New Remarks on the Concept in Logical Use

The main thesis of this paper is directed against the traditional (cognitivetheoretical) definition of the concept which claims that the concept is the '' thought about the essence of the object being thought'', i.e. that it is “a set of essential features or essential characteristics of an object''. But the '' set of essential features or essential characteristics of an object of thought'' is a '' content’’ of the thought. The thought about the essence of an object is definition and the concept is not definition but the part of definition! Besides as the part of formal structure of thought, the concept possesses calculative logical properties that in formal logic (be it syllogistics, or the logic of propositions, or the logic of predicates) come to the front place of formal logical computation. Without the calculative properties of the concept, there would be no calculative properties of propositions which express the thought (thought structures). The calculative properties of a concept include the (1) degree of its logical generality (degree of variability), the (2) logical relations it can establish within the whole of the conceptual content, the (3) operability of the concept in structure of affirmation and negation, the (4) deducibility of either axiomatic or probabilistic systems. Therefore, I believe that, from the logical point of view, the definition of a concept should be applied in favor of its calculative properties that it possesses.

The domination monoid in o-minimal theories

We study the monoid of global invariant types modulo domination-equivalence in the context of o-minimal theories. We reduce its computation to the problem of proving that it is generated by classes of [Formula: see text]-types. We show this to hold in Real Closed Fields, where generators of this monoid correspond to invariant convex subrings of the monster model. Combined with [C. Ealy, D. Haskell and J. Maríková, Residue field domination in real closed valued fields, Notre Dame J. Formal Logic 60(3) (2019) 333–351], this allows us to compute the domination monoid in the weakly o-minimal theory of Real Closed Valued Fields.

Formal logic and natural ways of reasoning

In the paper I ask the question about the relation between formal logic and the natural logic of human mind. By a natural logic I mean the ways of thinking of a person that is intelligent but untrained in formal logic. As it turns out that the laws, rules or properties of formal logic in some cases diverge from the natural ways of reasoning, I explain the causes of this divergence. Since the majority of research in this area has been carried out from the standpoint of psychology, as a logician I suggest a slight change of the angle from which we look at the problem. I argue that certain narrowing of an interdisciplinary research would be helpful in getting a better picture of natural logic, and might provide a new stimulus for formal investigations.

Unsaid Thoughts: Thinking in the absence of (some) verbal logical connectives

Combining two thoughts into a compound mental representation is a central feature of our verbal and non-verbal logical abilities. We here approach this issue by focusing on the contingency that while natural languages typically verbalise only two of the sixteen connectives from formal logic to express compound thoughts —"and" and "or"— the remainder appear to be entertainable as non-verbal, conceptual representations and this suggests a way to probe how linguistic and non-linguistic thinking processes relate. In a visual world experiment aimed at tracking both comprehension-related and reasoning-related aspects of the capacity to represent compound thoughts, we found that participants are capable of learning and interpreting a made-up word for logic’s NAND operator, indicating that unlexicalised logical connectives are nonetheless conceptually available.

Dialectical logic or logical dialectics? The Polish discussion on the principle of non-contradiction (1946–1957)

The discussion on the principle of non-contradiction (1946–1957) between Marxist and non-Marxist philosophers was one of the major philosophical discussions in Polish philosophy of this period. In my text, I carefully reconstruct this discussion and outline its relation to Soviet debates on the subject. I show that the change in Schaff’s position happened in the early 1950s under the combined influence of the Lvov–Warsaw School and the changes in the official Soviet position regarding formal logic. I discuss the aftermath following Schaff’s change in attitude towards the analytic tradition for the development of Polish philosophy, as well as the critique of this change by Jarosław Ładosz. In my reconstruction of the latter, I focus on the problem of the historical development of science. I refer to Ilyenkov’s critique of Schaff, opposing synchronic (“positivist”) and diachronic (“dialectical”) concepts of knowledge. As I argue, these opposing concepts of science can be seen as a genuine issue at stake in the Polish discussion as well, especially in the polemic between Schaff and Ładosz.

Real Options for Risk Analysis in Estimating the Capitalization Rate

A suitable cap-rate is generally determined through an analogical process in order to estimate the value of any real estate through the capitalization of the incomes. The analogy relates to the risk and duration of similar investments. There are numerous methods to rationalize the valuation of the cap-rate. Appraisals have a certain degree of uncertainty in all these methods. This paper proposes a methodology which removes any uncertainty when evaluating the cap-rate. This is achieved through the combination of the formal logic of the Ellwood’s model and the Real Options Analysis.

Eptonyms in German: An Attempt of Typological Distinction (on the Example of Maxims and Aphorisms)

The present paper provides an outline of the German eptonym, as a quotation-like utterance that can be traced back to the name of its real or alleged author, a precedential text / a part of a precedential text connected with the concept AUTHOR. The eptonyms are examined from the point of view of the specifics of the AUTHOR's position regarding the topic of the utterance determining the type of eptonym. The four-step algorithm shown in the paper involves modelling the degree of the author's personality prominence in the eptonym. Two polar points – maximal social experience and maximal individualised author-based approach – are represented in the eptonymicon by maxims and aphorisms respectively. It is stated that the maxim objectifies the moral norms of a certain national language collective. It is rational, contains an immanent moral component, has a directive character, explicates the rules of behaviour, ethical principles, objective laws, norms. The aphorism is paradoxical, reflecting the depth and originality of individual author's multi-vector thought, formal symmetric, dialogic, breaking the rules of formal logic. The provided method can be used with the purpose of distinguishing and defining other types of German eptonyms.

Methods, principles and presumptions of constitutional and conflict diagnostics

The article examines the main elements of constitutional and conflict diagnostics, which is a system of consistently applied methods, legal principles and presumptions, aimed at obtaining information about the causes, content, consequences and methods of preventing and resolving a constitutional conflict. Constitutional and conflict diagnostics is theoretically justified by the author as a new method of the science of constitutional law, which allows lawyers to study constitutional conflicts and constitutional norms of the conflictological type. The use of constitutional and conflict diagnostics will allow to establish and investigate the causal relationship between the formation of law, its normative expression and subsequent law enforcement, which will reflect the constitutional conflict. The author believes that the following methods are used in the course of diagnosing a constitutional conflict: dialectical, systematic, historical, statistical, methods of formal logic, formal-legal method, method of legal modeling, and other methods. The author also proposes to consider as the principles of such diagnostics: the principle of taking into account the specific historical situation, dialectical unity, systematic study of the conflict and the principle of the rule of law. The author suggests considering the following presuppositions used in the course of constitutional and conflict diagnostics: the presumption of the inevitability of constitutional conflicts, the presumption of the solvability of constitutional conflicts, and the presumption of the prevention of conflicts.

Maximality of bi-intuitionistic propositional logic

In the style of Lindström’s theorem for classical first-order logic, this article characterizes propositional bi-intuitionistic logic as the maximal (with respect to expressive power) abstract logic satisfying a certain form of compactness, the Tarski union property and preservation under bi-asimulations. Since bi-intuitionistic logic introduces new complexities in the intuitionistic setting by adding the analogue of a backwards looking modality, the present paper constitutes a non-trivial modification of the previous work done by the authors for intuitionistic logic (Badia and Olkhovikov, 2020, Notre Dame Journal of Formal Logic, 61, 11–30).