PIERRE GASSENDI, DESPRE ATOMI ȘI LIBERTATE
Review of: Pierre Gassendi, Despre atomi și libertate (ed. Ratio et Revelatio, Oradea2021, 411 p.)
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Review of: Pierre Gassendi, Despre atomi și libertate (ed. Ratio et Revelatio, Oradea2021, 411 p.)
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In this paper, we study bounded versions of some model-theoretic notions and results. We apply these results to the context of models of bounded arithmetic theories as well as some related complexity questions. As an example, we show that if the theory S1/2(PV) has bounded model companion then NP=coNP. We also study bounded versions of some other related notions such as Stone topology.
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Moral conflicts are the situations which emerge as a response to deal with conflicting obligations or duties. An interesting case arises when an agent thinks that two obligations A and B are equally important, but yet fails to choose one obligation over the other. Despite the fact that the systematic study and the resolution of moral conflicts finds prominence in our linguistic discourse, standard deontic logic when used to represent moral conflicts, implies the impossibility of moral conflicts. This presents a conundrum for appropriate logic to address these moral conflicts. We frequently believe that there is a close connection between tolerating inconsistencies and conflicting moral obligations. In paraconsistent logics, we tolerate inconsistencies by treating them to be both true and false. In this paper, we analyze Graham Priest’s paraconsistent logic LP, and extend our examination to the deontic extension of LP known as DLP. We illustrate our work, with a classic example from the famous Indian epic Mahabharata, where the protagonist Arjuna faces a moral conflict in the battlefield of Kurukshetra. The paper aims to avoid deontic explosion and allows to accommodate Arjuna’s moral conflict in paraconsistent deontic logics. Our analysis is expected to provide novel tools towards the logical representation of moral conflicts and to shed some light on the context-sensitive paraconsistent deontic logic.
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In our previous work we proved the conjecture NP = PSPACE by advanced proof theoretic methods that combined Hudelmaier’s cut-free sequent calculus for minimal logic (HSC) with the horizontal compressing in the corresponding minimal Prawitz-style natural deduction (ND). In this Addendum we show how to prove a weaker result NP = coNP without referring to HSC. The underlying idea (due to the second author) is to omit full minimal logic and compress only “naive” normal tree-like ND refutations of the existence of Hamiltonian cycles in given non-Hamiltonian graphs, since the Hamiltonian graph problem in NPcomplete. Thus, loosely speaking, the proof of NP = coNP can be obtained by HSC-elimination from our proof of NP = PSPACE.
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In this paper, we utilized triangular conorms (S-norm). The essence of using S-norm is that the similarity order does not change using different norms. In fact, we are investigating for a new conception for calculating the similarity of two Fermatean fuzzy sets. For this purpose, utilizing an S-norm, we first present a formula for calculating the similarity of two Fermatean fuzzy values, so that they are truthful in similarity properties. Following that, we generalize a formula for calculating the similarity of the two Fermatean fuzzy sets which prove truthful in similarity conditions. Finally, various numerical examples have been presented to elaborate this method.
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In the first sentence of his preface to the Tractatus Logico-Philosophicus from 1918, Ludwig Wittgenstein says that it is, in fact, a work that can only be understood by a person who has already thought about the ideas set forth in that work, or at least thoughts similar to them. Bertrand Russell wrote the second Introduction to Wittgenstein’s Tractatus in 1922, after Wittgenstein, in his letters, noted that Russell had misunderstood his work. Therefore, the paper aims to present Russell’s introduction to Wittgenstein’s Tractatus, which begins with the words that it is a work that should be considered an important event in the philosophical world. Thus, in his final Introduction, Russell points out the elements he considers most significant in the Tractatus: the logical structure of proposition, the nature of logical in ference, the theory of knowledge, the principles of physics, ethics, and Mystical (das Mystische). In this regard, the aim of the paper is to present Russell’s understanding of the fundamental teachings of Wittgenstein and linking them with Wittgenstein’s remarks on Russell’s misunderstanding. The hypothesis of the paper is to prove Wittgenstein’s remarks on Russell’s misunderstanding, which are found in the letters, but also to present basic examples of Russell’s (mis)understanding of Wittgenstein’s teachings from his Introduction.
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The presented text performs a conceptual analysis of the second part of the doctrine of being in Hegel’s logic – quantity. The analysis is conducted through the prism of the principle of particularity, of the mediating function of the middle term in Hegel’s triad. The methodological potential of the middle term generates the possibility for differentiation and topological specification of philosophy and mathematics. Through the dialectical connection of quality and quantity (in the logical course of the transition from quality to quantity and the return of quantity back again to quality), the essence of the universal evolution of philosophical and mathematical knowledge is explained.
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The semantic method of extension and intension presented by Rudolf Carnap may have some problems from the current perspective in cognitive science. For example, that method is strongly linked to logic, and it is hard to determine where its state-descriptions come from, how many they are, and what the relation of accessibility between them is. This paper tries to solve difficulties such as those by updating the method resorting to the theses and results of a contemporary reasoning theory: the theory of mental models. Basically, the update consists of replacing the state-descriptions of the original method with the possibilities of the theory of mental models. That allows reformulating several relevant concepts in Carnap’s method in order to better adjust them to the real characteristics of human language.
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Introduction. The main intellectual competence of IT professionals includes culture of thinking, the ability to generalize, analyze, and perceive information. But what do we mean by the culture of thinking today? If it is based on consistency and creativity, as leading IT-companies require from university graduates, it immediately indicates the complexity and even inconsistency of the requirements for the expected qualities of thinking from newly-qualified professionals. Because, on the one hand, they need to be able to systematize the available data into a certain structure; on the other hand, they have to abandon the existing one and achieve a fundamentally different solution. The purpose of this article is to identify the core of thinking tools in professional practice and describe precisely them using set-theoretical analysis. Materials and Methods. We proceed from the fact that thinking, as a part of the nature of reality, reaches the level required for professional practice when it satisfies at least three conditions: stability, accuracy and completeness of the description of a particular system or process. Since we cannot extract thinking from historical and cultural way of cognition, which is sometimes called an episteme, it is necessary, first of all, to rely on examples of such a context as the evolution of the linguistic state of the human population and the evolution of the architecture of the design of distributed systems in the information space. The mathematical basis is taken from the experience of teaching and using the set theoretical method in mathematics disciplines within computer fields of study. Results. Within the framework of the proposed methodology, some important tools of professional thinking are formulated in the precise language of computer science. The structures of stable retention of objective thinking, the accuracy of retention of meaning, the minimum completeness of the system, bricolage and the option of the basic figure of creativity visualization are described. This methodology allows to see the logic of branching in the evolution of different languages, as well as the logic of the evolution of software systems. Conclusions. The set-theoretical tools of thinking reveal the logic within the development of distributed systems in the modern information environment and, apparently, significantly affect the tools of thinking in various fields of knowledge.
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A number of versions of Zeno’s ‘Dichotomy’ is being discussed in literature. Some of them are versions of a paradox that can be called ‘the paradox of logical causality’. It can be traced back to Benardete; in recent decades it has been discussed by Priest, Yablo, Hawthorne, Uzquiano, Shackel, Caie, and others. Unlike the original ‘Dichotomy’, the paradox of logical causality is an open problem for it has no generally accepted solution. In the paper, I examine the solution to the paradox proposed by Hawthorne and argue that it has an essential flaw caused by Hawthorne’s rejection of what he calls ‘the Change Principle’. I also compare the paradox and Zeno’s ‘Dichotomy’ and specify features shared by them, and features distinguishing the paradox. Their shared features are using infinite open series and reasoning from logical premises to physical conclusions. What distinguishes the new paradox is presupposing motion, and applying Zeno’s series to phenomena of physical interaction.
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This paper continues my discussion with Michael Dummett on Frege’s senses, published in The Philosophy of Michael Dummett and further developed in Diametros. In his reply to my original paper, Dummett came to agree with me that senses are neither objects nor functions, since they have a categorially different kind of linguistico-metaphysical function to perform. He then asks how we might quantify over senses, if they are neither objects nor functions. He discusses two main options, and finds one unviable and the other “very un-Fregean.” I then offer a Fregean or neo-Fregean option in my rejoinder. And I still hold that this way out will do the job, or is at least plausible enough that the burden of persuasion is on those who disagree. But I hope to show in this paper that on a more complete examination of Frege, there are at least twenty Fregean or neo-Fregean ways out, with the one I proposed being option (17).
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D. E. Watt replied to Ramsey’s attacks on Keynes’s Logical Theory of, as originally contained in Keynes’s A Treatise on Probability, in the January 1922 issue of Cambridge Magazine, in the republished British Journal for the Philosophy of Science version. Watt overlooks that all 15 of Ramsey’s paragraphs in the original Cambridge Magazine version of the paper are erroneous. Watt concentrates only on the issue of numerical versus non numerical probabilities that was raised by Ramsey. Watt is correct in his assessment that Keynes was right and Ramsey was wrong, but gives probability answers that would not have been given by Keynes, or Keynes and Russell. Watt overlooks the errors contained in each paragraph of Ramsey’s review. Keynes’s main point on the issue of numerical versus non numerical probabilities is that many probabilities, especially initial or a priori probabilities, will have to be specified by interval probability. Keynes’s Principle of Indifference (POI) has nothing to do with this issue, due to Ramsey’s inchoate and erroneous understanding of the conditions Keynes laid out in the A Treatise on Probability for the sound application of the POI, as enunciated by Keynes on pp.52-56, and not on p.42, which is the Laplace -Bernoulli version of the POI. Sound applications of the Keynesian POI require that the alternatives must be a) discrete, b) indivisible, c) finite, d) represented by conditional probability, e) perfectly symmetrical, and f) based on the available, positive evidence. This, of course, rules out any application to states of equally balanced ignorance (no positive information). Of course, there will be only one answer that can be calculated by all rational decision makers. The obvious example is the first Ellsberg urn problem, which is nearly identical to the problem used by Keynes as an example on pp.75-76 of his A Treatise on Probability.
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The foundations of mathematics cover mathematical as well as philosophical problems. At the turn of the 20th century logicism, formalism and intuitionism, main foundational schools were developed. A natural problem arose, namely of how much the foundations of mathematics influence the real practice of mathematicians. Although mathematics was and still is declared to be independent of philosophy, various foundational controversies concerned some mathematical axioms, e.g. the axiom of choice, or methods of proof (particularly, non-constructive ones) and sometimes qualified them as admissible (or not) in mathematical practice, relatively to their philosophical (and foundational) content. Polish Mathematical School was established in the years 1915–1920. Its research program was outlined by Zygmunt Janiszewski (the Janiszewski program) and suggested that Polish mathematicians should concentrate on special branches of studies, including set theory, topology and mathematical logic. In this way, the foundations of mathematics became a legitimate part of mathematics. In particular, the foundational investigations should be conducted independently of philosophical assumptions and apply all mathematically accepted methods, finitary or not, and the same concerns other branches of mathematics. This scientific ideology contributed essentially to the remarkable development of logic, set theory and topology in Poland.
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The purpose of this paper is to analyze the concept of the interdisciplinary problem using the categories of the logic of questions. The problem is seen in a logical and epistemic sense: the problem is the meaning of the question, and the question is a formulation of the problem in a particular language. Demonstrating that the interdisciplinarity of an interdisciplinary problem is understood in terms of a particular kind of complexity, I indicate the places where it is realized in the structure of the problem-question, in the problem’s solution-answer to the question, and in the cognitive context of the problem solving – answer to the question. The paper also displays how an interdisciplinary problem is situated within the broader structure of an interdisciplinary research process. Thus, the paper provides not only a metatheoretical characterization of the interdisciplinary problem but also a general methodological tool for analyzing particular interdisciplinary problems.
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Both Lowe and Tsai have presented their own versions of the theory that both indicative and subjunctive conditionals are strict conditionals. We critically discuss both versions and we find each version wanting.
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Review of: John Perry, Frege’s Detour: An Essay on Meaning, Reference, and Truth, Oxford University Press, 2019, xii + 148 pp.
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The scientific development touches on significant problems in the development of scientific knowledge, present in the research of thinkers of the XX century. A set of principles, approaches and criteria in science, corresponding to the new priorities, is presented. In the context of the relationship between philosophy and the private sciences, interpretations take place and complex methodological dilemmas unfold. The focus of the development is the understanding of neo-positivist philosophers with their methodological concept of „logic of science”.
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This paper proposes a fuzzy logic model for evaluating the level of stakeholder motivation for high-quality publications. Conceptually, the model is based on stakeholder theory and Vroom’s expectancy theory of motivation. Instrumentally, tools of fuzzy sets, fuzzy logic, and expert evaluations are at its core. The model is suitable for any university. Further, it reflects university specificity, using specific motivational factors in one of the evaluation procedures. The model easily evaluates the level of motivation by processing vague, subjective perceptions. It was applied at a Bulgarian university through a comprehensive survey that included 106 participants and performed well. The model contributes to the advancement of management science by theoretically enriching research management and organizational behaviour and complementing their tools. Expected practical implications are improved university management and higher scientific results based on well-grounded decisions about research, people, and performance.
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It is my intention in this article to present some consequences of Quine’s thesis on the dependence of ontology on ideology (Quine, 1980), seeking an argument for my own thesis on the dependence (theoretical) existence of entities on identity type or ontology dependence on logic and language. If Quine's thesis is correct, then we can expand the resolution of this conclusion and say that ontology depends on the identity or on identification of the "identity criteria for conceptual schemes" (Davidson, 2001) which is constructed in the theory. Consequently I will speak about types of identity which adapts choice of ontology and of which depends ontology of a theory. Here I want to connect the different types of use of the term identity in Aristotle's writings and the different types of predications that are based on them with the concept of identity as the equivalence of symbols in modern logic. I want to reinterpret Quine's statement: "There is no entity without identity " in the form of implication "What (kind of) identity such (kind of ) entity."
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