*: Refereed article.
^: Secondary (minor) field of study.
Original Research
[*5] Yamada, T. (2024), `Wright's First-Order Logic of Strict Finitism', in Studia Logica, [pages to be assigned], https://doi.org/10.1007/s11225-024-10137-x. [Preprint in arXiv]
[Abstract] A classical reconstruction of Wright’s first-order logic of strict finitism is presented. Strict finitism is a constructive standpoint of mathematics that is more restrictive than intuitionism. Wright sketched the semantics of said logic in Wright (Realism, Meaning and Truth, chap 4, 2nd edition in 1993. Blackwell Publishers, Oxford, Cambridge, pp.107-75, 1982), in his strict finitistic metatheory. Yamada (J Philos Log. https://doi.org/10.1007/s10992-022-09698-w, 2023) proposed, as its classical reconstruction, a propositional logic of strict finitism under an auxiliary condition that makes the logic correspond with intuitionistic propositional logic. In this paper, we extend the propositional logic to a first-order logic that does not assume the condition. We will provide a sound and complete pair of a Kripke-style semantics and a natural deduction system, and show that if the condition is imposed, then the logic exhibits natural extensions of Yamada (2023)’s results.
[*4] Yamada, T. (2023), `Wright's Strict Finitistic Logic in the Classical Metatheory: The Propositional Case', in The Journal of Philosophical Logic, 52, 1081–1100, https://doi.org/10.1007/s10992-022-09698-w. [Preprint in arXiv]
[Abstract] Crispin Wright in his 1982 paper argues for strict finitism, a constructive standpoint that is more restrictive than intuitionism. In its appendix, he proposes models of strict finitistic arithmetic. They are tree-like structures, formed in his strict finitistic metatheory, of equations between numerals on which concrete arithmetical sentences are evaluated. As a first step towards classical formalisation of strict finitism, we propose their counterparts in the classical metatheory with one additional assumption, and then extract the propositional part of ‘strict finitistic logic’ from it and investigate. We will provide a sound and complete pair of a Kripke-style semantics and a sequent calculus, and compare with other logics. The logic lacks the law of excluded middle and Modus Ponens and is weaker than classical logic, but stronger than any proper intermediate logics in terms of theoremhood. In fact, all the other well-known classical theorems are found to be theorems. Finally, we will make an observation that models of this semantics can be seen as nodes of an intuitionistic model.
[*3] Yamada, T. (2012), `Two Realisms: An Analysis from the View Point of `Worldview'', in Tetsugaku-Ronso, 39: 98-109, in Japanese. [Repository]
[^2] Yamada, T. (2012), `A Deception by a Style of Play: Philosophy of Game and Play', in Prospectus, 15: 13-24, in Japanese. [Repository]
[*1] Yamada, T. (2010), `The `Truth-Value Links' Problem for Anti-Realism', in Chubu-Tetsugakukai-Nempo, 42: 65-80, in Japanese.
Translation into Japanese
[^1] A Japanese translation of Bernard Suits, The Grasshopper: Games, Life and Utopia (first published by University of Toronto Press in 1978, reprinted with the Introduction by Thomas Hurka, published by Broadview Press in 2005), as Kawatani, S. and Yamada, T. (translation) 『キリギリスの哲学 ――ゲームプレイと理想の人生――』 (2015), Nakanishiya Publication, Kyoto, except the Introduction by Thomas Hurka. [Publisher]
Review Articles
[2] Yamada, T. (2010), `Epistemology of Testimony: Reductionism and Anti-Reductionism', in Tetsugaku-Ronso, 37 (supplementary volume): S 61 - S 72, in Japanese. [Repository]
[1] Yamada, T. (2010), `Anti-Realism and `Truth-Value Links' Problem', in Tetsugaku-Ronso, 37 (supplementary volume): S 49 - S 60, in Japanese. [Repository]
Miscellaneous
[^1] Kawatani, S. and Yamada, T. (2019), `On the Japanese Translation of Bernard Suits, The Grasshopper: Games, Life and Utopia: キリギリスの哲学―ゲームプレイと理想の人生 (Romanization: kirigirisu no tetsugaku―gēmupurei to risō no jinsei. Lit.: The Philosophy of the Grasshopper: Game-playing and the ideal life})', in: Sport, Ethics and Philosophy, vol.13, issue 3-4, pp.471-6, DOI: 10.1080/17511321.2019.1614974. [Publisher]