How Does Reality Get Botstrapped?

If we take the Mathematical Universe Hypothesis (or any form of logical monism) seriously—that reality just is a formal system—then Tarski's theorem becomes not just a linguistic curiosity, but an ontological crisis. You are correct: it generates a metaphysical bootstrap problem.

Let me trace the logic of your concern carefully, because it exposes a fork in the road that forces us to abandon at least one of three intuitions:

  1. Reality is a complete formal system (complete in the sense of being fully describable by mathematics)
  2. Truth is definable/accessible within reality (semantic closure)
  3. There is no infinite regress of realities (ontological foundationalism)

Tarski forces us to pick two.

The Crisis of the Mathematical Universe

If reality = a formal system $S$, then: – By Tarski, the predicate $True^S$ (truth-in-reality) cannot be defined in $S$ – Therefore $True^S$ must exist in a meta-system $S^1$ – But if $S^1$ is also “real” (part of existence), then reality = $S \cup S^1$ – Now we need $True^{S \cup S^1}$ defined in $S^2$... – Result: Either infinite ontological regress, or reality is not semantically closed

This is exactly the dilemma you identify. If reality tries to “know itself” completely, it explodes into an infinite tower of meta-realities, never reaching a ground floor. Reality cannot bootstrap its own semantics.

Possible Escapes from the Regress

1. Reality is not a formal system (Reject premise 1)

Perhaps reality is not a syntactic structure but a semantic field. The physicist Lee Smolin argues that the universe is not a mathematical object but a process—history fundamentally real, timeless mathematical structures derivative.

On this view, truth is not a predicate to be defined but a primitive feature of how situations disclose themselves. Reality doesn't need a definition of truth because it is not a language—it is the referent, not the syntax.

2. Truth is transcendental (Reject premise 2)

Kant's solution: Truth is not “in” reality as an object, but is the condition of possibility for any reality to appear to a knower. The “metalanguage” isn't another reality—it's the transcendental structure of cognition (or in modern terms, the observer).

The infinite regress stops because the meta-level is not ontological but epistemological. We don't need Reality+1 to define truth for Reality; we need a subject who stands in a relation to Reality. Truth emerges in the gap between knower and known, not in infinite nesting.

3. The “Strange Loop” (Reject premise 3 in a specific way)

Some philosophers (Graham Priest, Douglas Hofstadter) embrace a non-well-founded reality where the hierarchy collapses into a loop. The metalanguage is “inside” the object language through self-reference.

Tarski's theorem assumes classical logic. In paraconsistent or dialetheist frameworks, we can define a truth predicate that includes its own negation (the Liar is both true and false), avoiding the regress by accepting local contradiction. Reality bootstraps itself by tolerating the glitches where self-reference occurs.

4. Truth as Indexical/Operational (Dissolve the problem)

Wittgenstein and pragmatists suggest that “truth” is not a substantial property to be defined but a speech-act marker (“I confirm this”) or a success condition (it works).

If reality is a formal system, then “truth” is not a predicate within that system but the relation between the system and us. We are the “metalanguage.” The infinite regress only appears if we imagine reality existing without observers. But if reality necessarily includes observers (a participatory universe), then the bootstrap happens at the boundary between system and subsystem—we are the strange loop that closes the hierarchy.

The Bootstrap Problem

You ask: How does reality get bootstrapped?

If we insist on both (1) and (3)—that reality is a formal system and there is no infinite regress—then we must accept that reality cannot contain a complete semantics of itself. It can exist, it can compute, it can evolve, but it cannot say what is true about itself in a complete way.

This suggests a division: – Ontology: What exists (the formal system) – Semantics: What is true about what exists (requires an external frame)

Perhaps reality “bootstraps” not by containing its own truth, but by producing subsystems (like us) that function as local metalanguages. We are the fragment of reality that evolved to represent other fragments. The “infinite regress” is cut off by the fact that we are inside the system we describe—we use the same reality to talk about reality, creating a virtuous (if logically incomplete) circle.

The Deepest Cut

Your intuition points to something profound: If reality is purely mathematical/formal, then meaning and truth are impossible within it. This is essentially the argument that a universe of pure structure cannot account for intentionality or semantics (the “symbol grounding problem” applied to cosmology).

The implication might be that reality must contain something more than formal structure—perhaps qualia, intentionality, or primitive reference—that allows truth to anchor without infinite regress. Or, more radically: Reality is the model, not the language. Truth is always defined externally because truth is the relationship between reality and something else (a representation, a mind, a measurement).

Tarski's theorem, applied to metaphysics, suggests that reality cannot be both complete and self-transparent. It can be vast, consistent, and lawful—but to know it as true, something must stand outside it, even if that “outside” is just us, looking back at the water from within the fishbowl.