Determinability, Intelligibility, and Logos

Preface: Scope, Status, and Method

This essay arises from a philosophical pressure sustained over many years rather than from a decisive encounter with a particular text or debate. It is not the product of having read the right book at the right moment, but of repeatedly returning to the same question while thinking seriously about transcendental conditions, explanation, and intelligibility. Over time, that question has clarified itself into the claim defended here.

The text should therefore be read neither as a finished treatise nor as a narrowly targeted journal article. It is a programmatic working paper: an attempt to place a conceptual kernel in public view, to articulate its internal structure with some rigor, and to test its resistance to the most obvious misunderstandings. Much of what follows will receive fuller and more formal treatment in later book-length work. Here the aim is not exhaustion but orientation.

Two methodological commitments govern what follows. First, philosophical conviction is treated as a legitimate mode of rational insight. The argument advanced here is not offered because it is fashionable or easily situated within existing schools, but because it survives sustained internal scrutiny. Second, the essay deliberately moves between discursive exposition and schematic reconstruction. Where informal explanation risks obscurity, formal articulation is introduced; where formalism would distort the issue, ordinary philosophical language is retained.

Readers should not expect a complete metaphysical system or a comprehensive engagement with the secondary literature. They should expect a tightly focused question—how determinacy is possible at all—and a sustained attempt to answer it without regress, stipulation, subjectivism, or mystification.

Orientation: Why This Question Cannot Be Avoided

Any serious metaphysical account eventually confronts a question that is more often displaced than answered: under what conditions can anything be determinate at all? This is not a merely epistemological or semantic question. It is ontological, and it concerns intelligibility as such. To be is to be determinate; yet determinacy cannot be self-grounding. If every determination required a further determination to account for its determinacy, explanation would dissolve into infinite regress. If, on the other hand, determinacy were simply posited as brute, metaphysics would collapse into stipulation.

The central claim defended here is simple but far-reaching: determinability is not itself a determination. It is the condition under which determinations are possible at all. Because it is not a determination, it does not stand in need of further conditions of the same kind. Properly understood, this halts regress without dogmatism and avoids both reductionism and negative mysticism.

The task of this essay is fourfold. First, it clarifies the distinction between determination and determinability. Second, it formalizes the regress argument and diagnoses the category mistake that generates it. Third, it introduces the notion of teleo-spaces as regions of intelligible determinability. Finally, it explains why the traditional concept of Logos names this condition more adequately than its modern competitors, even while remaining ontic in its historical deployments.

I. Determination and Determinability

To speak of determination (Bestimmtheit) is to speak of what is articulated, structured, or fixed: a form, a law, a property, a proposition, a norm, a state of affairs. Determinations are always many. They admit of revision, correction, refinement, and replacement. Scientific theories, metaphysical categories, linguistic meanings, and ethical norms are all determinate in this sense.

Determinability, by contrast, is not one more determination. It is the condition under which anything can count as a determination at all. It is what allows distinctions to hold, meanings to stabilize, and norms to bind, without itself becoming one more item among those distinctions, meanings, or norms.

This distinction is not optional. Any attempt to treat determinability as itself a determinate entity—whether material, conceptual, linguistic, or subjective—reintroduces the very regress it was meant to avoid. If determinability had conditions of the same kind as determinations, those conditions would themselves presuppose determinability, and explanation would never get started.

The key insight is therefore this: determinability is determinability all the way down. It does not bottom out in a more basic determination, because it is not a member of the series it makes possible. The condition for determinability would be determinability itself—not by circular stipulation, but by structural necessity. This is not a vicious circle but the recognition of ontological priority.

II. Formalizing the Regress and the Category Mistake

The informal distinction between determination and determinability can be sharpened by introducing minimal formal machinery. The purpose of this formalization is not technical completeness but diagnostic clarity: it allows us to see precisely where the regress arises and why it depends on a category mistake.

II.1 Minimal Ontological Typing

Let us distinguish two ontological types:

• Type D₁ (Determinations): items that can be determinate or indeterminate in the ordinary sense—properties, propositions, laws, norms, forms, states of affairs.

• Type D₂ (Conditions of Determinability): that in virtue of which D₁-items can be determinate at all.

Introduce a predicate Det(x) meaning “x is determinate.” This predicate is well-formed only for x ∈ D₁. This restriction is not stipulative. It reflects the functional role of determinacy: only items that can enter into relations of identity, difference, correctness, and truth-aptness are candidates for being determinate.

II.2 The Regress Schema

Any determinate item raises the question of what accounts for its determinacy. Formally:

1. For any x ∈ D₁, if Det(x), then there is some y such that y conditions Det(x).

2. If every such y were itself an element of D₁, then Det(y) would likewise require conditioning.

3. This generates an infinite regress of the same explanatory kind.

The regress is vicious not merely because it is infinite, but because the explanandum—determinacy—is never reached. Explanation is indefinitely deferred.

II.3 Exhaustive Responses and Their Failure

There are only four possible responses to this regress:

1. Accept the infinite regress and abandon explanatory completion.

2. Introduce a brute stopping point.

3. Posit a self-determining entity.

4. Draw a category distinction between determination and determinability.

The first three options either abandon explanation or collapse into circularity. Only the fourth avoids both.

II.4 The Category Mistake

The regress arises only if one assumes that the condition of determinacy must itself be determinate in the same sense. That assumption commits a category mistake. Determinacy is a predicate applicable only to what stands within the space of distinctions, identities, correctness, and truth-aptness. Determinability, by contrast, is the condition under which that space exists at all.

To ask whether determinability is determinate is therefore not to raise a deeper metaphysical question, but to misapply a predicate beyond its domain of sense. The demand for further determination does not go unanswered; it fails to get a foothold. Once this distinction is respected, the familiar regress dissolves—not by stipulation, but because the demand for further determination no longer has coherent application.

This is not an ad hoc exemption. It is a restriction on applicability analogous to asking whether a rule is heavy, whether a number is blue, or whether validity is taller than soundness. In each case the predicate has sense somewhere, but not here. The same holds for determinacy when applied to determinability.

III. Likely Objections and Replies

Objection 1: Is this a brute stopping point?

No. A stopping point is brute only where an applicable explanatory demand is refused. Here the demand for further determination does not apply. Determinability does not belong to the class of determinate items to which such demands attach.

Objection 2: Why not treat determinability as a higher-order determination?

Higher-order determination is still determination. Treating determinability as such simply reproduces the regress at a different level. The problem concerns the kind of explanation required, not the level at which it is given.

Objection 3: Can formal systems or structures ground determinacy?

Formal systems presuppose determinacy: symbols must already be distinguishable, rules applicable or misapplicable, correctness conditions intelligible. Structure articulates intelligibility once given; it cannot generate intelligibility as such.

Objection 4: Is this transcendental idealism without the subject?

No. The argument distinguishes epistemic access from ontological dependence. Determinability is encountered only through acts of judgment, but it is not constituted by them. Subjects participate in intelligibility; they do not produce it.

IV. Teleo-Spaces: Regions of Intelligible Determinability

Determinability is not an abstract vacuum. It is always encountered as oriented intelligibility: regions in which certain kinds of determination make sense and others do not. These regions may be called teleo-spaces.

A teleo-space is a space of possible sense, not a set of rules or a horizon of disclosure. Scientific explanation, ethical normativity, mathematical proof, and theological discourse each inhabit distinct teleo-spaces with their own internal standards of success and failure. These standards are not imposed from without, nor reducible to convention; they are made possible by determinability itself.

Teleo-spaces also mark the limits of formalization. Formal systems operate within teleo-spaces: they presuppose a prior orientation toward what would count as adequacy, correctness, or satisfaction within a given region of inquiry. No amount of formal articulation can by itself generate that orientation, because it is precisely what renders formalization intelligible as formalization. Teleo-spaces thus explain both the power and the limits of formal systems: why formalization succeeds locally, and why it necessarily leaves a remainder that cannot be absorbed into syntax or model alone.

Teleo-spaces therefore mediate between determinability and determinate practices. They orient without necessitating, ground without fixing, and enable identity without closure. They are not historical horizons that open and close, but stable regions of intelligible determinability presupposed by historical practice.

V. Why the Name “Logos” Is Not Optional

Once determinability is recognized as a non-determinate condition of intelligibility, the question is no longer whether such a condition exists, but how it is to be named without distortion. Appeals to structure, normativity, modality, or inferential roles all presuppose what they purport to explain, since each operates only within an already determinate space of sense.

At this point, recourse to Logos is not optional but practically unavoidable. Even the most rigorously naturalistic and materialist accounts of order and intelligibility—most notably in Stoic philosophy—were compelled to invoke Logos in order to account for the objectivity of reason, normativity, and order. In Chrysippus, Logos names the rational principle pervading and organizing the cosmos, the source of lawlike necessity and intelligible structure. The persistence of this appeal is not accidental; it registers the pressure to acknowledge an objective ground of intelligibility that is neither subjective nor conventional.

Yet precisely here the limits of Stoic Logos become visible. Chrysippean Logos is a determinate, ontic, and causally operative principle within the world. As such, it belongs to the very order of determinate explanation whose intelligibility it is meant to secure. The present argument explains why such a move is both inevitable and insufficient. Logos must be invoked, but it cannot finally be located as one more determinate principle among others without reintroducing the regress it was meant to halt.

The Logos identified here is therefore not a revival of Stoic cosmology, nor an importation of theology by fiat. It names a deeper role: the non-determinate condition of intelligibility as such, forced by a regress argument concerning determination. Formal systems, scientific theories, and languages do not create intelligibility; they inhabit it. They presuppose a teleological orientation toward sense that cannot be formalized without remainder. That remainder is not a defect. It is the condition of possibility for meaning itself.

VI. Concluding Orientation

The argument presented here does not offer a new metaphysical system. It clarifies the condition under which metaphysical systems are possible at all. Determinability is not what lies beneath beings, behind beings, or beyond beings, but that by virtue of which beings can be determinate in the first place—without itself becoming one more thing that must be explained.

Without this clarity, metaphysics oscillates endlessly between regress and dogma, formalism and mysticism. With it, intelligibility can be affirmed as real, irreducible, and grounded—without closure and without despair.

See a more complete version at academia.edu: https://ilt.academia.edu/DennisBielfeldt/Foundations%20of%20Theological%20Reasoning%20(2025-26)

On Intelligibility, Determinability, and the Logos Who Makes Meaning Possible

For many years I have been puzzled by a question that refuses to dissolve: how are transcendental arguments possible at all? How can one speak meaningfully about the conditions for the possibility of experience, knowledge, or formalization without already presupposing what one claims to ground?

Logic and mathematics have sharpened this question rather than resolved it. Formal systems are extraordinarily powerful. They model relations, generate derivations, and articulate vast domains of structure. Yet the more rigorous they become, the more clearly they reveal something they cannot contain: the space in which they are intelligible as systems in the first place.

Gödel made this unavoidable. A sufficiently expressive system can represent its own syntax, yet it cannot secure from within the distinction between truth and provability. Even when meta statements are themselves formalized, the recognition that the formalization is adequate occurs at a higher level still. The meta recedes as it is captured. What is gained in rigor is accompanied by a renewed excess.

This excess is not merely epistemic. It is not simply a limitation of human cognition or a gap in symbolic technique. It belongs to intelligibility itself. Formal systems presuppose a horizon in which interpretation, relevance, adequacy, and meaning are possible at all. That horizon is not a theorem. It is the condition under which theorems can appear as meaningful.

Here a structural parallel becomes visible. The transcendental I cannot be thought as an object without ceasing to be transcendental. An I that is thought is already a higher order self, something represented rather than that by virtue of which representation occurs. The condition of objectivity cannot itself be an object in the same register without contradiction. This is not a contingent limitation. It is structural.

Something analogous occurs with intelligibility itself. Once a teleological space of meaning is determined, named, or even ontologically affirmed, that determination presupposes another horizon within which it is intelligible as a determination. The sine qua non of the determined as determined is not a further determination, but an indeterminate field that allows for determinability. The indeterminate does not issue in form. It makes form possible.

This is the insight Kant reached most clearly in the Third Critique. Determining judgment subsumes particulars under given rules. Reflecting judgment seeks the rule under which particulars may be unified without possessing that rule in advance. Reflecting judgment operates within a teleological space, oriented toward coherence and purposiveness without algorithmic closure. This space is not subjective whim. It is the condition under which object languages can be coordinated at all.

Seen in this light, intelligibility is teleological not because it aims at a humanly imposed end, but because it orients formal structures toward meaning without compelling their form. Formal systems are not self originating. They are drawn into being by the possibility of meaning that precedes them. This possibility is real, but it is not itself formal. It orders without determining. It attracts without necessity.

This is why attempts to algorithmize theory change inevitably fail. To formalize the rules of revision presupposes prior judgments of relevance, adequacy, and success that exceed the system being revised. The ladder by which a system ascends cannot be retained within the system without contradiction. The indeterminate that allows for determinability cannot be collapsed into determination without loss.

Here the question of Logos re emerges with new clarity. Logos is not first a word spoken, nor an idea grasped, nor a system constructed. Logos names that by virtue of which meaning is possible at all. It is the order that permits articulation without exhausting itself in articulation. It is the ground that calls without coercing, that grants intelligibility without dictating form.

“In the beginning was the Logos” is therefore not a temporal claim but an ontological one. In the beginning was that by virtue of which anything could be said, meant, or understood. Formal systems, scientific theories, languages, and even our most advanced machines live within this space. They do not create it. They respond to it.

To remember this is not to retreat from rigor but to fulfill it. Logic itself teaches that intelligibility cannot be fully objectified without remainder. That remainder is not a defect. It is the sign that meaning is grounded more deeply than any system can contain.

On Christmas, it is fitting to recall that the Logos who grounds intelligibility did not abolish finitude, form, or history, but entered them. The Word became flesh. Meaning did not collapse into mechanism, nor did transcendence remain aloof. The determinate was upheld by the indeterminate, and the finite was made capable of bearing what it could not generate on its own.

This is not sentiment. It is metaphysics. And it is, perhaps, the deepest reason theology and philosophy still find themselves speaking about the same thing—if only we are patient enough to listen.

Transcendental Reflection and the Divine Other

I

Transcendental reflection investigates those conditions necessary for there to be the kind of experience that we have. Immanuel Kant (1724-1804) famously inquired into the "transcendental conditions for the possibility of experience as such," finding that pure priori forms of sensibility and pure a priori concepts of the understanding are both necessary to deliver the world as it is: one filled with objects having properties causally related to one another. Without these, the universality and necessity of Newtonian physics could not obtain.  

Kant inaugurated a type of thinking that has in many respects dominated theology for the last couple of hundred years.  Kant argued that in order to have a unity to experience there must be a transcendental unity of apperception, a unifying activity that is itself possible to reflect upon. In writing the Critique of Pure Reason, Kant was thinking about his own thinking, about the way that thinking grants unity to experience.  His thinking about thinking was neither an empirical thinking, a thinking of mathematics or geometry, nor a thinking about the ultimate nature of things as Leibniz and Wolff would have thought.  It was a reflective thinking that offered insight into how the unity of experience is possible, a thinking that sought the truth of this unity of experience.  It was not a metaphysical thinking of the transcendent, but a transcendental thinking that brought into the light of day those structures employed but not noticed, a thinking that sought a hermeneutical retrieval of that which is closest to us but remains unnoticed. 

Fichte, Schelling and Hegel were convinced of the profundity of Kant's project which reflected upon, and ultimately coaxed into the open, those transcendental structures making experience possible. A transcendental unity of apperception did not commit one to Descartes' "thinking substance'; such a unity of thinking that did not entail old school metaphysics. Fichte and followers followed Kant's lead after pointing out that the good philosopher could not sustain his famous distinction between things as they are in themselves and things as they appear for us. 

If thinking is that which unites our experience, then why must such thinking be turned back by a putative thing-in-itself? This too could be thought, and thinking this actually dissolves problematic dualisms. Of course, there is something one bumps up against in experience (Anstoss), but such a bumping does not entail that that what is bumped is of a wholly disparate ontological lineage.  Perhaps nature which, as Kant pointed out, is already the result of the synthesizing activity of the transcendental unity of apperception, is not a joint product of something out there and our synthesis.  Perhaps it simply is the result of our synthesis, a synthesis that does not have to hook to the disparate, but can simply connect to itself in appropriate ways.  And so it is that the I posits the very world with which it must deal, the world that it can know, the world that serves as the backdrop to the moral life and all the loftiest of the human heart.  

Transcendental reflection is born in the security of the transcendental unity of apperception, a security that finally cannot admit the Other, for to admit that is to destroy the very grounds upon which transcendental reflection is based.  To posit the Other is to return to the problematic between things as they appear and things in themselves; it is to bark up the Kantian tree and return to an aporia once thought solved and vanquished.  Thinkers in the Kantian tradition knew that this could not be progress.  After the Kantian critique of old-style metaphysics, the security of the transcendental provided a felicitous place for the narrative of God and His incursion into history to took place.  

II

At the risk of oversimplification, I claim that in the days prior to Kant, the days running from the Old Testament prophets through Plato and Aristotle to the steppes of the Enlightenment, the alterity or otherness of God was simply taken for granted by the Church and society generally. Although one could not know the nature of God, the regnant assumption was that God did have a nature that was not dependent upon human awareness, perception, conception or language.  God's being did not depend upon human being, particularly not upon human thinking.  

The story of how Neoplatonic thought forms gradually gave way to Aristotelian categories is important to tell, however, for our present purposes, I will just remark that both types of thinking generally assumed that the Being of God is externally related to human being.  Whether God is regarded as being itself or as the highest being, the tradition acknowledged that God is causally related to the universe.  God's creation of the universe is a causing of the universe to be. Without God's act of creation, the universe would not have being.  Divine power is needed to bring being out of non-being.  Accordingly, the theological tradition was generally committed to the reality of God apart from human being -- the thesis of theological realism -- and the possibility of causal connections between God and the universe -- the thesis of theophysical causation.  

At the dawn of the Reformation, there were a number of differing theological schools that read Augustine, Plato and especially Aristotle in different ways, ways that reflected differing philosophical positions on the ontology of universals and the relationship of these universals to particulars.  While it is an oversimplification to say that Aristotle had become the philosopher of the Christian tradition, many theological traditions assumed with him that there were basic things in the world (substances) and that these substances had properties, some of which were necessary for the substance itself, and some which were accidental to the substance, that is, some of which could either be had by the substance or not possessed by it  without changing the being of the substance. God's creation was a creation of substances with properties.  These substances were the effects of God's creativity activity.  Adam and Eve were individual substances bearing the kind-identifying properties of being both rational and animal. The contour of Adam and Eve's particularity was due to the contingent properties each possessed.  

All of this is important for Christology. That God is in Christ reconciling the world unto Himself meant that the particular entity Christ had both divine and human properties and that Christ had causal power.  The miracle stories suggest all of this, of course.  The being (or substance) Jesus caused it to be the case that 5,000 men (plus women and children) were fed with two fish and five loaves of bread. This being caused it to be true that the man Lazereth was no longer dead.  

Christ was the God-man, He is the second person of the Trinity that had assumed human flesh.  The Second Person eternally existed; there was never a time when Christ was not.  This means inter alia that Christ is simply other than any human who might think, love or trust in Him.  Christ is not a category of human thinking, but a name for a being that exists apart from human awareness, perception, conception or language.  To say that Christ is externally related to anybody ether accepting or rejecting him is to assume that Christ is other that anybody either accepting or rejecting Him.  

When it came time for Enlightenment rationalists to do theology, it was very natural to do it in a metaphysical key. God who is other than worldly being or human thinking must ultimately be seen as the sine qua non of the created order. The principle of sufficient reason claiming that for anything that is there must be some reason why it is, when applied to the universe seemed to point univocally to God.  

One might claim that the time before Kant's Critique of Pure Reason was a "pre-critical" time where the primary objects of religious thought and experience were not yet dissolved into the fog of rational doubt.  Reason, properly applied in discovering many truths fully consonant with the Bible, attested to the same reality as the Holy Scriptures themselves.  

While Kant himself seemed to leave room for there to be a God that is other than human thinking, this God could not be known, and accordingly, the enterprise of rational theology had to be profoundly rethought. The idealist tradition following Kant wished to think God within the security of transcendental subjectivity. Reason had found a place for God that could protect God from the contingencies of the other.  When one thinks about it, the post-Kantian theological tradition can be read in part as an attempt to rescue theology from Lessing's "broad ugly ditch."  Clearly, this theological tradition could insulate the "necessary truths of reason" from the "accidental truths of history."  

III

Martin Heidegger knew the tradition well, understood Kant, and had read Martin Luther.  In the Freiburg lectures from 1919-23, Heidegger shows himself increasingly dissatisfied with a thinking in theology that leaves out the life of the one thinking.  Heidegger's early attraction to Martin Luther (and fueled by Kierkegaard) was his attempt to find a way out from the security of the transcendental project.  For Luther, death was part of the very life of the theologian, an experienced life.  Luther famously uttered "experiential macht die Theologum".  There is nothing secure about finitude, about the life of the believer beset with "sin, death and the power of the devil."  The reality of all three is part of the experience out of which and in which theology is done.  Theological thinking must always be tied to the Otherness of God and the divine project of the salvation of the sinner.  It is a bold thinking of infinite things done by flesh-and-blood finite human beings whose thinking always happens under the Cross.  

Human thinking can never be wholly secure, because the otherness of sin, death and devil is always already besetting it. Such thinking is ecstatic, it is a thinking that is "outside oneself" because it is a thinking in the light of the Cross, a thinking that is a trusting in a Savior that is not a projection of one's own being, not an aspect of the nobility of human being with its cultivated intellectual and moral virtues, not a thinking that is grounded in reason.  Luther, who lived 250 years prior to the heyday of transcendental reflection, already knew that such reflection, if possible, could not end in human salvation.  To be saved is to be saved by that which is other than oneself.  Salvation happens in a world of flesh-and-blood believers dying and sinning.  Thirty-year old Martin Heidegger understood that if theology is to be a serious discourse, this discourse must not hide what is basic to the theologian: The theologian in her now is always already running ahead of herself in encountering that possibility of their being no more possibilities.  The theologian in her now is always already living death, sin and the power of the devil.  This triumvirate does not allow for calm, calculating thinking on the wonders of the grace-filled life.  Life is filled with death.  Our lives, like Christ's life, are lived in the shadow of our crucifixion.  We are now the not that we shall once be when we are no longer being the one for whom the not of the future is no longer.  

Heidegger wanted to bring reflection upon ultimate things back to the phenomenological-ontological-existential ground from which all metaphysical reflection arises. He wanted to call us back from the forgetfulness of this ground, a forgetfulness of being which gives rise both to our absorption in the world and our flights into metaphysical abstraction.  Heidegger's reading of Luther buttressed his conviction that it was time for philosophy to rediscover again the one for whom philosophy means, the one who in its being, has be-ing at issue for it.  With Heidegger, the spector of the Other comes into sight.  We are in our be-ing, beings for whom and by whom the question of being and meaning arise.  This questioning of be-ing by that being who cares about be-ing, is a questioning that opens to the Other of being, a questioning done over the pit of non-being, a questioning that itself is the conduit of the presencing of the absence of being.  Death, after all, cannot be taken up into the life of being; it is the boundary of being that establishes the conditions of being itself.  

IV

But the early Heidegger did not get to the Other.  His project remained curiously within the province of transcendental thinking and subjectivity.  Laying out (interpreting) the existential-phenomenological-ontological roots of our reflection upon being is at some level a continuation of transcendental subjectivity. In our thinking, we think Dasein which is open to its Other, but we can only think this alterity as part of the transcendental existential-ontological conditions for the possibility of ontic engagement with an Other, an Other that may for Dasein have profound existentiell significance.  No longer does the transcendental thinker lay out the unity of the categories of human thinking by which the world is known, now this thinker is engaged in highlighting the unity of the existential structures themselves by which and through which the unity of care is possible, a caring that grounds any thinking in the first place.  

The problem is clearly seen in Heidegger's treatment of other Daseins.  They are Mitsein for Dasein who can have Fuersorge for them, but they themselves in their otherness from Dasein cannot be be in themselves other.  The early Heidegger is simply unable to bring the world into focus.  He can and does get to the world from a certain position in the world, but cannot get to the world itself.  Being cannot ultimately be refracted by considering profoundly being as it is da (there).  What gets thought when considering Da-sein is Dasein, not Sein.  Ironically, Heidegger finds himself in the position of Leibniz.  One has a take on the world within any monad, but monads are windowless, and the world itself can only be reconstructed as describable above the fray of the monadic descriptions themselves.  To get to that world, one needs theological commitments not presenting themselves within the metaphysics of the monad.  

So wither comes the Other?  Can it be brought into focus beyond the security of the transcendental project?  Did Levinas accomplish its encounter with the face? Can phenomenological encounter ground the Other?  Can it give a basis for a radical theological of the Cross where one finds oneself living without metaphysical and ontological nets, as it were?  Can alterity be thought of ontically in the way of those of the Reformation, as an otherness of being toward being?  Must we finally admit that it can only be shown and never said, but that in its showing that we discern the real ontological position of human beings eviscerated by sin, death and the power of the devil as they live their lives in the shadows of the hidden divine.  The Theology of the Cross is about showing, but not about a metaphysics of presence.  Showing here cannot be said without the said Showing turning into such a presence. Wittgenstein knew that showing happens in words, but not in truth-claims. To say what can only be shown is to turn preaching into a dogmatics that must always miss the glimpse of Divine alterity.  

Bringing this Other into the open will demand an overturning of the very identity that has grounded the security of our theology of glory project of transcendental reflection.  At the end of the day, human beings cannot save themselves.  Salvation demands an overturning of the ontological of identity, an identity that has closed the clearing of the divine other, a clearing that finds in God's traces its own footsteps. At stake is the fundamental question: Can otherness show itself as what it is, or must if always show itself as what it is for us.  At stake is the fundamental question of the Garden: Did God really say?  

The Logic of Transcendental Logic

Immanuel Kant employs transcendental logic to show that the synthesis involved in judging that the conceptual "presentation" (Vorstellung) P applying to the conceptual "presentation" (Vorstellung) S also applies to intuitional presentations (Vorstellungen). In other words, the syntheses involved in the act of judgment in general ultimately make possible the world of our experience, a world in which we know objects. 

According to Kant, while general logic abstracts from the particular content of concepts related, concentrating instead on the formal features involved in relating the concepts, transcendental logic deals with the most general features of our experience of objects in space and time.  Unlike general logic, transcendental logic is not about the capacity for thinking as such, but concerns itself with our thinking in relation to our experience of objects as such.  Accordingly, transcendental logic deals with rules of synthesis in so far as this synthesis applies to intuitions as well as to concepts.  It is left to Kant's transcendental deduction to show that the necessary condition for the possibility of experience as such is that there exists a transcendental unity of apperception, an "I think" that is presupposed in all activity of knowing objects.  

Kant famously offers a transcendental deduction in the first edition of the Critique -- the "A deduction" -- which he completely rewrites in the second edition six years later -- the "B deduction." There is a pronounced difference in emphasis between the two deductions with the first being predominantly a "subjective deduction" while the second attempts an "objective deduction."  

The precise contour of the transcendental arguments are a matter of considerable debate, but one might broadly paint the  "B deduction" as follows: 

• Our experience is one of a succession of awarenesses, that is, a succession of contents of consciousness.

• The condition for a succession of awarenesses, however, is an awareness of the succession itself, that is, the successive contents of consciousness must be combined and held together in a unity of consciousness. Such a unity is a necessary condition for an experience of succession. 

• For this synthesis to be presented (represented), I must think it. 

• But this analytic unity of the self thinking its objects presupposes a synthetic unity of the manifold.  In other words, presupposed is a transcendental unity of apperception, a unity of the "I think" that is neither the empirical "self" of psychology, nor a metaphysical thinking substance a la Descartes. (The "I" could never know itself if it were not possible to unify the manifold through synthesis.)

• The transcendental unity of apperception is an objective, not a subjective, unity.  The conditions for this unity are the conditions by which we have consciousness of objects in general. 

• An object is that under the concept of which the manifold is united.  The necessary conditions for uniting the manifold is a unity of consciousness, a unity that bestows objective affinity to transcendental apperception.  

• Since there is an objective unity in the transcendental unity of apperception, the synthesis must proceed according to the categories and the rules required for experience as such.  

My aim in this brief blog post is not, however, to discuss the differences between the deductions, nor to talk about the differing views on the structure of the deductions within the voluminous secondary literature seeking to understand them. Rather I want to highlight the general modal features of transcendental arguments. I am not the first to do this, of course, but sometimes people reading Kant miss the forest for the trees. Sometimes people simply forget to mention that Kant is engaged in a modal argument of a particular kind.  Let us look at the logical structure of Kant's transcendental argument. 

Kant is interested in the necessary conditions for the possibility of experience as such.  Clearly, the argument is difficult to state if we do not include its modal features.  So what is the argument structure, when these are included? 

• Premise I:  There is the possibility of experience as such.  Using Polish notation of L for the necessity operation and M for the possibility operator, we might say 'Me', experience is possible.  

• Premise II:  It is necessary that, if experience is possible, then there exist conditions C for that experience.   We might express this as 'L, if Me, then o'.  (I am using 'o' for 'conditions'.) 

• Conclusion: Lo. 

Kant is claiming that from the mere possibility of experience we can conclude to some necessary features making possible that experience.  He is not arguing that as a matter of contingent fact some conditions (or other) obtain -- that is, empirical conditions -- that would account for that experience.  He is saying that in each and every possible world, the same conditions C must obtain, if there is a possible world where experience E is had.   

Those familiar with modal logic will understand that Kant is presupposing Lewis' S5 in order to conclude to the necessity of C.  Let us review basic modal systems briefly. 

• We might have a system that might allow us to move from necessity to possibility.  Using Polish notation, we have the distinguishing axiom 'CLpMp', if p is necessary, then p is possible.  (Read the 'C' as the conditional 'if, then', e.g., 'if Lp, then Mp'.) That is, if p obtains in all possible worlds, p obtains in some possible world.  (It is hard to conceive how something appearing in all possible world is not possible, for it is in every world that is, by definition, possible.)

• We could add to this first system another axiom this one from actuality to possibility: 'CpMp', if p obtains then p is possible.  That is to say, if p obtains in the actual world, then p obtains in a possible world.  (This seems plausible since the actual world is a possible world.)

• We can add to this second system another plausible theorem: 'CMMpMp'. We have now arrived at Lewis' system S4 holding that if something is possibly possible, then it is possible.  In other words, if p is possible in a possible world, then p is itself in a possible world.  (This seems plausible since all there are are possible worlds, and it would be strange were something possible in a possible world to somehow not simply be possible.) 

• Finally, we get to S5, sometimes assumed to be the "standard" system of model logic.  This system is generated from 'CLpMp', 'CpMp', CMMpMp' and the distinguishing assumptions of S5, 'CMLpLp', that is, if it is possible that something is necessary, then it is necessary.  Simply put, if there is possible world where some necessity holds, then, since for something to be necessary it obtains in all possible worlds, that which is necessary in that possible world is now ingredient in every possible world. (It is hard to see what being necessary in a possible world might be, if that necessity does not extend over all possible worlds.)  

Those familiar with ontological arguments for the existence of God should immediately recognize the importance of S5. Assume it is possible that God exists. Now reflect on the nature of God. Is God the kind of being that could exist contingently like a rat or an apple, or is God the king of being who, were God to exist, would exist necessarily?  If one's intuitions are of the latter, then God either exists in all possible worlds or in no possible worlds. But how do we know?  We know by checking whether or not God's existence involves a self-contradiction.  If God's existence is self-contradictory, then God does not exist in a single possible world. However, if God's existence is not self-contradictory and God's existence is not contingent, then the very possibility of God existing entails that God exists in all possible worlds including the actual world!  

So how do we apply S5 here?  Let us look at the argument again, and see if we can arrive at the conclusion. 

• Premise I: Me

• Premise II: LCMeo   (This says that necessarily, if possibly e then o.)

• S5 Assumption: CMLpLp

• But (2) is logically equivalent in all modal systems to 'CLMeLo'

•  From(3), 'C~Lp~MLp'. 

• (5) is equivalent to 'CM~pLM~p'. 

• Substituting 'e' for '~p' uniformly, we get, 'CMeLMe'. 

• Thus from (1), we derive 'LMe'. 

• Now by (4) through modus ponens we get 'Lo', and thus 'o' constituted necessary conditions for the possibility of 'e'.  QED. 

It is not immediately apparent what is wrong with this proof. Kant is engaged in critical or immanent metaphysics in the Critique. He is not talking about his believing or knowing primarily, but those states of affairs making true his believing and necessary for his knowing. The transcendental unity of apperception constitutes a necessary condition for any possible experience, that is to say, if there is a world in which there is experience 'e', then there can be no worlds in which transcendental unity fails to obtain.  The very possibility of 'e' entails the necessity of 'o'.  

Now the question of the claim: Is Kant really trying to say that 'o' obtains in all worlds, or simply that there is no world having 'e' that does not have 'o'? Are we saying that worlds in which 'e' does not obtain have 'o'?  In other words, are we asserting a necessity of consequence or a necessity of the thing consequent.  

In the medieval tradition God's foreknowledge was figured as a necessity of consequence, not a necessity of the thing consequent.  If God foreknows that S rejects God, does God's foreknowledge itself logically entail S cannot reject God? The solution was to discriminate the scope of the modal operator.  In worlds in which God foreknows S rejects God, S cannot not reject God.  However, in worlds where God does not have this foreknowledge, then S is presumably not logically determined to reject or not reject.  Are we saying that the transcendental argument is more like a necessity of consequence: In worlds were 'e' occurs, it cannot be that 'o' fails to obtain.  But how about those worlds in which 'e' does not transpire?  Must 'o' be ingredient in them as well?  And if 'o' is not ingredient, then how must we adjust the transcendental argument?  Clearly, these questions motivate a deeper investigation.