Prof. Richard Zach PhD.
September 8 until Dezember 31, 2025
Affiliation: University of Calgary, Canada
Research for a study about:
History of Logic / Collected Works of Rudolf Carnap
A first line of research concerns the history of logic at the time of the Vienna Circle: The 1920s saw important and influential advances in the development of symbolic logic. One of these was the development of logical metatheory, especially the semantics of predicate logic. Work carried out in Hilbert’s research group in Göttingen centered, inter alia, on the decision problem of predicate logic. This problem was considered by Hilbert to be one of the main open research questions in symbolic logic, and his students Ackermann, Behmann, and Bernays all worked on it, as did Gödel, Herbrand, Kalmár, Ramsey, Schönfinkel, and Schütte. It was shown undecidable independently by Church and Turing in 1935. However, the partial successes to prove various special cases decidable in the 1920s occasioned some fundamental changes in the way symbolic logic was conceived (e.g., a change from a syntactic-combinatorial conception of logic as what can be derived in a calculus to a semantic perspective), and with it certain mathematical tools for proving results about symbolic logic. This research project that was responsible in large part for adoption and development of model theoretic methods. A second line of research continues after WWII. Between 1945 and 1965, the development of proof-theoretic methods lead to the actual implementation of logical reasoning on digital computers. A surprising number of analytic philosophers (such as Chisholm, Dreben, Putnam, Quine, Wang) had significant roles to play in this development.
Both projects have connections to the Vienna Circle and the wider logical empiricist movement. The first involves a member of the Circle (Gödel) directly. Some connections between the Hilbert school and Vienna are well-known (e.g., Hilbert’s obvious influence on Gödel, the debate between Behmann, Bernays, Gödel and Kaufmann was studied by Mancosu), but perhaps a bit under-explored: e.g., Behmann and Carnap had plans to co-author a textbook on symbolic logic (a project that was eventually abandoned; Carnap wrote his Abriß der Logistik by himself). There are also connections to the second project, e.g., the inventor of the most well-known automated reasoning method (the resolution calculus), J. Alan Robinson, was a student of Arthur Pap.
The Collected Works of Rudolf Carnap (CWRC) aims at a complete edition of Carnap’s published writings. The CWRC project has so far published two volumes (with Oxford University Press). Volume 4 which collects Carnap’s writings on epistemology after the Aufbau, including the well-known “Pseudoproblems,” “Elimination of metaphysics,” as well as the manifesto of the Vienna Circle. It is co-edited by Richard Creath (Arizona State), Thomas Uebel (University of Manchester), and Richard Zach, and they aim to complete by the end of 2025. Volume 3 of the CWRC focuses on Carnap's writings on logic in the 1920s (i.e., before Logical Syntax). Zach has joined the editorial board—Erich Reck (UC Riverside), Georg Schiemer (Vienna), and Dirk Schlimm (McGill)—and aims to make significant progress on the remaining translation and editorial work of that volume.
Lecture
Theories and Models from Hilbert to Tarski
Philosophy of Science Colloquium
Date: December 18, 2025
Time: 4.45 pm -6.15 pm CET
Venue for all talks: Lecture Hall 2i, NIG Universitätsstraße 7, 2nd floor, NIG/ Neues Institutsgebäude, Universitätsstraße 7, 1010 Vienna
Abstract:
In the 1920s and 30s, the tools of symbolic logic began to be applied to the study of axiomatic theories and their models. Two main traditions can be identified in this regard. The first is the work of David Hilbert on the axiomatic method. He and his students such as Paul Bernays began to formulate axiomatic theories in the predicate calculus at the beginning of the 1920s. On the other hand, Rudolf Carnap and later Alfred Tarski used the simple theory of types as a background theory to formulate axiom systems and their consequences. The talk will survey these traditions and compare their metatheoretical approaches. In Hilbert's case the focus was on proof theoretic questions and investigations such as consistency; in the case of Carnap and Tarski the focus was on model theoretic concepts and questions such as consequence and categoricity.
Lecture
Institute Vienna Circle fellow Richard Zach is giving a talk at the Department of Mathematics, University of Vienna:
Semantics of First-order Logic: The Early Years
Logic Colloquium | 06.11.2025 15:00 - 15:50
R. Zach (U Calgary, CA)
The model and proof theory of classical first-order logic are a staple of introductory logic courses: we have nice proof systems, well-understood notions of models, validity, and consequence, and a proof of completeness. The story of how these were developed in the 1920s, 30s, and even 40s usually consists in simply a list of results and who obtained them when. What happened behind the scenes is much less well known. The talk will fill in some of that back story and show how philosophical, methodological, and practical considerations shaped the development of the conceptual framework and the direction of research in these formative decades. Specifically, I'll discuss how the work of Hilbert and his students (Behmann, Schönfinkel, Bernays, and Ackermann) on the decision problem in the 1920s led from an almost entirely syntactic approach to logic to the development of first-order semantics that made the completeness theorem possible.
Organiser: KGRC
Location: Department of Mathematics, HS 11, 2. OG, Oskar-Morgenstern-Platz 1
Workshop Epsilon Calculus: Logic, History and Philosophy
Workshop
Epsilon Calculus: Logic, History and Philosophy
Place: November 25 – 27, 2025,
Department of Philosophy – University of Vienna,
Lecture Room 3A (Room D0312, 3rd floor)
Universitätsstraße 7, 1010 Vienna
Organized by: Ludovica Conti (ESPRIT Program, Austrian Science Fund (FWF): “The Logic of Abstraction”) Georg Schiemer, Benjamin Zayton (University of Vienna, ERC Project: “The Formal Turn – The Emergence of Formalism in Twentieth-Century Thought”) and Richard Zach (University of Calgary/IVC Vienna)
Day 1 Tuesday | November 25, 2025
09:00 (s.t.) – 09:15 Opening
09:15 – 10:15 Hannes Leitgeb (LMU Munich) “Carnapian Logicism and Semantic Analyticity. Epsilon Terms Applied”
10:15 – 10:30 Tea/Coffee
10:30 – 11:30 Ludovica Conti (University of Vienna) “Arbitrariness via Epsilon Terms”
11:30 – 11:45 Tea/Coffee
11:45 – 12:45 Nicola Bonatti (LMU Munich) “Intuitionistic Free Logic with epsilon-operator”
14:45 – 15:45 Benjamin Zayton (University of Vienna) “Interpretations with Parameters, Bi-interpretability, and the ε-calculus”
15:45 – 16:00 Tea/Coffee
16:00 – 17:00 Mariami Gamsakhurdia (TU Vienna) “Epsilon Calculus: Between Existence and Error”
Day 2 Wednesday| November 26, 2025
10:00 – 11:00 Rosalie Iemhoff (Utrecht University) “Quantifiers and Skolemization in nonclassical logics”
11:00 – 11:15 Tea/Coffee
11:15 – 12:15 Elio La Rosa (LMU Munich) “Conservative Extensions of Intuitionistic Logic by Epsilon Terms over Predicate Abstraction”
14:15 – 15:15 Norbert Gratzl (LMU Munich) “Logical Pluralism as Higher-Order Logical Monism”
15:15 – 15:30 Tea/Coffee
15:30 – 16:30 Moritz Bodner (University of Vienna) “The Origin Story of the Epsilon-Calculus”
16:30 – 16:45 Tea/Coffee
16:45 – 17:45 Georg Schiemer (University of Vienna) “How to eliminate ideal elements”
Day 3 Thursday| November 27, 2025
10:00 – 11:00 Richard Zach (University of Calgary, IVC Wien) “The Logic of Epsilon”
11:00 – 11:15 Tea/Coffee
11:15 – 12:15 Marianna Antonutti Marfori (Université Paris 1-Panthéon Sorbonne) “TBA”
For further information please visit: formalism.phl.univie.ac.at or contact florian.kolowrat@univie.ac.at
Report
My stay at the IVC was productive and rewarding. My main aim was to finish work on the Collected Works of Rudolf Carnap, vol. 4. My part of this work is now essentially complete and the volume should soon be ready to send to the press. I have also begun work on vol. 3, together with Erich Reck, Georg Schiemer, and Dirk Schlimm. I actively participated in the life of the Institute and the Philosophy Department. I attended all meetings of the Logic Café and the Philosophy of Science colloquium as well as an IVC-internal reading group. I co-organized the workshop Epsilon Calculus: Logic, History and Philosophy on November 25–27, 2025 with Ludovica Conti, Georg Schiemer, and Benjamin Zayton. On that occasion I taught a 3-hour introductory seminar on the epsilon calculus in the Logic Café and myself gave a presentation in the workshop (“The Logic of Epsilon”). In addition to my own IVC fellow presentation on December 18 (“Theories and Models from Hilbert to Tarski”), I gave talks at the Kurt Gödel Research Center and the IHPST at the Université Paris 1 Sorbonne-Pantheon, and taught a course on the epsilon calculus as part of the LMU Proof and Computation Autumn School in Herrsching near Munich.