Gödel & the End of Physics and Abelard et al & the End of Trinitology

In my trinity-talk, I try to mindfully inhabit one mode of discourse at a time.

I approach creedal trinitology as a rather formal subject, where there seems to be a great deal of consensus, phenomenologically, regarding the requisite vague categories and their rules of predication (e.g. essence, existence, hypostasis, person, relation, energeia, oikonomia, univocal, analogical, distinctions: real, conceptual, formal; causes: formal, final, efficient, material; determinacies & necessities, etc). This consensus sets our theological contours, metaphysically, without specifying a given metaphysic.

In a systematic trinitology, staying with those contours, many specify a given metaphysic employing an apt root metaphor: substance, process, experience, social, relational, etc All such metaphors eventually collapse & paradoxes ensue. This is no less unavoidable in trinitology than it is in quantum interpretations or philosophies of mind. Alas, we press on in search of that meta-idiom.

Most of us, beyond our essential creedal formulae, engaged liturgically & explicated catechetically, are otherwise familiar with what I call trinitophany or trinity-talk in various common sense idioms, which are largely informal. In our local idioms, we employ metaphors but not as root metaphors and not in any formal syllogistic sense. Here our metaphors cascade & collapse and usually, but not always, change from one to the next. Here our discourse is poetic, celebratory, prayerful. Trinitophanies don’t aspire to universal models, only believable imgages.

In the consideration below, I’m trying to focus on a creedal trinitology.

Some of my favorite thinkers wonderfully integrate dogmatic, philosophical & sacramental-poetic discourse and/or creedal & systematic trinitological and theophanic approaches, e.g. Bulgakov & von Balthasar.

When we use concepts like consubstantial to refer to determinate secondary substances or essences, all 3 modes of being are in play, temporal acts in potency – of existence to essence and efficient to material & formal to final causations. There’s a LOT going on!

But we must check ALL of that conceptual baggage at the epistemic door, as we board the divine essence sleeper car, meta-ontologically, or we’ll derail our trinitarian train of thought, for NONE of that is going on!
None of that needs to go on for divine realities b/c they ALREADY ARE whatever they’re willed to be, while we are, instead, BECOMING what we’re willed to be.
We can thus identify & refer to an object as God if we know either its essence OR its person OR its energeia-oikonomia.
To completely identify & describe a determinate creature, we must know its essence AND its haecceity AND its relations (e.g. generalities, regularities, in/determinacies).
Note: Both determinate modes of being & meta-ontological modes of identity remain irreducibly triadic, the former an ontological subcategory of the formal mode of identity, which applies to both divine & determinate realities.

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The meta-ontological modes of identity in divine syllogistics merely assert (analytically) THAT there’s 1 ousia & 3 hypostases.

Unlike the modes of being in Aristotelian syllogistics, neither the essential propria nor the hypostatic idiomata of the divine modes of identity intimate (ontologically) HOW divine realities are variously nondeterminate, self-determinate, noncomposite, unoriginate, begotten, etc.

Tritheism, subordinationism, modalism & various paralogisms can appear as valid conclusions when ontological rather than meta-ontological categories are applied to classical trinitarian discourse. They thus amount to category errors.

A separate concern typically arises regarding the degree of intelligibility conveyed by modes of identity & it must be conceded that they gift us far more dispositionally than propositionally. Such gifts, however, remain eminently actionable, existentially, and particularly indispensable, theopoetically & theo-poi-etically.

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Consider 5 major aporia of determinate reality re types of origins: quantum, cosmic, life, consciousness & language. Not only do they defy explanatory adequacy, physically, they resist any adjudicatory attempts between competing metaphysical heuristics.

Still, even without a specific ontology or metaphysic, meta-ontologically, we can reasonably infer & successfully refer to such realities in terms of putative unknown causes.

From definitive determinate effects, which are proper to no known causes, we can identify such putative causes even though we’re unable to comprehensively describe them.

We vaguely refer to quantum gravity, dark matter, hidden variables, qualia & such, not unreasonably speculating that, like the long-hypothetical Higgs boson, those or related hypotheses could be experimentally confirmed (or not).

Such inferential, metaphysical reasoning from known effects to unknown causes (via relational reality) refers to a meta-ontological mode of – not being, but – identity, specifically, the mode of formal identity.

Formal identity thus includes both robust descriptions & vague references. Some such references (e.g. quantum gravity) have perennially resisted, while others (Higgs boson & field) have eventually yielded to, comprehensive description in terms of meta/physical properties (e.g. precise quiddities & specific regularities).

This meta-ontological, formal mode of identity maps to that relational, ontological subcategory, which, in a modal ontology, would include those laws, regularities & in/determinacies that mediate between quiddities & haecceities, possibilities & actualities, essences & substances.

This formal mode of identity applies, meta-ontologically, to both the divine syllogistics of nondeterminate & self-determinate realities as well as the Aristotelian syllogistics of determinate realities. Its ontological subcategory applies to all determinate effects, whether their putative causes are, themselves, determinate, or otherwise non- or self- determinate.

In addition to formal identity, nondeterminate & self-determinate divine realities exhibit two other modes of identity: the essential (re ousia) & personal (re hypostases). These apply ONLY in the syllogistics of divine realities, meta-ontologically, but do not map, for example, to such ontological subcategories of determinate realities, where, per Aristotelian syllogistics — re: essences, the act of existence remains in potency to essence; re: hypostases, efficient acts in potency to material causes; & re: relations, formal acts in potency to final causes — all such temporal dynamics are totally foreign to divine ousia & hypostases, which are eternal.

So, while there’s a semantical univocity & minimalist analogy of the meta-ontological categories of being, realities & relations, which apply in both created & Uncreated spheres, the modes of identity for the Uncreated categories of being (ousia) & realities (hypostases) not only do not map to any ontological subcategories in the sphere of creation but also remain silent, ontologically, in the Uncreated sphere.

Any univocity and/or analogy of beings & realities, created vs Uncreated, remain strictly meta-ontological in both essential & hypostatic/personal modes of identity.

A univocity and/or analogy of relations, however, can map, ontologically, the determinate effects within a modal ontology to putative causes, both created & Uncreated, and do so, meta-ontologically, via the formal mode of identity.

Thus natural theology reasons from the divine vestigia in the gratuity of creation back to certain attributes or propria of a divine essence and/or idiomata of, for example, a pneumatological hypostasis.

Thus special revelation reasons from divine theotic effects in the gratuity of grace, from the energeia back to the propria of divine ousia & from the oikonomia back to the idiomata of trinitological hypostases.

While such divine propria & idiomata successfully refer to putative causes of Uncreated realities, non- & self-determinate, those realities remain, at once, utterly incomprehensible & infinitely intelligible.

This is not unrelated to the constraints we encounter for determinate realities:

Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind. I’m now glad that our search for understanding will never come to an end, and that we will always have the challenge of new discovery. ~ Stephen Hawking

See:

http://www.hawking.org.uk/godel-and-the-end-of-physics.html

A more concrete take on the practical upshots of divine essence-talk might unpack these dense theoretical abstractions.

In our temporal reality, however it may be that we conceive essences, universals, properties, ie as nominalists, conceptualists, realists, etc, we can still manage to successfully describe realities & reason formally about them with terms, sentences & propositions. One mustn’t imagine that – by invoking a univocity & analogy of being, even mindfully tending to apophatic vs kataphatic predications – we can similarly reason about the Trinity.

We aspire, then, not to robustly ontological, theoretical descriptions w/propositional significance for divine-discourse, but to merely semantical, heuristical references w/dispositional impetus for divine-intercourse.

So, even without fully comprehending what it could possibly entail to be infinite, unoriginate, nondeterminate, noncomposite, etc vis a vis being, truth, beauty, goodness, freedom, etc, these otherwise meager conceptions can help properly dispose us – theopoetically, in our life of prayer, liturgies & devotions, also theo-poi-etically, fostering our ongoing theotic transformations.

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For starters, one mustn’t confuse meta-ontological phenomenologies and metaphysical ontologies, or quite simply that which is beyond being & being.

For another, one mustn’t confuse epistemic attributes and ontic properties.

Importantly, one must also not confuse nondeterminate, self-determinate, kenotically determinate & contingently determinate realities. In that regard, it might be best to engage Divine syllogistics by speaking in terms of essences, hypostases & formalities, while, analogically, employing quiddities, haecceities & quasi-formalities, when engaging Aristotelian syllogistics.

That’s pretty much it.

One can dig deeper, though.

To wit:

Meta-ontological categories of modal identity apply to nondeterminate, self-determinate & kenotically-determinate objects and include the essences, hypostases & telicities of such necessary realities.

This could include the ens necessaria of any meta-architectonic (e.g. materialist, pantheist, panentheist, classical theist, etc).

Such a necessary object can be identified either essentially or hypostatically or telically (formally) as attributes of any of those categories are, alone, sufficient to successfully identify such objects.

For determinate realities, only the meta-ontological category of telic (formal) modal identity applies. To successfully identify such contingent objects, essential, hypostatic & telic properties are all necessary, none – alone – sufficient.

For nondeterminate, self-determinate & kenotically-determinate objects, essential & hypostatic properties are epistemically unavailable, ontically occulted, in principle.

Hence, only vague attributes can be applied, such as, for example, divine propria, essentially, or divine idiomata, hypostatically.

For nondeterminate, self-determinate, kenotically-determinate & contingently determinate objects, telic (formal) attributes & properties afford, respectively, successful references & descriptions.

Hence, vague attributes can be applied, such as, for example, divine energeia, essentially, or divine oikonomia, hypostatically, in order to successfully refer to divine realities.

Also, for contingently determinate objects, precise essences & specific telicities can be applied in order to properly identify the (meta)physical properties that are necessary to successfully describe individual hypostases.

For such objects, beyond their modal identity & description, a dynamical modal ontology can be applied as various ontological categories represent different temporal acts in potency, for example, 1) hypostatic act of existence in potency to essence; 2) hypostatic efficient causation in potency to material causation; 3) telic formal causation in potency to final causation.

For nondeterminate, self-determinate & kenotically-determinate objects, beyond their modal identity & reference, their determinate effects ensue – not from acts in potency, temporally, but – from eternal acts.

Because of these distinctions, I prefer to distinguish eternal necessities from temporal contingencies by referring to the former in terms of essences, hypostases & telicities or formalities, the latter in terms of quiddities, haecceities & quasi- telicities or quasi-formalities. This approach flips that script which refers to divine telicities as quasi-formal (e.g. Rahner). It renders our metaphysical-talk metaphorical & our meta-ontological references as primally real. The path to authenticity thus involves eternalization or the transformation of quasi-telic temporal ends to the eternal ends of Divine Telos.

Amplification:

I think of modal identity in primarily epistemic terms, but it certainly also entails at least some vague ontological specifications (even when only via apophasis) & imparts some dispositional axiological implications.

This is to say that I believe that divine syllogistics regarding essential propria (e.g. truth, beauty & goodness) & hypostatic idiomata (e.g. Father, Son & Spirit) very much matter for our worship, our transformation & such.

Meta-ontologically, I conceive divine being as nondeterminate and/or self determinate, while contingent being presents as variously (in terms of degrees) in/determinate. I categorize in/determinate realities per a modal ontology, which recognizes its radical temporality.

Divine syllogistics & Aristotelian syllogistics intersect determinately, only in the category of formal modal identity. Otherwise, regarding modal identities, it’s a clear category error to equate divine essences & hypostases, for example, with contingent quiddities & haecceities, because they are otherwise distinguished as eternal vs temporal, as non- & self-determinate vs variously in/determinate, and so on.

In the category of formal modal identities, however, we can consider determinate effects, whether their causes are nondeterminate, self-determinate or in/determinate. Even allowing for divine determinate causes, still, those would be distinguishable from ordinary contingent determinate causes by their kenotic natures.

Divine determinate causes would include incarnational realities.
Divine determinate effects would originate from divine realities, including nondeterminate, self-determinate & kenotically determinate and would include, for example, vestigial effects in the gratuity of creation & theotic effects in the gratuity of grace, such effects as would otherwise be proper to no known contingent, determinate causes & which would be communicated via general & special divine revelations.

The Word remained what he was when he became flesh so that he who is over all & yet came among all through his humanity should keep in himself his transcendence & remain above the limitations of creation…he was alive even when his flesh was tasting death. (Cyril of Alexandria)

In the –

paterological ur-kenosis, the Father remained what He was in the generation of the Son & procession of the Spirit;

pneumatological kenosis, the Spirit remained the Holy Breath, when immanentized/presented in the gratuity of creation;

Christological kenosis, the Son remained divine, when incarnated/presented (via dyo/mia-physitism) in the gratuity of grace.

So kenosis has only ever entailed a qualified self-limitation or tzimtzum (not self-annihilation but self-contraction).

Formal identities of divine determinate realities (e.g. oikonomia & energeia) present via kenotic & synergistic trinitarian acts of the divine hypostases (personal identities), whether unoriginately nondeterminate, eternally self-determinate &/or kenotically determinate.

Essence, Hypostasis, Person, Relation, Energy & Economy

Many New Testament statements by Jesus are interpreted by some in terms that are – not just ontological and/or economical, but, also – relational (e.g. mutual interabiding or indwelling). In my tradition (informed by the Pontifical Biblical Commission), when in doubt, even re John 10, for example, they assume no one in the NT is talking metaphysics, in general, much less a substance ontology, in particular. Rather, they say such verses refer to economic mission & relational indwelling, i.e. w/implications for us. Even conceding that, all such verses when taken together in their NT context as well as in early liturgical traditions will certainly have metaphysical implications, theologically. Most Fathers thought they were ontologically suggestive (&, I’d add, meta-ontologically decisive)?

Hypostatic Asymmetries & Subordinationism

There’s an asymmetry of the homoousion imputed to Athanasius that, seems to me could, involve the distinction between individual vs general essences, qualities that identify hypostases vs properties that identify ousia, any asymmetry applying only hypostatically. Athanasius didn’t employ Cappadocian-like nuances, so, if we plausibly interpret him as talking about individual essences, hypostatically, that asymmetry isn’t truly subordinationist, because such an essential dependence is – not causal, but – merely definitional.

It seems that hypostatic order or taxis, for some, won’t involve originations &/or causes but – ways of self-revealing. For example, maybe active/passive revelatory “images,” while unique for each hypostasis, needn’t entail unique “ways of relating” to the essence. Whatever the case, hypostatic idiomata, whether originationist or revelatory, might best be interpreted in definitional terms of essential dependence & individual essence, not without ontological implications but merely metaphysically (meta-ontologically), bracketing any specific metaphysic (ontologically).

One practical upshot of trinitarian modes of identity seems to me to be that hypostatic asymmetries needn’t imply subordinationism because essential dependencies aren’t causal (not saying they don’t have other ontological implications).

Preserving analogy does seem indispensable to any theotic approach that suggests we can participate in or partake of the divine nature? And, of course, it implies, also, dissimilarities, since divine realities “be what they are” & we “become” what we are. What about dissimilarities between hypostases in relating to essence?

Hypostatic Kenoses

For Bulgakov & Balthasar’s kenotic models, the same activity engaged by each hypostasis would be possession through dispossession. That hypostatic activity can otherwise be uniquely identified as we consider whether a given relation is active, passive, mediated, inverted, etc? Such essential dependencies & interdependencies could still be expressed in terms of individual not general essence.

We have to distinguish between ontological attempts to describe how the hypostases might variously relate to the divine nature & meta-ontological references to same.

The former employ root metaphors of substance, process, social experience or other relations & are less interesting to me because they aspire to say more, in principle, than we can prove. But I affirm those who strive to formulate better idioms.

The latter are “merely metaphysical” and more “vaguely phenomenological.”

I can’t always readily tell which approach people are taking.

For example, Neville’s hypothetical neo-Whiteheadian process approach seems clearly ontological; it would interpret the divine nature, itself, as a product of the Father’s creatio ex nihilo – a rather radical conception of principium sine principio?

In a merely metaphysical approach (perhaps), von Balthasar would kenotically differentiate the hypostatic relations to the divine nature in terms of 1) stripped of 2) thankful for and 3) bridged by, respectively, Father, Son & Spirit.

See: https://mobile.twitter.com/John_S_Sylvest/status/1084862911758168064

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In what amounts to my pan-semio-entheistic theory of truth, I conceive five transcendentals per terms of an Ens Necessarium as Necessary Truth, Necessary Beauty, Necessary Goodness, Necessary Unity (Love) & Necessary Freedom. These five categories map to my conceptions of Lonergan’s conversions & imperatives as well as to a fivefold missiology, both pneumatological & Christological.

This is neither a Kantian nor transcendental Thomist approach, however, but grounded in a semiotic realism and advanced abductively from that naturalized epistemology, deriving from those participatory engagements with reality that rely on an axiological epistemology (per my Peircean-like theory of knowledge).

There’s a leap of faith required, to be sure, at an existential disjunction where nihilism, pantheism & classical theism present.

see Note Below
See: https://paxamoretbonum.wordpress.com/2018/12/04/classical-theism-doesnt-really-compete-tautologically/

Can one take my pan-semio-entheistic leap, within the contours of a classical theism, employing a logic that wouldn’t be considered adhocery & unamenable to normal syllogistic logic?

I believe so.

Conceiving my approach as a fallibilist abduction, then formalizing its phenomenology via a consistent predicate & propositional logic, employing modes of identity, we could establish that its reasoning regarding existents (creatures) would be a special case or reduction of the phenomenological syllogizing of my putative transcendentals.
Put more simply, creature-talk would employ metaphors of our normative Creator-talk, not vice versa.

My five transcendentals, then, will be imported into a classical trinitology. The conceptual bridges between it and Aristotelian logic have already been built by Sara Uckelman.

See: Uckelman, Sara L. (2010). Reasoning About the Trinity: A Modern Formalization of a Medieval System of Trinitarian Logic. In Logic in Religious Discourse. Schumann, Andrew Ontos. 216-239.

I will try to summarize her discourse below & apply it to my heuristics.

In avoiding both modalism & tritheism, while remaining consistent in trinitarian predication, one must recognize three modes of identity. Unlike modalism, which refers to a single object existing in one of these modes, a modal identity entails one object as being the same as another object in one of the modes of identity.

  • Essentially identical objects share the same essence (extensional identity).
  • Personally identical objects share the same properties & definitions (intentional identity).
  • Formally identical objects share a genus, sufficiently similar to be placed therein.

(Abelard originally distinguished extensional from intentional identity.)

The above modes of identity can be applied to the trinitarian logic of the Athanasian Creed, but this divine syllogistics collapses when applied to existents, where Aristotelian syllogistics, instead, apply.

My modal schema, influenced by Peircean categories, where

Being > Reality > Relations > Existents

roughly & analogously maps to these modes of identity

Essential | Personal | Formal | Creatures

employing a predicate or propositional logic, which is meta-logical (while Aristotelian syllogistics employ a term logic).

See:
https://paxamoretbonum.wordpress.com/2018/08/26/simply-divine-or-a-divinity-fudge-cooking-with-dionysius-scotus-peirce-aquinas-palamas/

Also see:

So, Trinitarian discourse can be affirmed as formally consistent and roughly maps, heuristically, to our meta-logical categories.

Still, that affords us only analytical conceivability, a rather minimalist intelligibility?

Can a bridge be constructed to Aristotelian syllogistics? that we might gain some additional modicum of intelligibility?

Yes.

First, we would recognize that, for existents (creatures), only the formal mode of identity obtains and essential & personal predications do not (i.e. in Aristotelian syllogistics).

So, can Aristotelian syllogistics yet be extracted from the mode of identity framework mindful of where such predications obtain or not?

If so, our trinitarian logic needn’t be considered adhocery & unamenable to normal syllogistic logic. Instead, our reasoning regarding existents (creatures) would be a special case as a reduction of trinitarian syllogizing.

We should remain mindful that, in relating propria of the essence, idioma of the hypostases & energeia of the Trinity, per Abelardian modes of identity (essentially, personally & formally), even if we suitably predicate these realities using apophasis, analogy, gerundives & such and remain otherwise consistent —-
still, because we only ever use partial references and not exhaustively complete definitions, a radical incompleteness will still afflict our trinitarian discourse.
For example, even when we’ve managed to avoid paralogisms by properly attending to our modes of identity, in order to disambiguate our categorical predications of divine terms (thereby making explicit identity types essencialiter vs personaliter vs formaliter), while we will have saved some of our most meaningful intuitions, still, mystery will perdure.

While our Peircean-like categories analogously map to our Aristotelian, Scotist & Thomist categories (like quiddity, haecceity, ousia, hypostasis and such), it’s not counterintuitive that the dissimilarities — between all of our approaches to temporal being (Peirce, Scotus, Thomist, etc) and our approach to nondeterminate & self-determinate being (with three modes of identity) — will be located essentially & hypostatically vis a vis the modes of identity.

The categories of essential-hypostatic nondeterminate being (ad intra), where an act-potency distinction will not obtain, simply will not, by definition, correspond to temporally modal categories of essential-hypostatic determinate being.

It makes perfect sense, otherwise, to draw on the formal mode of identity to locate the similarities between, on one hand, the determinate effects of the divine energeia (essentially or substantially of ousia) & economy (personally or hypostatically of haecceities), and, on the other, those of created, determinate beings.

Is that not precisely what we find in the Palamitic distinction between essence & energies, Thomist distinction between esse naturale & intentionale, Scotus’ formal distinction and Peirce’s thirdness?

There’s a divine-creaturely nexus, a semiotic locus, where we can reason, abductively, from effects that are proper to no known causes, to putative causes, whether the Actus Purus of nondeterminate & self-determinate divine causes, or the acts in potency of in/determinate creaturely causes, both physical & metaphysical.

While we are often epistemically constrained, methodologically, unable to exhaustively define such putative causes, whether divine, metaphysical or even physical, this moderate realism affords us the prospect of nevertheless, really, making successful references – per a univocal mode of identity vis a vis effects.

That’s what my project has been about — establishing that our God-talk, including a classical trinitology, remains robustly intelligible & coherent:

See:
https://independent.academia.edu/SylvestJohn

https://paxamoretbonum.wordpress.com/2018/12/03/how-gelpis-inculturated-north-american-theology-graced-my-encounter-with-eastern-orthodoxy/
https://paxamoretbonum.wordpress.com/2018/12/04/classical-theism-doesnt-really-compete-tautologically/

Note re: leaps of faith

Monist
nihilism
pantheism

Dualist
panen-theism (dipolar or whole-part relation)
classical theism (created tehom – staged vs lapsarian)

Pluralist
pan-entheism (uncreated tehom)

Appendix – application to physical systems

1ns, 2ns, 3ns applies to particles & to systems, or to particles as triadic systems, and to systems of systems or meta-systems

As isolated quanta variously rest & interact, isolated systems variously rest & interact, formatively (1ns – entropic), trans-formatively (3ns – telic) & in-formatively (2ns – equilibric).

1ns or the virtual or intrinsic characteristics of an energy system = system energies’ “forming” = system energies’ intrinsic spontaneous changes of placement and/or of time = spatio-temporal waveform-ing or self-visualization or self-potentialities; approaching & realizing massless energy

2ns or the actual or characteristics of an energy system = system energies “resting” or existing or being or instant-aneously at an “instant” in time & place in space or materio-energetic characteristics (efficient/material) or self-actualization or self-actualities of authenticity of Here I Am, Lord or nonstrict identity; approaching nonenergetic mass but there is no energyless mass (asymmetry there, converse or transitivity not in play as energy is THE fundamental)

3ns or the real or extrinsic characteristics of an energy system = system energies “interacting” or “trans-forming” or be-coming or system energies’ extrinsic con-temp-oraneous changes of placement and/or of time or relating or the invitatory-participatory or spatio-temporal characteristics (formal/final) or “hold on, I’m coming!” or “I be coming!) as the I = true self or self-real-ization or self-realities of sustained authenticity of “I will go, Lord” or ultimate eternalization; approaching unique or designated mass-energy specifications

energy system = wave-particles
isolated, resting together, interacting

massless/massive particles

1ns isolated = no signal, only carrier or baseband-ing or pure potentiality or epistemically unmanifest &/or ontically isolated; approaching massless energy (e.g photon) – no frame in which an isolated photon has mass, i.e. no rest mass & no rest energy

2ns resting = signal or decoding or demodulation or epistemically manifest & ontically actual or acting/efficacious or approaching nonenergetic mass (e.g. rest mass or invariant mass) — all relative to an observer

3ns interacting = signal + noise or disturbance or modulation, or codes & errors, encoding or epistemic-ontic omelet of in/determinacy; eternalized as near-pure act or quasi- actus purus vis a vis approaching unique or designated materio-energetic specifications (e.g. )

3 thoughts on “Gödel & the End of Physics and Abelard et al & the End of Trinitology

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