Publications

This article investigates Charles Peirce’s development of logical calculi for classical propositional logic in 1880–1896. Peirce’s 1880 work on the algebra of logic resulted in a successful calculus for Boolean algebra. This calculus, denoted by PC, is here presented as a sequent calculus and not as a natural deduction system. It is shown that Peirce’s aim was to present PC as a sequent calculus. The law of distributivity, which Peirce states in 1880, is proved using Peirce’s Rule, which is a residuation, in PC. The transitional systems of the algebra of the copula that Peirce develops since 1880 paved the way to the 1896 graphical system of the alpha graphs. It is shown how the rules of the alpha system reinterpret Boolean algebras, answering Peirce’s statement that logical graphs supply a new system of fundamental assumptions to logical algebra. A proof-theoretic analysis is given for the connection between PC and the alpha system.

This paper compares Peirce’s and Hintikka’s logical philosophies and identifies a cross-section of similarities in their thoughts in the areas of action-first epistemology, pragmaticist meaning, philosophy of science, and philosophy of logic and mathematics

This paper presents and defends an integrated view of the placebo effect, termed “affective -meaning- making” model, which draws from theoretical reflection, clinical outcomes and neurophysiological findings. We consider the theoretical limitations of those proposals associated with the „meaning view‟ on the placebo effect which (i) leave the general aspects of meaning unspecified, (ii) fail to fully analyse the role of emotions and affect, and (iii) establish no clear connection between the theoretical, physiological and psychological aspects of the effect. We point out that a promising way to overcome these limitations is given by grounding the placebo effect on Peirce's theory of meaning, in which the role of the meaning constitution and change is placed in logical and objective structures. We also show the connection between our theoretical proposal and the appraisal theory, and integrate it with emotion regulation.

First-Order Tolerant Logics

The paper critically discusses two prominent arguments against closure principles for knowledge. The first one is the “argument from aggregation”, claiming that closure under conjunction has the consequence that, if one individually knows i premises, one also knows their i-fold conjunction—yet, every one of the premises might exhibit interesting positive epistemic properties while the i-fold conjunction might fail to do so. The second one is the “argument from concatenation”, claiming that closure under entailment has the consequence that, if one knows a premise, one also knows each of its remote consequences one arrives at—yet, again, the premise might exhibit interesting positive epistemic properties while some of its remote consequences might fail to do so. The paper firstly observes that the ways in which these two arguments try to establish that the relevant closure principle has the relevant problematic consequence are strikingly similar. They both crucially involve showing that, given the features of the case, the relevant closure principle acts in effect as a soritical principle, which is in turn assumed to lead validly to the relevant problematic consequence. There are however nontransitive logics of vagueness (“tolerant logics”, developed elsewhere by the author) where soritical principles do not have any problematic consequence. Assuming that one of these logics is the correct logic of vagueness, the paper secondly observes that both arguments describe situations where knowledge is arguably vague in the relevant respects, so that a tolerant logic should be used in reasoning about it, with the effect that the relevant soritical principle no longer validly leads to the relevant problematic consequence. This shows an interesting respect in which the gap between validity and good inference that arguably arises in a transitive framework can be bridged in a tolerant one, thereby approximating better certain features of our epistemic lives as finite subjects. Moreover, even for those who do not subscribe to tolerant logics, the paper’s two observations jointly indicate that, for all the arguments from aggregation and concatenation show, the status of the relevant closure principles should be no worse than that assigned by one’s favoured theory of vagueness to soritical principles, which only rarely is plain falsity and can indeed get arbitrarily close to full truth.

The main tenet of this paper is that human communication is first and foremost a matter of negotiating commitments, rather than one of conveying intentions, beliefs, and other mental states. Every speech act causes the speaker to become committed to the hearer to act on a propositional content. Hence, commitments are relations between speakers, hearers, and propositions. Their purpose is to enable speakers and hearers to coordinate their actions: communication is coordinated action for action coordination. To illustrate the potential of the approach, commitment-based analyses are offered for a representative sample of speech act types, conversational implicatures, as well as for common ground.

The received notion of axiomatic method stemming from Hilbert is not fully adequate to the recent successful practice of axiomatizing mathematical theories. The axiomatic architecture of Homotopy type theory (HoTT) does not ft the pattern of formal axiomatic theory in the standard sense of the word. However this theory falls under a more general and in some respects more traditional notion of axiomatic theory, which I call after Hilbert and Bernays constructive and demonstrate using the Classical example of the First Book of Euclid’s Elements. I also argue that HoTT is not unique in the respect but represents a wider trend in today’s mathematics, which also includes Topos theory and some other developments. On the basis of these modern and ancient examples I claim that the received semantic oriented formal axiomatic method defended recently by Hintikka is not self-sustained but requires a support of constructive method.

Finally, I provide an epistemological argument showing that the constructive axi omatic method is more apt to present scientifc theories than the received axiomatic method.

In a Hilbert-style non-logical axiomatic theory the semantics of logical symbols is rigidly fixed, while the interpretation of non-logical symbols usually varies giving rise to different models of the given theory. All non-logical content of such a theory is comprised in its non-logical axioms (e.g., axioms of ZF) while rules, which generate from these axioms new theorems, belong to the logical part of the theory (aka underlying logic). An alternative approach to axiomatization due to Gentzen amounts to a presentation of formal calculi in the form of systems of rules without axioms. Gentzen did not try to extend his approach to non-logical theories by considering specific non-logical rules as a replacement for non-logical axioms. However the more recent work in Univalent Foundations of Mathematics [2] suggests that the Gentzen-style rule-based approach to formal presentation of theories may have important applications also outside the pure logic. Areasonwhy onemay prefer a rule-based formal representation is that it ismore computerfriendly. This, in particular, motivates the recent work on the constructive justification of the Univalence Axiom via the introduction of new operations on types and contexts [1]. However this pragmatic argument does not meet the related epistemological worries. What kind of knowledge may represent a theory having the form of a bare system of rules? Is such a formof a theory appropriate for representing a knowledge of objective human-independent reality? How exactly truth features in rule-based non-logical theories? Using HoTT as a motivating example I provide some answers to these questions and show that the Gentzen-style rule-based approach provides a viable alternative to the standard axiomatic approach not only in logic but also in science more generally.

Opinion dynamics in network structures of special type are considered. Each node consists of two agents interacting with each other. The properties of consensus arising in such structures are studied using the DeGroot model.

We describe distributed reflexive complex mechanisms of decision-making in a SMART city. These complex mechanisms are a cognitive self-organizing decision support system for development governance. These mechanisms utilize local information from all nearby sensors of city sensors on buildings, sensors on other cars, sensors on pedestrians and some additional information. We describe the way to a new level of safety of citizens by additional vision and automated reasoning.  It provide transparency in Augmented Reality Devices by virtually eliminating obstacles e.g. buildings. The problem is that development of a city is a process so people still have to make suggestions and now these suggestions are about awareness of other agents. Distributed reflexive complex mechanisms can assist and support their decisions in solving these problems.

Discussions on the scientific pluralism typically involve the unity of science thesis, which has been first advanced by Neo-Positivists in the 1930-ies and later widely criticized in the late 1970-ies. In the present paper the problem of scientific pluralism is examined in the context of modern logic, where it became particularly pertinent after the emergence of non-Classical logics. Usual arguments in favor of a unique choice of “the” logical system are of an extralogical nature. The conception of Universal Logic as a theory of mutual translatability and combination of alternative logical systems allows for a more constructive approach to the issue. Logical pluralism gives rise not only to the ontological pluralism but also to non-Classical mathematics based on various non-Classical logics. Our analysis of ontological pluralism rises the following question: is our mathematics globally Classical and locally non-Classical (i.e. having non-Classical parts) or rather, the other way round, is globally non-Classical and only locally Classical? We conclude that in the context of post-non-Classical science the logical pluralism justifies one’s freedom to chose logical tools in conformity with one’s aims, norms and values.

The paper studies Russian metalinguistic comparatives. Specifically, it argues that Russian exhibits three single meta-comparatives (skoree ‘sooner’, bol′še ‘more’, and lučše ‘better’, lit.), which are derived as a result of grammaticalisation of corresponding standard comparatives and three double meta-comparatives (skoree bol′še, bol′še skoree, and skoree lučše). From a morphological and syntactic point of view, these meta-comparatives are quite distinct from standard comparatives. Unlike standard comparatives, they have only synthetic forms, are ungrammatical with Genitive and show prosodic restrictions and linearly syntactic preferences. Moreover, the metacomparatives are divided into two major groups: skoree, bol′še, skoree bol′še, bol′še skoree vs. lučše, skoree lučše. Each of these two groups imposes specific restrictions on a syntactic category and/or grammatical form of the two compared phrases. Last but not least, due to a relatively free combination of skoree with other single meta-comparatives, which results in double metacomparatives, the paper reveals that skoree is the most grammaticalised metacomparative in Russian.

Although mathematicians often use it, mathematical beauty is a philosophically challenging concept. How can abstract objects be evaluated as beautiful? Is this related to the way we visualise them? Using a case study from graph theory (the highly symmetric Petersen graph), this paper tries to analyse aesthetic preferences in mathematical practice and to distinguish genuine aesthetic from epistemic or practical judgements. It argues that, in making aesthetic judgements, mathematicians may be responding to a combination of perceptual properties of visual representations and mathematical properties of abstract structures; the latter seem to carry greater weight. Mathematical beauty thus primarily involves mathematicians' sensitivity to aesthetics of the abstract.

Frankfurt-type cases with covered manipulation received a great attention in the debates about freedom of will and moral responsibility. They pretend to give the refutation of the Principle of Alternative Possibilities (PAP) and to show that we can intuitively blame or praise an agent who was not able to do otherwise. In this paper, I will try to make explicit some basic intuitions underlying the agent's responsibility in Frankfurt-type cases, which were surprisingly ignored in the contemporary debates. The key intuition is that the responsibility of the agent in Frankfurt-type cases is always grounded at the point of overcoming the uncertainty preceding action. This overcoming is crucially important for agent's responsibility and immune to any manipulation of counterfactual intervener.

We extend the language of the modal logic K4 of transitive frames with two sorts of modalities. In addition to the usual possibility modality (which means that a formula holds in some successor of a given point), we consider graded modalities (a formula holds in at least n successors) and converse graded modalities (aformula holds in at least n predecessors). We show that the resulting logic, GrIK4, is both locally and globally undecidable. The same result is obtained for all logics between GrIK4 and its reflexive companion GrIS4 and for some other modal logics. As a consequence, for the “unrestricted version” of the description logic SIQ, the problem of concept satisfiability (even with respect to the empty terminology) is undecidable. We also give a survey of results on the local and global decidability, complexity, and the finite model property for fragments of GrIK4.

It is well-known that the concept of da Costa algebra [3] reects most of the logical properties of paraconsistent propositional calculi Cn, 1< n <w introduced by N.C.A.da Costa. In [10] the construction of topos of functors from a small category to the category of sets was proposed which allows to yield the categorical semantics for da Costa's paraconsistent logic. Another categorical semantics for Cn would be obtained by introducing the concept of potos { the categorical counterpart of da Costa algebra (the name \potos" is borrowed from W.Carnielli's story of the idea of such kind of categories)

In this paper we reconstruct a famous Severin Boethius's reasoning according to the idea of the medieval obligationes disputation mainly focusing on the formalizations proposed by Ch. Hamblin. We use two different formalizations of the disputation: first with the help of Ch. Hamblin's approach specially designed to formalize such logical debates; second, on the basis of his formal dialectics. The two formaliza-tions are used to analyze the logical properties of the rules of the medieval logical disputation and that of their formal dialectic's counterparts. Our aim is to to show that Hamblin's formal dialectic is a communicative protocol for rational agents whose structural rules may differ, thus, varying its normative character. By means of comparing Hamblin's reconstructions with the one proposed by C. Dutilh-Novaes we are able to justify the following conclusions: (1) the formalization suggested by Hamblin fails to reconstruct the full picture of the disputation because it lacks in some the details of it; (2) Hamblin's formal dialectic and the medieval logical disputation are based on different logical theories; (3) medieval logical disputation, represented by the formalization of C. Dutilh-Novaes, and the two ones of Hamblin encode different types of cognitive agents

 In 1926 D.Mourdoukhay-Boltovskoy introduced a hypersillogistic which according to him relates to the traditional syllogistic as a four-dimensional space relates to the three-dimensional space. Unfortunately, his note was too brief to understand the conception introduced. His remark from 1929 in which he refers to N. Vasiliev’s metalogic furnishes the clue to hypersyllogistic. In the paper the semantic of model schemes for hypersillogistic is proposed and some possible translations into traditional syllogistic are discussed.

It is not news that we often make discoveries or find reasons for a mathematical proposition by thinking alone. But does any of this thinking count as conducting a thought experiment? The answer to that question is “yes,” but without refinement the question is uninteresting. Suppose you want to know whether the equation [8x + 12y = 6] has a solution in the integers. You might mentally substitute some integer values for the variables and calculate. In that case you would be mentally trying something out, experimenting with particular integer values, in order to test the hypothesis that the equation has no solution in the integers. Not getting a solution the first time, you might repeat the thought experiment with different integer inputs.