A logical calculus with descriptions

Journal of Philosophical Logic -     

A logical calculus for controlled monotonicity

In this paper we introduce a new deductive framework for analyzing processes displaying a kind of controlled monotonicity. In particular, we prove the cut-elimination theorem for a calculus involving series-parallel structures over partial orders which is built up from multi-level sequents, an interesting variant of Gentzen-style sequents. More broadly, our purpose is to provide a general, syntactical tool for grasping the combinatorics of non-monotonic processes.     

On the consistency of a three-valued logical calculus

[This résumé was published in English in Matematicheskii Sbornik along with the article.]The present paper contains an investigation of a three-valued logical calculus (the system) previously described by the author [Recueil Mathématique 4 (46), 2 (1938)].A constructive consistence proof is given for a part of this calculus rendering the results previously published concerning the Russell paradox. A method for a non-constructive completeness proof for the complete calculus is briefly indicated.     

On a three-valued logical calculus and its application to the analysis of the paradoxes of the classical extended functional calculus

A three-valued propositional logic is presented, within which the three values are read as ‘true’, ‘false’ and ‘nonsense’. A three-valued extended functional calculus, unrestricted by the theory of types, is then developed. Within the latter system, Bochvar analyzes the Russell paradox and the Grelling-Weyl paradox, formally demonstrating the meaninglessness of both.     

Some implications of the logical calculus for empirical classes for social science methodology

An exposition of a calculus for empirical classes (CEC), one of the few attempts by logicians to deal with the problem of constructs and indicators, is presented. The CEC provides the groundwork for a formal structure for the situation in which individuals have a degree of membership in various classes rather than having either membership or nonmembership—a situation nearly always true in empirical research. The CEC is presented and its relation to various social science concepts is mentioned. An application of the CEC model to latent structure analysis (LSA) suggests alternatives to the local independence assumption including one called the local scale assumption, which has a close relation to a Guttman scale.     

An approach to why-questions

The purpose of this paper is to give a semantical analysis of why-questions. Why-questions will be construed as requests for knowledge. Special attention will be paid to considering what the conditions for conclusive answerhood are in the case of why-questions. Since explanations can often be thought of as answers to why-questions, we also discuss some topics in the theory of explanation.This study was supported by the Academy of Finland (Valtion humanistinen toimikunta) and by NSF grant No. IST-8310936 (Information Science and Technology), principal investigators Jaakko Hintikka and C. J. B. Macmillan. Scholarships from the Emil Aaltonen Foundation and the Finnish Academy of Sciences (Suomalainen Tiedeakatemia) are gratefully acknowledged.     

An ecological approach to disjunctivism

In this paper I claim that perceptual discriminatory skills rely on a suitable type of environment as an enabling condition for their exercise. This is because of the constitutive connection between environment and perceptual discriminatory skills, inasmuch as such connection is construed from an ecological approach. The exercise of a discriminatory skill yields knowledge of affordances of objects, properties, or events in the surrounding environment. This is practical knowledge in the first-person perspective. An organism learns to perceive an object by becoming sensitized to its affordances. I call this position ecological disjunctivism. A corollary of this position is that a case of perception and its corresponding case of hallucination—which is similar to the former only in some respects—are different in nature. I show then how the distinguishability problem is addressed by ecological disjunctivism.

     

An approach to intensional logic

A system of tensed intensional logic excluding iterations of intensions is introduced. Instead of using the type symbols (for ‘sense’), extensional and intensional functor types are distinguished. A peculiarity of the semantics is the general acceptance of value-gaps (including truth-value-gaps): the possible semantic values (extensions) of extensional functors are partial functions. Some advantages of the system (relatively to R. Montague's intensional logic) are briefly indicated. Also, applications for modelling natural languages are illustrated by examples.     

An ecological approach to learning

This paper introduces a special journal issue devoted to the study of learning in ecological and developmental contexts. In the past, the dominant approach to the study of learning has depended upon the choice of arbitrary problems, stimuli, and responses to guarantee the generality of principles discovered in the laboratory. Recently, though, there has been considerable interest in integrating an ecological (functional) account of learning with the strengths of the classic laboratory approach. One form of integration is to use the technology of the laboratory to look for the operation of general learning laws in ecological problems. The approach favored here is to treat learning as a biological phenomenon by first placing it within a functional system of behavior, and then by analyzing where and how learning modifies the operation of that system. Because the results of such analyses are defined with respect to functioning systems rather than procedural paradigms, the ecological approach readily makes contact with issues in evolution, development, and physiology, an ability not completely shared by the classic general-process approach. Concerns about laboratory versus field, function versus mechanism, generality of results, and adaptive “storytelling” can be resolved or further clarified by the present approach. The papers in this issue represent a cross-section of research stemming from an ecological approach to learning, and provide specific analyses of how learning modifies and is expressed in functional systems of behavior.     

A dialogical route to logical pluralism

This paper argues that adopting a particular dialogical account of logical consequence quite directly gives rise to an interesting form of logical pluralism, the form of pluralism in question arising out of the requirement that deductive proofs be explanatory.

     

An extension of the deontic calculus DSC1

The chief aim of the paper is to extend the calculusDSC ₁ (see [4]) in such a way as to satisfy all the requirements listed in [4] as well as a further stipulation — called ‘the principle of uninvolvement’ — to the effect that neither deontic compatibility nor deontic incompatibility of codes (see [2]) should be presupposed in deontic logic.