The paper addresses how empirical rationality developed in cognitive science and AI can be bridged to epistemic knowledge argued in epistemology and philosophy of science, as a part of the effort for bridging the former, empirical sciences to the latter, philosophical inquiries. The empirical concepts of bounded and procedural rationality are applied to interpret the procedural theories of learning by doing and interaction by information sharing; empirical notions of knowledge and expertise widespread but underspecified in cognitive science and AI are more rigorously defined as cognitive knowledge and expertization process; and concepts of view, composite view, shared view and shared cognitive knowledge are introduced. Then, those arguments are deployed altogether to provide sufficient conditions for cognitive knowledge of a goal-directed adaptive agent to be epistemic knowledge (or justified true belief), and to demonstrate that cognitive knowledge shared by socially interacting agents exists (in the sense of epistemological realism) as epistemic knowledge under assumptions on motivateness, expertise and evolutionary processes of those agents.

Disagreement is widespread in mathematics. In this paper, I focus on disagreement about new axioms, which in our time means chiefly new axioms for set theory. Set theorists seek new axioms because the currently accepted axioms of Zermelo-Fraenkel set theory (ZFC) do not resolve key questions about sets like the continuum hypothesis. One way to resolve this disagreement would be to find reasons for choosing one or another new axiom. Philosophers classify such reasons as ‘intrinsic” and “extrinsic”, where the former are based on intuition or the content of the concept of set, and the latter are based on the value of the consequences such an axiom would have for set theory. Our modest goal in this article is to argue that this distinction, between intrinsic and extrinsic reasons for resolving a disagreement about new axioms, is not well-defined.

In the last decades there have been attempts at building relativist logical frameworks. These might prove helpful in the context of the present discussion about relativism. Their philosophical presuppositions, however, should be questioned. In this context, John MacFarlane's construction is particularly interesting. Using a formalism borrowed from temporal logic, it introduces an assessment index on which the truth-value of the proposition would depend. This picture helps make sense of the situations of conflicts or of retractions: the content is the same, but it seems that depending on who judges, truth-value varies. The author of this article feels uneasy about this relativization of truth to the assessor. By making the assessor a mere factor to be taken into account it seems to ignore assessment as an epistemic activity essentially involving responsibility. Drawing upon MacFarlane's interesting way to distinguish between contextualism and relativism, the article shows how in contextualism as such another sense of subjectivity is involved, as sensitivity to context.

There are quite serious disagreements among claims using counterfactuals. However, when we attempt to analyze such disagreements among counterfactual claims, we also find that there is disagreement among quite different manners of analizing the truth conditions of such counterfactual claims, among which two major theoretical analyses are David Lewis's similarity analysis and Judea Pearl's causality analysis. Meanwhile, Hosokawa (2023) provides a third up-to-date candidate for logical analysis of counterfactuals, i.e., temporality analysis based on hybrid temporal logic. In this article, we see what view emerges if each of similarity analysis and causality analysis is seen from the temporal point of view, and suggest that similarity analysis and causality analysis can be considered as two types of abstraction from temporality analysis. Furthermore, we present prospective contributions by temporality analysis not only to disagreement in counterfactuals but also a wider range of disagreement, i.e., disagreement in projects and policies proposed in the real world.

In this paper, I argue that given what variables enable us to express, although there may be disagreements about which statement expresses a rule one has been following, such disagreements do not lead to any paradoxes such as the one Kripke finds in Wittgenstein's Philosophical Investigations.To follow a rule is to undertake a commitment to the applicability of a certain condition over a domain of items, and variables can be used to express one's understanding of the condition and domain of a rule.These notions couched in inferentialist terms enable us to explain how we can resolve a disagreement about the expression of a rule and also why even if we cannot resolve one, we do not find anything paradoxical there.

We first analyze MacFarlane's Natural Deduction style presentation of Williamson's proof of collapsing of the classical negation and intuitionistic negation in a merged language; we show how the collapsing proof process is blocked by making the hidden (classical and intuitionistic) contexts explicit. Then, we consider a safe (conservative) merge between the classical rule system and a finitist (implication) rule, system and claim that the approach of safely merging the rules does not necessarily help the mutual understanding of the difference between different logical standpoints in general. MacFarlane (2020), in Sec.6, suggests the mutual embedding approach as an alternative approach for mutual understanding of the difference between the classical logicians and the intuitionistic logicians. At the Appendix Section, we argue on this. Then, we show that the situation is different in the linear logic setting; the embedding approach provides a new positive insight. Importance of semantic consideration is claimed in this paper.

The implementation of a normative system causes disagreement, more often than not. Variations in interpretation are involved, and also differences in advice-giving and inconsistencies between the correlated choices. In spite of these difficulties and for various reasons, a decentralized pattern of implementation is often preferred, in which agents are able to elaborate interpretations and to act or organize accordingly. It is argued that this causes patterns of disagreement which do not reduce to direct disagreement and call for a discussion of the alliance of objective and subjective elements.

This paper establishes the Craig interpolation for the logic FOC+J, studied in [14, 43]. This logic is known as a logic that “combines” first-order intuitionistic and classical logic, i.e., that is conservative over the both logics. As a corollary, the Robinson Joint Consistency is established. From this property we obtain a sufficient condition for consistently combining two consistent theories, described in the syntax of a combination of first-order intuitionistic and classical logic. Preceding to the Craig interpolation and the Robinson joint consistency, this paper describes Popper's [29] original formulation of the collapsing problem, a problem occurring when we try to combined two logics, and briefly explains how FOC+J avoids this problem.