transcendental

Etymology

noun

1. (obsolete) A transcendentalist.
2. (philosophy, metaphysics, Platonism, Christian theology, usually in the plural) Any one of the three transcendental properties of being: truth, beauty or goodness, which respectively are the ideals of science, art and religion and the principal subjects of the study of logic, aesthetics and ethics.
   In deference to Christian usage we can say that the transcendentals constitute the Logos within which everything has its being and according to which everything is made. 2002, Robert C. Neville, Religion in Late Modernity, State University of New York Press, page 72
   These predicates of Being are what the Medievals called, using a term that will have a fertile future, "transcendentals" (often called the "universals") because they transcend all particular genera, following the example of Being.⁹⁶ A quarrel over these transcendentals even shook the later Middle Ages. The quarrel stemmed from the question of whether the existence of these transcendentals was real or intellectual (also called nominal). 2012, Jean Grondin, translated by Lukas Soderstrom, Introduction to Metaphysics: From Parmenides to Levinas, Columbia University Press, page 105
   The medieval doctrine of the transcendentals is closely connected with a metaphysical conception of reality, but is there a science of being in William of Ockham (ca. 1285-1347)? 2012, Jan Aertsen, Medieval Philosophy as Transcendental Thought: From Philip the Chancellor (ca. 1225) to Francisco Suárez, BRILL, page 515
   Another fascinating thing about the transcendentals is that each is fully contained in the others. When you appreciate beauty, for example, you recognise the presence of goodness and truth. When you grasp the truth about something you experience a moment of beauty in, perhaps, the simplicity or power of the insight. When you observe goodness in the actions of another person you are seeing truth and beauty in operation. 2015, Anthony Howard, Humanise: Why Human-Centred Leadership is the Key to the 21st Century, Wiley, page 70

adj

1. (philosophy) Concerned with the a priori or intuitive basis of knowledge, independent of experience.
   The best way to demonstrate the possibility of something is to show its actuality, for actuality implies possibility. At least since Kant, transcendental philosophies have been on the scene. However, such simple demonstration of the possibility of transcendental philosophy has not been effective and is not likely to be so — so strong is the presumption that transcendental philosophy just could not be possible, or, if it was possible earlier, it is not possible now. 1985, J. N. Mohanty, The Possibility of Transcendental Philosophy, Kluwer Academic (Martinus Nijhoff), page xiii
   1999, Robert Stern, 4: On Kant's Response to Hume: The Second Analogy as Transcendental Argument, Robert Stern (editor), Transcendental Arguments: Problems and Prospects, 2003, Oxford University Press (Clarendon Press), Paperback, page 47, Whilst it was once held that transcendental arguments could provide a direct and straightforward refutation of scepticism, this view now seems over-optimistic.
   2007, Steven Crowell, Jeff Malpas, Chapter 1: Introduction Steven Crowell, Jeff Malpas, (editors), Transcendental Heidegger, Stanford University Press, page 1, Not only does Heidegger's early work stand within the framework of transcendental phenomenology as established by Husserl—even though it also contests and revises that framework—but that thinking also stands in a close relationship to the critical philosophy of Immanuel Kant, and specifically to the transcendental project, and modes of argument, of Kant's Critique of Pure Reason.
2. Superior; surpassing all others; extraordinary; transcendent.
3. Mystical or supernatural.
4. (algebra, number theory, field theory, of a number or an element of an extension field) Not algebraic (i.e., not the root of any polynomial that has positive degree and rational coefficients).
   The theory of transcendental numbers was originated by Liouville in his famous memoir^† of 1844 in which he obtained, for the first time, a class, très-étendue, as it was described in the title of the paper, of numbers that satisfy no algebraic equation with integer coefficients. 1975, Alan Baker, Transcendental Number Theory, 2nd edition, Cambridge University Press, published 1990, page 1
   If the distribution of decimal digits of π (or any other transcendental number) is truly random (suspected but not yet mathematically proven!), given any arbitrary finite sequence of whole numbers, that sequence would be included an infinite number of times in the decimal expansion of π. 2005, Juan G. Roederer, Information and Its Role in Nature, Springer, page 28
5. (algebra, field theory, of an extension field) That contains elements that are not algebraic.
   2006, Steven Roman, Field Theory, Springer, 2nd Edition, Graduate Texts in Mathematics 158, page 108, Suppose that F<E is purely transcendental. Show that any simple extension of F contained in E (but not equal to F) is transcendental over F.