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.
Highlights
This work is an original attempt to provide some clues to a connection, on the interpretational level, between A.N
Epperson’s interpretation of quantum mechanics, this is characterized as a clear ontological principle, in the sense that “every fact is a determinant in the becoming of every new fact, such that the evolution of any fact entails both temporally prior facts and logically prior potentia as data, and an integration of these data that is unique to that evolution." (Epperson (2004), p. 120)
To the extent that the Whiteheadian process entails a metaphysical character inasmuch as it is associated with an actual entity as the outcome of a real concrescence of a multiplicity of potentia, otherwise indescribable but only in its outcome, it will be associated on the interpretational level with the underlying assumptions in axiomatizing the existence of nonstandard entities
Summary
This work is an original attempt to provide some clues to a connection, on the interpretational level, between A.N. 287), a major deficiency of the corresponding Whiteheadian approach, which initially led to a confusing notion of ‘point’ defined in terms of a theory of durations, may be found out in suspending the question of a subjectivity that underlies extensive connection, the latter being merely thought of as an objectified state of things In this respect, Whitehead admitted in his earlier works, The Principles of Natural Knowledge, Whitehead (2007a) and The Concept of Nature, Whitehead (2007b), to a certain inaptitude of the extensive abstraction method to define a ‘point’ without entering a theory of duration, whereas his ambiguous re-evaluation of the notion of point further in Process and Reality does not seem to much clarify things (Whitehead (1978), pp. In a formal-mathematical context, points in the sense of irreducible individuals of standard mathematical theories are associated with zero-level elements within a general cumulative structure (mainly by means of the Foundation Axiom of ZFC Theory), whereas in the version of non-standard theories by ultrapower construction they are associated with a definition of infinitesimals of various orders in which the infinitesimals of a given order appear to be atoms without inner structure to the immediately higher order until we unravel their own structure in a kind of Russian doll game and reveal a class of elements of a lower order playing provisionally the part of indecomposable atomspoints.
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