Ryota Akiyoshi

J-GLOBAL         Last updated: Sep 15, 2018 at 18:11
Ryota Akiyoshi
Waseda University
Institue for Advanced Study
Job title
Adjunct Researcher
PhD (Philosophy)(Keio University)
Other affiliation
Keio UniversityL'Institut d'Histoire et de Philosophie des Sciences et des Techniques


My research fields are philosophy of mathematics and logic, mathematical logic (proof theory), and theoretical computer science (type theory). The main philosophical question in my research is "what is a proof ?".

The origin of modern philosophy of mathematics was the foundational debate in the beginning of 20th century. This debate had involved mathematicians, logicians, and philosophers. After this debate, many philosophical works have been done independently of the modern development of mathematical logic. I'm doing philosophy of logic and mathematics, mathematical logic (proof theory) and theoretical computer science (type theory) in the way that they are essentially related to one another. In particular, by analyzing finitism (Hilbert), intuitionism (Brouwer), and logicism (Frege) by proof-theoretic methods, I would like to find a common base for these seemingly different positions in philosophy of mathematics.

More recently, I'm interested in the formalization of mathematics using Coq or Minlog and in the question "what is a proof ?" from this point of view too. These are based on my philosophical or historical interest in early Husserl's logical philosophy (for example, his "Logische Undersuchungen"). Moreover, I started to work on Gaisi Takeuti's finitism behind his proof theoretic works and cyber security as an application of proof theory.

Research Topics:

(i) Goedel's theorem and Hilbert's program,
(ii) Gentzen's consistency proofs,
(iii) Brouwer's proof of bar induction,
(iv) early Husserl's philosophy of logic,
(v) proof theoretic analysis of Frege's logical system,
(vi) the meaning of logical constants, proof theoretic semantics,
(vii) proof theory of impredicative subsystems of second-order arithmetic, ordinal analysis (cut-elimination, normalization theorem),
(viii) intuitionistic analysis (point-free topology),
(xi) Gaisi Takeuti's finitism,
(x) cyber security as an application of proof theory.

Research Areas


Academic & Professional Experience

Sep 2018
Associate member, L'Institut d'Histoire et de Philosophie des Sciences et des Techniques
Sep 2018
Part-time lecturer, Faculty of Letters, Arts and Sciences, Waseda University
Sep 2018
Part-time lecturer, Faculty of Science and Engineering, Waseda University
Apr 2018
Adjunct researcher, Institute for Advanced Study, Waseda University
Apr 2018
May 2018
Part-time lecturer, College of Industrial Technology, Nihon University

Awards & Honors

Nov 2014
The Japan Association for Philosophy of Science Research Award, The Japan Association for Philosophy of Science
Winner: Ryota Akiyoshi, Yuta Takahashi
Oct 2009
The Japan Association for Philosophy of Science Research Award, The Japan Association for Philosophy of Science

Books etc

Consistency proofs of arithmetic: Introduction to proof-theory (in Japanese)
Ryota Akiyoshi (Part:Joint Work, Consistency proofs by cut-eliminatiom methods)
Kyoritsu Publisher   2018   
Philosophical Logic: Current Trends in Asia – Proceedings of AWPL-TPLC 2016
Ryota Akiyoshi, Yuta Takahashi (Part:Contributor, Contentual and Formal Aspects of Gentzen’s Consistency Proofs (refereed))
Springer Verlag   Nov 2017   ISBN:9789811063541
Yokuwakaru Tetsugaku and Shisou (textbook on philosophy)
Ryota Akiyoshi (Part:Contributor, 「論理学」(article of "logic"))
Minerva Publisher   2018   

Published Papers

Towards proof-theoretic semantics for second-order logic
Ryota Akiyoshi and Alberto Naibo
in preparation      2018
Takeuti’s finitism and ordinal-theoretic proofs of consistency
Ryota Akiyoshi and Andrew Arana
in preparation, 30 pages      2018
Ryota Akiyoshi
Proceedings of the XXIII World Congress of Philosophy   56 5-9   2018   [Refereed]
The Upperbound of the Length of the Reductions in a Subsystem of Girard's F
Ryota Akiyoshi
in preparation, 17 pages      2018
“Proofs as Programs” in Parameter-Free Fragments of System F
Ryota Akiyoshi
submitted, 17 pages      2018


"Proofs as Programs" Revisited (abstract)
Ryota Akiyoshi
The Bulletin of Symbolic Logic, to appear      2018   [Invited]
A uniform idea behind Gentzen’s three consistency proofs (abstract)
Ryota Akiyoshi, Yuta Takahashi
The Bulletin of Symbolic Logic   22 382   Sep 2016   [Refereed]
Proof-Theoretic Analysis of Brouwer's Argument of the Bar Induction (abstract)
Ryota Akiyoshi
The Bulletin of Symbolic Logic   21 53-54   Mar 2015   [Refereed]
An Interpretation of Brouwer's Argument for Bar Theorem via Infinitary Proof Theory (abstract)
Ryota Akiyoshi
Abstract Volume of XXIII World Congress of Philosophy   18   2013   [Refereed]
Complete Cut-Elimination Theorem for Ω-Rule (abstract)
Ryota Akiyoshi and Grigori Mints
The Bulletin of Symbolic Logic   18 438   2012   [Refereed]

Conference Activities & Talks

Cut-elimination methods by Gentzen and Schuette [Invited]
Ryota Akiyoshi
Summer School on Foundations of Mathematics   Sep 2018   
"Proofs as Programs" Revisited [Invited]
Ryota Akiyoshi
Logic Colloquium 2018 (Udine, Italy)   Jul 2018   
"Proofs as Programs" Revisited
Ryota Akiyoshi
Oberseminar Mathematische Logik (LMU München, Mathematisces Institut)   Feb 2018   
"Proofs as Programs" Revisited [Invited]
Ryota Akiyoshi
"Philosophy of Logic and Mathematics" with special focuses on "Philosophy of Proofs" and the Study of Euclid's Elements   Jan 2018   
Gentle Introduction to the Omega-Rule: Part II
Ryota Akiyoshi
Atelier autour de la théorie de la démonstration (Institut d'histoire et de philosophie des sciences et des techniques, Université Paris)   Sep 2017   

Association Memberships