ELFT HÍRADÓ

[Gömöri Márton <gomorim AT gmail.com>]

Logic and Philosophy of Science Seminar
Department of Logic, Institute of Philosophy
Eötvös Loránd University
Budapest, Múzeum krt. 4/i Room 224
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P R O G R A M

The seminar is held in hybrid format, in person (Múzeum krt. 4/i Room 224)
and online. Zoom link
<https://us02web.zoom.us/j/84594385686?pwd=a7KPWoNLrPg11xNTi5Ug91YR5mHmmS.1>


20 March (Friday) 4:15 PM  Room 224 + ONLINE

Tibor Papp
Eötvös Loránd University, Department of Logic
Title: Introduction to Universal Logic

*The talk will be in Hungarian.*
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ABSTRACT:
The first part of my doctoral thesis is a self-developed metalogical
theory, called Universal Logic (UL). The doctoral thesis outlines UL as
follows:








*There is a hidden internal architecture of logic that is obscured by the
implicit paradigms governing syntax, semantics, and consequence. By
explicating and reformulating these paradigms in two distinct directions,
this hidden architecture becomes visible.First, modern (post-Fregean) logic
has typically approached traditional (pre-Fregean) logic by reformulating
its categories within modern logical frameworks. To make the internal
architecture of logic visible, however, this direction must be reversed:
modern logic must be reconstructed on the basis of the categorical
distinctions already present in traditional logic.Second, the internal
architecture of logic has typically been sought through its algebraisation.
Yet algebraic abstraction, while structurally powerful, necessarily
suppresses certain features specific to logical construction, and therefore
cannot render the full internal architecture of logic visible. To make this
architecture fully explicit, it is not logic that must be algebraised, but
algebra that must be logified.As a result of this reformulation, the
completeness theorem emerges in a new light. It is a universal property of
the internal architecture of logic itself, rather than a result tied to
particular logical calculi, and it can be formally proved within the new
paradigms that make this architecture explicit. In other words, the absence
of a completeness theorem in higher-order logics does not reflect an
intrinsic limitation of logic itself; it reveals instead that the implicit
paradigms governing syntax, semantics, and consequence are insufficient to
support completeness in higher orders.*
Of course, I cannot present the entire UL during the seminar lecture, as it
is a mathematical construction of over 100 pages. The aim of the lecture is
to show the basic ideas on which UL is based.

Finally, an important note: I will give the lecture* in Hungarian*.
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The seminar is open to everyone, including students, visitors, and
faculty members from all departments and institutes! Format: 60 minute
lecture, coffee break, discussion.
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Organizers: Márton Gömöri and Zalán Molnár
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LPS - Logic and Philosophy of Science (Student and Faculty Seminar)
Department of Logic, Institute of Philosophy
Eötvös University Budapest
http://phil.elte.hu/lps