## How Logical Foundation of Quantum Theory Derives from Foundational Anomalies in Pure Mathematics

**Authors:** Steve Faulkner

Logical foundation for quantum theory is considered. I claim that
quantum theory correctly represents Nature when mathematical physics embraces
and indeed features, logical anomalies inherent in pure mathematics.
This approach links undecidability in arithmetic with the logic of quantum
experiments. The undecidablity occupies an algebraic environment which is
the missing foundation for the 3-valued logic predicted by Hans Reichenbach,
shown by him to resolve `causal anomalies' of quantum mechanics, such as:
inconsistency between prepared and measured states, complementarity between
pairs of observables, and the EPR-paradox of action at a distance.
Arithmetic basic to mathematical physics, is presented formally as a logical
system consisting of axioms and propositions. Of special interest are all
propositions asserting the existence of particular numbers. All numbers satisfying
the axioms permeate the arithmetic indistinguishably, but these logically partition
into two distinct sets: numbers whose existence the axioms determine by proof,
and numbers whose existence axioms cannot determine, being neither provable
nor negatable.
Failure of mathematical physics to incorporate this logical distinction is seen
as reason for quantum theory being logically at odds with quantum experiments.
Nature is interpreted as having rules isomorphic to the abovementioned axioms
with these governing arithmetical combinations of necessary and possible values or
effects in experiments. Soundness and Completeness theorems from mathematical
logic emerge as profoundly fundamental principles for quantum theory, making
good intuitive sense of the subject.

**Comments:** 17 pages

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### Submission history

[v1] 13 Jan 2011

[v2] 25 Feb 2011

[v3] 26 Feb 2011

[v4] 18 Apr 2011

[v5] 20 Apr 2011

[v6] 13 May 2011

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