There are three main types of paradoxes:

  1. 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.
  2. 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.
  3. 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.