Common Objections to Logic Realism

The fifth in a series exploring how the laws of logic constrain physical reality

Logic Realism (the thesis that logical laws are ontological constraints on physical instantiation) generates predictable resistance. Here we address the most common objections, showing that each rests on misunderstandings of what the position actually claims.

“Logic Is Just Human Convention”

The Objection: Logic is a human invention, like language or mathematics. Different cultures could develop different logics. There’s nothing “out there” that corresponds to logical laws.

The Response: This objection confuses notation with constraint. Yes, the symbols “¬” and “∧” are conventional. The words “contradiction” and “identity” are human inventions. The impossibility of something being both A and not-A simultaneously is not conventional; it’s what makes any notation possible in the first place.

Could a culture develop a “logic” where contradictions are permitted? They could say they permit contradictions, but their actual practice would betray them. The moment they distinguish “this word” from “that word,” they’re relying on the law of identity. The moment they treat “yes” and “no” as different answers, they’re relying on non-contradiction.

The objection is self-undermining. To argue that logic is conventional, you must use logic. You must assume your words have stable meanings (identity), that your position differs from its negation (non-contradiction), and that your argument either succeeds or fails (excluded middle).

“What About Non-Classical Logics?”

The Objection: Intuitionistic logic rejects excluded middle. Paraconsistent logics tolerate contradictions. Quantum logic violates distribution. These prove that classical logic isn’t necessary.

The Response: This objection conflates different uses of the word “logic.” L₃ (the conjunction of Identity, Non-Contradiction, and Excluded Middle) functions at a different level than these variant systems.

Intuitionistic logic denies that we can assert “P or not-P” without proof. This is an epistemic restriction. Intuitionists still assume non-contradiction; they just have higher standards for assertion.

Paraconsistent logics explore what happens in formal systems when contradictions appear. These are tools for managing inconsistent databases or modeling belief revision. No paraconsistent logician claims you can build a physical system that is simultaneously red and not-red in the same respect.

Quantum logic describes the structure of quantum propositions, not a replacement for classical reasoning. The physicist using quantum logic still assumes their paper either is or isn’t on the desk.

None of these alternatives demonstrate that L₃ can be violated in physical instantiation. They’re all downstream of L₃.

“You Can’t Derive Physics from Pure Logic”

The Objection: Physics is empirical. You can’t deduce the structure of the universe from armchair reasoning. Any attempt to derive quantum mechanics from logic alone is rationalist overreach.

The Response: Logic Realism doesn’t claim to derive the specific values of physical constants, the existence of particular particles, or the contingent features of our universe. The claim is more modest: certain structural features of physics are constrained by the requirements of coherent instantiation.

Here’s the key distinction:

• Contingent: Which particles exist, their masses, the value of constants
• Necessary: That distinguishable states exist, that measurement produces definite outcomes, that probability governs irreversible transitions

The claim: if there is to be a physical world at all (if instantiation rather than merely representation), certain structural features follow. This recognizes that constraints on coherent instantiation have physical consequences.

Compare: we can’t derive the specific content of a book from the constraints of language, but we can recognize that any book must use discrete symbols with stable meanings. That’s recognizing transcendental constraints on the possibility of text.

“This Is Just Anthropomorphizing Reality”

The Objection: Saying reality “obeys” logic anthropomorphizes physics. Logic describes how humans reason, not how quarks behave. You’re projecting human cognitive structures onto the universe.

The Response: This objection gets the direction of dependence backwards. Logical constraints are conditions on the possibility of any coherent system, including human cognition.

If non-contradiction were merely a human quirk, we’d expect to find systems that violate it. We don’t. Every physical system ever observed respects identity, non-contradiction, and excluded middle. Incoherent systems cannot be instantiated.

The objection proves too much. If logic is anthropomorphization, so is physics: physics describes reality using human concepts, mathematics, and measurement procedures. The correct conclusion: human cognition has access to genuine constraints on reality.

“Quantum Mechanics Violates Classical Logic”

The Objection: Quantum superposition shows that a particle can be both spin-up and spin-down simultaneously. This violates non-contradiction. Therefore, physical reality doesn’t obey classical logic.

Crucially, measurement always yields definite outcomes. When you measure spin, you get “up” or “down”: never both, never neither. The Born Rule gives you probabilities, and the actual outcome is perfectly classical: either this or that, not both.

Superposition appears paradoxical only if you insist on describing quantum states using classical predicates. Quantum systems require a richer descriptive vocabulary than classical particles. The underlying logic remains classical, as evidenced by the fact that quantum mechanics is formulated in standard mathematics, which presupposes classical logic.

“You’re Committing the Epistemic Fallacy”

The Objection: Just because we can’t conceive of contradictions doesn’t mean they can’t exist. You’re confusing what we can know with what can be. Maybe reality is fundamentally illogical and our logical minds simply can’t access it.

The Response: This objection is self-defeating. To state that “reality might be illogical” is to make a claim, and claims presuppose logic. If reality were genuinely illogical, the statement “reality is illogical” would be neither true nor false (violating excluded middle), would be identical to its negation (violating non-contradiction), and wouldn’t refer to any definite state of affairs (violating identity).

More fundamentally: “Illogical reality” is a pseudo-concept, words combined in grammatically correct form without any possible referent. Compare: “colorless green ideas sleep furiously” is grammatically valid but semantically null. “Reality that violates non-contradiction” has no content.

The objection asks us to consider the possibility that possibility itself might not apply. This is asking us to use logic to consider its own inapplicability: a performative contradiction.

“This Is Old-Fashioned Rationalism”

The Objection: We moved past rationalism with Hume and Kant. Science is empirical. Any attempt to establish necessary truths about physical reality is pre-critical metaphysics.

The Response: Hume showed that specific causal claims can’t be established a priori. Kant showed that pure reason has limits. Neither claimed that all structural constraints on physical reality are empirical.

Kant’s project was precisely to identify transcendental conditions on the possibility of experience: conditions that must obtain if experience is to be possible at all. Logic Realism is in this tradition. It identifies transcendental conditions on the possibility of physical instantiation.

Treating this as “old-fashioned rationalism” misunderstands the claim. We’re identifying constraints that any physical instantiation must satisfy. This is compatible with robust empiricism about the specific content of physics.

“It’s Not Falsifiable”

The Objection: If Logic Realism makes no falsifiable predictions, it’s not scientific. It’s metaphysics or philosophy, not physics.

The Response: Logic Realism does make claims that could in principle be falsified:

1. No physical system will ever violate non-contradiction. If we found a particle that was simultaneously present and absent at the same measurement, that would falsify the claim.

2. Quantum mechanical structure is not arbitrary. If we could construct a coherent physical theory that predicted interference without superposition, or measurement without state reduction, that would undermine the claim that these features follow from instantiation constraints.

3. The Born Rule is necessary, not contingent. If we found a physical system where probabilities followed a different rule (say, the cube of amplitudes rather than the square), that would falsify the derivation.

A deeper point: claims about the constraints on physical instantiation may be philosophical rather than physical, yet still true and important. The claim that science requires logic is itself a precondition for science.

“Why These Three Laws and Not Others?”

The Objection: You’ve picked Identity, Non-Contradiction, and Excluded Middle. But why these? There are infinitely many logical principles. The selection seems arbitrary.

The Response: These three aren’t arbitrarily selected from a menu of options. They’re the minimal conditions for distinguishability, the possibility of there being distinct things at all.

• Identity: Without A = A, nothing would be itself. There would be no “things” to distinguish.
• Non-Contradiction: Without the impossibility of A ∧ ¬A, nothing would differ from anything else. Everything would merge into everything.
• Excluded Middle: Without A ∨ ¬A, there would be no determinate boundaries. Things would neither be nor not-be various properties.

Together, these three constitute the possibility of plurality. Any world with multiple distinct entities necessarily satisfies L₃. And since our world has multiple distinct entities, L₃ obtains.

Other logical principles (modus ponens, transitivity, etc.) are important but derivative. They follow from L₃ given the structure of implication. The trinity of identity, non-contradiction, and excluded middle is foundational in a way other principles are not.

The Core Insight

Most objections to Logic Realism share a common structure: they try to use logic to argue against the necessity of logic. This is self-defeating. The very act of arguing (distinguishing positions, ruling out alternatives, drawing conclusions) presupposes that L₃ obtains.

You can’t argue your way out of the conditions that make argument possible.

Logic Realism is the recognition that certain constraints cannot be contested without presupposing them. The question is whether to acknowledge what we’re already committed to.

This concludes our five-part series on Logic Realism. For the technical details and formal derivations, see the Papers section.