LIMIT. – Limit (Greek πέζα, Latin *terminus*, German *Grenze*) is defined by Aristotle as “the extreme point of a thing: that is, the first point beyond which there is nothing, and on this side of which there is all of it” (Met., V, 17, 1022 a 4–5; trans. by A. Carlini, Bari 1928, p. 174).
This notion therefore originally derives from extension, in which the surface, the line and the point are limits respectively of the volume, the surface and the line. Later, as Aristotle himself and St Thomas note in his commentary on the passage cited, the concept of limit is transferred to movement, action and time, as the point of departure and the point of arrival of these or of a determined part of them; and more generally still it is applied to any entity that is not infinite. In this sense the limit is nothing other than the negation of further perfection, and, according to the Thomistic thesis, it has its principle in the limiting power of act (St Thomas, *In V Met.*, lect. 19).
Aristotle also notes another sense of limit, namely “the essence, the quiddity of each thing: for this is the term of cognition; and if of cognition, also of the thing” (Met., loc. cit., 9–10); for, as St Thomas explains in the commentary cited, “knowledge of a thing begins from certain external signs by which one arrives at knowing the definition of the thing; and when this is reached, perfect knowledge of the thing is had.” By contrast, Kant calls a limit-concept (*Grenzbegriff*) the concept of the noumenon, inasmuch as it limits the objective validity of sensible intuition, thereby indicating that such knowledge cannot extend its domain to what the understanding thinks. Nevertheless, of the possibility of such a noumenon it is not possible to have a positive account, but only a problematic one, because we lack any possibility of intuition other than the sensible; and thus the territory beyond the sphere of phenomena for us is empty. “The concept of noumenon is therefore only a limit-concept to circumscribe the pretensions of sensibility and is therefore used purely negatively” (Critique of Pure Reason, *Analytic of Principles*, III; trans. by G. Gentile and G. Lombardo-Radice, I, Bari 1924, p. 251). A similar notion is also found in Lange, Riehl, Ardigò, Höffding and other positivists; while others, such as Paulsen, Max Wundt, Heidegger and Carabellese, attribute to the concept of noumenon also a more positive sense.