On The Triune Problem of Indexicals
Indexicals, Omniscience, and the Triune Mind
Introduction
In the age-old battle between Muslim and Christian online Philosophy-Bros, there is one argument that resurfaces every couple of years. Recently, I’ve seen this issue addressed in different ways, but mainly in two that are most prominent, which I will discuss here. As for the issue, we will call it: “The Triune Problem of Essential Indexicals”. It isn’t new. Anyone versed in the philosophy of language literature will recognize it as a localized version of Patrick Grim’s argument found in his famous 1985 paper, “Against Omniscience: The Case from Essential Indexicals”.
The Dialectic
In the world of online apologetics, the dialectic follows a predictable and fruitless loop; the one bringing the objection will be called “the skeptic”. The following will be expressed in plain language and in formal logical notation, for those only interested in the plain language, the formal notation can be ignored:
To track exactly how this challenge is laid, we need to define our logical domain of discourse. Let us define our terms and symbols:
1. The Skeptic’s Opening
The skeptic steps up with a classic move, establishing a fundamental rule for what it means to share a single mind. If the Father and the Son share the same divine (omniscient) mind, then they must share the exact same knowledge.
Next, they introduce a basic fact about the Father: The Father knows the first-person proposition, “I am the Father”.
Then the big moment, the skeptic points out a fact about the Son, based in the epistemic rule that you cannot know a falsehood: The Son cannot know that same first-person statement for Himself, because for the Son, it is false. Therefore, the Son can not and does not know it.
2. The Apologists’ Overcorrection
The Christian apologist feels the trap closing in, and instead of questioning the setup of the argument, they attack basic grammar. Arguing that the propositions are identical, that “I am the Father” means the exact same thing regardless if it’s the Father or the Son saying it.
And in doing so, they walk directly into the trap by accepting that the two propositions are identical (P4), they allow a substitution of identicals inside a knowledge operator.
The laws of logical substitution forces them to conclude that the Son lacks knowledge held by the Father:
Which immediately leads to the next conclusion: There is a truth that is not shared by both.
The apologist has just broken basic logic by trying to maintain that the same single proposition can be true and false at the same time, and the skeptic claims that they exposed a total collapse of the Trinity because their knowledge is divided:
The main worrying inference step is at P4; it relies on a “transparent” theory of belief contexts that many in philosophy has since thoroughly rejected. The issue here is rather simple; you probably heard of it in the Superman example:
P1. Lois knows Superman can fly.
P2. Superman is Clark Kent.
P3. Therefore, Lois knows Clark Kent can fly.
The conclusion does not follow, as we all know, Lois does not know that Superman is Clark Kent. The terms might refer to the same person, but Lois relates to that person under different cognitive guises. The apologist assumes that since two expressions refer to the same reality, they can be substituted inside a knowledge operator, but knowledge contexts are not transparent like ordinary identity contexts (i.e. X knows Y, Y = Z, therefore X knows Z). If this is already true for ordinary names like “Superman” and “Clark Kent,” then it is even clearer for indexicals like “I,” where the reference shifts depending on the speaker.
The Christian need not say φ = ψ. He only needs to say that both φ and ψ concern the same divine reality but under different hypostatic self-locations; we will explore this solution further after the next defense.
The Academic Retreat
I’ve come across a more sophisticated defender. We will call him “Defender 2”. They correctly look at the above and reject the first defender’s blunder. They know that changing the speaker changes the proposition.
They see the technical breakdown and recognize we are dealing with de se (Knowledge of oneself, from the inside, i.e. self-location) indexicals. But because they don’t know how to disconnect indexical propositions from underlying factual knowledge, they panic at the sight of the divided propositions, and their solution is a tactical retreat: to stop the final conclusion, we must go back to the very first premise and rewrite it. They argue that we must “filter” or “exclude” these first-person indexical propositions from divine omniscience altogether.
His version of P1: “If the Father and the Son have the same divine mind, then the Father and the Son share the same beliefs”.
He justifies this exclusion by arguing that it is not ad hoc because every monotheistic religion must make the exact same exception to avoid having God claim the identities of creatures (i.e., I’m Jeremy and I like Ice Cream). To explain how a single mind can have differing thoughts, he uses Alexander Pruss’s metaphysical model of a single undivided divine act operating through three distinct personal relations. In this framework, the single divine intellect is “filtered” through Paternity as “I am the Father” and Filiation as “I am the Son”. To preserve the system, they willingly shrink what God is allowed to know, and in doing so, unknowingly fall into the same trap they so desperately tried to avoid.
To see why Defender 2 also completely misreads the situation, we have to look closely at his first premise and the skeptic’s third premise: (The Son does not know the proposition “I am the Father”).
Does God believe anything?
The issue starts with the new P1, his switch from “Knowledge” to “Belief”. It seems to me that this is a category mistake that actually cements the skeptic’s argument. A belief is a mental representation of reality that lives inside an agent’s head. Creatures need these representations to bridge the gap between our consciousness and reality, given our limited minds. Our beliefs can be true, false, justified, or completely mistaken.
The divine mind has direct and unmediated access to all of reality. God exists purely in the fundamental state of Knowing. Belief is an epistemic tool for limited and error-prone creatures who have to fill in gaps of uncertainty. But an omniscient being does not have said gaps.
This is Classical Theism, which holds that divine intellection is not discursive. God does not move from premise to conclusion, and does not form representations in his mind that map to reality.
To say God “believes” is to say God thinks discursively and, in doing so, he has accidentally conceded to the skeptic that the Son’s personal relation actively blocks out the Father’s de se truths. If a de se truth is a concrete piece of data, and the Son’s relation is a filter that blocks it out, then there is a real fact about reality that the Son lacks. Conceding C2, C3, and anthropomorphizing God in the process.
The Solution
Since we are dealing with omniscient agents rather than fallible believers, we must not use the belief operator(Bx) but instead use knowledge (Kx). This is important because this distinction carries a crucial property that the belief operator lacks: factivity.
The skeptic frames P3 as a negative omission to make it sound like a void inside the Son’s intellect, but because knowledge is factive, an omniscient mind can only know things that are actually true.
The proposition “I am the Father”, when expressed by the Son, is false, and because knowledge is factive, it cannot be an object of knowledge. What omniscience would instead require is knowledge of the true proposition: “I am not the Father”, ¬ψ.
Since ψ is false for the Son, and being omniscient entails knowledge of every truth (while factivity excludes knowledge of falsehoods), it follows that the Son does not know ψ but instead its negation, ¬ψ, and so the skeptic’s claim can be restated in the positive as:
From
to
Plainly, the Son has perfect, positive knowledge of His own relational identity, His self-location.
And notice this isn’t the only positive knowledge where the skeptic claimed to find a void. The Son also fully affirms φ, the objective fact that the Father is the Father. But expressing it not as “I am the Father” but “He is the Father.” Therefore, there is no gap; the Son has exhaustive knowledge of what the Father is and exhaustive knowledge of what/who He is not. That is not a void, that is perfect, complete self-location.
The Symmetric Omniscience Check
If we run ¬ψ back through the original P1, using it to serve as the universal rule for a shared mind, the quantifier survives and we see that there is no missing data anywhere in God:
The Father knows the true fact that the Son is not the Father.
The Son knows the true fact that He Himself is not the Father:
But from here, one might ask, how is this not an ad hoc arbitrary patch? First, shifting the scope of negation is a classic diagnostic tool in logic. By forcing the skeptic to consider the internal negation Ks¬ψ, you catch them in a scope fallacy. This move shows that the external negation is merely the consequence of the Son possessing perfect internal knowledge of a negative fact.
Using a test for bivalent completeness, a law that states that every proposition is either true or false, and defines omniscience. If p is true, then an omniscient mind, by definition, would know p. If p is false, then ¬p is true, and an omniscient mind therefore knows ¬p. If there is ever a case where a mind doesn’t know p AND doesn’t know ¬p, only then can one truly say there is ignorance.
If a proposition is false, then by definition, an omniscient mind cannot know it, and with the law of bivalence, that mind must know its negation. There is no new rule being invented; we’ve just exposed that the skeptic is conflating the lack of a falsehood with a lack of omniscience.
The Verdict
The skeptic’s premise ¬Ksψ isn’t tracking a lack of omniscience in the Son; instead, it is merely stating a lack of falsehood. The Son doesn’t lack the knowledge that the Father is the Father; He simply lacks the personal identity of the Father. And knowing that you aren’t another person isn’t ignorance; it is the very definition of perfect self-location.
This closes the epistemic charge. But a smarter skeptic doesn’t need the Son to be missing a proposition, but, which to me seems like the real charge, they only need the Son to be a distinct center of first-person access. That move doesn’t depend on any gap in knowledge at all, which means it survives everything we’ve established up until this point. And to answer it, we need to look more carefully at what an indexical actually is.
The Indexical and the Inversion
The indexical “I” is not irreplaceable because it carries extra factual content, but because the thinker is oriented within the state of affairs.
This is what is called a de se or a self-locating belief.
As John Perry, in his 1979 paper on essential indexicals, showed, the skeptic’s argument assumes that utterances like “I am making a mess” are truths that only the one identified as the one making the mess can know, and therefore an omniscient God who cannot think the man’s first-person thought is missing a fact. But the indexical “I” does not make the proposition true. The state of affairs, the making of the mess, is what makes it true. The indexical merely locates the thinker within the state of affairs. It tells the mess maker which coordinate on the map they are; it adds no new facts to the map.
Applying this to God, an omniscient mind knows the state of affairs exhaustively. Who, where, when, why. What God does not have is the individual’s de se act, the first-person mental orientation that only comes with being the individual. And that is not a missing fact, but a missing identity.
So the Son doesn’t lack knowledge about the Father. The Son lacks being the Father.
Let’s suppose that the skeptic is careful; they could concede everything above, that no proposition is missing, and that the Son has 100% of the data. They could then press that the father engages in a reflexive act regarding his own fatherhood that the Son cannot perform. This is no longer an issue of a propositional gap. It’s an asymmetry in their cognitive lives, and wouldn’t a real asymmetry in cognitive acts mean two minds?
No, because the question is simply incoherent. The Father’s “I am the Father” act is not something the Son is blocked from performing as a kind of deficiency in his intellect or anywhere else. It is an act the Son cannot perform for the same reason any distinct person cannot perform another’s first-person act. That is not a limitation; it is, by definition, what first-person thought is. To demand that the Son perform the Father’s de se act is not asking for a stronger unity. It is asking for the Son to be the Father.
Comparing Analogies, the Symmetry Breaker
You might now be thinking, “Defender 2 said that de se perspectives are not considered within ‘knowledge’ held by an omniscient mind, but you are seemingly saying the same thing. So what’s the difference?”
Defender 2, I believe, had the correct instinct that the skeptic was doing something sketchy and was attempting to avoid it by reframing the whole syllogism. But the difference between his solution and mine is that I’m not saying God “believes” anything, nor am I treating de se perspectives as propositional content.
He invents a “relational filters” model to serve as a firewall, blocking the Son from accessing certain data the Father has. Whereas I’m using the Map/Coordinate model to show that the indexical “I” carries zero unique factual content and is just a linguistic pointer for self-location. The Son has 100% of the data. The analogy is natural once we notice that there are three distinct parts of reality being collapsed by all the previously mentioned parties.
The “Map”: the objective state of affairs, independent of perspective. The Father is the font of the Godhead, the Son is begotten of the Father, and the Spirit proceeds from the Father. These facts simply are: the Father saying “I am the Father” doesn’t constitute his Fatherhood.
The “Mind”: the exhaustive knowledge of the Map. The Persons have numerically identical knowledge. Every relational truth is held in one undivided act of knowing.
The “Coordinate”: The self-locating act by which a person orients themselves within the Map. This is the only level where Father and Son differ, and that difference is the relational distinction itself, expressed at the level of self-location.
Conclusion
“I’m the Father” is not a proposition on the Map (reality) to be known simpliciter by all three persons. Instead, it is the self-locating (Orientating) expression of the underlying truth, “The Father is the Father”. The Son not expressing it as the Father does is a perfect affirmation of His own self-location (Coordinate).
What the Son doesn’t have isn’t a fact; it’s an identity. The Son doesn’t lack knowledge about the Father, but He lacks being the Father. That is not a bug but a feature: the Father and Son are distinct by relation, identical in nature, and share one undivided act of knowing.
The skeptic thought he had found a hole in the Trinity; instead, he found the Trinity.