Najkrótsze aksjomaty modalnej logiki Łukasiewicza
We show that the formula CLpEqLq axiomatizes Łukasiewicz’s modal logic and that there exists no shorter axiom for it.
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We show that the formula CLpEqLq axiomatizes Łukasiewicz’s modal logic and that there exists no shorter axiom for it.
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Od Fregeho pochádza myolienka, že vyznam vety môže byu dany stanovenIm podmienok, pri ktorych je pravdivá. Tento názor zastávali po Fregem okrem inych Wittgenstein, Carnap, Quine a v súčasnosti je jeho hlavnym obhajcom D. Davidson.
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V 1. a 2. ročníku ORGANONu Pavel Cmorej v e svých Kapitolách z logické syntaxe předváděl, jak je přirozený jazyk možné nahlížet prismatem 'standardní' logiky.
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Každý človek je determinovaný historicky, svojou spoločenskou príslušnosť'ou; existencialisti hovoria, že osud ho vrhá do určitej konkrétnej situácie.
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This paper focuses on two interrelated issues about the prospects for research projects in experimental philosophical logic. The first issue is about the role that logic plays in such projects; the second involves the role that experimental results from the cognitive sciences play in them. I argue that some notion of logic plays a crucial role in these research projects, and, in turn, the results of these projects might inform substantive debates in the philosophy of logic.
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Warrant and Conditions for Warrant in Alvin Plantinga’s Philosophy. Warrant is the central concept of Alvin Plantinga’s epistemology. As Plantinga suggests it, warrant is that quantity or quality which together with belief and truth constitutes knowledge. This paper, intends to present broadly the concept of warrant and to analyze the conditions for warrant in order to see if the conditions proposed by Plantinga are necessary and sufficient for a belief to be considered knowledge.
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The Limits of the Formal Treatment of Language. Within the philosophy of language there is a distinction between the natural language philosophers and the ideal language philosophers. The distinction is drawn based on the way these philosophers reflect on language and the world. Natural language philosophers stress the context-based feature of meaning, while the ideal language philosophers emphasize the context-free feature of meaning. In my study I want to show that that even within the formal study of language, in the apparent absence of any context, the notions of valuation and interpretation help us to understand the meaning of sentences.
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Self-reference and the Limits of Thought. This paper explores the connection between the natural language and a formal language from a particular point of view: self-referential constructions. Such constructions lead to some kind of limits of thought, either in the form of paradoxical constructions (Liar-type or Grelling-type), or in the form of the so called limitative theorems in mathematical logic (e.g. Gödel’s theorem). By deriving Gödel’s significant results from paradoxical constructions the limitative character of such self-referential constructions is preserved, but they open the ways for a new representation of a great variety of arguments in the field of logic, mathematics and philosophy.
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Modern logic owes an important debt to C.I. Lewis and his students. In addition to Lewis’s five modal logics, they are responsible for the creation (or discovery) of the logic of analytic implication and connexive logic. In this paper, we examine E.J. Nelson’s connexive logic as an attempt to formalise the notion of entailment while avoiding the paradoxes of strict implication. We also look briefly at the reception of Nelson’s logic and at Lewis’s reply to it.
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The central result of the paper is an alternative axiomatization of the conditional system VC which does not make use of Conditional Modus Ponens: (A > B) ⊃ (A ⊃ B) and of the axiom-schema CS: (A ∧ B) ⊃ (A > B). Essential use is made of two schemata, i.e. X1: (A ∧ ♢A) ⊃ (♢A >< A) and T: □A ⊃ A, which are subjoined to a basic principle named Int: (A ∧ B) ⊃ (♢A > ♢B). A hierarchy of extensions of the basic system V called VInt, VInt1, VInt1T is then construed and submitted to a semantic analysis. In Section 3 VInt1T is shown to be deductively equivalent to VC. Section 4 shows that in VC the thesis X1 is equivalent to X1∨: (♢A >< A) ∨ (♢¬A >< ¬A), so that VC is also equivalent to a variant of VInt1T here called VInt1To. In Section 6 both X1 and X1∨ offer the basis for a discussion on systems containing CS, in which it is argued that they cannot avoid various kinds of partial or full trivialization of some non truth-functional operators.
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This paper is a critical study of an argument put forward by Kwasi Wiredu in his engagement with C. I. Lewis on choosing the right modal logic for logical necessity. Wiredu argues that Lewis “could have been more adventurous modally with perfect logicality” and could justifiably have accepted S4 rather than being “to the last cautious of any system stronger than S2” (Wiredu 1979). I address terse, incomplete, and provocatively incongruous notes on Wiredu’s paper by (Makinson 1980) and (Humberstone 2011), as well as a paper by (Cresswell 1965) that Humberstone cites, and I draw on recent work by (Lewitzka 2015; 2016). I conclude that Wiredu’s argument cannot be accepted as sound but a variant argument can be accepted as sound.
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This is a review of the book Jedność i wielość logik modalnych (The Unity and Diversity of Modal Logics) edited by Marcin Tkaczyk. The book contains discussions of the most recent results of contemporary modal logic, focusing on regular modal logics, epistemic logic, and temporal logic. The book comprises four chapter, each of which deals with selected formal-logical and philosophical problems associated with modal logic.
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The purpose of the current paper is to develop the beginning of logical calculation for a first variant of actional impossibility interpretation. It is about the interpretation by modal logic. Human action requires several kinds of ability. A special kind of them is the ability to stand against the acts or forbearances ability of the others. That is to create the actional impossibility by an action agent for another one. This can be interpreted in two ways: as actional impossibility by modal operators and as a lack of ability. In this article we deal with actional impossibility by modal operators. This means a shift through modal concepts as necessary and şi possible. It also means the appeal to the set of possible worlds. And involves at least two drawbacks: contradiction and circularity. As such it remains to try the other interpretation: the lack of ability. Which is also, an opening for a further concern.
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Amending Mark Colyvan's views, I develop a Quinean view of the indispensability of abstract objects, according to which the indispensability of objects does not extend beyond the truth of existential claims involving them, conditional upon the truth of the theory positing those objects.
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After a brief reminder of the, so called, Linda problem and its solution by Kahneman & Tversky (KT) (the tame solution), I point out the implications of the solution adopted by the KTs. Among these implications, I emphasize the importance of the relation of probability between the sentences: eLinda is active in a feminist movementf (F) and eLinda is a bank teller and active in a feminist movementf (TČF); while in KTfs paper the main emphasis was put on considering the relationship between the probability of sentences: eLinda is a bank tellerf (T) and eLinda is a bank teller and active in a feminist movementf (TČF). I offer a critical argument against the zero hypothesis H0 that eat least 85% of the respondents will choose the sentence F as more likely than the sentence (TČF), and the opposite consequently will be selected at most by 15% of the respondents;f being drawn from the assumptions made by Kahneman and Tversky. This hypothesis will be further partially refuted by means of results from the surveys N0.1. and N0.2. Then the reasoning supporting the result of surveys is presented and finally critical conclusions will be derived.
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Reflection on Kvasz's thinking about geometry
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Reflection on Kvasz's book
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Anton Dumitriu is a representative Romanian philosopher and logician, well- known across the world as the author of the History of Logic and the English translation of the Treaty published by Abacus Press, Kent, in 1977. Our study investigates how the author summarizes Romanian contributions, to the development of logic in the postwar period, spoiled by massive Communist ideological interference into Romanian culture. In the last part of the treaty, dedicated to the Romanian postwar logic, the author includes both philosophers and logicians repressed during the decade of the Stalinist Cultural Revolution (DD Rosca, Dan Bădărău, Aram Frenkian and Constantin Noica) and persecutors of logicians and philosophers, as the Pavel Apostol, C.I. Gulian and Athanase Joja. In presenting these authors, considered the representatives of the current ideas of dialectical logic, Anton Dumitriu made only a presentation exercise, and not criticism, proper for reasons of self-defense. We highlighted this issue to prove the thesis that during the cultural revolution in Romania even logic, the science of the eternal forms of human thinking, was achieved by unlawful interference of the communist ideology. This totalitarian ideology, having suppressed an entire generation of Romanian thinkers of the interwar period, including arrests and deportations, aims to prevent recovery of the free mind in thinking. Towards the end of the study we wonder why the Romanian logician has not intervened in the earlier editions of the History of Logic, since 1990, when he had worked for the preparation of the third edition, published posthumously between 1993 and 1998.
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This work aims to formulate an important issue of contemporary philosophy of mathematics – Church’s thesis [CT] – by taking advantage of the richness of the conceptual system of St. Thomas’ philosophy and using its type of notions. The indicated aim was first tried to achieve through an in-depth analysis of Thomas’ definition of truth as “adaequatio rei et intellectus.” This analysis revealed a great wealth of underlying philosophical content and showed its nontriviality. The final result is an attempt to formulate Church’s thesis as a specific instance of Thomas’ definition of truth. The result of the work is ambiguous and therefore it constitutes a specific challenge for the supporters of Thomism to discuss this topic.
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