Topic of the issue: LOGIC PROBLEMS, INTERPRETATIONS, APPLICATIONS (https://doi.org/10.58945/QIHF7433)
Issue editors: Doroteya Angelova
CONTENTS & Abstracts & Keywords & Authors in the issue
Let a Hundred Flowers Bloom, or on Cryptomorphism
Abstract: The paper discusses a possible way of justifying the existence of a multiplicity of cryptomorphic axiomatic theories. It is argued that what renders this multiplicity inevitable are the applications of the theory. They give rise to difficulties whose solution necessitates the application of different conceptual tools. The paper is organized as follows: (§1) introduces the concept of cryptomorphism and the canonic example for the phenomenon: matroid theory; (§2) discusses five cryptomorphic approaches to the definition of rationality in the framework of decision theory: through utility functions, weak orders, choice operators, layered permutations, and pop-stack sortability; (§3) shows that each of these different approaches can serve as a basis for the introduction of a different modification of the original theory. This establishes the heuristic value of cryptomorphic approaches in the domain of decision theory.
Keywords: philosophy of mathematics; cryptomorphism; matroids; decision theory; utility function; weak order; choice operator; layered permutations; pop-stack sortability; series-parallel partial orders
Evgeni Latinov (Associate Professor, DSc at Sofia University “St. Kliment Ohridski”)
Conditions and Conditional Sentences
Abstract: The terms “sufficient condition” and “necessary condition” are related to conditional sentences (those of the form “If A, then B”). The meaning of the former depends on the use of the latter, and conditional sentences are used differently. A conditional sentence could express material implication, but it could also express formal implication. The terms “sufficient condition” and “necessary condition” reflect this difference, each taking on respectively (at least) two different meanings. In the text, I indicate and analyze these meanings. The difference between them is significant because, as it turns out, according to one of them (corresponding to the cases where conditional sentences express material implications), if several conditions together are a sufficient condition for something, then (by logical necessity) only one of them is also a sufficient condition for it, which is not the case with the other meaning (corresponding to the cases in which conditional sentences express formal implications). If the difference in meaning is not taken into account, it is not improbable for situations to arise where mixing them up leads to logical problems. An example of this is given in the text.
Keywords: conditional sentences; sufficient condition; necessary condition
Silviya Kristeva (Associate Professor, Ph.D. at South-West University “Neofit Rilski”)
Grounding and Schematics of Induction
Abstract: Induction is a major challenge for logical theory in its quest to build a comprehensive theory of inference. In the contest between deduction and induction for awarding and deriving the crown of the theory of reasoning, induction more often gives up first place. But here we must trust John St. Mill, who declares induction to be the fundamental and absolutely prime question of the “Science of Logic”. The article will follow the way Mill defines induction and how is the logical axiom of inductive inference formulated by him on this basis. For the general construction of induction, however, Hegel offers a structure that will take us even further in entering into the inner mechanism of induction as well as towards the schematization of the logical path to the derivation of the inductive conclusion.
Keywords: logic; theory of reasoning; Mill; Hegel; induction; general axiom of induction
LOGIC AND SCIENCE
On Symbolization in Mathematics
Abstract: In this paper we discuss the importance of the symbolization in mathematics through the analysis of four aspects we judge to be the most important ones. Our discussion will be centralized in some syntactical aspects of mathematics and the four aspects we are going to discuss are: i. precision and concision; ii. the possibility of extension to other problems; iii. heuristics; iv. structure revelation.
Keywords: Symbolic knowledge; philosophy of mathematics; mathematical notations
Doroteya Angelova (Associate Professor, Ph.D. at the Institute of Philosophy and Sociology, BAS)
Some Philosophical and Logical Aspects About Artificial Intelligence
Abstract: The article examines some philosophical and logical aspects that are present in the definitions of the concept of artificial intelligence (AI) and in the different views about its essence and goals. The main focus will be on the place of logic, including non-classical logics, in the context of the mentioned views. The question of the boundaries of AI will be also discussed and it will be proposed to be considered in several different contexts.
Keywords: artificial intelligence; philosophy; non-classical logics; boundaries
LOGIC, PHILOSOPHY, LANGUAGE
Application of Grice’s Theory in Linguistic Research
Abstract: Two tasks are assigned to this article, related to Grice's theory of conversational implicatures. One of them is concerned with the distinction that Mark Jary proposes between behavioral and material conversational implicatures and the idea that, if this distinction is accepted, then Grice’s notion of non-natural meaning is reduced to cases of behavioral implicatures. An attempt is made to disprove this position and simultaneously maintain the distinction between the two types of implicature. The second task is related to the application of Grice’s theory in linguistic studies to further develop explanations for the processing of utterances containing metaphor or irony.
Keywords: implicatures; speaker’s meaning; Grice; irony; metaphor; speech act theory
Kristiyan Enchev (Associate Professor, Ph.D. at Institute of Philosophy and Sociology, BAS)
(Im)Possibility, (Im)Potentiality, Death: Heidegger and Blanchot
Abstract: This text aims to trace, through Darin Tenev's thesis on the relationship between possibility and negativity, how Heidegger's thinking proposes death as a self-possibility and how not- being-able-to-be in superposition against the horizon of the world ultimately can be interpreted as “sublated” in death as “Dasein's ownmost possibility”. Blanchot, who follows Heidegger in many respects, takes a radically different position towards death, speaking of death as an impossibility, which in the process of dying is less and less owned death.
Keywords: impossibility; possibility; negativity; impotentiality; potentiality; death
The Stoic Conception of Philosophy as an Art of Living and the Pursuit of Moral Beauty
Abstract: The Stoics argue that philosophy as an art of living (techne) is not only a theoretical and intellectual pursuit of knowing the rational order and harmony (or logos) of nature/physics/God but it is also a practical activity that aims to transform and shape our lives in accordance with this knowledge. In this sense, the Stoics argue that philosophy is not an abstract subject to be considered but rather a practical matter that has a direct influence on our way of living. Based on this main Stoic conception of philosophy, in this paper, I fundamentally take issue with the general claim about the the Stoic moralism entails that philosophy is solely grounded on the purpose of achieving moral virtue, suggesting that all other elements are excluded from its purview. By arguing that Stoic moralism is not contrasted with the conception of moral beauty, I adopt the view that Stoic moralism is not free from the conception of beauty, such that it encapsulates the idea that beauty is within the virtuous. In light of this, I focus on the conception of philosophy and suggest that, for the Stoics, although the ultimate goal of philosophy is to lead a virtuous life that is grounded on our understanding of the rational order and harmony (or logos) of nature, the philosophical life does also correspond to a moral life, which has the aesthetic aspect of embellishing our lives with beauty, harmony, and order.
Keywords: art of living; techne; philosophy; Stoicism; moral beauty; nature; physics; God.
About “Readings of Dante”
Miglena Nikolchina (Professor, PhD at Sofia University “Kliment Ohridski”; member of Academia Europea)
Socioanalytical Enlightenment: an Opportunity
Virginia Radeva (Associate Professor, Ph.D. at Sofia University “St. Kliment Ohridski”)
Оbsession. Laura and the Poet