Goal of research
The project aims to develop a unified conceptual framework for formal analysis of agency that combines logical-mathematical and linguistic methods and to detect the source of the normativity of logic as a formal theory of agency.
In the theoretical part of the research, traditional logical philosophical and linguistic approaches were supplemented by methodological apparatus of (1) dynamic epistemic logic; (2) game theory; (3) the semantics of possible worlds; (4) constructive type theory; (5) formal phenomenology; (6) category theory; (7) speech acts theory and post-Gricean pragmatics; (8) corpus linguistics; (9) psycholinguistics;
Empirical base of research
The results of linguistic experiments with native speakers of Russian language (with the DMDX platform) and Russian Sign Language (elicitation technique).
Results of research
1) An account of communication has been developed that explains communication in terms of a system of mutual obligations that facilitates the coordination of actions. This account, in turn, has been used to generalize the classical theory of implicatures introduced by P.G. Grice. The main advantage of the proposed generalization is its capacity to avoid using the mentalistic vocabulary and a new perspective that it provides on the process of language acquisition understood in terms of the normative practice of the division of commitments and planning. An original classification of expressives, speech acts that has no propositional content, has been developed on the material of several languages. The proposed classification distinguishes between three types of exclamatives depending on which pronouns they include. The principle of classifying speech acts by the complexity of their constitutive rules has been defended, and a hypothesis has been suggested according to which there are different stages of the development of speech acts (e.g. “proto-asserts”, “proto-commissives”).
2) The advantages of a dynamic interpretation of compositionality for binary semantic phenomena have been shown. A dynamic approach to binary quantifiers and mixed colors based on the interpretation of compositionality as a dynamic formality has been developed. A dynamic extension of modal intuitionistic logic, namely, the epistemic logic of IEL, with a public announcement operator, has been constructed. A game for Abelian logic A has been constructed and the correctness of this game has been proved for standard algebraic semantics for Abelian logic. An interpretation of this game as a game of agents with limited resources has been proposed. Complete axiomatic systems for graded modal logics with transitive dependent modalities have been constructed. The completeness theorem of such axiomatics for Kripke semantics has been proved. A classification of the hierarchies of binary relations has been obtained in terms of the relations of conservative extension. A decidability criterion has been formulated for graded modal logics with transitive and dependent modalities.
3) A category-theoretic semantics of quantum logic based on the modification of its category model has been proposed. The standard category model of quantum logics uses the concept of topos, a special kind of category which employs the Heyting algebra. In the proposed modification of topos, called quantum, Heyting algebra has been replaced by an orthomodular lattice. An interpretation of some systems of orthomodular quantum logic has been proposed. The completeness of these systems for the proposed semantics has been proved. A family of first-order tolerant logic has been constructed that allows formalizing the concept of vagueness.
4) A probabilistic epistemic model of social influence for agents with accurate general information has been proposed. The problems of combining a probabilistic epistemic model with an arbitrary relation of accessibility and function of social influence have been demonstrated. Mechanisms for overcoming these problems involving both a modification of the probabilistic function and an adjustment of the function of social influence have been proposed. The general form of the structural problem of indeterministic theories of action has been proposed. It has been shown that various forms of the argument from luck (rollback argument, promise argument, the argument from the lack of explanation, Hume’s argument) are dependent on the revealed structural problem. It has been proven that the determination of an action by the character of the agent is a necessary condition for the consistent attribution of moral responsibility for this action. It is demonstrated that causal indeterminism does not provide a satisfactory metaphysical platform for libertarian understanding of free will.
5) The necessity of epistemic approaches to the proof theory has been proven. The interpretation of Martin-Löf's theory of types and the homotopy type theory in terms of calculi with epistemically loaded theoretic-proof semantics has been presented. The importance of the balance between an “inductive risk” and the values of tychism, synehism, and uberty in C.S. Peirce's philosophy of science has been demonstrated. It has been shown that, according to Peirce, values help to choose what empirical hypotheses will be tested and to reduce the risk of error while using the inherently risky inductive method. The project of a modular scheme for creating prospective explanatory hypotheses for the interpretation of the data has been developed. A taxonomy of informal operations that are performed by mathematicians “before” and “around” a formal proof of mathematical theorems (thought experiments, work with mathematical bases and platforms) has been proposed.
6) Two senses of signification in the logic of W. Occam are clarified. In the first sense, the name or term of spoken language signifies something if the term supposes this thing in a non-modal present tense sentence and if it is truly predicated of this thing. In the second sense, a name signifies something when it can suppose what it signifies in a sentence about the future or past or modal sentence. The interpretation of the first sense of signification as a tripartite relation between term, the object to which the term refers and the moment of utterance has been proposed.
7) The first systematic description of sentential negation in Russian Sign Language is presented. It was shown that sentential negation in Russian Sign Language is a unique phenomenon among the languages of this linguistic group. The syntactic analysis of the structure of sentential negation in Russian Sign Language is conducted. Two types of negation have been distinguished: universal negation and type negation. This distinction has been employed to solve a series of problems related to the nonsensical sentences.
The project has resulted in 6 articles that have been published in a peer-reviewed journal, indexed in the Web of Science and/or Scopus databases; 4 articles from Additional List of Eligible Journals for Allocation of Academic Bonuses and Research Productivity Assessment at HSE; 1 article was published by publisher included in the list of publishers that are considered relevant for the assignment of a level 3 bonus at HSE; 1 monograph has been prepared for publication in the publishing house URSS.
Two international conferences were organized: «Formal Philosophy – 2019» and «Trends in Logic 19. Current Issues in Philosophical Logic» (in collaboration with the journal “Studia Logica”). All members of the project participated in the project as well as philosophers, mathematicians, linguists from the USA, France, Austria, Great Britain, the Netherlands, Germany, Brazil, Poland, Portugal, Belgium, Spain, Italy, Israel, the Czech Republic, Serbia, various Russian cities (Moscow, St. Petersburg, Novosibirsk, Ulyanovsk, Tomsk). Three seminars were working as a part of the project: the theoretical seminar “Formal Philosophy” (9 meetings), the research seminar “From the Logical Point of View” (24 meetings), the educational seminar “Logical Semantics” (10 meetings). The results of the project were also approbated in 33 reports of its participants at conferences and theoretical seminars at universities and research centers in Russia, France, Great Britain, Norway, Germany, Brazil, Croatia, Portugal, and the Czech Republic. Members of the project took part in a summer school in Latvia and visited research and educational centers in Portugal and France as visiting scholars.
Level of implementation, recommendations on implementation or outcomes of the implementation of the results
The results of research results are used in the teaching courses on logic, philosophy of language, history of philosophy, theory of language, cross-cultural pragmatics, contemporary Russian language, formal presentation of natural language, corpus methods of studying linguistic processes, formal and experimental pragmatics, formal epistemology. The results were also used in the research seminar “Logic, Epistemology and Methods of Philosophical Research”. The research problematics has been explored in the theses of undergraduate and graduate students of educational programs of the Faculty of Humanities of the Higher School of Economics. The Ph.D. thesis “W. Ockham's conception of supposition and signification” supervised by Elena Dragalina-Chernaya was defended by Anastasia Kopylova (cum laude).