There are three main types of paradoxes:
- Cognitive paradoxes (paracosmies)
When the reasoning is flawless and the contradiction arises from bringing together two incompatible realities, we are dealing with a cognitive paradox, a paracosmie.
Example: the “bright night sky” (Olbers’ paradox), which contradicts the observation that the night sky is dark.
This kind of paradox has always flourished in the sciences; hence they are often called scientific paradoxes. - Logical fallacies (paralogies)
When the incompatible premises may be true, but the contradiction arises from a faulty or deceptive line of reasoning, we speak of a logical paradox, a paralogie.
Example: “Socrates is mortal; a horse is mortal; therefore Socrates is a horse.”
In reality, no demonstration has taken place; it is a logic fault.
A paralogie is thus an unintentional error, whereas a sophism is an intentional attempt to deceive. - Logical dilemmas or antinomies (paradoxies)
When both the premises and the reasoning are correct, yet no reasonable conclusion can be reached, one speaks of a paradoxy, a genuine logical dilemma or antinomy.
Examples: the Liar paradox (“This statement is false”), or the Barber paradox.
More precisely
The word paradox (from Greek para-doxa, “against opinion”) refers to a proposition or situation that appears contradictory but reveals, upon examination, a deeper logical or ontological structure.
A paradox often emerges from a tension between different levels of reality, or between discourse and what it refers to — as in the Liar paradox, where language refers to itself.
Paracosmies, paralogies, and paradoxies reveal, in differing degrees, the limits of discursive thought:
— paracosmies show the limits of scientific conceptualization in the face of reality;
— paralogies reveal the limits of logic confronted with itself;
— paradoxies show that a rational resolution may be impossible without a change of level.
From a metaphysical perspective, paradoxes signal that discursive reason cannot encompass the whole of reality, and that a higher intellectual (intuitive) act may be required.
The paradox then becomes a gateway into the intelligible, allowing access to a higher vision — not by suppressing the contradiction, but by transfiguring the viewpoint.
✅ For further reading
- Zeno of Elea, Paradoxes — On motion and the infinite.
- Aristotle, Metaphysics, IV — On the principle of non-contradiction.
- Kant, Critique of Pure Reason, Antinomies — On inevitable contradictions when reason oversteps its limits.
- Lewis Carroll, “What the Tortoise Said to Achilles” — On infinite logical regress.
- Bertrand Russell — Russell’s paradox, set theory.
- Wittgenstein, Tractatus ; Philosophical Investigations — On the limits of language.
- Bruno Bérard, La métaphysique du paradoxe ; vol. 1: Paradoxes et limites du savoir ; vol. 2: La connaissance paradoxale (Paris, L’Harmattan, 2019) — Systematic reflection on paradoxes, their types, their intellectual meaning, and their metaphysical surpassing.