An Early Reflection on Divine Action and Ethical Decision-Making from the First Years of ILT

The following essay is an early reflection written during the founding years of the Institute of Lutheran Theology. It was written and shared likely around 2008 or 2009, when many of us were first gathering to think together about the future of theological education and the church’s intellectual vocation. I had recently returned to academic theology after many years of parish ministry, and I found myself increasingly struck by a gap that seemed rarely acknowledged in the academy.

In graduate school we had been taught—almost as a matter of intellectual hygiene—that serious theology after Kant must avoid speaking of God as a causal agent within the world. The dominant assumption was what Ian Barbour called the “independence motif”: theological language and scientific language speak about different domains and cannot refer to the same reality. Once this presupposition is granted, much of modern theology becomes an exercise in reinterpretation—finding ways to translate traditional religious language so that it no longer implies divine agency within nature.

Yet my experience in congregations had been very different. The people in the pews did not speak this way. They prayed as though God could act. They believed that God could guide, heal, forgive, and intervene. They did not regard such claims as poetic expressions of existential commitment. They regarded them as statements about reality.

The tension between these two worlds—the academic assumption of divine causal quarantine and the lived faith of ordinary Christians—raised a question that seemed to me unavoidable: What difference do our metaphysical assumptions actually make for the ethical judgments Christians must render in concrete situations? Ethical judgment never occurs in a metaphysical vacuum; what we take to be possible, necessary, or forbidden already presupposes a deeper account of how God, the world, and human agency are related.

What began to dawn on me at the time was that the issue was not merely pastoral or sociological. It was philosophical. If theology denies that God can act in the world, then the range of what counts as ethically possible is already silently restricted. Entire classes of moral reasoning—appeals to divine guidance, providence, vocation, or the transformative power of grace—are quietly ruled out in advance. Conversely, if divine action is metaphysically possible, then the moral landscape appears in a very different light. Ethical deliberation becomes inseparable from deeper questions about causality, agency, and the structure of reality itself.

The essay below was an early attempt to explore that question. Its central claim is simple: ethical judgments are never made in a metaphysical vacuum. Whether we believe that God can act in the world, how we understand human agency, and how we conceive the relation between scientific explanation and divine purpose all shape the way we evaluate moral claims.

Looking back nearly two decades later, I can see that the argument is exploratory and incomplete. Much of my later work has tried to develop a more rigorous account of theological reference, intelligibility, and divine action. In particular, I have come to see more clearly that questions about divine agency cannot be addressed merely by revisiting older debates about intervention, causation, or the relationship between science and theology. They require a deeper clarification of how theological language itself can meaningfully refer to reality—how truth, satisfaction, and reference operate in theological discourse, and how formal descriptions of the world relate to the ontological conditions that make intelligibility possible in the first place. Results from logic and model theory, which sharply distinguish syntax from semantics and proof from satisfaction, have increasingly convinced me that the structure of theological language cannot be reduced to the grammar of formal systems or to the interpretive practices of a community. The conditions under which theological speech can be true must ultimately be grounded in reality itself rather than in linguistic form or communal authorization. 

Still, the questions raised here remain important. If theology is to speak meaningfully within the church, it must reckon honestly with the metaphysical assumptions that underlie both academic theology and congregational faith.

What follows is therefore not a final position, but an early attempt to think through a problem that continues to shape the theological task.

I

I remember the response of one of my professors thirty-five years ago when I had tried to connect theology to science in one of my papers. “Ah, but that's all precritical,” he snorted. In those graduate school days we learned early on the Kantian truth that God could neither be a substance nor could causally relate to objects within the universe. Only after understanding this did we move on to the important business of studying the various post-Kantian options, all of which presupposed what Ian Barbour has called the independence motif: theological and scientific language cannot refer to a common reality.

I want to reflect today on how one's view of the causal relationship between God and the universe affects an activity in which Christians are always engaged: ethical judgment. My claim is simple. The metaphysical picture one presupposes about the causal relation between God and the world has direct consequences for the ethical judgments one is prepared to make.

While the greatest theological expressions of the past two centuries presuppose this Kantian-inspired “causal quarantine” of God, I have become increasingly concerned about the disconnect between this presupposition and the views of many who still occupy pews in the early twenty-first century. It seems that many faithful Christians actually believe that God is at work in the world. One of the things I like best about the science and theology discussion is the working assumption that God need not be a causally impotent being, that serious theological reflection can and should try to conceive how it is that God might actually causally link to the universe. In other words, in important respects the science and theology discussion is as precritical as the views of those to whom I regularly preached on Sunday mornings in the small rural congregations I once served. There is something refreshingly honest about serious theological work undertaken that actually connects to beliefs of those in the church.

I shall argue that adherents of the independence motif often find their ethical judgments at odds with those in the pews precisely because they adopt the assumption of divine causal impotence. It turns out that they may well judge certain propositions false that those rejecting that motif would regard as true, and vice versa. My point is simply this. In doing theological ethics, one must take into consideration the metaphysical picture one presupposes, especially the nature of the putative causal connection between God and the world.

In what follows I shall suggest that the ontological question of the relation between what theology talks about and what science talks about is critically important for how the Church responds to ethical issues. After discussing an especially clear example of this, I shall examine three general issues in the science and religion discussion that have great import at the congregational level for theologically informed ethical judgment and evaluation. While all are old issues in the science and religion conversation, I suggest that the effect of each upon ethical valuation has not been adequately appreciated.

II

Consider the example of Bob, a person engaged in homoerotic behavior who believes that these behaviors are genetically determined.  I shall argue that Bob may display a number of different ethical responses to his homosexuality depending upon what he takes to be the causal connections between God and the world.  For instance, imagine Sue says to Bob that he should pray that "God change his homosexuality." I claim that the moral propriety of the statement that "it is good to pray to God to have one's homosexuality changed" is contingent upon what Bob takes the underlying ontological situation to be regarding the causal link between God and world.  Let us examine four positions that Bob might adopt: 

1)    Bob might be convinced by the Kantian view that God can neither be a substance (physical or otherwise), nor can God enter into causal relations with other substances.  On this view, God-talk must be analyzed so that it makes no commitment to substance or causality.  Thus, "God changes homosexuality" cannot mean that some divine entity actually brings about a change in the natural order.  Instead, an alternate analysis of the statement must be given, an analysis that does not vitiate one's ontological scruples.  Accordingly, the statement might be construed as an expression of existential attitudes, a donation of courage in the face of future, or a moral recommendation or valuation.  For example, prayer to God that God might "change one's homosexuality" might be regarded as an expression of one's inability to accept oneself.  Many who accept the independence thesis would no doubt wince at such a prayer and regard it as wrongheaded or morally-corrupt precisely because they do not suppose it possible for God to cause events in the natural order.  Because they understand the proposition to be an expression of or statement about Bob's lack of acceptance of his own condition, they can quite plausibly claim that "it is good to pray to God to have one's homosexuality changed" is false.  Why?  If it is true that Bob's homosexuality is genetic and cannot be altered by God, then on utilitarian grounds his greatest happiness (and the happiness of those around him) is perhaps best realized by his accepting his genetic situation.  To not accept what cannot be changed is a prescription for unhappiness.  The fact that one might argue deontologically to another conclusion does not concern me here.  I merely want to indicate that on utilitarian grounds the statement "it is good to pray to God to have one's homosexuality changed" is plausibly false, given the underlying Kantian ontology.

2)    Bob might hold some variety of Thomism (or God-universe interactionistic dualism), and assert minimally that God is a substance, albeit not a natural one, and that God is causally related to the universe through primary causality and through supernatural intervention.  Leaving aside the theological question of why God would need to interrupt his continuous activity of bringing about actualizations in a primary causal way to intervene directly, we ask if the proposition "it is good to pray to God to have one's homosexuality changed" is false on a Thomistic ontology.  It is plausible to argue that this different ontology affects the ethical evaluation of the proposition, for presumably the ontology of Thomism does allow that God hears prayer and can act in accordance with that prayer.  Moreover, God's direct intervention is sufficient for the event of Bob's genetic predisposition being changed.  Given the challenges homosexuals continue to face in our society, it is credible to argue on utilitarian grounds that it now might be true that "it is good to pray to God to have one's homosexuality changed."  If God turns out not to do anything about Bob’s homosexuality, Bob can always subsequently accept his homosexuality by considering it to be God's will.  After all, if God is a real causal agent who can immediately bring about anything God desires, then if he does not change Bob's genetic predisposition, that predisposition must be regarded as passively willed by God. 

3)    Bob might believe that God acts in the world, but not through direct supernatural intervention.  Instead of violating the causal closure of the physical, God works at the quantum level in being part of the necessary cause of every particular quantum actualization.  While the philosophical difficulties with bottom-up approaches to divine agency are legion, we will not examine them here.  We are interested in determining how  such divine efficacy might affect the utilitarian evaluation of the statement that "it is good to pray to God to have one's homosexuality changed."  Unfortunately, the matter is not at all clear. Much depends upon what is physically possible and not possible for a God working at the quantum level to do regarding the change in genetic dispositions.  The factual question of how much divine action at the micro-physical level can percolate up into the macro-physical level is all important.  If one holds that God's action at the micro-physical level is basically consistent with macro-physical determinism, then it might seem that "it is good to pray to God to have one's homosexuality changed" is again false on utilitarian grounds.  However, another evaluation is possible.  Perhaps while "bottom-up” divine action cannot change Bob's genetic dispositions, such action is causally relevant in allowing Bob to act in accordance or at variance with those dispositions.  One might hold some version of Roger Penrose’s thesis that quantum gravitational effects in the brain make free-will or contra-causal agency possible.  If so, then perhaps "it is good to pray to have one's homosexuality changed" is true after all. 

4)    Finally, we might ask how the statement fares if Bob holds that God works as a top-down causal agent. Here things become murkier. The crucial question is this: What effects would top-down constraints have upon the causal story of Bob's genetic homosexual disposition?   While there is much that is not clear, it is plausible to hold that those top-down constraints, however specified, would not be of the kind to allow divine intervention or special providence.  Furthermore, they do not seem to be capable of providing resources for the contra-causal free act of acting in accordance or at variance with one's genetic disposition.  Although God would act in the world on the top-down approach, it seems unclear that He could act specifically enough to grant Bob freedom from his homosexual genetic leash.  If this is so, then it seems reasonable to conclude again that the proposition "it is good to pray to God to have one's homosexuality changed" is false. 

While much more needs to be said about the specifics of this example, I think that the general moral is clear enough: How we view the underlying ontological situation, and thus the reference of our theological language, has an effect on the evaluation of our ethical judgments.  Armed with this insight, I now shall talk directly about the reference of theological language in terms of three basic questions in the religion/science conversation. These three are critically important, in my opinion, if we are somehow to find a place for divine (and even human) activity in our world. They are all very old questions, questions oftentimes not taken seriously enough in the current religion/science dialogue.

1)    Can one really reconcile the standard efficient causal account of evolution with the teleology implicit in talk of creation?

2)    Can one really reconcile the teleology of personal agency and spirit-talk with efficient causal explanations assumed by current nonreductive physicalist proposals of mind?

3)    Can one really make sense out of a connection linking God and the universe, and if not, can one make sense out of the notion that divine emergent properties causally influence the complex configurations from which they putatively arise?

While I cannot say much about any of these, my hope is to at least raise the questions and indicate the effects their resolution might have at the congregational level upon ethical issues.

III

The first topic is evolution.  While some would say that there is no conflict between science and theology on the issue, that really is true only if one adopts the independence thesis.  In my opinion, there remains considerable difficulty in relating talk of God’s creation to evolutionary accounts.  The problem is that the neo-Darwinian evolutionary synthesis seems to allow no place for telos or purpose, yet such telos is necessary if God is to be somehow causally at work in the evolutionary process.

Teleology has traditionally been concerned with purpose in nature, purpose not predominantly resulting from conscious human intent.  Characteristic of teleology is talk of functions and goals.  For instance, one might say that the heart functions to pump blood or that the goal of the rabbit whose fur turns to white in the winter is to avoid predators.  Aristotle, of course, invested all of nature with goals, claiming bodies travel in perfect circles because it is their nature, and bodies tend to fall because that too is their nature.  Prior to the nineteenth century, natural theology commonly assumed that God created the world such that each entity in it tended to realize its God-given nature. The eye was designed such that it functioned to allow sight.  Purpose was thought to be immanent in all that was.

Darwinian theory offered an account whereby organismic functions and goals were no longer understood as due to conscious design.  In the last century, work in population genetics helped shed light on the process of the inheritance of variations.  Mutations and gene recombinations introduce variation in a seemingly random way, apparently unrelated to the requirements of the organism.  Natural forces subsequently act upon the diversity in population introduced through these mutations and genetic recombinations such that particular mutations survive in particular environmental contexts.  Subsequent generations of selected mutations produce complex higher-order life that, while appearing to be something towards which the universe is striving, is actually only the result of past events.  Higher-order complex life is what happens to survive within a given environmental context.  If environmental pressures were different (e.g., if radiation bathed us) then perhaps cockroaches would appear to be a goal of the universe’s evolution. 

What must be noticed in this story is the rejection of final cause in favor of the category of efficient causality.  Mutations and genetic recombinations occur and are subsequently selected.  While the mutations and recombinations are caused by antecedent events at the biochemical level, the natural selection is caused by antecedent events at the macro-physical level.  The result is that the movement to increasing complexity is a function of past events, not any teleological “lure” implicit in nature.  Richard Dawkins’ The Blind Watchmaker forcefully represents this view, claiming that “the only watchmaker in nature is the blind forces of physics, albeit deployed in a very special way” (Dawkins 1987, p. 15). 

While there are any number of ways to respond to the challenge of reconciling divine creation with mechanistic evolution, I shall not pursue them here.  What I am critically interested in is how one’s intuitions about whether an efficient-causal or teleological explanation is deeper can influence his or her evaluation of ethical issues.  For instance, Suzy the good Lutheran, believes that God created and continually creates the universe.  She holds that everything that God creates is good and that God has a purpose in creating everything.  On the other hand, she is a biochemist and knows full well the processes of genetic variation and determination.  After learning that her three-month old fetus has Downs Syndrome, she considers an abortion.  While she knows theologically that everything that God creates is good, she realizes scientifically that her fetus results from a most unlikely chance-like combination of genetic material.  She must decide whether this statement is true or false: “It is morally permissible to terminate the pregnancy.”  How will she decide?

Let us imagine that Suzy thinks clearly, and realizes that the same set of events cannot simply be both mechanistic and teleological at the same time.  Let us assume further that Suzy reads the philosophy journals and decides that the efficient causal explanation is the deeper one - - though she knows that one can allow teleological explanations for certain purposes.  Let us also assume that Suzy dislikes utilitarianism and is committed to a deontological approach to ethics.  Now consider Suzy’s “duty” to her fetus.  If she believes her fetus results from the teleology of divine creation, she is apt to regard it as a full-member of the kingdom of ends, for its purpose is to have a rational nature.  Arguably, she will thus be constrained so as to act upon it as an end rather than a means.  Consequently, she is likely to regard the ethical sentence “it is morally permissible in this instance to have an abortion” as false. 

Now let us imagine that while loving and using theological and religious language Suzy knows that the deepest explanation of her fetus’ Downs Syndrome is biochemical; it is a matter of chance-like recombinations of genetic materials.  It is plausible that even though Suzy understands the expressive and donational power of religious language, she will nonetheless be less inclined because of her understanding of the deep nature of the genetic explanation to regard her fetus as a full member of the Kantian kingdom of ends.  In short, she will be more prone to abort her pregnancy.  Consequently, she may on deontological grounds regard the proposition “it is morally permissible in this instance to have an abortion” as true.  The question of who belongs to the kingdom of ends seems here to be at least partially dependent upon what explanation really “carves the beast of reality at its causal joints.”

IV

The same problem between the efficient causal and the teleological explanation concerns our view of the self.  Recently, Nancey Murphy has adopted nonreductive physicalism with hopes of saving human agency from a reduction to brain states, or outright elimination in favor of neurostate description.  On this view, one can talk meaningfully about human freedom and rationality while at the same time affirming that all mental events are identical with some physical events or other.  Again it is important to get clear on the problem for theology. 

Study of the human brain proceeds methodologically like the study of other physical entities.  One attempts to understand brain behavior by uncovering the causal antecedents of that behavior.  This can be done by isolating the “general laws” at work in brain processes and understanding the underlying conditions that realize those general laws.  To understand the brain is to explain and predict how one neural event is related to another event, and how such events are related to causal inputs and outputs.  Thus, brain research seems to presuppose what philosophers call event-event causality.

Our experience of self is not an experience of one constituted by event-event causal chains, however.  We experience a unity of our various awarenesses, and we make normative judgments concerning all matters of things.  We experience ourselves as comprised of an agent who acts in the world.  The standard question in the philosophy of mind is how to reconcile our experience of agent-act causality with an underlying physicalist paradigm assuming event-event causality.  How can we reconcile our experience of one who acts from reasons with the fact that talk of “reasons” cannot arise in brain state description?  Furthermore, how can we square our talk of agency (particularly “free agency”) and “spirit” with the seeming determinism of brain processes?

Asking these questions is, of course, standard fare in any philosophy of mind course. Nancy Murphy’s particular contribution is to claim that nonreductive physicalism, one of the standard positions in the current literature, can square with Christian anthropology. Freedom and rationality can somehow be made consistent with their realization in wholly physical systems.  She rejects any mind/body dualism, claiming implicitly that the notion of downward causation can do the work once reserved for the immortal soul.  The idea is that human agency while realized in brain processes can somehow affect those brain processes such that they are actualized differently than they otherwise would have been actualized in the absence of that agency. 

I have written quite a bit on the problem of downward causality and the related problems of supervenience and mental causation, generally claiming that there is much less to downward causality than meets the eye.  I cannot enter here into that technical discussion, but will move immediately ahead to consideration of how one’s ontological commitments to event-event or agent-action explanation can influence one’s ethical reasoning. 

Imagine the scenario where Meg must decide whether or not to pull the plug on Aunt Mavis who has been comatose in her bed for weeks.  Brain activity has virtually ceased.  Imagine now that Meg is a nonreductive physicalist holding that all mental events are token identical to some brain events.  Now if Meg really is a nonreductive physicalist, she realizes that pulling the plug on Mavis really does kill her, for no self, no center of Mavis’ being can remain after the plug is pulled.  This view is clearly entailed by mind/brain token identity. 

Now consider that Meg is an idealist or dualist somehow claiming that an agent-act description is the deepest description of the mental. Because dualism or idealism rejects the token identity of brain states and mental states, Meg might more easily pull Mavis’ plug and usher her agency into another modality of existence.  The statement “it is morally permissible to disconnect Mavis from life support” may thus have different evaluations due to the different entailments of “disconnect” on the different views.  If  “disconnect” entails “allows to die” as in the nonreductive physicalist scenario, then the truth of the ethical proposition seems different than if it means “aids in ushering into another mode of existence” as on the dualistic assumption. 

Consider now Freda’s freedom.  It seems that saying that Freda has freedom is much different for the nonreductive physicalist than for the dualist.  We are interested in determining whether or not this statement is true: “Freda is morally responsible for her inveterate extramarital activity.”  Notice that if the agent-act explanation is the deepest and one can make profound sense of reasons causing action, then it is possible that Freda could have done other than what Freda did in fact do, and that thus Freda is responsible for her dalliances.  If, however, the event-event description is the deepest, and if all mental events are somehow token identical to physical events, then it seems to follow that nature being what it is, Freda cannot be held morally responsible for her clandestine trysts.  What is necessary in the case of Freda would then be good psychological and physiological treatment, not ethical and moral judgment.

We are confronted with the same scenario in this case.  Our ethical judgments about what we should do are influenced by our prior assumptions about the nature of God’s connection to the universe.  My point is simply this: Many of those in our pews will be faced with judgments of the kind I have presented.  They hear our theological language, they listen to talk of God’s “mighty acts in history and nature”; they listen to the church’s language about the importance of the human person or spirit.  Consequently, when they are forced to evaluate an ethical situation, they will take the words seriously and assume that the words have a particular meaning.  What they assume that meaning to be is, I argue, critically important for the task of applying their ethical standard to the concrete situation.  It makes a difference to Meg’s application of a deontological yardstick to Mavis, what Mavis really is. 

V

Finally, let us consider the general relationship between the domain of the divine and that of the universe.  I suggest that how we evaluate ethical claims depends in part on how we conceive this relationship.  A standard way of thinking the transcendent relation of God to the universe has been asserted by ontological dualism, the claim that there are two fundamentally different orders of reality: divine being and physical being.  Not surprisingly, such a God/universe dualism shares many of the same problems as its mind/body counterpart.  Firstly, there is the causal joint question: How can one kind of stuff causally affect another kind of thing?  What cosmic “pineal gland” can link the humors of the infinite and the finite? 

What of the question of conservation of energy?  How can something not in space and having no mass, momentum, and energy, bring about events in space with mass, momentum, and energy?  Moreover, how can a God located outside the domain of the physical causally influence events within the physical order without violating the causal closure of the physical?   These questions arise on standard mind/body dualism accounts, and have been thought to be so fundamental there that dualism has been largely abandoned.  So if dualism is so problematic philosophically, how about nondualism?

One could perhaps claim that irreducible divine properties somehow emerge at higher-levels of complexity and attain causal powers of their own that are in principle irreducible to the causal powers of the entities from which they arose.  On this view the human agent with her reasons and actions constitutes an emergent reality arising out of neural complexity.  Once emergent, however, the agent takes on a causal life of its own.  Similarly, God might be conceived to be an emergent, causally-efficacious reality arising out of extremely complex physical systems. 

My purpose in talking about these two general positions is again ethical.  Returning to our first example of Bob, I would say that the truth-value of  “it is good to pray to have one’s homosexuality changed” depends upon whether we embrace dualism, monistic divine emergence, or deny any God/universe causal connection.  My reasoning should be apparent.  As before, the moral propriety of the prayer seems to increase as a function of the degree to which God can actually bring about effects in the natural order. 

If you are like I am and studied theology in graduate school, you likely spent most of your time learning the various post-Kantian options for doing theology without a causal connection between God and the world. One typically begins with the presupposition that God and the universe cannot be causally connected, and that theological or religious language appearing to assert such a connection must therefore be reinterpreted. Because we generally agreed upon this paradigm of independence, our ethical judgments could proceed with at least some level of consensus.

What I wish to suggest, however, is that at the congregational level there has never been—nor will there likely ever be—any comparable agreement regarding the impossibility of a causal connection between God and the world. This fact complicates the task of doing theological ethics. Can those of us who function as theological elites responsibly advocate a definite ethical program if the people in the pews do not share the presuppositions from which that program flows?

Theology, Language and its Limits

A Brief History of Logos

Since the dawn of the 20th century, many disciplines have been concerned with the limits of what can be expressed. The story I want to tell today starts in Greece, jumps to Germany, and from there has spread around the North Atlantic and beyond. Theologians should be adept at hearing and understanding the story. The fact that they are sometimes not is likely a mark against the contemporary theological enterprise. There are many ways of telling the story, and I will endeavor to tell it both as simply and as broadly as possible.  

2,559 years ago, Heraclitus was born in the City of Ephesus. He argued, quite famously, that "everything flows," that is, that everything is in flux. Yet, despite universal change, he claimed that there is stability, that somehow opposition between things constantly in flux gives rise to a stable structure. He called the principle that gives rise to stability despite flux the Logos. It is the Logos which brings identity out of difference, an identity that is constituted in and by difference. (For example,  while I am always changing both physically and mentally, there is an identity in this difference of change, an identity that is me.)

The ancient Stoics made the Logos an important part of their worldview. Famously, they argued that human beings often find themselves despairing because the world does not conform to how human beings think that the world should go. Stoicism counsels its followers to replace trying to change the world to conform to their views about how the world should go with changing their views about the world so as to conform to how the world actually is. There is healing in this, they thought, a salvation borne of grasping the universal structure of the world, a world to which they themselves finally belong, although they mostly forget. 

The Stoics advocated that the Logos is the principle of universal reason coursing through the world. Lamentably, human beings have only a very limited grasp of the world and its underlying rationality, and thus they find themselves hoping, wishing and acting in ways that are incompatible with how the the world actually rationally is.  Yet, that they can sometimes obliquely apprehend some of the world's rationality witnesses to the "divine spark" of the universal Logos in them. Stoic philosophy teaches that the subject who often has but very limited rationality can participate more fully in the universal Logos and accordingly become more rational. Developing the rationality that lies within one happens through increasing one's harmony with nature. To develop virtue, for the Stoic, is to develop the capacity to live in accordance with nature and reason, for the universal Logos is reason as it determines the structure of the natural world. Through developing wisdom, courage, justice or other classical virtues, one attunes oneself to the movement of the Logos. Fear is conquered when one abandons the foolish project of trying to change that which cannot be changed.

From this, Greek philosophy inherited a notion of subjective and objective Logos. While the objective Logos is rationality and order as it presents itself in the world apart from the self, the subjective Logos is the rationality and order of the self as it seeks to attune itself to the world. Because the selfsame Logos ultimately courses through both the object and the subject, there is common structure between the two, an isomorphism by virtue of which the reason of the subject can come to grasp the reason in the world. 

The notion of the Logos is thus the background upon which knowledge of the world is possible. An isomorphism between structures points to similar forms and properties being present in the different structures. Isomorphisms claim similar functions and relations among compared structures. Consider P coming to know W. What are the conditions for the possibility of knowledge?  The answer is apparent: P can know W if and only if the structure of W and the structure of P are similar.  For instance, we can come to know the movement of macro-objects through space by differential calculus because the calculus by which the world is grasped has a common structure with the world that is grasped. Objects accelerating in physical space have, in fact, the same positions in time that differential calculus says that they will have. The common structure between objective and subjective Logos is the deepest meaning of the Logos.  

Aristotle's Organon while nonetheless silent on the Stoic notion of Logos, nonetheless presupposed that the world is a rational place and that human beings could come to understand the structure of the world through reason. In The Categories Aristotle articulates those basic categories by which the world is grasped, i.e., primary substance, secondary substance, quantity, quality, relation, place, time, position, action and affection, categories that seem to have existence in the world as well as in the mind. For instance, there really are substances and they really do have accidents. The categories thus cut the beast of reality at its joints; there is a basic sayability to the world that matches are ability to say it. Although Aristotle would not say it this way, one might claim that the great philosopher nonetheless presupposebasic isomorphism between our semantics and our metaphysics.  

Think of the claim of John 1: "In the beginning was the Word (Logos), and the Word (Logos) was with God, and the Word (Logos) was God. The same was in the beginning with God." Christians not understanding the philosophical and religious horizon of the late first century or early second century miss the semantic range of logos. While 'word' properly translates logos, the latter also means, reason, rule, regularity, and account.  To say "in the beginning was the Logos" is to say that the world is not chaotic, that is, that the principle of rationality has been present in the world from its very beginning. It is to say that a common principle orders both the realms of the object and that of the subject, that the world and the minds that grasp it are similarly structured.  The claim that this common principle both is alongside God and is God, is the claim that rationality itself, which is not what God is, nonetheless has such deep divine roots, that God would not be Trinitarian, and thus not be God without it.  

The entire medieval tradition operated out of the supposition of a deep rationality consonant with the notion of the Logos. In Neo-Platonic thought, the One as the source of all reality, transcends both existence and thought. From it rationally emanates first the Nous, then the World Soul (demiurge) and finally the material world. Each of these are hypostases, e.g. the hypostasis of the Nous emanates the World Soul and the hypostasis of the World Soul emanates the material world.  All of this is done in an orderly, rational fashion. Each lower hypostasis is an emanational "overflow" of a higher hypostasis. The nous is the first emanation of the One, and is closest to the One ontologically. This nous itself has a logos character, for it is both intellect and the divine mind whose forms are archetypes of all that exists. The nous contains the forms and organizes these forms in an intelligible way, synthesizing these forms into an intelligible whole, a whole that is rational, regular, rule-governed, and ultimately sayable.  

When humans speak, they speak out of the same organized reason that rationally organizes the world. Even in the thirteenth century, Thomas Aquinas (1225-74), following Augustine, assumes that God's mind was filled with archetypes, that is, the Divine mind contains the original types or forms of all that exists. Such archetypes for Thomas constitute the essence of anything that can be in the world. Since God has complete knowledge of all that is, God must know both the particulars of the world and all the universal forms or essences in which these particulars can be ingredient. Since these essences or forms are the possibilities of existing things, God knows not only what is actual, but what is possible. The divine archetypes thus function to undergird the commonality between the saying of the world and the sayability of the world said. Semantics and metaphysics are not alien from each other. The world can be known because the Word is both in the world and in the ones whose job it is to think the world. But the days of the logos were growing short. Soon there would be a divorce between language and the world, a divorce where already bitter parties would soon find themselves unable to communicate with each other.  

The via moderna could no longer assume universal structures that coordinated language and the world. Their work in logic and epistemology was careful, nuanced, and tended towards being skeptical of many of the traditional rational claims of theology.  It famously denied that general terms refer to universals, claiming instead that only individual and particular qualities actually exist. Late medieval nominalism tended to undermine the assumptions about the isomorphism among mind, language and world assumed by earlier medieval traditions. 

At the center of the via moderna critique of the earlier was its new understanding of the relationship between significatio and suppositio.  There earlier tradition, the so-called via antiqua, had assumed that a word has a significatio, that it caused the mind to think in a particular way, and on the basis of this the word could have various suppositiones, various references. The via antiqua spoke of three basic kinds of suppositiones, the personal suppositio where a word refers to a particular individual or thing, the simple suppositio where a word refers to a universal or abstract entity, and finally a material suppositio where a word refers to itself.  In contemporary parlance, we would say that in personal supposition the word 'tree' is used to mention a particular tree, in simple supposition it is used to mention the universal instantiated by the particular tree, and in material supposition the word ''tree" is used to mention the word 'tree.'  Because the word 'tree' has a significatio, it causes the mind to think about that to which it could refer. Accordingly, the suppositio of a term is the way that the term can stand for an individual, a universal or the term itself within an occasion of use or particular context. 

The via moderna prioritized the role of suppositio in semantics over significatio. What was important for Ockham and followers was that to which the term referred. Since terms refer to individuals, not to universals, reference to individuals is what is important in semantics, not the associated ideas that a term might connote. For him, while terms can undoubtedly bring to mind certain thoughts or connotations, these do not determine reference. There is a direct relationship between words and things, a relation not semantically mediated by the term's significatio. This is true, despite Ockham's insistence that context is indeed important in determining that to which a term refers. Simply put, context matters in determining suppositio.  

Ockham thought that written and language was inherently ambiguous. This was so, in part, because human beings have a more fundamental language, a mental language that allows human beings to represent the world in their minds. Names do not signify individuals in the world directly, but they do point to the concept associated with that to which the word supposits.  For Ockham, mental language is the language of thought prior to words.  Spoken language is that by virtue of which our mental language can be shared with others; it expresses our mental language.  Finally, written language preserves the spoken expression of our mental language. Because supposition is context dependent, and there is no one-to-one function from mental language to spoken language, and because the general terms in spoken and written language do not refer to universals or abstract entities, language cannot directly picture reality. Simply put, there is no isomorphism between language and the world, and thus no isomorphism between the subject's saying of the world and the sayability of the world said.  Thus, there is no logos structuring the subject and object such that the subject can encounter the object in itself, and the object is available for the subject's grasp.  

Further marginalization of the Logos can be seen in Kant. With the critical philosophy, the conditions of intelligibility are no longer sought in the structure of reality but in the structure of the knowing subject. The question that governs the Critique of Pure Reason is not what the world is, but under what conditions a world can be experienced by us. Intelligibility becomes transcendental rather than ontological. Space and time are forms of intuition; the categories are functions of judgment; the unity of experience arises from the synthetic activity of the understanding. What had previously been understood as the rational articulation of being is now understood as the contribution of cognition.

This move preserved the possibility of objective knowledge while abandoning the older confidence that the structure of knowledge mirrors the structure of reality itself. Kant did not deny that the world possesses its own order. What he denied was that human reason could know that order apart from the conditions through which experience becomes possible for us. The world as it is in itself remains beyond the reach of theoretical reason. The mind does not discover intelligibility already inscribed within being; rather, it supplies the forms through which phenomena become intelligible at all.

The consequences of this move were immense. The Logos no longer functioned as the ground of the intelligibility of the world. Instead, intelligibility became a function of transcendental subjectivity. The order of experience arises from the activity of synthesis, not from participation in a rational structure that precedes the mind. Reason becomes legislative rather than receptive. The world appears intelligible because it conforms to the conditions imposed by the subject.

Yet even in Kant the older intuition never entirely disappears. The Critique of Judgment introduces the idea of reflecting judgment, which operates where determinate rules cannot be given in advance. When we encounter organisms, aesthetic order, or the systematic unity of nature, we must judge “as if” nature were purposively ordered for our cognition. Teleology thus returns, but only as a regulative principle. The idea that reality itself is purposively structured cannot be affirmed as knowledge. It can only guide reflection.

The tension here is unmistakable. Kant relocates intelligibility within the subject, yet the practice of scientific inquiry continues to presuppose that nature is intelligible in itself. The mind legislates the form of experience, but the success of science suggests that something in the world cooperates with this legislation. The critical philosophy therefore stabilizes knowledge while leaving unanswered the deeper question: why should the structures of human cognition prove adequate to the structure of reality at all?

The Aftermath: From Transcendental Philosophy to Formal Logic

Once the mind becomes the source of intelligibility, the history of philosophy begins to move in two divergent directions. One trajectory attempts to radicalize the Kantian insight by dissolving the distinction between thought and being altogether. German Idealism pursues this path, culminating in Hegel’s claim that the rational structure of reality unfolds through the self-development of Spirit. The other trajectory abandons metaphysical speculation entirely and concentrates instead upon the analysis of language and logic. It is this second path that leads to modern analytic philosophy.

The analytic movement inherited Kant’s suspicion of traditional metaphysics but redirected attention from the structures of consciousness to the structures of language. If philosophy cannot know reality as it is in itself, it can at least clarify the forms of meaningful discourse. Logic becomes the privileged instrument of philosophical analysis. The task of philosophy is no longer to disclose the rational structure of being but to analyze the grammar through which propositions represent the world.

Frege’s work marks the decisive beginning of this transformation. In distinguishing between sense and reference, Frege sought to explain how language can express objective truth without relying upon psychological states. Meanings belong to a “third realm,” neither mental nor physical, within which the logical relations among propositions can be rigorously analyzed. Truth becomes a property of propositions understood within a formal structure of inference.

Russell and the early Wittgenstein extended this project by attempting to reveal the logical form underlying ordinary language. Propositions represent the world because they share a logical structure with the facts they depict. Philosophy becomes an activity of logical clarification, dissolving confusion by uncovering the form that language must possess in order to say anything meaningful about the world.

Yet something remarkable occurs in the course of this development. As logic becomes increasingly precise, the connection between formal structure and the world it purports to describe becomes increasingly tenuous. Logical systems specify the rules according to which propositions may be derived from one another. They determine what follows from what. But they do not determine what the symbols themselves refer to. The formal system governs syntax, not semantics.

This distinction is not a mere technicality. It marks a profound limitation within the logical enterprise itself. A formal calculus can generate indefinitely many theorems without ever determining the interpretation under which those theorems become true. Syntax governs derivability; semantics concerns satisfaction and reference. The two are related but irreducible. While syntactical conditions determine what counts as a possible utterance within a language, they cannot generate meaning or secure truth. 

Once this distinction is recognized, the ambitions of formal logic must be reconsidered. Logical systems can exhibit the structure of valid inference with extraordinary rigor. What they cannot do is explain why those structures successfully describe the world in the first place. The applicability of logic to reality remains a presupposition rather than a theorem.

Formal Systems and the Rediscovery of Excess

The twentieth century gradually made this limitation explicit. Gödel demonstrated that sufficiently powerful formal systems contain true statements that cannot be proved within the system itself. Tarski showed that truth for a language cannot be defined within that language without generating contradiction. Turing established that no general algorithm can decide every question of derivability within a formal system. Each of these results reveals, in a different way, that formal structure cannot close upon itself.

What emerges from these developments is not the failure of logic but the discovery of its horizon. Formal systems are indispensable for the articulation of reasoning, yet they presuppose conditions that they cannot themselves generate. The relation between syntax and semantics remains irreducible. Derivability does not exhaust truth; proof does not guarantee meaning; formal coherence does not secure reference.

At precisely this point the question of intelligibility returns with renewed force. If formal systems cannot ground their own applicability, then the intelligibility that makes their application possible must lie elsewhere. It cannot be reduced to syntactic derivation, algorithmic procedure, or the conventions of language. Rather, it must function as a condition of possibility for the very practices of reasoning that formal logic describes. As the presuppositions of the Disputationes make clear, intelligibility is therefore not an artifact of cognition but a real feature of the order within which cognition operates. 

The older language of the Logos now reappears in an unexpected form. Philosophy discovers that rational articulation cannot be manufactured by formal systems, even though those systems presuppose it everywhere. Logic clarifies the structure of reasoning but cannot explain why reasoning is possible at all. The intelligibility of the world precedes the languages through which we describe it.

The story therefore comes full circle. What began as a marginalization of the Logos in favor of transcendental subjectivity ends with the rediscovery that intelligibility itself cannot be grounded within subjectivity or formal structure alone. The rational order that makes truth possible cannot be reduced to syntax, algorithm, or convention. It remains the silent presupposition of every act of understanding.

And it is precisely here that philosophical theology begins.

 

The Löwenheim–Skolem Paradox and the Elusiveness of the Infinite

On What First-Order Logic Cannot Say

The development of modern mathematical logic in the late nineteenth and early twentieth centuries promised a remarkable achievement: the complete formal articulation of mathematical reasoning. A mathematical theory could be expressed as a set of sentences in a precisely defined language governed by explicit rules of inference. In principle, once the axioms and rules were specified, all legitimate consequences of the theory would follow from them by purely formal means. Mathematics would thus appear as a system of symbolic structures whose content could be fully captured in formal syntax.

Yet the very success of this program has revealed limits that are as philosophically significant as they are mathematically precise. Some of the most striking of these limits arise from the Löwenheim–Skolem theorems, results in model theory established in the early twentieth century that demonstrate a fundamental expressive limitation of first-order logic. These theorems show that first-order theories cannot control the cardinality of their models. A theory intended to describe an uncountable structure may have countable models; a theory intended to describe the natural numbers may have models of arbitrarily large infinite cardinalities.

At first glance this might appear to be a technical peculiarity of formal logic. In fact it discloses something deeper about the relation between syntax and reference, between the formal articulation of a theory and the mathematical structures to which that theory is intended to refer. The Löwenheim–Skolem theorems reveal that formal systems cannot determine their own intended interpretations. They describe a class of possible structures but cannot specify which of those structures they are about.

Once this point is appreciated, the philosophical implications become difficult to ignore. Questions arise concerning the determinacy of mathematical reference, the relation between formal systems and mathematical practice, and the broader conditions under which meaning and truth become possible. The results of modern logic do not simply clarify the structure of formal reasoning; they also expose the horizon within which formal reasoning itself takes place.

The Löwenheim–Skolem Theorems

The downward Löwenheim–Skolem theorem concerns the existence of smaller models for theories that already possess infinite ones. In one of its standard forms it states that if a first-order theory expressed in a countable language has an infinite model, then it has a countably infinite model. More precisely, if (M) is a structure for a language (L) and (A) is a subset of its domain, then there exists an elementary substructure (N) of (M) containing (A) such that the cardinality of (N) does not exceed the cardinality of (A) plus the cardinality of the language plus (\aleph_0). In the special case where the language is countable and the original structure is infinite, the theorem guarantees the existence of a countable elementary substructure.

The proof proceeds through the introduction of Skolem functions, which replace existential quantifiers with function symbols that witness their satisfaction. Beginning with a countable subset of the original structure, one repeatedly applies these functions to generate a domain closed under the definable operations of the theory. The resulting structure is countable yet satisfies exactly the same first-order sentences as the larger structure from which it was derived.

The upward Löwenheim–Skolem theorem moves in the opposite direction. If a theory in a language of cardinality (κ) possesses an infinite model, then it possesses models of every infinite cardinality (λ) greater than or equal to (κ). In a common formulation, if (M) is an infinite structure for a language (L) and (λ) is a cardinal at least as large as the maximum of (|M|) and (|L|), then there exists an elementary extension (N) of (M) whose domain has cardinality (λ).

Taken together, the two theorems establish a striking limitation of first-order logic: any first-order theory with an infinite model has models of many different infinite sizes. The formal theory cannot restrict the size of the domain it describes. A theory written in a countable language cannot rule out the existence of countable models, even if the structures it is intended to describe are uncountable.

From a purely mathematical perspective this is simply a theorem about the expressive power of first-order languages. Philosophically, however, it raises a deeper question. If the formal theory admits many non-isomorphic models, what determines which of these models the theory is about?

Skolem’s Paradox

The philosophical force of these results becomes especially vivid in what is traditionally called Skolem’s paradox. Although the phenomenon involves no genuine contradiction, it exposes an apparently paradoxical feature of formal set theory.

Consider the standard foundational theory of mathematics, Zermelo–Fraenkel set theory with the Axiom of Choice (ZFC). Among its theorems is Cantor’s result that the power set of the natural numbers is uncountable. There exists no bijection between the natural numbers and the set of all subsets of the natural numbers.

Yet the language of ZFC is countable, containing only the membership relation as a primitive symbol. If ZFC has any infinite model, the downward Löwenheim–Skolem theorem implies that it has a countable model. Let us call such a model (M).

From the external perspective of the mathematician studying the model, (M) is countable. Its entire domain can be placed in bijection with the natural numbers. But (M) nevertheless satisfies all the axioms of ZFC. In particular, within (M) the set corresponding to the power set of the natural numbers is uncountable.

How can a countable model contain an uncountable set?

The resolution lies in distinguishing between internal and external perspectives. Externally we can see that the domain of (M) is countable. Internally, however, (M) satisfies the statement that no bijection exists between the natural numbers and the power set of the natural numbers. The bijection witnessing countability exists outside the model but not inside it.

The notion of countability expressed in the theory is therefore model-relative. The structure contains what it regards as all subsets of the natural numbers, but from the outside we can see that this collection omits many subsets that exist in the surrounding universe.

Skolem emphasized that the phenomenon does not produce a contradiction but rather reveals a limitation of first-order formalization. The theory cannot guarantee that its models capture the intended notion of uncountability.

The Underdetermination of Interpretation

The Löwenheim–Skolem theorems do not themselves establish that mathematical reference is indeterminate. What they do establish is that first-order syntax alone cannot determine the intended interpretation of a theory. The axioms specify a class of structures satisfying them, but they do not select a unique member of that class as the object of discourse.

From the perspective of model theory this is simply a fact about the expressive limitations of first-order logic. Philosophically, however, it raises the question of what fixes the interpretation of mathematical language. If multiple structures satisfy the same formal description, what determines which structure mathematicians have in mind when they assert theorems about the real numbers, the natural numbers, or the universe of sets?

Different philosophical responses have been proposed. Some mathematicians adopt a form of structuralism, according to which mathematics studies structures abstractly rather than particular objects. On this view a theory does not aim to describe one privileged model but rather any structure satisfying its axioms. The multiplicity of models revealed by Löwenheim–Skolem therefore poses no difficulty.

Yet this description does not fully capture the character of mathematical practice. When analysts investigate the real numbers, they do not ordinarily regard themselves as studying an arbitrary complete ordered field. They speak and reason as though they were investigating the continuum itself. Similarly, set theorists studying the continuum hypothesis typically assume that their arguments concern the universe of sets rather than an arbitrary model of ZFC.

Formal theory reveals a symmetry among models that mathematical practice does not treat as symmetrical. Something beyond the formal syntax appears to orient interpretation toward certain structures as the intended objects of inquiry.

Intentionality and the Horizon of Meaning

This situation can be illuminated by drawing upon the phenomenological analysis of intentionality. In Husserl’s account, acts of meaning are always directed toward objects. A linguistic expression articulates an intention toward an object that may be fulfilled in different ways. The meaning of the expression includes not only what is explicitly stated but also the horizon within which possible fulfillments are anticipated.

Formal theories function analogously. A theory articulated in a symbolic language expresses a set of formal intentions toward a mathematical structure. The Löwenheim–Skolem theorems show that these intentions admit multiple fulfillments. Distinct structures can satisfy the same formal description.

The intended object of mathematical discourse therefore cannot be fixed solely by the formal sentences themselves. It is situated within a broader horizon of understanding that guides the interpretation of those sentences.

The presence of this horizon becomes visible precisely when formalization reaches its limits. The theory specifies conditions that any satisfying structure must meet, but it does not determine which satisfying structure is taken as the object of study.

Teleospaces and Mathematical Orientation

The background that guides interpretation in mathematical practice may be described as a teleospace: a field of purposive orientation within which mathematical concepts acquire their significance. A teleospace is not itself a formal system but the network of practices, intentions, and conceptual relations that orient inquiry toward particular structures.

Within such a field mathematicians acquire a sense of what their investigations are about. Certain constructions become canonical, certain problems become meaningful, and certain interpretations are regarded as natural while others appear artificial. The real numbers, the natural numbers, and the cumulative hierarchy of sets function as focal points within this space of orientation.

Formal theories crystallize within these teleospaces. They articulate and discipline patterns of reasoning that already possess a direction within mathematical practice. The formalism provides precision and rigor, but it does not generate the orientation that gives the symbols their intended reference.

The Löwenheim–Skolem phenomenon reveals the independence of this orientation from the formal system itself. The axioms permit many models, but the teleospace within which mathematicians operate selects certain structures as the objects toward which their reasoning is directed.

Structural Perspectives and Category Theory

Modern mathematics increasingly emphasizes relational perspectives that resonate with this description. In category theory, mathematical objects are characterized not primarily by their internal constitution but by their position within a network of morphisms connecting them to other objects. The significance of an object lies in the pattern of transformations in which it participates.

From this viewpoint, structures are often identified by universal properties that specify their role within a system of relations. The real numbers, for example, may be characterized through categorical constructions that situate them within a broader mathematical landscape.

Category theory can therefore be understood as partially formalizing aspects of the relational field that the concept of teleospace attempts to describe. It captures structural patterns that arise within mathematical practice and articulates them with remarkable generality.

Nevertheless, even categorical characterizations presuppose the interpretive horizon in which they operate. The significance of a universal property or a categorical equivalence is not determined solely by the formal definitions but by the mathematical practices that render those definitions meaningful.

Gödel and the Transcendence of Formal Systems

The limitations revealed by the Löwenheim–Skolem theorems are complemented by another set of results that transformed the foundations of logic: Gödel’s incompleteness theorems. Gödel demonstrated that sufficiently expressive formal systems cannot prove all truths about the structures they describe. In any consistent system capable of representing basic arithmetic, there exist true statements that cannot be derived within the system itself.

Where Löwenheim–Skolem reveals a gap between theory and interpretation, Gödel reveals a gap between provability and truth. The formal system cannot capture all truths about its intended domain, nor can it uniquely determine the domain to which it refers.

These two limitations point in the same direction. Formal reasoning presupposes a field of intelligibility that it cannot fully generate or articulate. Truth and reference both transcend the resources of formal syntax.

Gödel himself interpreted these phenomena as evidence that mathematical understanding involves a form of intellectual intuition directed toward objective structures. The logical results did not undermine the reality of mathematical truth; rather, they showed that truth cannot be reduced to formal proof.

Theological Resonance

The structure revealed by these logical discoveries has implications beyond the philosophy of mathematics. Theological discourse exhibits an analogous relation between formal articulation and the reality to which it refers.

The Christian tradition speaks through creeds, confessions, and scriptural texts that possess grammatical structure and inferential relations. These forms of speech may be analyzed using logical tools, and theological reasoning often proceeds through carefully articulated arguments.

Yet theological truth does not arise from syntax alone. The grammar of faith does not generate the reality to which it refers. Instead it presupposes that reality and seeks to articulate it faithfully.

The relation between theological language and divine reality thus resembles the relation between a formal theory and its models. The sentences of the theory do not determine their own interpretation; the reality to which they refer must be given.

Logos and the Ground of Intelligibility

At this point the discussion touches a deeper philosophical question. If formal systems presuppose both truths they cannot prove and interpretations they cannot determine, what grounds the intelligibility within which truth and reference become possible?

The Christian theological tradition answers this question through the concept of Logos. The Logos is not merely a principle within reasoning or a structure among structures. It is the source of intelligibility itself—the rational order through which beings become knowable and language becomes meaningful.

Formal systems operate within this intelligibility. They articulate patterns within it, refine them, and explore their consequences with extraordinary precision. But the field of meaning within which such articulation occurs cannot itself be generated by formal syntax.

The limits uncovered by modern logic therefore do not merely expose deficiencies in formal systems. They reveal the dependence of formal reasoning upon a deeper order of intelligibility.

The Logos, in theological language, names that order. It is the ground that makes both mathematical truth and meaningful discourse possible.

Conclusion

The Löwenheim–Skolem theorems demonstrate that first-order logic cannot determine the cardinality of its models and therefore cannot uniquely specify the structures it describes. Skolem’s paradox shows how this limitation appears even within the foundational theory of sets. Gödel’s incompleteness theorems reveal an analogous limitation concerning the relation between proof and truth.

Taken together, these results disclose a structural feature of formal reasoning. Syntax alone cannot secure either truth or reference. Formal systems function within a broader horizon of understanding that guides their interpretation and gives their symbols meaning.

Mathematical practice implicitly relies upon such horizons. The concept of teleospace names the field of orientation within which formal systems operate and within which mathematical objects are taken as the intended subjects of inquiry.

Modern logic thus reveals not the self-sufficiency of formal systems but their dependence upon the deeper conditions of intelligibility within which they arise. In theological terms, those conditions belong to the order of Logos—the rational ground that makes meaningful speech and rational understanding possible at all.