Takahiro Yamada

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.

ABSTRACTThe Japanese translation of Bernard Suits's The Grasshopper was published in 2015. We report in this article the background of the translation, the way our project was operated, some notable difficulties we had and the impact that our translation has had so far. The description of the difficulties with translation touches upon how we interpreted the terms ‘lusory’ and ‘prelusory’. This article also includes an appendix describing the history of how the word ‘grasshopper’ has been translated into Japanese.