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The
seminar is held in hybrid
format, in person (Múzeum
krt. 4/i Room 224) and
online.
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| 1
December (Friday) 4:15 PM
Room 224 + ONLINE |
Márton
Gömöri*
Carl
Hoefer**
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* Department of Logic,
Institute of Philosophy
Eötvös University Budapest
Institute
of Philosophy, Research
Centre for the
Humanities, Budapest
**
Department of Philosophy,
University of Barcelona
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Classicality
and Bell's Theorem
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A widespread view among
physicists is that Bell’s
theorem rests on an implicit
assumption of “classicality,” in
addition to locality. According
to this understanding, the
violation of Bell’s inequalities
poses no challenge to locality,
but simply reinforces the fact
that quantum mechanics is not
classical. The paper provides a
critical analysis of this view.
First we characterize the notion
of classicality in probabilistic
terms. We argue that
classicality thus construed has
nothing to do with the validity
of classical physics, nor of
classical probability theory,
contrary to what many believe.
At the same time, we show that
the probabilistic notion of
classicality is not an
additional premise of Bell’s
theorem, but a mathematical
corollary of locality in
conjunction with the standard
auxiliary assumptions of Bell.
Accordingly, any theory that
claims to get around the
derivation of Bell’s
inequalities by giving up
classicality, in fact has to
give up one of those standard
assumptions. As an illustration
of this, we look at two recent
interpretations of quantum
mechanics, Reinhard Werner’s
operational quantum mechanics
and Robert Griffiths’ consistent
histories approach, that are
claimed to be local and
non-classical, and identify
which of the standard
assumptions of Bell’s theorem
each of them is forced to give
up. We claim that while in
operational quantum mechanics
the Common Cause Principle is
violated, the consistent
histories approach is
conspiratorial. Finally, we
relate these two options to the
idea of realism, a notion that
is also often identified as an
implicit assumption of Bell’s
theorem.
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Related paper:
M. Gömöri and C. Hoefer,
“Classicality and Bell's Theorem,”
European Journal for Philosophy of
Science 13, 45 (2023)
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| 8
December (Friday) 4:15 PM
Room 224 + ONLINE |
Valérie
Lynn Therrien
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Philosophy,
McGill University,
Montréal
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The
Evolution of Cantor's Proofs
of the Non-Denumerability of
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The
primary aim of this paper is to
track the evolution of Cantor's
proofs of the non-denumerability
of ℝ -- which culminates in the
famous diagonal argument and
Cantor's Theorem. Why did Cantor
revisit his proof three times? The
secondary aim of this paper is to
explore the heuristic role of
arrays in his proof of the
non-denumerability of ℝ. Why did
Cantor return to the infinite
array he had abandoned for his
first two versions of the proof? I
will conclude that Cantor likely
had the means to arrive at the
diagonal argument by 1878, but
that the ways in which he had been
using arrays up until then would
have involved arbitrarily
constructing an irrational number
simply by manipulating numbers as
if they were mere symbols. While
this may seem natural to us now,
this would not have been an
acceptable way to construct an
irrational number to his peers.
Cantor's lengthy absence from
public mathematics likely provided
him with the time required to
distill the essence of the
diagonal argument, and to produce
a proof that did not require the
construction of an irrational
number at all.
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