Location






The seminar is held in hybrid format, in person (Room 224) and online by Zoom. Zoom Meeting link:

https://us02web.zoom.us/j/889933315?pwd=Q3U3V3VQdXpXckhJYWRrcWRiMUhhQT09



8 October (Friday) 4:15 PM  Room 224 + ONLINE
Zalán Gyenis
Department of Logic, Jagiellonian University, Krakow
 
The weak interpolation property
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.



15 October (Friday) 4:15 PM  Room 224 + ONLINE
Lászlo E. Szabó
Department of Logic, Institute of Philosophy
Eötvös Loránd University Budapest
 
On the basic premises of quantum theory LyX Document
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



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

New date: 12 November

Dániel Kodaj
Department of General Philosophy, Institute of Philosophy
Eötvös Loránd University Budapest
 
Metaphysical undecidability
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.