The possibility of formulating the expression “square circle,” despite the impossibility of thinking or conceiving it, shows that words indeed possess a lexical meaning, yet cannot substitute for signifying intention.
More specifically
Such an expression belongs to the category of contradictory concepts, revealing the internal limits of language when it claims to represent what is intelligible. Logically speaking, “square circle” juxtaposes two incompatible definitions: a circle is a figure in which all points are equidistant from a center, whereas a square presupposes four straight sides and four right angles. The constitutive properties of one necessarily negate those of the other; no being can simultaneously fall under both definitions without contradiction.
The “square circle” thus highlights the distinction between signifying thought, subject to the principle of non-contradiction, and the mere verbal manipulation that freely combines terms without regard for the conditions of possibility of the object. Aristotle already insisted on this: any meaningful discourse must bear upon a being; otherwise it collapses into logical nullity. Formulating an absurd concept amounts to producing an empty syntactical structure that sounds like an assertion but designates nothing intelligible.
This example proves valuable in metaphysics and negative theology: it reminds us that language can overstep the limits of intellection, and that grammatical coherence does not guarantee reality. Similar pseudo-concepts include “non-existent reality” or “uncaused cause” when understood univocally. By contrast, symbolic or analogical thought may legitimately articulate opposing terms, provided they refer to distinct orders (e.g. God as “beyond being”).
The “square circle” thus becomes a methodological exercise: it helps to distinguish the thinkable from the merely sayable, reminding us that reality is thinkable according to principles, whereas language can feign what it cannot signify. Signifying intention, inseparable from intelligibility, regulates proper conceptual usage and ensures that discourse does not merely assemble words, but truly conveys knowledge.
Further reading:
– Aristotle, Metaphysics, Γ (principle of non-contradiction).
– Thomas Aquinas, De veritate, q.1.
– Leibniz, Discourse on Metaphysics.
– Bruno Bérard, Metaphysics for Everyone (Angelico Press), trad of Métaphysique pour tous (Paris, L’Harmattan, 2021); It. Sui sentieri della metafisica; Sp. ¿Qué es la metafísica?; De. Was ist Metaphysik?