Showing posts with label Extensionality. Show all posts
Showing posts with label Extensionality. Show all posts

Saturday, November 22, 2025

Disputatio LIV: De Hyperintensionalitate Divinae Operationis:

 

On the Hyperintensionality of Divine Action

Quaeritur

Utrum actus divini, quoad identitatem, formam, et rationem essendi, non possint explicari per extensionalem aequivalentiam, modalem necessitationem, vel possibilia mundorum, sed sint essentialiter hyperintensionales; et utrum veritas theologica requirat talem hyperintensionalitatem ut Deus cognoscatur secundum actum, non secundum eventum.

Whether the identity and form of divine acts can be explained by extensional equivalence, modal necessity, or possible-world semantics, or whether they are essentially hyperintensional; and whether theological truth requires such hyperintensionality so that God is known according to the act God performs, not merely according to an outcome.

Thesis

Divine acts are hyperintensional. By this we mean that the identity of a divine act cannot be captured by any framework in which acts are considered the same whenever they yield the same outcomes, share the same extension, or hold necessarily across all possible worlds. A divine act is not defined by its effects, nor by the set of circumstances under which it occurs, nor by its modal profile. Instead, a divine act is individuated by its formal identity within the Logos, by the specific constitutive act through which the Logos brings a res into being or presence, and by the Spirit’s concrete donation of that act to creatures.

Thus, extension does not capture divine identity,modal equivalence does not capture divine identity, and possible-world semantics is too coarse-grained to describe divine agency. A hyperintensional account alone preserves the theological conviction that God’s acts are personal, irreducible, and internally differentiated modes of the one divine life.

Locus Classicus

1. Exodus 3:14 — אֶהְיֶה אֲשֶׁר אֶהְיֶה

“I AM WHO I AM.”

This is not a definition, but an identity of actBeing itself is hyperintensional, for it names a unique form of divine acting, not a property instantiated across possible worlds.

2. John 5:19 — ἃ ἂν ἐκεῖνος ποιῇ, ταῦτα καὶ ὁ Υἱὸς ὁμοίως ποιεῖ

“Whatever the Father does, the Son does likewise.”

The divine act is not duplicated or numerically separable. Rather, its identity is internal to the Trinity, not extensionalized in effects.

3. Athanasius, Contra Arianos I.21

ὁμοούσιος οὐ κατὰ θέλησιν ἀλλὰ κατὰ φύσιν.
“Of one being not by will but by nature.”

The divine act is identical with divine being; it is an identity finer than any modal equivalence.

4. Gregory of Nyssa, Ad Ablabium

Οὐ τὰ γινόμενα, ἀλλ᾽ ὁ τρόπος τῆς ἐνεργείας τὴν διαφοράν ποιεῖ.
“It is not the outcomes, but the manner of operation that makes the distinction.”

This is a classical statement of hyperintensionality clearly stating that the manner by which something obtains profoundly matters.

5. Luther, WA 40/III, 343

“Deus non est causa sicut causae creatae.”
“God is not a cause as created causes are causes.”

Thus God cannot be modeled extensionally.

Explicatio


1. Why extensional identity is inadequate

Extensional identity holds when two expressions apply to precisely the same set of objects. If two predicates pick out exactly the same individuals, classical extensional logic treats them as equivalent. For example, if every creature that is forgiven is also elected, and every creature that is elected is also justified, then these predicates are extensionally equivalent: they have the same extension.

Formally, if for all x, x is forgiven ↔ x is elected and x is elected ↔ x is justified, then the predicates forgiven, elected, and justified are coextensive.

Similarly, in the Spirit’s work, if for all x, x speaks in the Spirit ↔ x has been given the Spirit, and x has been given the Spirit ↔ the Spirit dwells in x, then Spirit-speaking, Spirit-giving, and Spirit-indwelling are extensionally equivalent expressions.

But extensional equivalence tells us nothing about what distinguishes these divine actions in God Himself. Forgiving is not the same divine act as electing, nor is electing the same divine act as justifying. Likewise, the Spirit’s giving, indwelling, and speaking are not identical divine operations simply because they coincide in the believer. Extensional identity collapses formally distinct divine works into a single undifferentiated outcome and therefore cannot serve as the framework for a theology that seeks to speak truthfully of God’s own acting.

2. Why modal equivalence is insufficient

A second temptation is to appeal to modal identity. Accordingly, if two acts occur in every possible world in which God acts toward creatures, or if one cannot conceive God performing one without the other, then they are treated as identical.

Creation and preservation offer a clear example. Classical theology holds that God’s preserving of the creature is nothing other than the continued giving of being. Because no creature could exist for a moment apart from God’s sustaining act, creation and preservation are necessarily coextensive: wherever one occurs, the other is already taking place.

So too with incarnation and redemption. In the Christian confession, the Son becomes incarnate for our salvation, and His incarnate life is unintelligible apart from His redeeming work. One cannot separate them modally, for in every possible description of God’s salvific activity, incarnation and redemption occur together.

Yet modal inseparability does not entail formal identity. Creation and preservation differ in their reason, because one brings being into existence, while the other maintains that being in existence. Incarnation and redemption differ likewise, for one is the assumption of human nature, the other is the reconciling act performed in that nature. Modal equivalence cannot register these distinctions because it treats any necessarily co-occurring acts as identical, thereby losing the finer structure of God’s activity that theology must retain.

3. Why divine acts require hyperintensional individuation

If theology is to speak truthfully, it must be able to say why this particular divine act grounds this theological statement. In our broader account, a theological utterance is true because the Logos performs a determinate act—Λ ⊨* Tₜ. But determinate truth requires determinate action. If divine acts could not be distinguished except by their extensions or modal profiles, then the truthmaker for any theological statement would be some undifferentiated divine activity, and doctrinal distinctions would lose their ontological grounding.

By hyperintensional identity I mean that divine acts differ not by their outcomes or by their modal placement but by their internal form in the Logos—the determinate way God is acting here and not otherwise. This internal form cannot be captured by appeal to effects, extensions, or modal profiles; it belongs to the act as God performs it. Forgiving is formally distinct from electing because each expresses a different aspect of the divine life, even when the same creature receives both. The Spirit’s indwelling is formally distinct from the Spirit’s giving because each arises from a different manner of divine self-communication. Hyperintensionality preserves the integrity of these differences.

4. The Spirit’s donation is hyperintensional

The Spirit does not donate to creatures a general divine presence or a generic divine favor. Instead, the Spirit donates the specific act that God is performing toward the believer. In one moment, this may be forgiveness; in another, consolation; in another, empowerment. The specificity of the Spirit’s donation presupposes a finely articulated structure of divine action in God Himself. Without this specificity, divine presence would become conceptual rather than real, and theology would lose the concreteness of God’s address.

5. Felicity is indexed to particular divine acts

A theological assertion is felicitous only if it corresponds to the act God is performing here and now—an act that is already individuated in God with a hyperintensional precision. The Spirit authorizes not theological grammar in general but this particular word because this particular divine act is being given. Thus the intelligibility of theology depends on a hyperintensional account of divine acting.

Objectiones


Ob I: According to classical extensionalism if two divine acts produce the same effects, they are the same act. If this is so, there is o need for hyperintensional identity.

Ob II: Modal realism holds that if God necessarily performs A and B, then He performs A and B in all possible worlds, and thus A = B. Therefore, modal equivalence suffices in individuation.

Ob III: Thomism claims that since God is simple, all divine actions are identical and distinctions collapse.

Ob IV: Deflationism asserts that hyperintensionality describes linguistic distinction, not metaphysical difference.

Ob V: Postliberalism holds that since all distinctions arise from use within the community, divine action adds nothing.

Responsiones


Ad I: Effects underdetermine cause. Divine acts differ in their formal ratio, not merely in outcome (Gregory of Nyssa). Thus, extension collapses personal identity.

Ad II: Possible-world semantics assumes shared structure with creaturely action. But divine acts exist outside modal ontology; they ground modality rather than inhabit it. God is not a node in a modal structure but its creator.

Ad III: While implicity entails no composition in God, it does not follow that divine acts lack distinct formal identities. The Fathers held simplicity alongside real distinctions of operation.

Ad IV: Hyperintensionality is not linguistic fineness but metaphysical precision. Divine act identity is not a function of language but of participation in the Logos.

Ad V: While usage explains how we talk, it does not identify what God does. Without hyperintensional divine action, grammar loses its anchor in reality.

Nota

Hyperintensionality is the ontological form of God’s personal action. We have seen that constitutive causation (L) requires fine-grained identity; that real presence (LI) is specific, not generic; that donation (LII) concerns a particular res, and that felicity (LIII) authorizes a particular act of creaturely speech. If theological semantics were simply extensional or modal, the Trinity collapses into one role, the sacrament collapses into symbol, revelation collapses into a proposition, grace collapses into an effect, and Christology collapses into monism.

Regarding the Trinity, hyperintensionality preserves the distinction of the trinitarian persons, Christ’s unique acts, sacramental specificity, and the performative depth of divine truth. Simply put, hyperintensionality is not an analytic embellishment but a theological necessity. Without it, we could not preserve the conviction that God acts personally and decisively for the creature, nor could we maintain the integrity of the Gospel’s claim that God’s work is addressed to us in its fullness and specificity.

Determinatio

We have determined that:

  1. Divine acts are intrinsically hyperintensional, distinct in their internal form even when extensionally identical.

  2. Neither extensional equivalence nor modal necessity suffices to individuate divine action.

  3. Hyperintensional identity flows from the Logos’ constitutive act (L) and is made present (LI), donated (LII), and authorized (LIII).

  4. Theological truth (Λ ⊨* Tₜ) requires such hyperintensional grounding.

  5. Therefore, theology must employ a hyperintensional semantics to speak truly of God.

Transitus ad Disputationem LV: De Intentione Divina et Identitate Actuum in Deo

Having established hyperintensionality in divine action, we proceed to the related question as to how divine intentions are related to divine acts, and how the Logos unifies them without collapsing distinctions. 

Thus, we turn to Disputatio LV: De Intentione Divina: Utrum Intentiones Dei Sint Actus et Quomodo Unitas in Logō Constituitur, where we shall inquire as to whether God’s intentions are identical with His acts, and how the Logos grounds their unity and distinction.

Thursday, April 06, 2023

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

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

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

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

Compare the following: 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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