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1. Proceedings of the XXII World Congress of Philosophy: Volume > 13
Valentin A. Bazhanov Heuristic Ground of Paraconsistent Logic: The Imaginary Logic of N.A. Vasiliev
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The paper deals with the heuristic prerequisites of paraconsistent logic in the case of imaginary logic of N.A. Vasiliev proposed in 1910.
2. Proceedings of the XXII World Congress of Philosophy: Volume > 13
Jean-Yves Béziau What is “Formal Logic”?
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“Formal logic”, an expression created by Kant to characterize Aristotelian logic, has also been used as a name for modern logic, originated by Boole and Frege, which in many aspects differs radically from traditional logic. We shed light on this paradox by distinguishing in this paper five different meanings of the expression “formal logic”: (1) Formal reasoning according to the Aristotelian dichotomy of form and content, (2) Formal logic as a formal science by opposition to an empirical science, (3) Formal systems in the sense of Hilbert, Curry and the formalist school, (4) Symbolic logic, a science using symbols, such as Venn diagrams, (5) Mathematical logic, a mathematical approach to reasoning. We argue that these five meanings are independent and that the meaning (5) is the one which better characterized modern logic, which should therefore not be called “formal logic”.
3. Proceedings of the XXII World Congress of Philosophy: Volume > 13
Chang Kyun Park A Philosophical Interpretation of Rough Set Theory
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The rough set theory has interesting properties such as that a rough set is considered as distinct sets in distinct knowledge bases, and that distinct rough sets are considered as one same set in a certain knowledge base. This leads to a significant philosophical interpretation: a concept (or phenomenon) may be understood as different ones in different philosophical perspectives, while different concepts (or phenomena) may be understood as a same one in a certain philosophical perspective. Such properties of rough set theory produce a mathematical model to support critical realism and the theory ladenness of observation in the philosophy of science.
4. Proceedings of the XXII World Congress of Philosophy: Volume > 13
Don Faust Explorationism, Evidence Logic and the Question of the Non-necessity of All Belief Systems
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Explorationism (see www.bu.edu/wcp/Papers/Logi/LogiFaus.htm, WCP XX, “Conflict without Contradiction”) is a perspective concerning human knowledge: as yet, our ignorance of the Real World remains great. With this perspective, all our knowledge is so far only partial and tentative. Evidence Logic (EL) (see “The Concept of Evidence”, INTER. JOURNAL OF INTELLIGENT SYSTEMS 15 (2000), 477‐493) provides an example of a reasonable Base Logic for Explorationism:EL provides machinery for the representation and processing of gradational evidential predications. Syntactically, for any evidence level e, for a proposition symbol P, Pc:e asserts that there is level e confirmatory evidence regarding P, while Pr:e asserts level e refutatory evidence (n‐ary predications, for n>0, are handled similarly). Semantically, EL has similarly enriched model spaces. The Boolean sentence algebras of the variety of EL languages, varying across stipulated families of predicate and functions symbols, have been analyzed, and EL is sound and complete. Belief Systems, we will argue, are all unnecessary: in science, as well as in all broader domains of human relations and activity, it is always sufficient to have simply commitments, which entail no assertion of Truth but rather simply entail agreed‐upon consequent actions. (Agent A believes a sentence S if A asserts S is True although A does not know (have absolute evidence) that S is True.) We will further seek to explore ways in which such a perspective may help in engendering more enhanced discourse, less absolutist and shrill advocacy and violence, and more rationality, in the Global Village of the new century.
5. Proceedings of the XXII World Congress of Philosophy: Volume > 13
Tzu-Keng Fu Translation Paradox and Logical Translation: A Study in Universal Logic
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Why do logicians develop so many different philosophical logics? All their aims focus on the same question--”What is logic?” Whether they have said it is the aim question which they want answer or not when they are doing logics, this is the presumed motivation for all studies of logics. In other words, the reason for logicians to do logics is try to answer what logic is. This kind of conceptual analysis on logic is the main problem style to be asked in Universal Logic, such as “What is classical propositional logic?”, “What is many‐valued logic?”, “What is paraconsistent logic?”, etc. In this paper, we discuss one of Béziau’s paradoxes, Translation Paradox in Logical Translation, due to this kind of conceptual analysis on logic. Universal Logic is not a new logic, according to Béziau, it is a general theory of logical structures analogy to Universal Algebra, even if we could see it as a new logical activity. It is not to find out a ‘universal’ logic to cover all aims of logical researches. And it is definitely not in the spirit of logical monism, that is there is only one true logic. Develop Universal Logic about 15 years, besides its own motivation and purposes, it increasingly induces to two main stream problems, one is Logical Translation and the other is Combination of Logics which are two new realms in logic research. We find it is an easier way to start with Béziau’s Translation Paradox to get involved into Translation of Logics.
6. Proceedings of the XXII World Congress of Philosophy: Volume > 13
Mario Gomez-Torrente Tarski on Variable Domains
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In earlier work I claimed that when Tarski wrote his seminal 1936 paper on logical consequence, he had in mind a now nonstandard convention, that he also used in his 1937 logic manual, requiring the domain of quantification of the different interpretations of a first-order mathematical language to covary with changes in the interpretation of a non-logical “domain predicate”. Recently Paolo Mancosu has rejected this claim, holding that it can be established on the basis of a passage from Tarski’s manual that he did not employ that convention. I show that Mancosu misinterprets the passage in question and that detailed examination of the surrounding text actually confirms my earlier claim.
7. Proceedings of the XXII World Congress of Philosophy: Volume > 13
Rolando M. Gripaldo The Rejection of the Proposition
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Part of rethinking philosophy today, the author believes, is to rethink our logical concepts. The author questions the ontological existence of the proposition as the content of sentential utterances—written or spoken—as it was originally proposed by John Searle. While a performative is an utterance where the speaker not only utters a sentential or illocutionary content such as a statement, but also performs the illocutionary force such as the act of stating, the author reasserts John Austin’s constative as the general label (genus) of specific utterances (species) that can be rendered true or false such as a statement, assertion, description, and prediction. In the remainder of the paper, the author tries to show that it is a category mistake for someone to assert a statement or to state an assertion.
8. Proceedings of the XXII World Congress of Philosophy: Volume > 13
Beomin Kim The Translation of First Order Logic into Modal Predicate Logic
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This paper deals with the translation of first order formulas to predicate S5 formulas. This translation does not bring the first order formula itself to a modal system, but modal interpretation of the first order formula can be given by the translation. Every formula can be translated, and the additional condition such as formula's having only one variable, or having both world domain and individual domain is not required. I introduce an indexical predicate 'E' for the translation. The meaning that 'E(a)' is true is 'this world is 'a' '. Because of this meaning, I call 'E' an indexical predicate. 'E' plays an important role for the translation. In addition that the modal formulas can be translated into first order formulas, we can conclude that the first order logic and modal predicate logic isintertranslatable.
9. Proceedings of the XXII World Congress of Philosophy: Volume > 13
Robert K. Meyer Fallacies of Division
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What do well-known theories look like if formulated with a relevant rather than a standard classical or intuitionist logic? Do familiar reconstructions of these theories go through, or do we change the reconstruction when we change the logic? I show in this paper that a new class of fallacies arises when we take the familiar Peano postulates as the foundation for a relevant theory of the natural numbers N. For these postulates fail in the relevant context to establish the relevant cancellation theorem. Put otherwise, there are fallacies of division in arithmetic formulated relevantly!
10. Proceedings of the XXII World Congress of Philosophy: Volume > 13
Sergey Pavlov Semantics with Only One Bedeutung: Rethinking Frege's Semantics
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The modification of Frege's semantics that consists in using only one reference (Bedeutung, denotate) truth instead of two references truth and falsity is proposed. According to Frege 1) every true sentence stands for truth, 2) every false sentence stands for falsity. We modify the second statement: 2*) every false sentence doesn't stand for truth. The modification of sentential logic interpretation will consist in change of semantic rules: a) every formula A stands either for truth or falsity, b.1) the formula A has value T iff the formula A stands for truth, b.2) the formula A has value F iff the formula A stands for falsity. Let’s change rules a) and b.2) on: a*) every formula A either stands or doesn't stand for truth, b.2*) the formula A has value F iff the formula A doesn't stand for truth. So, we have only one reference but still two values. The proposed approach can be extended to non-classical cases, for which the bivalence principle doesn't take place. An ordered pair of the sentences A, ~A is put in correspondence to the sentence A. Each sentence of ordered pair can either stands or doesn't stand for truthindependently from the other. Thus for each pair of sentences we have four possible variants of reference which are generate four functional values.