Omnipotent gods cannot be asserted by minds bound by sense data
Below is the result of a writing project I have been doing for nearly 4 years now, here and offline.
Three results are established in sequence.
D: For any classically transcendent agent G, no natural-order signal carries mutual information about G's causal identity: I(V₁;V₂) = 0 necessarily, across all accessible worlds.
F: No W-mind (a mind bounded by sense data) is assertorically entitled to assert any proposition whose truth conditions require identifying G's causal contribution: ¬Asrt(p_G).
E: The propositions so barred are not merely unassertible but truth-apt-defective for W-minds: ¬TA(p_G).
##Definitions##
G. The proposed transcendent causal agent. Variable α ranges over all agents proposed as causes of religious experience-type events R(x).
W. The class of worlds accessible to sense-data-bounded minds (W-minds). W is our modal working space for the thesis. Result D's □ quantifies over all possible worlds; the rest of the chain operates within W.
V₁(α, w). The natural-order phenomenological signal associated with α-attributed events in world w, the measurable, instrument-accessible causal output.
V₂(α, w). The agent-identity variable: whether α is the actual cause of V₁ in w.
I(V₁;V₂). Shannon mutual information between V₁ and V₂. Equals zero iff V₁ is statistically independent of V₂ — i.e., V₁ carries no discriminating information about V₂.
I₀(α). ∀w₁ w₂ ∈ W: V₁(α, w₁) = V₁(α, w₂). The natural-order signal is world-invariant with respect to α's causal presence.
D(α). α-attributed events possess discriminating power: the V₁ signal carries differential information about α's causal identity. Formally: I(V₁(α); V₂(α)) > 0.
S(x). Proposition x is truth-apt for W-minds: it has modal structure sufficient for evaluation within W.
Asrt(a, p, w). Agent a is assertorically entitled to assert p in world w under Brandom's inferentialist norms.
TA(p). Proposition p is truth-apt for W-minds in the stronger semantic sense: it is capable of bearing a truth value relative to states of affairs accessible within W.
T(G). Proposition p carries a truth-maker whose verification or falsification requires identifying G's causal contribution to a natural-order state.
Ref(p, G). Proposition p refers to G as its causal agent — G is the semantic referent of the agent-causal component of p.
□ₙ (causal-metaphysical necessity). The modal operator governing Layer 0. Source: the essential nature of the transcendent agent G. Accessibility structure: S5 (every possible world accessible from every other). Primary content: □ₙ InfoZero(G). Inclusion: Acc_s ⊆ Acc_n ⊆ Acc_c.
□ₙ (normative necessity). The modal operator governing Layer 1. Source: InfoZero(G) — the total absence of discriminating information — operating at the normative level. The □ₙ does not derive from an independent argument about assertion norms; it derives from the same source as □ₙ. I(V₁;V₂) = 0 means there is no informational input at all: no normative framework can generate assertoric entitlement from nothing. The prohibition is the causal result expressed at the normative level. Accessibility structure: S5. Primary content: □ₙ ¬Asrt(p_G).
□ₛ𝕌 (semantic necessity, W-indexed). The modal operator governing Layer 2. Source: the Dummettian manifestation requirement, indexed to cognitive type W (sense-bounded minds).
Accessibility structure: S4 (reflexive, transitive; indexed to worlds reachable by W-mind cognition; symmetry not claimed). Primary content: □ₛ𝕌 ¬TA(p_G).
Modal force is non-decreasing across the chain: Acc_s ⊆ Acc_n ⊆ Acc_c ensures no weakening at each modelling transition. As such, the notation below will just be dealing with necessity without these transitions, as the transition is not material to the effectiveness of the argument.
#Result D:#
>Premise 1 — Identity of Phenomenology: □∀α: (V₁(α) = V₁(α)). Grounded in the Law of Identity. The phenomenological character of α-attributed experiences is exactly itself and nothing more.
>Premise 2 — Information Exclusion: □∀α: ¬I(V₁(α), V₂(α)) . For any α defined as causally transcendent, no natural-order instrument can discriminate α -caused from internally-caused states, because a transcendent agent’s causal activity is defined as leaving no natural-order signature detectable by any instrument operating within that order (Thomas Aquinas, Summa Theologica, I, Q. 105, Art. 5 ; Placher 1996 ; Saunders 2002 ). The □ derives from the concept of transcendence: in any possible world where α is defined as transcendent, α’s causal identity is necessarily beyond the reach of the phenomenological component of the states α is claimed to cause. This □ is not grounded in A=A: if the agent is truly "other" or “transcendent,” its "causal joint" (Saunders) must be indistinguishable from natural noise. Agents cannot, even in theory, discriminate between a "G caused X" and a "G not caused X" as the causal chain terminates on the border of the natural order, and any link on that chain is definitionally indistinguishable from the natural order itself.
>Premise 3 — Definition of Discriminating Power: □∀α: (D(α) → I(V₁(α), V₂(α))). Definitional: for α -attributed experiences to possess discriminating power, their phenomenological component must contain information identifying α as the cause. Necessarily true as a definition across all possible worlds.
>Step 4: □∀α: (¬I(V₁(α), V₂(α)) → ¬D(α)). By TRP on Premise 3.
>Step 5: □∀α ¬I(V₁(α), V₂(α)) → □∀α ¬D(α). By K-axiom.
>Step 6: □∀α ¬D(α). By MP on Premise 2 and Step 5.
Necessarily, no proposed transcendent causal agent α is such that experiences attributed to α possess discriminating power regarding α’s causal identity.
>Step 7: □¬D(G). By UI on Step 6, instantiating α = G.
Necessarily, R(x)-type (internal mental states) experiences attributed to the Christian god G do not possess discriminating power regarding G’s causal identity. This is the conclusion the thesis requires for the specific case.
(For additional discussion on why this result obtains for all sense-bound minds: https://plato.stanford.edu/entries/davidson/#ThreVariKnow)
>Identifying the content of attitudes is a matter of identifying the objects of those attitudes, and, in the most basic cases, the objects of attitudes are identical with the causes of those same attitudes (as the cause of my belief that there is a bird outside my window is the bird outside my window). Identifying beliefs involves a process analogous to that of ‘triangulation’ (as employed in topographical surveying and in the fixing of location) whereby the position of an object (or some location or topographical feature) is determined by taking a line from each of two already known locations to the object in question – the intersection of the lines fixes the position of the object (this idea first appears in ‘Rational Animals [1982]). Similarly, the objects of propositional attitudes are fixed by looking to find objects that are the common causes, and so the common objects, of the attitudes of two or more speakers who can observe and respond to one another’s behaviour. In ‘Three Varieties of Knowledge’, Davidson develops the idea of triangulation as a means to elaborate the three-way conceptual interdependence that he argues obtains between knowledge of oneself, knowledge of others and knowledge of the world. Just as knowledge of language cannot be separated from our more general knowledge of the world, so Davidson argues that knowledge of oneself, knowledge of other persons and knowledge of a common, ‘objective’ world form an interdependent set of concepts no one of which is possible in the absence of the others.
>The idea of triangulation has important implications that go far beyond questions of knowledge alone, and the idea is one of the most important and enduring, but also controversial elements in Davidson’s later thinking (see Myers and Verheggen, 2016). Moreover, although the idea may appear at first sight to be intended purely as a metaphor, the structure of triangulation seems actually to direct attention to the way in which knowledge, action, and content are fundamentally dependent on the genuinely embodied and located character of speakers and agents. As Davidson presents matters, it is only through their concrete engagement in the world, in relation both to objects and to other speakers or agents, that a putative speaker or agent can be capable of genuine speaking or agency; only then can they speak, act, or think.
##Layer 0 - Shannon Mutual Information Model##
Transcendence (Df): (From D) G is causally prior to and constitutively exterior to the natural causal order. G's causal contribution to any natural-order event e is constitutively indistinguishable, by any instrument operating within the natural causal order, from e occurring without G's contribution.
From the Transcendence Definition: P(e | G-caused) = P(e | ¬G-caused) for all natural-order events e in all accessible worlds. Shannon mutual information I(V₁;V₂) = H(V₁) − H(V₁|V₂). Since P(V₁ | V₂ = G-caused) = P(V₁ | V₂ = ¬G-caused), conditioning on V₂ does not reduce uncertainty about V₁.
Therefore H(V₁|V₂) = H(V₁), and I(V₁;V₂) = 0.
Theorem (I₀) [Modal type C]: □∀α[Transcendent(α) → I₀(α)].
It is causally necessary that, given the definition of transcendence of agent alpha, any phenomenology in a W-mind of that agent acting carries exactly 0 bits of discriminating information concerning that agent's causal identity.
##Layer 1, Route 1 — Sellars: No Valid Language-Entry Transition##
Wilfrid Sellars distinguished the empirical Space of Causes from the Space of Reasons (Sellars, Empiricism and the Philosophy of Mind). Entry into the Space of Reasons (the normative space where claims can be made, inferred, and contested) requires a causal event that carries discriminating information about the relevant classification.
The Entry Requirement
Sellars Entry (Sel): For any classification C to be licensed by a causal trigger τ, τ must carry I(τ; C) > 0. In other words, the trigger must reduce uncertainty (Shannon information entropy) about whether C obtains.
Where I(τ; C) = 0, the trigger is causally present but informationally inert with respect to the classification. It cannot license a normative move, not because the move is poorly evidenced, but because the move has no informational ground at the pre-semantic level. The Space of Reasons definitionally cannot "touch" or "be bumped by" the Space of Causes. This result is reached by the definition of information: I is that which reduces uncertainty about a claim's relationship in the Space of Reasons to a referent in the Space of Causes. If I=0, no such reduction can occur in any possible world.
Application to G
From I₀(G): I(V₁(G); V₂(G)) = 0. Therefore, by Sellars: the V₁ signal does not carry information sufficient to license the language-entry transition for any classification of the form "G caused this." The move into the Space of Reasons (which would be the precondition for any subsequent assertoric claim about G) is blocked at the causal level.
This is a pre-semantic result, before the brain even conceives of the linguistic model to represent G in the space of reason. The objection that God's recognition-transcendence is a well-understood theological concept arrives too late: the recognition-transcendence objection is already in the Space of Reasons. Sel establishes that G's causal signature is insufficient to trigger entry into that space in the first place. The objection presupposes what I₀(G) positively denies.
The Constitutive Force of the Sellars Condition
The transition from Layer 0 (□ₙ) to Layer 1 (□ₙ) does not require an independent argument about the constitutive structure of assertoric practice. It requires only the result already established: I(V₁;V₂) = 0. This is not a low information threshold that better norms might clear, it is a total absence.
H(V₂|V₁) = H(V₂): knowing V₁ at all, any observation, any number of them, any quality of instrument, reduces uncertainty about V₂ by exactly zero bits. The □c therefore rides on the □n. It does not derive from what assertion norms require; it derives from what 'nothing' (I=0) provides the reasoner in the space of reasons. The only available choices for the observer are attempts to restore informational footing. Each fails for the same reason: they do not establish information where I = 0; they either confirm the absence or relocate it.
Any attempt to restore assertoric entitlement must supply an informational footing where there is none. Reference, even on the most robust non-verificationist account (Kripke, Putnam), requires some causal-historical grounding: names and natural-kind terms refer in virtue of causal chains connecting uses to the entity named. An entity that constitutively leaves no causal signature in the natural order provides no 'hook' for any causal theory of reference, and no alternative route produces information that was not there. Three choices are available:
(a) Deny the causal theory of reference. Fall back to descriptive theories: “God” refers in virtue of satisfying certain descriptions. But the descriptions constitutive of classical theism (pure actuality, impassibility, modal transcendence) are precisely what generate I₀(G). The descriptive route relocates the information problem; it does not supply information, and the lack of information is the result that must be changed for the discriminating power to be reestablished.
(b) Maintain that divine action leaves a causal signature W-minds cannot detect. This is not a distinct position, it is a restatement of I₀(G). “Leaves a signature W-minds cannot detect” and “leaves no signature detectable by W-minds” are informationally identical: I(V₁;V₂) = 0 in both cases. The position does not contest the premise; it confirms it.
(c) Accept that G-reference is ungrounded but insist truth-aptness is unaffected. Some normative frameworks may lower the threshold for assertion. But no normative theory of meaning framework generates entitlement from I = 0, because this is not a threshold question. A framework that licenses assertion where there is zero informational contact with the referent is not a lower-threshold account of assertion; it is the abandonment of the referential relationship, and denies reasoning itself, because without the ability of social scorekeepers to evaluate the claim by interacting with the cause, no normative scorekeeper (Brandom, Dummett) could ever resolve the proposition in any way. The assertion would not be about G; it would be a noise event whose content relation to G is empty.
There is no epistemic 'gas' in any framework ('car') that allows any normative system to do any work at all.
All three choices confirm the same absence. The □c therefore has the same source as the □ₙ: I(V₁;V₂) = 0.
#Theorem (F3 via Sellars): I₀(G) ∧ Sel → ¬Asrt(p_G) for any W-mind#
For any W-mind, it is normatively necessary that since the Sellars Language Boundary condition is not met, W-minds lack entitlement to assert G or -G in the Space of Reasons, even if G is causally present in the Space of Causes, as there is definitionally 0 mutual information between those 2 spaces.
##Layer 1, Route 2: The TAAC Interaction Horn:##
Ax1 (Information Threshold). Valid assertion requires that the asserter's epistemic access to the referent carry I > 0. Formally: Asrt(a, p, w) → I(V₁(a, referent(p)), V₂(referent(p))) > 0.
Grounded in Shannon Layer 0: where I = 0, no finite sequence of observations reduces uncertainty about the referent.
Ax2 (Pragmatic Constraint). Valid assertion requires that the asserter be able to discriminate the referent from relevant alternatives. Formally: Asrt(a, p, w) → D(referent(p)) for agent a in world w. Grounded in Sellars Layer 1: the language-entry transition requires a discriminating causal trigger.
Note: Ax1 and Ax2 are independently grounded in Layers 0 and 1 respectively. They are not ad hoc constraints on assertion. Ax2 is the Sellarsian articulation of a condition that any account of genuine assertion practice must respect: assertion is not merely the production of a sound correlated with a belief, but a normative move that stakes a claim and undertakes a commitment trackable within the Space of Reasons.
Suppose one wanted to object, as Plantiga does, that the human brain can have a transcendent-detection faculty, a "sensus divinitatis". This would, he claims, provide discriminating information about G (V2) to the physical phenomenology (V1).
For any transcendent faculty F proposed as a mechanism by which a W-mind receives G-content:
Horn 1: F causally interacts with the W-mind's physical brain → F leaves a V₁ receipt → by Ax3 (Causal Closure), F is a natural-order causal event → F is not transcendent. Contradiction.
G is a natural-order causal force (I(V1;V2) --> I(V1;0)=0, regardless of V1's magnitude). To the agent, then, this G is indistinguishable from a natural order object with incoherent predicates: G is both natural and not natural, and contradicitons are taken as meaningless in all semantic understanding of meaning and truth.
Horn 2: F does not causally interact with the W-mind's brain → F makes no causal difference to the W-mind's cognitive states → the assertion is generated by natural-order processes alone → ¬Asrt(a, p_G, w). As any assertion in Horn 2 is barred from the space of reasons.
Both horns yield ¬Asrt(p_G). The dilemma is not merely epistemological. Horn 1 naturalizes G: G becomes a detectable natural-order cause, and the classical theistic apparatus (aseity, incomprehensibility, worship-worthiness) dissolves. This arbitrary G is now subject to full Humean analysis. Horn 2 confirms that the assertion is a noise event in the natural causal order, not a valid inference in the Space of Reasons.
Theorem F3 (Pragmatic Foreclosure) [Register N]: □∀x[Ref(p, G) ∧ T(G) ∧ W-mind(a) → ¬Asrt(a, p, w)].
##Result E — ¬TA(p_G): The Semantic Void##
E3 is a downstream consequence of F3. It moves from the normative/pragmatic level (assertion norms) to the semantic level (truth-aptness conditions). It requires one additional axiom (Ax4) which is defensible but contested.
Ax4 — The Semantic Bridge
Ax4 (Semantic Bridge). □(¬D(α)) → □(¬◊true(x) ∧ ¬◊false(x)) for any x with Ref(x, α) and T(α).
Where discriminating power is necessarily absent, no W-mind can be in a position to recognize what would count as verification or falsification of x. The proposition lacks the modal structure that truth-aptness requires for W-minds.
Ax4 is Dummett's manifestation thesis applied to the W-restricted modal frame. It is not a verificationism revival: it does not say propositions must be verified to be meaningful. It says that meaning requires a manifestable capacity to recognize what would count as verification or falsification (the claim must be able to be true or false in order to be a proposition), and that where this capacity is constitutively absent, the proposition fails the semantic preconditions for truth-aptness within the relevant practice.
The □ₙ → □ₛ𝕌 transition. The same information absence drives the semantic result. Truth conditions require informational content to track. I(V₁;V₂) = 0 means there is no content for truth conditions to attach to. The Dummett bridge (Ax4) is not doing independent work, it is the semantic-level expression of the same total absence that drives F3. The semantic void is not a consequence of verification conditions being unsatisfied; it is a consequence of there being no informational basis on which propositional content could be grounded in the first place. The □ₛ𝕌 of ¬TA(p_G) is S4 rather than S5 because it is indexed to W-minds, not because the necessity is weaker.
#E3 Stated#
Theorem E3 (Semantic Void) [Register S, W-indexed]: □∀x[Ref(p, G) ∧ T(G) ∧ W-mind(a) → ¬TA(p)].
Derivation: By F3, ¬Asrt(a, p_G, w) for all W-minds a and accessible worlds w.
By Ax4: □¬D(G) [from Result D] → □(¬◊true(p_G) ∧ ¬◊false(p_G)) for W-minds.
Therefore p_G is not truth-apt for W-minds — not merely unverified, not merely uncertain, not merely beyond current evidence, but lacking the modal structure that truth-aptness requires within the W-restricted frame.
E3 is the strongest result in the chain. It forecloses not only assertion but propositional status. The claim is not false. Not true. Not undetermined. It lacks the modal structure that propositional content requires for minds of our kind.
The Terminal Equation
I(V₁;V₂) = 0 → ¬Asrt(p_G) → ¬TA(p_G) □
The conclusion is not that classical theism is false. Falsity requires propositional content that truth-aptness conditions can be applied to. The conclusion is that the proposition in question lacks the modal structure that truth-aptness requires for W-minds. The question of its truth or falsity does not arise for minds of our kind, not because we lack sufficient evidence, not because the claim is empirically unfalsifiable, but because the non-assertoric claim constitutively cannot make contact with reality in any way that W-minds can track.
The transcendent god shares a linguistic structure to one of my favorite sentences that highlight this problem:
Proposition: 7 is heavier than 2, True or False?