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.  

Extensionality, Description and the Question of Good Works: Towards An Anomalous Monergism?

 The great American philosopher Donald Davidson (1917-2003) wrote the following about causality:

The salient point that emerges so far is that we must distinguish firmly between causes and the features we hit upon for describing them, and hence between the question whether a statement says truly that one event caused another and the further question of whether the events are characterized in such a way that we can deduce, or otherwise infer, from laws or other causal lore, that the relation was causal ("Causal Relations," The Journal of Philosophy, 64 (1967), 691-703).  

Davidson's point in this famous article is that causality has an extensional nature.  If a causes b, it is, in fact, the event a that causes b to obtain, and this is a causal relation that obtains apart from however a and b might be described.   

Compare the following: 

1. Jack fell down and broke his crown.
2. That Jack fell down explains the fact that Jack broke his crown. 

Clearly, (1) bespeaks extensionality and (2) intensionality.  Very simply put, extensionality concerns what there is, while intensionality deals with how we might pick out or refer to what there is.  For example, in f(x) = y +2 for natural numbers N where 1< y < 5, the intension is the rule 'y +2' applied to either 1, 2, 3, 4, or 5, while the proposition's extension is {<1, 3>, <2, 4>, <3, 5>, <4, 6>, <5, 7>}. 

What is there a difference between (1) and (2) above?  (2) is concerned with the relation between two descriptions, 'Jack fell down' and 'Jack broke his crown'. These two sentences are related by the operation of causally explaining.  Notice, however, that (1) does not connect to descriptions at all, for the 'and' in (1) is concerned with the actual events of Jack falling down and Jack breaking his crown.  

Assume that d is the event of Jack falling down and c is the event of Jack breaking his crown. Notice that event d  may cause event c without any recourse to modal terms.  Clearly, the singular event d and the singular event c, both denizens of the extensional, cannot be connected by a modal operator, for modality applies to events only in so far as they are properly described.  Modality is de dicto and not de re.  In Humean terms, it concerns the relations of ideas, not the matters of fact.  

One could, I suppose, have a general law claiming that for all x, if x falls down then x breaks x's crown.  Such an occurrence may be so regular that one might, I suppose, claim that it is necessarily the case, that for all x, if x falls down then x breaks x's crown. But this modal operator which concerns relations between ideas (or language) might be replaced by a far more modest operator in intensional contexts, the causal explanation operator.  We have our stories about the world and the behavior of objects within it.  We know that there are features instanced in Jack's falling down and Jack's breaking his crown, such that the features of the first causally explains the features of the second.  Thus, it is true that Jack's falling down causally explains the breaking of Jack's crown.  

But Jack is the man most to be pitied on Beecher Street, and while his falling down is the most unfortunate event of his lifetime,  his breaking of his crown is that that issued in his wife leaving him. Does causal explanation still work as we substitute descriptions for singular events salve veritate?

3. That the man most to be pitied on Beecher Street suffered the most unfortunate event of his lifetime causally explains the fact that his wife left him. 

Clearly, any law connecting fallings and breakings is now no longer at issue. Here the connection is between unfortunate events happening to guys on Beecher Street and their wives abandoning them.  While one might think the causal explanation operator in (2) is apt, its use in (3) seems much more problematic.  But how can causal relations depend upon the descriptions of d and c?  Is it not simply about the relations between these two events however they might be described? 

Davidson developed a theory of token identity in the philosophy of mind that exploits the difference between causal relations and causal explanation.  Imagine that there is some event e such that it can be given both a neuro-physical and psychological description.  The neural event that e is is presumably related to other neural events, but the mental description of that event -- perhaps a particular thinking of one's particular mother when she was 36 -- cannot seemingly be relatable to other mental events causally in the same way.  After all, neural events do not swim in the waters of the normative.  My thinking of my mother when she was 36 might be followed by a particular thought of the appropriateness of my love for her, and this is clearly a matter of normativity.  One ought to love one's mother, after all; it is right to do so.  

One might generalize from these reflections into the philosophy of action.  What is the best explanation why Bob gets in his vehicle and drives the 25 miles to the airport at 4:50 p.m. on April 23?  It is that Bob believes that his wife Jan is flying home on the 6:00 p.m. plane from Chicago, and that Bob has a desire to see her.  Causal explanations for why we do what we do our routinely cast in the language of beliefs and desires, and not in the language of neural states.  It would be odd, after all, to say that Bob is getting in his vehicle at 4:50 on April 23 because Bob's neurophysiological states coupled with appropriate external sensations caused it to be so. What kind of causal explanation for Bob's behavior refers simply to brain states and perceptual inputs?  How could knowing the neural events of Bob causally explain the purpose he had when entering his auto? 

Davidson's token identity theory of the mental and physical simply points out that our mental life with its complexities of purpose in beliefs in desires is physically realized, that is to say, that some set of neuro-events realizes our mental states.  Davidson is not a substance dualist, after all, claiming that there is an ontic realm of mental events, entities, properties, relations or functions that can exist on its own, and whose processes are simply coordinated with physical events, entities, properties, relations of functions in the brain, and that, in principle, one might be able to draw causal connections between the mental and the physical.  By claiming a token identity between mental states and some brain states or other realizing these mental states, Davidson believes he can protect the anomalousness of the mental while not acquiescing to dualism.  His position is appropriately called anomalous monism.  The point is that one event can have different descriptions, and that there is a certain irreducibility of the mental to the physical.  Accordingly, the complexities of our mental life cannot be either explained or predicted by pointing to the existence of strict scientific law -- if there actually is such -- at the neuro-level.  

Whether or not Davidson's position of anomalous monism is finally defensible is not my concern here.  I advert to this only because I want to show again the importance of description when it comes to events. Causal explanation is possible because of the descriptions we give to a particular event.  Causal explanation involves language, in our use of language to highlight features of events we want to explain.  Causal relations, however, are ultimately extensional, they are drawn between events however they might be described.  That event e causes event e', is a feature of the world, not a feature of our description of the world -- or so one might argue.   But what might any of this have to do with theology? 

In the Lutheran tradition there has been since the beginning profound controversy about the status of good works in salvation.  Classically, one might ask, "are good works necessary for salvation?"  An unreflective quick response is simply "no!"  "Good works do not save us before God, so good works are not necessary for salvation."  It is perhaps a response like this that underlies the suggestion by Amsdorf and others that good works might even be harmful for salvation. 

But reflecting on the logical form of the statement, 'Good works are necessary for salvation' does not mean 'if good works, then salvation'.  If 'if A then B' obtains, then A is sufficient for B, and B is necessary for A.  The proper translation of 'good works are necessary for salvation' is 'if salvation, then good works', that is, 'if not good works, then no salvation'. Those claiming that good works are necessary for salvation are clearly not claiming that by doing good works, one might be saved; they are not saying that good works are sufficient for salvation.  Good trees bear good fruit.  If God makes the tree good, then good fruit will follow.  Therefore, good works are necessary for salvation. 

But merely pointing to the logic, does not seemingly solve the controversy.  Those espousing monergism, that we are saved wholly by God apart from our own agency, want to protect divine autonomy.  They are deeply suspicious of language having to do with human working and doing, of language having to do with human discipling, for such language suggests human agency; the language itself suggests synergism.  Luther was profoundly critical of the category of created grace, the notion that God through his agency might create in human beings ontologically-extended dispositions to behave, and thus that there might be something in human beings on the basis of which the divine imputation of righteousness rests.  Luther accordingly rejects the notion that human beings have been made right, and on that basis, they are pronounced right; the Gerechtmachung grounds the Gerechtsprechung.  But if this were so, were we given such goods, then why and how could we who have benefitted so deeply utter as did Luther in his final hours, "Wir sind bettler, hoc est verum?"  

There are standard moves in this debate, a debate that is connected to the so-called "third use of the law." My purpose here is not to get into the debate and follow the lines of reasoning that have a certain plausibility no matter upon which side one finds oneself.  My purpose here is simply to propose something new that might move the conversation forward.  

What if we took seriously the distinction between the event of the person doing a good work and its description?  Let me be more clear, what if we took seriously the distinction between d, the event of a person behaving in a particular way, with its description as to what the person was doing in that event d?  After all, Paul's ingredience in d could be described as both the doing of a good deed through Paul's own agency or as a divinely-gifted doing where it is no longer I who live but He who lives in me.  The point is this, the same event d is multiply describable. It can be described on the basis of a human agent believing that he must do the act and desiring so to do it, or it can be described as a behavioristic input/output function, or it can be described as wholly caused by the Holy Spirit. Our background assumptions and theories deeply influence how the event might be described.  The same event can be given a description in terms of beliefs and desires and the intent by the person to "do what is within them."  It can be described, solely in monergistic terms; the event is that work that is worked by God in us propter Christum and by grace through faith; or the event could be described perhaps without averting to so-called "folk psychological ascriptions" at all.  If we were to give a neuro-description to the event, it would make no sense in giving a casual explanation to the event to speak of the Holy Spirit's causality or the desire to be saved and the belief that that a particular doing, a suitable description of d, motivates the doing.  

The language of discipleship -- what is it to be a fisherman that follows -- is clearly a different language than the language of apostolicity -- what heralds does God establish in His Wording of the world.  Both languages can be developed quite thickly, with language available to speak of all sorts of events, and both languages can provide causal explanations.  This being said, however, there still is some underlying events that are what they are because of causal relations they sustain with other events. The fact that no language can mime the contour of these causal relations does not tell against their presence.  The extensionality of causal relations of such d doings by Paul might not be able to be articulated in the languages by which events like d are described.  Here we are talking about propositional attitudes, about the believings of people doing d.  Here we are at the level of the intensional.  

Although I have not defended anamolous monism, in closing I want to open up the possibility of an anamolous monergism.  What if Davidson is right, and that there are simply causal relations at the neuro-level that support mental descriptions where causal explanation is possible?  What if one could be a nonreductive physicalist of such a kind?  Does this have relevance for the theological issue at hand? 

Imagine that the Holy Spirit has a causality such that some human events are caused by the Holy Spirit.  After all, maybe Luther is right in that we are either ridden by the devil or Christ.  If the Holy Spirit causes that event we might describe as a good work, then clearly no human agency is determinative in its doing.  Clearly, this is an embrace of monergism.  But what about our description, our own self-understanding of that event?   

Surely, we could causally explain that act in terms of beliefs and desires.  We could have an intent to do what God would have us do, and we could believe that that doing is meritorious somehow before God.  We live lives that are thus pleasing to God, and we try in all we do to keep God's commandments.  We learn more about God and we attempt to follow Christ in all we do.  All of this description of our life of faith, as thick or thin as we might want, could be seen as realizable within the underlying divine causality upon human events. Clearly, the language of belief, desire, intentionality, and following is not reducible to the language that describes the Holy Spirit's causality upon our behavior.  From the standpoint of the extensional, God authors are events, but from the standpoint of the intensional, are doings realized by those events can be explained in therms of the motivations of living the Christian life.  

What I am suggesting here is an anamolous monergism that neither undercuts the reality of monergism, nor does it downplay the complex experience of living out the Christian life. There are deep philosophical and theological objections to this view, of course, but I do think that the main point might be defendable: The penchant to good works is a way of talking or describing Christian lived existence, and this way of talking or describing does not have to contradict the reality that I cannot cause that event that might be described as a Christian following.  Similarly, third use of the law talk need not contradict the reality that there are only two proper uses.  But this topic must await a later treatment.