Yusuke Kaneko

As Nagel suggested (sec.2.4-sec.2.5), all the troubles of other minds are not reduced to that epistemological problem which analytic philosophers have eagerly tackled (sec.2). Other minds exist; they are not zombies nor automata, which we can directly conrm as a matter of fact. We learn it from Sartre’s philosophy as well as Nagel’s. is new stance on the problem is called an ontological turn (sec.3). Taking the stance, however, even Sartre’s motif of the Look appears insucient (sec.5.2). Other minds become a problem not due to their Looks, but due to their existence. We learn it from Hume nally, whose principle of comparison reveals the genuine problem we should have tackled.

The practical syllogism of the customary type, “desire, belief /∴ action”, which we may also formulate as “WI (q), BI (p→q) /∴ p”, is the main topic of the following discussions. This syllogism is not valid, viewed at the level of rigid, symbolic logic. That is the initial claim made in this article (§2). Kant may save us from this dead end (§1); but his logic of the imperative is never always provided for our ordinary lives (§3.1). Contrasting the two, Kant’s logic and the customary syllogism, we look into where the invalidity of the latter resides in: individuality of the belief (§1.4), a fallacy of affirming the consequent (§2.1), propositional attitudes (§2.3), irrationality (§3.2), concretely. Although the validity is finally given up, we find another dimension of understanding in the formulation of utilitarianism; this point has been passed over by former thinkers (§4). Before jumping to this conclusion, we look through the landscape of their discussions as well, especially those held under the name of Humeanism. Readers who wonder how this article relates to the main stream of modern debates are recommended to see those parts (§3.3-3.4) first.

This article is mainly composed of two discussions. First, we introduce event-expressions, individual constants of a new type referring to events, not things. We learn this from Davidson’s famous formulation of event-sentences (§§1-3). The first half or more of this article is occupied with this discussion. The second half is devoted to the creation of a new analysis of probability, especially conditional probability. As seen in the author’s other work (Kaneko 2022), probability theory can be reconstructed with predicate logic in the name of inductive logic. This article includes its development and its application to the notion of conditional probability (§§4-6).

Crucial Note (April 9, 2026) This edition has already been replaced with the 2026 revised edition:  "What Is LK? Vol.2-I--As a Meta-Theory of NK: A Fully Revised Edition of Vol.2 (Textbook Series in Symbolic Logic)". For reference, the author, although hesitantly, has left this former version (What is LK? Vol.2. Structural Inference-Figures) , which includes numerous incorrect passages. ******the following is the previous abstract******** LK is much more difficult than NK, and to make matters worse, Gentzen's intention is still unclear when it comes to that system (LK). The second and third volumes of the series titled What is LK? conduct the detailed survey of each inference-figure in a toe-to-toe way, as it were, which most mathematicians looked through. The present volume, Vol.2, looks deeper into structural inference-figures, which is never an easy task.

The original interest of this article lies in existential import. It provides a broader view on the problem by reference to modern, symbolic logic (ch.1). Gradually, however, our interest will change into the amalgamated expressions often used in logic; that is, why are such expressions as “x is a round triangle” applied in logic? We critically discuss this question from an extensional viewpoint, namely model theoretic semantics (ch.2). We also touch on Church’s λ-calculus in the appendix (app.2).

This article handles a series of articles written by Suzuki (2016a; 2016b; 2018), in which he put forward the anti-psychologism, a new standpoint of action theory. This standpoint, however, has lost the path Anscombe originally opened up, seemingly. Anscombe’s point (called “Anscombe’s motif” in this article) was: the agent him/herself responds, by revealing his/her original motive, to the question “Why did/do you do…?” Leaving this ground, in modern theories, one sees an unfamiliar idea like a normative reason flow into the debate on human action. We review this academic environment critically in terms of Kaneko (2017), whom Suzuki criticized in one of his papers (2018).