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Vol.:(0123456789)

Foundations of Physics (2021) 51:84

https://doi.org/10.1007/s10701-021-00488-z

1 3

A Note onBell’s Theorem Logical Consistency

JustoPastorLambare1 · RodneyFranco1

Received: 9 February 2021 / Accepted: 20 July 2021 / Published online: 31 July 2021

© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature

2021

Abstract

Counterfactual deﬁniteness is supposed to underlie the Bell theorem. An old con-

troversy exists among those who reject the theorem implications by rejecting coun-

terfactual deﬁniteness and those who claim that, since it is a direct consequence of

locality, it cannot be independently rejected. We propose a diﬀerent approach for

solving this contentious issue by realizing that counterfactual deﬁniteness is an

unnecessary and inconsistent assumption. Counterfactual deﬁniteness is not equiv-

alent to realism or determinism neither it follows from locality. It merely reduces

to an incongruent application of counterfactual reasoning. Being incompatible with

falsiﬁability, it constitutes an unjustiﬁed assumption that goes against the scientiﬁc

method rigor. Correct formulations of the Bell theorem’s bases show it is absent

either as a fundamental hypothesis or as a consequence of something else. Most

importantly, we present a coherent Bell inequality derivation carefully devised to

show explicitly and convincingly the absence of incompatible experiments or coun-

terfactual reasoning. Thus, even admitting that counterfactual deﬁniteness could

be a consistent assumption, the necessary conclusion is that it is irrelevant for the

inequality formulation and can be safely ignored when discussing Bell’s inequality

philosophical and physical implications.

Keywords Bell inequality· Counterfactual deﬁniteness· Falsiﬁability· Realism·

Locality

* Justo Pastor Lambare

jupalam@gmail.com

Rodney Franco

francorodney03@gmail.com

1 Facultad de Ciencias Exactas y Naturales, Ruta Mcal. J. F. Estigarribia, Km 11 Campus de la

UNA, SanLorenzo, Paraguay

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