Model-Theoretic Considerations for Theological Semantics

I

I have for many years been convinced that the theological enterprise cannot survive in our age without affording to its language robust truth conditions.  Contemporary men and women presuppose what Jaegwon Kim once called Alexander's Dictum, that is, "to be is to have causal powers."  We don't live in the 19th century where ideas themselves are thought to have a kind of reality; we don' t live in a time in which the conceptuality of God can remain important for vast numbers of people. 

In our days, people are not generally searching to find some overarching concept or principle that grounds our rational thinking about life and existence, a notion that might somehow explain why human experience is given as it is, and accordingly, somehow ground the preciousness and value of that experience.  While Madonna once sung of a "material girl," we generally acknowledge that, even in our churches, the cultural primacy of the physical reigns.  The new atheism talks breathlessly of its discovery of a worldview without divine agency and causality -- as if such a view of things is in any way new.  There is an assumption of the causal closure of the physical among many unwashed in the complexities of the actual relations holding among experience, theory and truth, among those who simply believe that the theories of the natural and social sciences simply state the way things are.  

The idea is easy enough to grasp.  Consider this structure <{x | x is a natural event}, C>.  This is a structure consisting of the set of all natural events and a causal operator C relating members of this set of events to each other.  This structure can satisfy these two assertions:  1) For all x, there is some x (or other) that causes x, and 2) For all x, if x is caused, then it is caused by some x (or other).  What is precluded by this structure is that there is an x that can be caused by some event or agency that is outside the set {x | x is a natural event}, or that x causes some event or state of affairs outside the set {x | x is a natural event}.  Simply put, there are no non-physical events causing physical events, nor no physical events causing non-physical events.  

In addition to the causal closure of the physical assumed by many impressed with the results and progress of the natural and social sciences, it is also supposed, though not always as clearly, by the heralds of late nineteenth century radical criticism, that human beings are somehow alienated when they fail to come to terms with the physicality of their fate.  Feuerbach, Freud, Marx, and Nietzsche, all, in their own way, argued that the illusion of the traditional God connects with the fundamental alienation of men and women.  Marx, for instance, argued that human value and ideology is determined by underlying economic processes, and that the concept of God simply operates to block human beings from understanding the basic materiality of their existence.  The God concept sanctions prevailing ideology and functions to keep in place value ideologies grounded in the unequal distribution of economic materiality.  

Most people that continue to practice the Christian life believe that there is a God and that God is active in the world, i.e., they assume that "to be is to have causal powers" and that God has causal powers.  They speak about the divine design of the universe, and about the power of prayer, particularly prayers of petition.  They assume that there are things that have come about that would not have come about were there no God, and that there are events and processed that have not come about that would have come about were there no God.   

The structure they assume is perhaps this: <{x | x is an event}, g, C, D> where there is a set of natural events and there is God, and that there is a binary natural causal operator C linking natural events to other natural events, and a binary divine causal operator D, linking natural events to divine agency, e.g., 'Dgp' means God divinely produces event p, with p being a member of the set of all natural events.  

Metaphysics remains crucial in theology because claims about that beyond the physical are by nature metaphysical, and assuming God to be with causal powers means that something beyond the physical is bringing about something physical.  This is clearly a metaphysical claim. To afford to theological language robust truth conditions in an age that assumes that to be is to have causal powers means that theology must be self-consciously and boldly metaphysical.  There must be intellectual honesty here.  Either theological language is broadly expressive of the self, its experiences and existential orientations and possibilities, or it is a rule-governed customary discourse by and through which human communities function and operate in the world, or it is a type of discourse that non-subjectively donates possible ways of being, or perhaps it is realist in its motivations; it states what its utterers believe is the ultimate constitution of things.  

One needs to think through these issues very clearly.  What are either the truth or assertibility conditions of theological language if one eschews realism?  Are sentences in the language rightly assertible simply because my tribe (the theological tradition) has traditionally asserted them?  But clearly the assertibility condition cannot simply be 'x is properly assertible' if and only if x has been asserted by normative theologians of tradition T over time t.  Why? In order even to begin to evaluate that claim we must know the identity conditions of 'normative theologian' and 'tradition' and 'time'.   

Are the assertions of theology then either descriptions of the self -- its experience and existential orientations -- or are they expressions of the self?  Clearly, embracing the latter is to give up on truth,  for it entails that assertibility must be understood broadly in terms of a "boo hurrah" theory of theological language.  But the former alternative is not much better, for on its assumption the truth-makers of all theological language are not theological.  On this view, models satisfying a set of theological assertions are not theological models at all because the sets, functions and relations of the models deal with the human.  Since human dispositions, experiences, and orientations are operated upon by relations and functions, these functions and relations ultimately concern the human. The fact that such models can satisfy a class of theological statements, should give us pause about what it is we are doing when we provide theological models. 

But there is another alternative, for we might hold that theological language somehow operates to disclose truth, that language, the Word, in its wording grants world and our place within it must itself be given a theological model.  But it is to me unclear exactly how this model can be constructed coherently.  Models or structures concern domains with functions and relations drawn upon those domains. But what can be the domain of the creative Word?  Remember that revelation is not insight.  Insight concerns an intellectual grasp of that which is already present.  Revelation, on the other hand, is a daring grasp of what is not present, but which shows itself eschatologically.  There is so much that can be said here, but I cannot in this brief essay say it.  We must move to the central issue of the influence that model-theoretic arguments might have for one who in her theological semantics, is broadly speaking realist. 

II

While I could only sketch briefly in the last section my prima facie reservations with non-realist construals of theological language, I will assume in this section that the reader is sufficiently persuaded by what I have said to give theological realism a try.  Theological realism, simply put, is the view that God, and divine states of affairs generally, exist and have the particular contour they have apart from human awareness, perception, conception and language.   Theological realism is thus a species of external realism, the view the world consists of entities, properties, events, relations and states of affairs which, broadly speaking, exists independently of our human perceptual and conceptual processing, or, more to the point, apart from our epistemic structures and capabilities.   We might call this the independence thesis with regard to external realism. 

I am convinced with many others that external realism makes two other important claims as well.  The first is the correspondence thesis which claims that statements about the world are true if and only if they correspond in appropriate ways with how the world actually is. (Clarifying what 'correspondence' and 'appropriate' might mean here is notoriously difficult.)  The other thesis of external realism one can be called the Cartesian thesis which states that although our theories about the world might meet all theoretical and operational constraints of an ideal theory, we could still be wholly wrong in our theory.  Since the theory is made true (or false) by how the world is apart from us, it is always logically possible to be wrong about everything that we might say about it.  Satisfying all theoretical and operational constraints does not a theory true make.  Only the way the world is can make the theory true or false.  The external realist thus seems committed to all of these: the independence thesis, the correspondence thesis, and the Cartesian thesis.  

Hilary Putnam in his famous "Models and Reality" distinguishes among three positions in the philosophy of mathematics.  These positions deal with both truth and reference in mathematics, and are thus, for him and for us, relevant to considerations of truth and reference with respect to external realism generally.  These positions are: 

• Platonism which, according to Putnam, "posits nonnatural mental powers of directly 'grasping' the forms" (Models and Reality, p. 24). This notion of grasping is primitive and cannot be further explicated.  Those familiar with Husserl's description of phenomenological intentionality will understand this quickly.  
• Verificationalism replaces the classical Tarskian notion of truth with verificational processes or proof.  Mathematic assertions are not true in any deep sense, but they are assertible on the basis of other mathematical procedures. Verificationist proposals within the philosophy of science of the last century are connected to this. 
• Moderate Realism, for Putnam, "seeks to preserve the centrality of the classical notions of truth and reference without postulating nonnatural powers" (Ibid.).  The idea here is that mathematical assertions are true, but that their truth does not involve one in a deep process of grasping or understanding the structure of some Platonic heaven.  

Putnam believes that arguments built upon the "Skolem-Paradox" are germane to a moderate realist perspective within mathematics and the external realist perspective in metaphysics generally.  These arguments are known in the literature as "model theoretic" arguments, and they basically exploit the difference in model theory between what might be intended and what might be said.  If one is a non-naturalist when it comes to semantics -- that is, if one thinks that semantic objects, properties, relations and functions are natural objects and does not involve non-natural magic -- then one has a problem with reference, because many models can make true the very same class of sentences.  This means, that one cannot naturally fix reference, that is, what the sentences say is logically independent from what one might mean to say in their saying.  

Putnam draws conclusions from this that are quite far reaching.  For instance, he claims that metaphysical realism (external realism generally) in incoherent, and that 'brain in vat' or 'evil demon" (Descartes) scenarios cannot even be coherently stated.  Putnam throughout tries to show that, because of the problem of reference, one cannot even state the conditions necessary to formulate the brain-in-vat/evil demon hypothesis. In other words, the necessary conditions for the possibility of posing the brain-in-vat scenario cannot obtain because a certain type of reference must be had by the language in stating the scenario, and since this type of reference cannot be had, the scenario cannot be coherently stated.  In other words, while it might appear that we could be a brain in a vat, we really can't be one, for to be one demands that we can refer to being a brain in a vat, and this we cannot do.  

Putnam employs a bit of a technical branch of logic known as model theory and there are considerable arguments in the literature about the effectiveness of his employment of these resources.  There are arguments as to the number and effectiveness of distinct model-theoretic arguments that Putnam uses, and their ultimate effectiveness in attacking metaphysical realism. All of this, I will lay out at another time.  What is important for us, however, is this question: Why is any of this important for theology? 

III

I believe that theological language must be given a realist construal if we are to retain it.  Long ago, I argued that the arguments for the elimination of theological language are strong, and that only a realist interpretation of theological language will likely stem the collapse of such language into reduction and ultimate elimination.  I can't rehearse that here, but know that I believe that theological realism best coheres with the principle that to be is to have causal powers. 

Notice now that if we afford to theological language realist truth conditions we seem to be interpreting it in ways that best connect to the classical Christian tradition.  Believers throughout the centuries assumed that there is a God, that one could refer to God, and that once could talk meaningfully about God's relationship with His universe, both in terms of creation and redemption.  It is extremely difficult, I think, to argue that the horizon of the Reformation is one in which one of the three following is not presupposed: theological realism, semantic realism, and theophysical causation.  The Reformers thought that God exists apart from human awareness, perception, conception and language, that our language about God is true or false apart from the ways in which we verify or come to hold it true or false, and that God is in principle capable of causal relations with nature and the historical realities of nature.  

So on the assumption of external realism when it comes to theology, what are the repercussions of model-theoretic arguments on theological semantics?  

At this point we must appreciate how important reference is for theological language.  We are using theological words and phrases, and if we must ultimately give a realist construal to theological language then reference turns out to be the key to theological semantics generally.  'God is in Christ reconciling the world unto Himself' is true only if 'God' refers, 'Christ' refers, 'world' refers, and the relation of 'reconciling' can be drawn between the world and Christ.  But now the question, if reference is so important, why cannot it be something intended?  Why can we not simply say that intentionality fixes reference and that we don't need to worry about model-theoretic considerations at all?   Remember, Putnam had said that model-theoretic arguments really apply to the moderate realist in mathematics and the metaphysical realist; they are not aimed at one who holds that intentionality can be fixed nonnaturally by something like Husserl's "ego rays."  If one wants to hold intentionality as a nonexplicatable primitive, then can't we simply say that our intentionality determines reference in the theological order, as well as the mathematical and metaphysical orders? 

Here is the problem with this response.  While one might hold that one can intend cherries or trees by nonnaturally fixing one's gaze upon them, one cannot seem easily to do that when it comes to God or the inner workings of the Trinity.  After all, "nobody has ever seen God."  How can one intend that which has no clear content?  The theological tradition knew the apophatic nature of God-talk.  We can never be given the proper content to think God, because the content of our thoughts pertain to the finite order and God is infinite. Our thoughts of God do not thus determine our reference to God; our intentionality cannot issue in reference, because we cannot be given that by virtue of which reference is determined. Instead of intentionality granting an intensionality that determines reference, our theological language -- the language of the tradition -- speaks about God and God's relationship to His creation.  The ways of talking about God are very important indeed!  God's name is that by virtue of which reference is established, and maybe for Christians -- or perhaps all the monotheistic religions of the west -- this happened at the burning bush.  (Recall here Kripke's "initial baptism" of the tretragrammaton at the burning bush in Exodus.) 

It is important here to grasp what is at stake. If intentionality cannot fix reference to the divine, and if we don't want to give up truth to some verificationist-inspired theological position -- that is to say, if we want to be realists in theology -- then we seem to find ourselves in theology with no other option than to have to take the model-theoretic arguments seriously with regard to theological realism.  This means that not only are model-theoretic arguments relevant to theology, they might be crucial to its very future.  If model-theoretic arguments yield a knock-out blow to external realism, of which theological realism is a species, and if realism is essential in providing a defendable semantics for theology, then model-theoretic arguments may pose a much deeper threat to theological discourse than we previously might have thought. 

So what is at stake with respect to model-theoretic consideration in theological semantics?  I think it likely that the future of theology itself might be at stake. But consideration of this must await another time.  It is upon that which I am toiling a new manuscript.