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| 11 October (Wednesday)
5:00 PM
Room 226 |
Péter Juhász* and Gergely Székely**
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*Institute of Philosophy, Eötvös University, Budapest
**Rényi Institute of Mathematics, Budapest
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On using iteration and fixpoint theorems for resolving causal paradoxes connected to time travel
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This talk is a revisited
version of a previous LaPoM presentation, focusing more on the
technical parts of the framework. We are going to discuss the topic in a
self-contained way, begin with the introduction of temporal paradoxes:
causal loops and consistency paradoxes, outdraw possible solutions and
present our framework developed to be a general method of giving a
self-consistent model for every possible initial data.
The main subject of the talk is going to be the framework itself. The
goal is to delve into the details of the formal components, that is, to
display our ideas by explicit and precise definitions. Then discuss the
results and setbacks of our approach, such as a local counter example
showing that the self-consistent solutions cannot always be found in
nearby worlds by simple iteration.
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| 18
October
(Wednesday) 5:00
PM Room 226 |
Gábor Forrai
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Institute of Business Economics, Eötvös University, Budapest
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Hibáztathatóak vagyunk-e hiteinkért? Doxasztikus deontológia akaratlagos ellenőrzés nélkül
(Can we be blamed for our beliefs? Doxastic deontology without volumtary control)
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A doxasztikus
deontológia szerint az ismeretelmélet területén éppúgy beszélhetünk
kötelességről és felelősségről, mint az etika területén, azaz bizonyos
körülmények fennállása esetén kötelező vagy éppen tilos ebben vagy abban
hinnünk, és számon kérhető rajtunk, ha nem így teszünk. Az előadásban
első felében William Alstonnak a doxasztikus deontológia ellen szóló
érvével vitatkozva el fogom magyarázni, hogy a deontikus kifejezéseket a
doxasztikus állapotokra vonatkoztatva hogyan kell értelmezni. A második
felében azt vizsgálom, hogy ez a felfogás összeegyeztethető-e a
naturalista programmal, s Hilary Kornblith naturalizált felfogását
elemezve amellett fogok érvelni, hogy a deontológiának legfeljebb egy
része illeszthető be a naturalizált ismeretelméletbe.
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| 25
October
(Wednesday) 5:00
PM Room 226 |
Koen Lefever
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Centre for Logic and Philosophy of Science, Vrije Universiteit Brussel |
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Comparing Classical And Relativistic Kinematics In First-Order Logic*
*Joint research with Gergely Székely (Rényi Institute of Mathematics, Budapest)
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The
aim of the research presented in this talk is to establish a new
logic-based understanding of the connection between classical kinematics
and relativistic kinematics. We work in the framework and the tradition
of the Andréka--Németi school of axiomatic relativity as developed at
the Algebraic Logic department of the Alfréd Rényi Institute of
Mathematics.
We show that the axioms of special relativity can be interpreted in the
language of classical kinematics. This means that there is a logical
translation function from the language of special relativity to the
language of classical kinematics which translates the axioms of special
relativity into consequences of classical kinematics.
We will also show that if we distinguish a class of observers
(representing observers stationary with respect to the “ether”) in
special relativity and exclude the non-slower-than light observers from
classical kinematics by an extra axiom, then the two theories become
definitionally equivalent (i.e., they become equivalent theories in the
sense that the theory of lattices as algebraic structures is the same as
the theory of lattices as partially ordered sets).
Furthermore, we show that classical kinematics is definitionally
equivalent to classical kinematics with only slower-than-light inertial
observers, and hence by transitivity of definitional equivalence that
special relativity theory extended with “ether” is definitionally
equivalent to classical kinematics.
So within an axiomatic framework of mathematical logic, we explicitly
show that the transition from classical kinematics to relativistic
kinematics is the knowledge acquisition that there is no “ether”,
accompanied by a redefinition of the concepts of time and space.
The above allows us to introduce a metric "conceptual distance" between
theories: theories which are equivalent have a conceptual distance of
zero, while the distance between non-equivalent theories is the number
of concepts which need to be added or subtracted to make them
equivalent. Since the only concept which need to be added to
relativistic kinematics to make it equivalent to classical kinematics is
the "ether", the conceptual distance between both theories is "one".
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