Institute of Philosophy of Saint-Petersburg State University
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Reply to the Opponents
Get PDFВ статье я отвечаю на комментарии и возражения, высказанные оппонентами, фиксирую точки расхождения между нами и отмечаю проблемы, которые лично мне кажутся особенно интересными.I reply to comments and objections made by my opponents, specify disagreements between them and me, and the topics of discussion that I find especially interesting
Шаг назад в межмировой предикации
Get PDFThe note contains two objections to the syntactic and semantic architecture of Borisov’s logic for cross-world predication. First, I point out that Borisov’s language is unable adequately to formalise contingent propositions with zero-place predicate (e.g. ‘It is raining’) due to the inflexible connection between the number of world arguments of a predicate and the number of its individual arguments. Second, I argue that Borisov’s VP-functions, whose job is to map individuals to possible worlds where they are to be considered, are redundant even if our goal is to handle cross-world predication.В реплике выдвигается два возражения против синтактико-семантической архитектуры логики межмировой предикации Е. В. Борисова. Одно состоит в том, что в языке Борисова невозможно адекватно формализовать контингентные пропозиции с нуль-местными предикатами (типа ‘Светает’), поскольку число аргументов-миров у предиката привязано к числу аргументов-индивидов. Второе основано на избыточности вводимой Борисовым VP-функции, сопоставляющей индивидам возможные миры, для интерпретации термов даже с учётом межмировой предикации
Penalty Logic: Paraconsistency and Applications
Get PDFPenalty logic is a non-classical non-monotonic logic which allows us to demonstrate the power of belief, the level of truth or the reliability of data that we are using. This logic can be useful to model human reasoning or to replace the penalty function in the sphere of Machine Learning. We can also talk about paraconsistency of this logic and suggest the definition of contradiction without negation.Penalty logic is a non-classical non-monotonic logic which allows us to demonstrate the power of belief, the level of truth or the reliability of data that we are using. This logic can be useful to model human reasoning or to replace the penalty function in the sphere of Machine Learning. We can also talk about paraconsistency of this logic and suggest the definition of contradiction without negation
Mr. Frege, The Platonist
Get PDFAlthough Frege is one of the prominent figureheads of analytic philosophy, it is not surprising that there are still issuessurrounding his views, interpreting them, and labeling them. Frege’s view on numbers is typically termed as Platonistic orat least a type of Platonism (Reck 2005). Still, the term ‘Platonism’ has views and assumptions ascribed to it that may bemisleading and leads to mischaracterizations of Frege’s outlook on numbers and ideas. So, clarification of the term‘Platonism’ is required to portray Frege’s views more accurately (Reck 2005). This clarification gives us a better picture of what Frege is interested in and what he does not emphasize. Moreover, in such a clarifying process, we find that Frege draws heavy influence from Rudolf Hermann Lotze, who is frequently called a Neo-Kantian (Vagnetti 2018). InLotze’s major work, Logik, Lotze has a central focus on validity, in its most general form as he used it, that investigatesvarious related topics, i.e., concepts, language, etc. (Vagnetti 2018; Lotze 1888). Furthermore, we observe that Frege’s work is so similar to Lotze, that it seems questionable to call his outlook ‘Platonism’. Therefore, attributing ‘Platonism’ to Frege may be a slight misnomer. This paper’s entirety is mostly a synthesis of a variety of articles related to Frege,Lotze, and their respective outlooks and the original works of Frege and Lotze that I use to support the view that the term ‘Platonism’ is a slight issue when predicated to Frege. As such, I include an overview of Frege’s treatment incontemporary literature that highlights the usage of the term ‘Platonism’ and how broad its uses tend to be utilized (Balaguer 2006; Burge 1992). In sum, it is observed that the general label ‘Platonism’ becomes less appropriate when we consider Lotze in the picture and contrast Lotze alongside Mr. Frege. Overall, this paper is just an explanatory one of Mr. Frege, the Platonist, and the issues of applying the term ‘Platonism’ onto him as his views are seemingly more of a segue from Lotze.Although Frege is one of the prominent figureheads of analytic philosophy, it is not surprising that there are still issuessurrounding his views, interpreting them, and labeling them. Frege’s view on numbers is typically termed as Platonistic orat least a type of Platonism (Reck 2005). Still, the term ‘Platonism’ has views and assumptions ascribed to it that may bemisleading and leads to mischaracterizations of Frege’s outlook on numbers and ideas. So, clarification of the term‘Platonism’ is required to portray Frege’s views more accurately (Reck 2005). This clarification gives us a better picture of what Frege is interested in and what he does not emphasize. Moreover, in such a clarifying process, we find that Frege draws heavy influence from Rudolf Hermann Lotze, who is frequently called a Neo-Kantian (Vagnetti 2018). InLotze’s major work, Logik, Lotze has a central focus on validity, in its most general form as he used it, that investigatesvarious related topics, i.e., concepts, language, etc. (Vagnetti 2018; Lotze 1888). Furthermore, we observe that Frege’s work is so similar to Lotze, that it seems questionable to call his outlook ‘Platonism’. Therefore, attributing ‘Platonism’ to Frege may be a slight misnomer. This paper’s entirety is mostly a synthesis of a variety of articles related to Frege, Lotze, and their respective outlooks and the original works of Frege and Lotze that I use to support the view that the term ‘Platonism’ is a slight issue when predicated to Frege. As such, I include an overview of Frege’s treatment incontemporary literature that highlights the usage of the term ‘Platonism’ and how broad its uses tend to be utilized (Balaguer 2006; Burge 1992). In sum, it is observed that the general label ‘Platonism’ becomes less appropriate when we consider Lotze in the picture and contrast Lotze alongside Mr. Frege. Overall, this paper is just an explanatory one of Mr. Frege, the Platonist, and the issues of applying the term ‘Platonism’ onto him as his views are seemingly more of a segue from Lotze
Yablo’s Paradox, The Liar, and Referential Contradictions from a Graph Theory Point of View
Get PDFF-systems are useful digraphs to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and the one of Yablo can be analyzed with that tool to find graph-theoretic patterns. In this paper we studied this general model consisting of a set of sentences and the binary relation ‘ affirms the falsity of ’ among them. The possible existence of non-referential sentences was also considered. To model the sets of all the sentences that can jointly be valued as true we introduced the notion of conglomerate, the existence of which guarantees the absence of paradox. Conglomerates also enabled us to characterize referential contradictions, i.e., sentences that can only be false under a classical valuation due to the interactions with other sentences in the model. A Kripke-style fixed-point characterization of groundedness was offered, and complete (meaning that every sentence is deemed either true or false) and consistent (meaning that no sentence is deemed true and false) fixed points were put in correspondence with conglomerates. Furthermore, argumentation frameworks are special arguments and argued about the usefulness of the concept for the argumentation theory.F-systems are useful digraphs to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and the one of Yablo can be analyzed with that tool to find graph-theoretic patterns. In this paper we studied this general model consisting of a set of sentences and the binary relation ‘ affirms the falsity of ’ among them. The possible existence of non-referential sentences was also considered. To model the sets of all the sentences that can jointly be valued as true we introduced the notion of conglomerate, the existence of which guarantees the absence of paradox. Conglomerates also enabled us to characterize referential contradictions, i.e., sentences that can only be false under a classical valuation due to the interactions with other sentences in the model. A Kripke-style fixed-point characterization of groundedness was offered, and complete (meaning that every sentence is deemed either true or false) and consistent (meaning that no sentence is deemed true and false) fixed points were put in correspondence with conglomerates. Furthermore, argumentation frameworks are special arguments and argued about the usefulness of the concept for the argumentation theory
Hinges, Deep Disagreement and Fixed Points in the Argumentation Logic
Get PDFIn his treatise ‘On Certainty’ (1969) L. Wittgenstein compared the propositions ex- pressing basic principles to the hinges enabling both doubting and justifying knowledge. In 1985 Robert Fogelin proposed the conception of deep disagreement in argumentation analysis and in his description of it he referred to the hinges. We continue Wittgenstein’s hinges metaphor and compare pulling and pushing the door of knowledge to adopting contrary standings about principal issues, which can result in the deep disagreements. We suggest looking at the hinges enabling those door moves as at the fixed points in the extension semantic of the argumentation logic. Interpreting the hinges as the fixed points allows viewing rejected arguments as isolated deadlocks of the deep disagreements, or anti-extensions, and opens a possibility for a compromise on the basis of certain extensions.В трактате «О достоверности» (1969) Л. Витгенштейн сравнил предложения, выражающие ключевые принципы знаний людей, с дверными петлями, без которых невоз- можно ни обосновывать знание, ни сомневаться в нём. В 1985 году Роберт Фогелин предло- жил понятие глубокого несогласия для анализа аргументации и, описывая его свойства, со- слался на дверные петли Витгенштейна. Если продолжить метафору дверных петель Вит- генштейна, то, если дверь познаниятолкают или тянут, это ведет к глубоким разногласиям по принципиальным вопросам. В русле этого мы предлагаем посмотреть на дверные петли как на неподвижные точки в семантике расширения логики аргументации. Это позволяет рассматривать отклоненные аргументы как изолированные тупики глубоких разногласий и открывает возможность длякомпромисса на основе определённых расширений
К проблеме расширения матричной семантики, адекватной классической импликативной логике, до матричной семантики, адекватной классической конъюнктивно-импликативной логике
Get PDFIn (Popov 2019), a list of all logical matrices is given, the carrier of each of which is {1, 1/2, 0} and the designated set of each of which is {1}, adequate to classical implicative logic. In particular, to this list belong the logical matrices ⟨{1, 1/2, 0}, {1}, ⊃ (1, 0, 0, 1)⟩ and ⟨{1, 1/2, 0}, {1}, ⊃ (1/2, 0, 0, 1/2)⟩. This article contains the construction of the binary opera- tion& on {1, 1/2, 0} and the proof that ⟨{1, 1/2, 0}, {1}, &, ⊃ (1, 0, 0, 1)⟩ there is an �&⊃-matrix adequate to the classical conjunctive-implicative logic, as well as a proof that there is no op- eration for which ⟨{1,1/2, 0}, {1}, , ⊃ (1/2, 0, 0, 1/2)⟩ is an �&⊃-matrix that is adequate to the classical conjunctive-implicative logic.В (Попов 2019) дан перечень всех логических матриц, носитель каждой из которых есть {1, 1/2, 0} и выделенное множество каждой из которых есть {1}, адекватных классической импликативной логике. В частности, этому перечню принадлежат логиче- ские матрицы ⟨{1, 1/2, 0}, {1}, ⊃ (1, 0, 0, 1)⟩ и ⟨{1, 1/2, 0}, {1}, ⊃ (1/2, 0, 0, 1/2)⟩. Настоящая статья содержит построение бинарной операции & на {1, 1/2, 0} и доказательство того, что ⟨{1, 1/2, 0}, {1}, &, ⊃ (1, 0, 0, 1)⟩ есть �&⊃-матрица, адекватная классической конъюнктивно-импликативной логике
НОВАЯ МОДУЛЯРНОСТЬ. ЛОГИКА И РАССУЖДЕНИЯ
Get PDFOver the centuries, logic has studied reasoning. Later reasoning turned into a question of cognitive science, which is not always friendly to logic. Using the example of the relatively new philosophico-cognitive theory due to Sperber and Mercier, in which logic plays a modest role, we demonstrate the productivity of their cooperation. Sperber and Mercier develop a theory of the functioning of reason which fits perfectly with the epistemological tradition of Modern philosophy. The reasoning is the core of this theory. However, it is based not on logic but on intuition reinforcedby the concept of modularity. The paper argues that reasoning can hardly be conceived beyond logical sequences. Sperber and Mercier’s approach confirms this position as we clarify how contemporary logic can fill the lacunae in their theory shaped by vague concepts of intuition and modularity.Изучение рассуждений на протяжении столетий входило в круг интересов логики. Позднее этот прием познавательной деятельности вошел в сонм вопросов когнитивной науки, которой временами с логикой ужиться совсем не просто. На примере относительно новой философско-когнитивной теории Спербера и Мерсье, отводящей довольно скромное место логической рациональности, мы показываем, почему сотрудничество этих двух наук все же может быть продуктивным. Вполне в духе эпистемологической традиции Нового времени Спербер и Мерсье строят теорию функционирования сознания. Ключевую роль в ней играют рассуждения, которые, однако, подчиняются не правилам логики, а интуиции, подкрепленной идеей модулярности. В статье отстаивается позиция, что рассуждения сложно помыслить вне логических последовательностей, и данная теория это только подтверждает: современная логика вполне органично способна заполнить ее лакуны, которые образуют смутная интуиция и не менее непонятная модулярность
In defense of the self-referencing quantifier Sx. Approximation of self-referential sentences by dynamic systems
Get PDFArguments in defense of introducing the self-referencing quantifier Sx and its approxi- mation on dynamical systems areconsistently presented. The case of classical logic is described in detail. Generated 3-truth tables that match Priest’s tables (Priest 1979). In the process of constructing 4-truth tables, two more truth values were revealed that did notcoincide with the original ones. Therefore, the closed tables turned out to be 6-digit.Arguments in defense of introducing the self-referencing quantifier Sx and its approximation on dynamical systems are consistentlypresented. The case of classical logic is described in detail. Generated 3-truth tables that match Priest’s tables (Priest 1979). In the process of constructing 4-truth tables, two more truth values were revealed that did not coincide with the original ones. Therefore, the closed tables turned out to be 6-digit
Антикритериализм и нечёткость миров. По поводу кросс-мировой семантики Евгения Борисова
Get PDFThe study is focused on two problems related to cross-world semantics: anticriterialism (the idea that identity cannot be defined by any criteria whatsoever) and fuzziness of possible worlds (possible world semantics where the worlds are fuzzy). These two problems are important, in particular, for the logic of indirect meanings in natural language and the logic of narrative.Рассматриваются главным образом две проблемы, решение которых может быть особенно важным для кросс-мировой семантики: антикритериализм (представление о том, что идентичность не может до конца определяться какими бы то ни было критериями) и нечёткость миров (возможные миры, границы между которыми нечёткие). Эти проблемы важны, в частности, для таких приложений кросс-мировой семантики, как логика образований непрямых значений в естественном языке и логика нарратива