This study develops a Metaverse Set based on an uncountable infinity of special instances of Univ... more This study develops a Metaverse Set based on an uncountable infinity of special instances of Universal Sets of the type relevant to W. V. O. Quine's, "New Foundations for Mathematical Logic, (1937)" [9], and his revision, "Set Theory and its Logic, (1963)" [10], that are each constructed by a transposition of a pair of real numbers. This is done for the purpose of wrapping a Non-Ordinal generalization of set theory and mathematical objects to be considered as operationally determined symbolic objects [1], around Quine's NF Universal Set. This study presupposes the internal consistency of NF as a resolvable difficulty for its proponents subject to the difficulties of uncomputability and infinitesimals, and demonstrates that by assembling Quine's Universal Set as a Metaverse Set of inconsistent Universal Sets it is possible to create an Erroneous Set as a constrained dialethia [21, 22], that accounts for all false statements of identity. Such that by utilizing this Erroneous Set with an antithetical Not-Erroneous Set of all true statements of identity it is possible to prove the discreteness of convergence theorem based identities as was done for Naive Set Theory [7], in my article, "An Analysis of Paradox, A Context for Error, P. R. Fidler (2018)" [1]. Since the creation of a similar Erroneous Set is also possible for axiomatic set theories such as ZF and ZFC or NBG or Russell's variety of Type Set Theory [2, 3, 16, 17], this application of my dialectical approach adapted for NF resolves the problem of utilizing NF or NFU as well as TST+(Typical Abigiuty), that have a Universal Set [2, 9, 10, 11], for similar proofs of the discreteness of convergence theorem based identities.
This study requires familiarity with concepts from Predicate Calculus, Real and Complex Analysis ... more This study requires familiarity with concepts from Predicate Calculus, Real and Complex Analysis and provides an unusual analysis of convergence paradoxes. This analysis is based on a generalization beyond recursive ordinal assumptions regarding numbers. Numbers are considered as categorically discrete identity objects and contrasted with false identity statements that lack categorical discreteness. The analysis proceeds from a modified axiomatic system that may seem unexpected. But this modification provides an entirely new analytic branch from Real and Complex Analysis while at the same time demonstrating how it is possible to move back and forth and reconcile the new analytic branch with more traditional analysis.
This study develops a Metaverse Set based on an uncountable infinity of special instances of Univ... more This study develops a Metaverse Set based on an uncountable infinity of special instances of Universal Sets of the type relevant to W. V. O. Quine's, "New Foundations for Mathematical Logic, (1937)" [9], and his revision, "Set Theory and its Logic, (1963)" [10], that are each constructed by a transposition of a pair of real numbers. This is done for the purpose of wrapping a Non-Ordinal generalization of set theory and mathematical objects to be considered as operationally determined symbolic objects [1], around Quine's NF Universal Set. This study presupposes the internal consistency of NF as a resolvable difficulty for its proponents subject to the difficulties of uncomputability and infinitesimals, and demonstrates that by assembling Quine's Universal Set as a Metaverse Set of inconsistent Universal Sets it is possible to create an Erroneous Set as a constrained dialethia [21, 22], that accounts for all false statements of identity. Such that by utilizing this Erroneous Set with an antithetical Not-Erroneous Set of all true statements of identity it is possible to prove the discreteness of convergence theorem based identities as was done for Naive Set Theory [7], in my article, "An Analysis of Paradox, A Context for Error, P. R. Fidler (2018)" [1]. Since the creation of a similar Erroneous Set is also possible for axiomatic set theories such as ZF and ZFC or NBG or Russell's variety of Type Set Theory [2, 3, 16, 17], this application of my dialectical approach adapted for NF resolves the problem of utilizing NF or NFU as well as TST+(Typical Abigiuty), that have a Universal Set [2, 9, 10, 11], for similar proofs of the discreteness of convergence theorem based identities.
This study requires familiarity with concepts from Predicate Calculus, Real and Complex Analysis ... more This study requires familiarity with concepts from Predicate Calculus, Real and Complex Analysis and provides an unusual analysis of convergence paradoxes. This analysis is based on a generalization beyond recursive ordinal assumptions regarding numbers. Numbers are considered as categorically discrete identity objects and contrasted with false identity statements that lack categorical discreteness. The analysis proceeds from a modified axiomatic system that may seem unexpected. But this modification provides an entirely new analytic branch from Real and Complex Analysis while at the same time demonstrating how it is possible to move back and forth and reconcile the new analytic branch with more traditional analysis.
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Papers by Paul Fidler