Culture can transmit knowledge, whether scientific or normative, and arguments can work at a cultural level. It could be that a theistic culture where the existence of God was known grew into a culture where (1) was known. The knowledge of (1) can remain even if the culture non-rationally rejects the existence of God (as American culture has not done, and might or might not do in the future). And then the individual can acquire the knowledge of (1) from the culture (we don't need to attribute knowledge to the culture if we don't want to; we can just talk of knowledge had by individuals participating in the culture), and then infer (3).

I think there are probably many consequences of theism that are embedded in the culture, from which consequences one can infer back to theism. If the participants in the culture knew theism to be true when these consequences were derived, then it is perfectly legitimate to reason back from these consequences to theism.

A variant of the genetic fallacy

Consider the following argument form:

1. p is believed because of argument A.
2. If A is a good argument, then q.
3. Not q.
4. Therefore, not p.

This is a kind of cross of the genetic fallacy with a denial of the antecedent (in the conditional: If A is a good argument, then p). For example:

5. The Immaculate Conception (the doctrine that Mary was saved by grace alone in the first moment of her existence) is believed because of the argument that Jesus would be subject to original sin if Mary was.
6. But if Mary's original sin would have infected Jesus, then the original sin of Mary's parents would have infected Mary, and so on, and hence all of Mary's ancestors would need to be without original sin.
7. But not all of Mary's ancestors are without original sin.
8. Therefore, the Immaculate Conception is false.

Notice, however, that there is an argument form in the vicinity of (1)-(4) that is better. Namely, we replace (4) with:

9. Therefore, the belief that p is not justified.

However, if we do that, we need to read (1) as saying "p is only believed because of argument A". But people are not very good at figuring out the reasons why they themselves believe something, and are much worse at figuring out why others believe something (that explains why so much political discussion is heated—for it is often difficult for people to figure out why someone might take a political position that disagrees with theirs, unless that person is stupid or vicious). So if the implied epistemic agent in (1) and (9) is someone other than the person offering the argument (1)-(3),(9), the argument is likely to be unsound in step (1). I think that when the argument form is found in the wild, it is common for (1) to fail.

Furthermore, it is important to keep constant the epistemic agent constant between (1) and (9).

I think the Marian case likely screws up on all of these counts. First of all, in (5) the epistemic agent is likely some ordinary believer or at best an incautious rookie apologist. In the analogue of (9), the epistemic agent is the Church. Second, even in the case of the ordinary believer or the rookie apologist, (5) ceases to be true if we read "is believed" as "is only believed", because in fact the ordinary believer and the apologist believe in the Immaculate Conception not just on the basis of their flawed argument, but primarily on the basis of the Church's authority.

Moreover, arguments of the form (1)-(3),(9) are often annoying to the interlocutors. I remember a job interview where a candidate tried to convince me that I only rejected his or her view because of thinking about a topic under the influence of a certain other position. This bit of mind-reading not only was incorrect (I can be accused of many things, but not of that particular influence; I rejected the candidate's view cause the conjunction of its claims obviously entailed some absurd proposition that we were both committed to the denial of), but I found it annoying and a bit offensive, and the other members of the interview committee did not like it either. That was a somewhat different version of the genetic fallacy, but the genetic fallacy is generally annoying.

There are places for arguments of the form (1)-(3),(9). But when one gives such arguments, danger is all about.

An argument form in ethics

Consider the following argument form:

1. It would be good if A were forbidden (respectively, permitted).
2. Therefore, probably, A is forbidden (respectively, permitted).

For instance, it would be bad if one were forbidden to fail to fulfill (apparent) promises made under duress. For then people could place one under duress, and force one to promise to serve them for life, and one would be obliged to keep to that. So, probably, it is permitted to break such (apparent) promises. On the other hand, it would be good if one were obliged, ceteris paribus, to fulfill promises to self, since such promises would be a useful tool for self-mastery. Therefore, probably, one is obliged to keep such promises.

As a technical point, we probably want to boost the antecedent in (1) to say not just that A is forbidden (permitted) but that it is additionally known or at least believed to be such.

Consequentialists will be friendly to a version of the argument form, assuming that there is an inference to be made from something's being believed forbidden to its being less likely to be done.

The interesting question is whether there is anything non-consequentialists can make of this argument. I think divine command theorists can. A good legislator, makes prohibitions that are good for his subjects. So divine command theorists will accept this argument form, and this counts in favor of divine command theory.

Natural law theorists will have to accept the argument form when "good" is restricted to mean "good for the agent", because of the tight link between the right and the perfective of the agent. It takes a little bit more work for natural lawyers to accept the argument form when "good" is not restricted to the agent's own good. If the agents are people, some work can be done by the fact that flourishing in a flourishing community is one of the basic goods. But to get the argument form in all generality, one might need to add theism to natural law (and a sociological matter of fact, natural lawyers overwhelmingly seem to be theists)—for theism will give one reason to think that the natures of the existent beings are in some significant degree of harmony.

What about other non-consequentialist theories? Social contract ones will probably respect this argument form. Kantian ones? Here, things are much less clear. The historical Kant's theory is theistic or at least deistic, and Kantianism plus theism or deism does make this argument form plausible: it is likely that God would arrange things such in the Kingdom of Ends that acting well is connected with flourishing. But a non-theistic Kantianism might be unable to give us good reason to think the argument form is right. That is an argument against non-theistic Kantianism.

One worry. The argument form may suffer from some circularity. After all, as Socrates taught, it's bad to do what is forbidden, simply because it is forbidden. So in evaluating what is good in (1), one needs to avoid taking the mere fact of the action's being forbidden into account.

Arguments and sincerity

When we write down a complex logical argument, it seems there is a pretty good chance that while writing down the proof, we will write down sentences that express propositions which we do not believe. Some of these sentences will be as part of a conditional proof, and those are not puzzling. But some of the sentences that express propositions which it seems we do not believe will be simply asserted. For instance, in the middle of our argument, we might make a claim that involves some complex logical or mathematical formula, which we then expand out using appropriate manipulation rules. But the expanded out claim may well exceed our mental capacities: we can handle it on paper, but it is just too complex for us to believe, it seems.

If this is right, then sincerity does not require that I believe what I say. (I assume the rules for sincerity do not depend on whether I am writing or speaking.) All that is required is that I believe that what I am saying is true. (What should I say about the speaker meaning in such a case?)

Or so it seems. But here is a curious test case. Politician reads a speech that her speechwriter wrote. She trusts her speechwriter to write only truths. The politician did not read over the speech ahead of time. She enunciates the sentences carefully, but she is distracted and pays no attention to what the text says. I think we would say that she is not being fully sincere. Maybe, though, our standards for sincerity are unfairly high in the case of politicians. Or maybe there are different kinds of sincerity—there is the bare sincerity which is one's duty in speech, and there is something that one might call "real sincerity" which entails conviction (where conviction is belief and more).

On the other hand, there is a different way of looking at the case of the complex sentence in an argument (this is inspired by some things that David Manley said based on his book with John Hawthorne). Maybe we can simply gain access to the proposition by means of the sentence, without having ourselves to understand or even parse the sentence.

Or maybe the things in the middle of proofs should not count as assertions. Perhaps making steps in proof is a mechanical procedure, akin to punching buttons on a calculator and likewise intrinsically devoid of propositional content, aimed at producing empirical evidence of the truth of some entailment. (That the evidence produced by a complex proof is empirical in nature is clear to me, weird as it may sound. One reason is that memory is intricately involved.)

An argument against shaving

The argument is a reductio.

1. Shaving is sometimes permissible.
2. There is a relation I such that IxP holds if and only if P is a property which x has.
3. Define the property N by NP=~IPP.
4. Either N has N, N does not have N.
5. If N has N then ~INN by definition of N, and so N does not have N, which is absurd.
6. If N does not have N then by definition of N we do not have ~INN, and so by double negation, we do have INN, and so N has N, which is absurd.
7. Thus absurdity ensues on both horns of the dilemma in (4).

The reader will, of course, notice that (1) is not used anywhere in the argument. Instead, the argument gives (1), and then launches into a standard variant of Russell's paradox. It's obvious, thus, that we learn nothing from the argument about the permissibility of shaving.

But one can dress up the argument if one so desires, so that (1) gets used further on down. For instance, instead of working with I, one can work with I_s where I_sxP holds if and only if P is a property which x has and shaving is sometimes permissible. If N_sP=~I_sPP, then absurdity ensues from assuming that N_sN_s only assuming that shaving is sometimes permissible. (If shaving is not permissible, then N_sN_s holds because I_sN_sN_s unproblematically fails as the second conjunct in its definition fails.) Thus, we can take the paradox and dress it up into an argument against the permissibility of shaving. But of course we still learn little about shaving from it.

I claim that Patrick Grim's arguments against omniscience are another such dressing up of this paradox, and hence we learn little about omniscience from them. But I am not going to argue for this here, since I am still working on the paper where I show this.

Bringing theology into metaphysical discussions

As readers of this blog know, I am not a big fan of the compartmentalization of knowledge, and specifically of a compertmentalization on which theological knowlege does not affect one's philosophical beliefs. Here I just want to note one thing. A lot of contemporary metaphysical arguments have some form rather like this:

Here's a phenomenon F. Look, it's puzzling. Here are three accounts of F. Look, they all fail. Here's a fourth account of F. Look, it doesn't fail for the reasons for which the three fail.

We're then supposed to accept the fourth account.

But of course such arguments are weak (there is nothing wrong with weak arguments, except that strong ones are preferable). Unless there is a further argument that any account must be one of the four, while such argument provides evidence for the fourth account, it should not give one very strong confidence in the fourth account. And at least in such a case, if the theology has a rational basis (e.g., in apologetic arguments), it seems clearly unproblematic to say, e.g., "Ah, but the fourth account fails, too, because it contradicts transubstantiation."

After all, if the fourth account of F contradicts transubstantiation, then the philosopher who accepts the fourth account and accepts transubstantiation needs to revise her beliefs. She could do so by rejecting transubstantiation. But assuming there is the kind of rational basis for her acceptance of transubstantiation that we might expect an intelligent Catholic to have (e.g., she is appropriately convinced by the apologetic arguments that show that Christ founded a Church whose basic beliefs would always be true and by the historical evidence that transubstantiation was, at least at one point in history, one of the basic beliefs of the Church), wouldn't it be silly for her to reject transubstantiation merely on the grounds of the fact that we have not yet found a satisfactory account of F that coheres with transubstantiation, but we have so far found an otherwise satisfactory account of F that does not cohere with transubstantiation? The confidence engendered by arguments of the form that was given for the fourth account of F is just too low to make it rational to reject transubstantiation.

Consider, too, that the revision to her web of beliefs in rejecting the fourth account of F is likely to be much smaller than the revision in rejecting transubstantiation if she is Catholic. (If she rejects transubstantiation, she will need to reject conciliar infallibility or else go Orthodox and deny that Trent was an ecumenical council. In either case, a lot of other beliefs would likely have to change.) It would be strange indeed if such significant transformation of one's belief system were to be made rational merely by the fact that three accounts of F are unsatisfactory and the only one we know of that doesn't fail in this way contradicts transubstantiation.

What is further typically true of these kinds of metaphysical arguments is that the fourth account, while not subject to the deficiencies of the first three, has some implausible consequences, too, which the author finesses. Even if in fact the author of the argument is right that these implausible consequences are less problematic than those of the first three accounts of F, it seems really clear that at least in such a case bringing in the theological consequences is entirely appropriate.

(I sometimes argue for a significantly weaker conclusion than the one I hold. This is certainly true in this post.)

Bioethics without God

It is considered in bad taste to bring God into contemporary bioethics discussions. Why? Well, one reason is that if one does so, one's argument will be irrelevant to atheists and agnostics. But note that in the American public, the percentage of people who accept the existence of God is significantly greater than the percentage who are Kantians, or utilitarians, or virtue ethicists, etc. Thus, say, an argument in favor of cloning based mainly on the premise that God exists (I don't know of any such argument off-hand) will be relevant to a much greater percentage of people than an argument for the same conclusion based on Kantianism. Moreover, while among academics there are significantly more atheists and agnostics, it still may be that the claim that God exists is at least as widespread as a belief in Kantianism, or in utilitarianism, or in virtue ethics.

Another reason it's in bad taste is that it allegedly brings faith into what should be a reasoned discussion. But this presupposes that the existence of God cannot be argued for rationally, a claim that is false (clearly false if we use as our standard of rationality the level of compellingness of arguments in applied ethics). Now one might with greater plausibility claim that no argument for the existence of God will be compelling to all, or even to a majority, of intellectuals. But it is in perfectly good taste to give serious bioethics arguments based on premises that are not compelling to the majority of intellectuals. Thus, one can give Kantian, utilitarian or virtue ethics arguments.

A third, though very pragmatic (but so is the first), reason is contingencies involving legal issues about church and state in the U.S., and cultural hangups connected with this. For better or worse, it is likely that the Supreme Court would see a law grounded in the existence of God, even if the law included a preamble giving a very powerful rational argument for the existence of God, as violating the separation of church and state.

I have theistic friends whom I respect highly and who try very hard to avoid making use of the existence of God in their work in applied ethics. While I think such work is very important both intellectually and practically, I also think there is a danger of distortion in bioethics if one confines oneself to working in this way. When one does have to do non-theistic work in bioethics, one should think of it as a way of tying one hand behind one's back, because that's what the rules of the game call for, not because that's what is appropriate to the enterprise of truth-seeking. For when we are talking about appropriate treatment of the beginning and end of life, it is plausible that the question of the relation between life and God is highly relevant. Some people think that the way science can explain all kinds of facts without invoking God is an argument against the existence of God. That's a bad argument. But if ethics, especially the ethics that deals with the beginning and end of life, could do without God, that should be quite surprising to a theist.

In the above, I talked of mere theism. I have a strong suspicion that, at least in our fallen state, more than mere theism is relevant. John Paul II somewhere said that we can only understand man through Christ. If that's right, then non-Christian bioethics is doomed to incompleteness. And incompleteness in a philosophical enterprise runs the danger of leading to distortion, through onesidedness.

Art as argument

I once ran a panel discussion between an Islamic theologian and a philosopher of art. The Islamic theologian was defending what she claimed was traditional Islamic jurisprudence, that for the sake of freedom of inquiry it is legally permitted to write anything in the context of intellectual verbal argument (even really nasty things about the founder of Islam, as long as long as they were supported by argumentation), but that there are restrictions on, say, what is permitted in art. The idea was that in intellectual inquiry, verbal expressions have a privileged status.

It seems to me that this account of inquiry is somewhat impoverished. While argument can be made in words, it can also be made in other ways. In their fun Handbook of Christian Apologetics Kreeft and Tacelli give this argument for the existence of God:

There is the music of Johann Sebastian Bach.
Therefore there must be a God.
You either see this one or you don't.

I may not see it, because my own appreciation of music is most deficient[note 1], but I see the kind of argument that is made here, and it is not an argument in words—simply asserting that there is the music of J. S. Bach doesn't do the job. The music is an essential part of the argument itself.

Or consider the following argument:

1. 
2. Therefore, war is wrong.

Does it make sense to simply incorporate a work of art as a premise to an argument. One problem—and this may be the reason for the apparent Islamic privileging of verbal arguments—is that arguments that incorporate a work of art as a premise are hard to criticize. I am not a pacifist. So I accept that the above argument is unsound. But it is really hard to see what I deny. Do I deny premise (1), i.e., deny Guernica? That seems to be a category mistake. Or do I deny that (2) follows from (1)? So there is something unfair about the use of art in argument—one is putting oneself beyond criticism, except maybe by a competing work of art.

Difficulties with this notwithstanding, I do think the idea that a work of art can express an otherwise ineffable proposition is defensible. Perhaps Guernica expresses the proposition that war is like this (isn't it fun to use hyperlinks to indicate referrents of demonstratives?). If so, then while denying Guernica is a category mistake, denying the proposition expressed by Guernica is no category mistake.

If so, then poems, songs, novels, etc. can express propositions that have truth value. This might be relevant to an account of Biblical inerrancy that includes the full range of genres found in Scripture.

Final note: I think the Bach and Guernica arguments may have different logical forms. It may not be that the music of Bach itself expresses something that implies the existence of God, so that the music is not a premise, but only a part of a premise—the premise that there is this [mp3 download is from here].