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Titre

Three Logical Proofs of Ontological Agnosticism
From Aristotle to Propositional Logic

Phronetic essay, Published ; August 2025

Introduction

Ontological agnosticism rests on a simple idea:

If all knowledge is conceptual, and no concept is identical to the thing itself, then no knowledge can coincide with Being.

This idea can be formulated within several logical systems — from the oldest, Aristotelian logic, to Boolean logic, and up to modern propositional logic.

We will see that, no matter which logical language is used, the conclusion is always the same. This shows that ontological agnosticism is not merely an opinion, but a structural result.

I. Aristotelian Logic

Aristotelian logic uses categorical syllogisms — reasonings made up of two premises and a conclusion, arranged in strict forms.

Form used: Barbara (AAA-1)

• Major premise : All human knowledge is conceptual. (All K are C)
• Minor premise : No concept is identical to the thing. (No C is I)
• Conclusion :No human knowledge is identical to the thing. (No K is I)

Venn Diagram Visualization:

• Circle K (knowledge) entirely contained in circle C (conceptual).
• Circle I (identical to the thing) is disjoint from C.
• Result: K is necessarily disjoint from I.

II. Boolean Logic

Boolean logic expresses relationships through variables and truth values (True or False).

Let’s translate the statements:

• K: “Human knowledge”
• C: “Conceptual”
• R: “Represents reality as it is”

Formulas:

1. K ⇒ C — If something is human knowledge, then it is conceptual.
2. C ⇒ ¬R — If something is conceptual, then it is not identical to reality as it is.

K ⇒ ¬ R — If something is human knowledge, then it is not identical to reality.

K	C	R	P1 : K ⇒ C	P2 : C ⇒ ¬ R	Conclusion : K ⇒ ¬ R
V	V	F	V	V	V
V	V	V	V	F	F
F	V	F	V	V	V
F	F	F	V	V	V

→ In all rows where the premises are true, the conclusion is true.

III. Propositional Logic

Modern propositional logic allows a more general and abstract formulation.

Notations:

• K(x): “x is human knowledge”
• C(x): “x is conceptual”
• I(x): “x is identical to Being

Premises:

1. ∀x (K(x) → C(x))
2. ∀x (C(x) → ¬I(x))

Conclusion:

∀x (K(x) → ¬I(x))

Demonstration:

1. From (1), if 𝐾(𝑥) then 𝐶(𝑥).
2. From (2), if 𝐶(𝑥) then ¬𝐼(𝑥).
3. By transitivity of implication, if 𝐾(𝑥) then ¬𝐼(𝑥).
4. Therefore, the conclusion is logically necessary.

Conclusion

Whether we reason like Aristotle, use Boolean algebra, or adopt modern propositional logic, the result is identical: "If all human knowledge is conceptual, and if no concept is identical to the thing, then no human knowledge can coincide with Being."

This convergence shows that ontological agnosticism is not speculation, but a logical consequence independent of the formal language used. It is on this basis that infraphysics and phronetics propose not a system of knowledge, but a lucid attitude toward reality.

∀ x [ K(x) → Illus(x) ]

For all x: K(x) -> Illus(x)

Meaning: If something is human knowledge, then it is non-coincident with Being (therefore “illusory” in the ontological sense).

Minimal premises (click to view)

• ∀ x [ K(x) → C(x) ]
• ∀ x [ C(x) → ¬ I(x) ]
• ∀ x [ ¬ I(x) → Illus(x) ]

Chaining: K(x) → C(x) → ¬I(x) → Illus(x).

Postscript: This article is part of a larger project exploring the limits of conceptual thinking. See the home page.