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| 8
October (Friday) 4:15 PM
Room 224 + ONLINE |
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Zalán
Gyenis
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Department of Logic,
Jagiellonian University,
Krakow
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The weak
interpolation property
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This talk centers around
a weak version of the Craig
interpolation property which
states that whenever an
implication is a logical
tautology, then in every model
there exists an interpolant
formula, that is, the interpolant
in Craig's interpolation may
depend on the model. We discuss
several examples, and show, in
particular, that the n-variable
fragment of first order logic has
the weak interpolation property.
The weak interpolation property of
an algebraizable logic can be
characterized by a weak form of
the superamalgamation property of
the class of algebras
corresponding to the logic, and
thus finite dimensional cylindric
set algebras enjoy this weak
superamalgamation. This is a joint
work with Zalán Molnár and Övge
Öztürk.
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| 15
October (Friday) 4:15 PM
Room 224 + ONLINE |
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Lászlo
E. Szabó
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Department
of Logic, Institute of
Philosophy
Eötvös Loránd University
Budapest
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| On the
basic premises of quantum
theory
LyX Document
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Within the framework
of a joint project with Márton
Gömöri and Zalán Gyenis, we have
proved a representation theorem,
according to which, everything
LyX Document
that can be described in empirical/operational
terms can be -- if we want --
represented in the Hilbert space
quantum mechanical formalism, no
matter whether the phenomena in
question belong to classical or
quantum physics. Namely, there
always exists:
(Q1) a suitable Hilbert space,
such that
(Q2) the outcomes of each
measurement can be represented
by a system of pairwise
orthogonal closed subspaces,
(Q3) the states of the system
can be represented by pure state
operators with suitable state
vectors, suitable density
operators, and
(Q4) the probabilities of the
measurement outcomes can be
reproduced by the usual trace
formula of quantum
mechanics.
(Q5) A measurement yields a
given outcome with probability 1
if and only if the state vector
of the system is contained in
the subspace representing the
outcome event in question.
Moreover, in the case of
real-valued physical quantities,
(Q6) each quantity, if we want,
can be associated with a
suitable self-adjoint operator,
such that
(Q7) the expectation value of
the quantity, in all states of
the system, can be reproduced by
the usual trace formula applied
to the associated self-adjoint
operator,
(Q8) each measurement result is
equal to one of the eigenvalues
of the operator, and
(Q9) the corresponding outcome
event is represented by the
eigenspace belonging to the
eigenvalue in question.
Beyond the
discussion of the baffling
conclusion that the basic
premises of quantum theory
seem to be analytic statements
-- they do not tell us
anything new about a physical
system beyond the fact that
the system can be described in
empirical/operational terms --
I would like to say a few
words about the style and the
main technical steps of the
proof itself.
LyX Document
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22
October (Friday) 4:15
PM Room 224 + ONLINE
Postponed!
-- as all classes are
cancelled in the Institute
of Philosophy for 20-22
October, due to the Rawls
conference
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Dániel
Kodaj
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Department of
General Philosophy,
Institute of
Philosophy
Eötvös Loránd
University Budapest
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Metaphysical
undecidability
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This paper
aims to adapt an
undecidability theorem from
computer science to
metaphysics, examining its
potential formal and
substantive message there.
Specifically, my goal is to
see how the Scott–Curry
theorem from lambda calculus
affects metaphysical realism.
Very roughly, the SCT entails
that no computer program that
is capable of
self-interpretation can
express nontrivial properties
of its own terms (such as
function identity). I will
argue that this result is
relevant in the context of
metaphysics too, and what it
says there is that either
properties are not abundant
(either fundamentally or
non-fundamentally) or there
are no semantic facts.
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