trascendentali

Trascedentali is a plural term used in Italian to refer to concepts in both philosophy and mathematics that are described as transcendent as opposed to merely empirical or algebraic. The exact sense depends on the field.

In philosophy, trascendentali (plural of trascendentale) denotes aspects of the Kantian program concerning the a priori conditions that make experience possible. The term is used to describe forms and principles that constrain how we perceive and think about objects, such as the a priori forms of sensibility (space and time) and the categories of the understanding. In Italian Kantian literature, trascendentale appears in expressions like estetica trascendentale (transcendental aesthetics) and logica trascendentale (transcendental logic). The concept is distinct from trascendente, which refers to what lies beyond possible experience, and from ordinary empirical inquiry.

In mathematics, trascendentali refers to transcendental numbers, i numeri trascendenti. A transcendental number is a real or complex number that is not a root of any nonzero polynomial equation with rational coefficients. This class contrasts with algebraic numbers, which are roots of such polynomials. Famous examples are π and e. The study of transcendental numbers shows that most real numbers are transcendental, and it includes results such as the Liouville construction of explicit transcendental numbers and the Lindemann–Weierstrass theorem, which implies the transcendence of numbers like e^π. The term also appears in discussions of transcendental functions and related topics, though the core idea remains the distinction from algebraic numbers.

Overall, trascendentali designates either Kantian a priori conditions that structure knowledge or mathematical numbers and concepts that lie outside algebraic roots, depending on the disciplinary context.