The notion of process in nonstandard theory and in Whiteheadian metaphysics

Abstract

In this article I intend to show that certain aspects of A.N. Whitehead's philosophy of organism and especially his epochal theory of time, as mainly exposed in his well-known work Process and Reality, can serve in clarify the underlying assumptions that shape nonstandard mathematical theories as such and also as metatheories of quantum mechanics. Concerning the latter issue, I point to an already significant research on nonstandard versions of quantum mechanics; two of these approaches are chosen to be critically presented in relation to the scope of this work. The main point of the paper is that, insofar as we can refer a nonstandard mathematical entity to a kind of axiomatical formalization essentially 'codifying' an underlying mental process indescribable as such by analytic means, we can possibly apply certain principles of Whitehead's metaphysical scheme focused on the key notion of process which is generally conceived as the becoming of actual entities. This is done in the sense of a unifying approach to provide an interpretation of nonstandard mathematical theories as such and also, in their metatheoretical status, as a formalization of the empirical-experimental context of quantum mechanics.

El proceso analítico, considerando lo aritmomórfico, la aducción y la complejidad. La importancia de la investigación teórica en la ciencia económica: Reflexiones sobre la contribución de Georgescu-Roegen

“…Naturally, these moments must be at a finite distance; otherwise, we would not know all that has gone into the process or all that the process does.» (Georgescu-Roegen, 1970: 3) Véase: Georgescu-Roegen (1996: 120). Respecto a la noción de proceso planteada por Whitehead y la teoría no estándar, véase Livadas (2013) Se puede escoger la escala de tiempo, y expresar la duración del proceso que puede representarse por el intervalo temporal cerrado. [t 0 , t 1 ]…”