The criterion of naturalness represents David Lewis’s attempt to answer some of the sceptical arguments in (meta-) semantics by comparing the naturalness of meaning candidates. Recently, the criterion has been challenged by a new sceptical argument. Williams argues that the criterion cannot rule out the candidates which are not permuted versions of an intended interpretation. He presents such a candidate the arithmetical interpretation (a specific instantiation of Henkin’s model), and he argues that it opens up the possibility of Pythagorean worlds, i.e. the worlds similar to ours in which the arithmetical interpretation is the best candidate for a semantic theory. The aim of this paper is a) to reconsider the general conditions for the applicability of Lewis’s criterion of naturalness and b) to show that Williams’s new sceptical challenge is based on a problematic assumption that the arithmetical interpretation is independent of fundamental properties and relations. As I show, if the criterion of naturalness is applied properly, it can respond even to the new sceptical challenge.
{"title":"Lewisian Naturalness and a new Sceptical Challenge","authors":"Matej Drobňák","doi":"10.12775/LLP.2021.002","DOIUrl":"https://doi.org/10.12775/LLP.2021.002","url":null,"abstract":"The criterion of naturalness represents David Lewis’s attempt to answer some of the sceptical arguments in (meta-) semantics by comparing the naturalness of meaning candidates. Recently, the criterion has been challenged by a new sceptical argument. Williams argues that the criterion cannot rule out the candidates which are not permuted versions of an intended interpretation. He presents such a candidate the arithmetical interpretation (a specific instantiation of Henkin’s model), and he argues that it opens up the possibility of Pythagorean worlds, i.e. the worlds similar to ours in which the arithmetical interpretation is the best candidate for a semantic theory. The aim of this paper is a) to reconsider the general conditions for the applicability of Lewis’s criterion of naturalness and b) to show that Williams’s new sceptical challenge is based on a problematic assumption that the arithmetical interpretation is independent of fundamental properties and relations. As I show, if the criterion of naturalness is applied properly, it can respond even to the new sceptical challenge.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":"1"},"PeriodicalIF":0.5,"publicationDate":"2021-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49039425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
One of the most often explored, repeatedly interpreted, and recognized again and again as a valuable achievement of Kant’s philosophy, is his transcendental philosophy, a new methodological approach that – as Kant believed – will allow philosophy (metaphysics) to enter upon a secure path of science. In this paper, I explore Nicolai Hartmann’s reinterpretation and development of this methodology in both the historical and systematic context of his thought. First, I will deal with the Neo-Kantian’s understanding of the transcendental method as a starting point of Hartmann’s own understanding of it. Then I will analyze in detail his only paper devoted entirely to the problem of the method, (Hartmann, 1912), to present how he understands the necessary development of this methodology. I will claim that despite the fact that Hartmann – following Kant – never denied that the real essence of philosophy is the transcendental method, he tried to show that this methodus philosophandi cannot be reduced to the Neo-Kantian’s understanding of it. He argued that the core of all true philosophical and scientific research is the transcendental method, but only insofar as it is accompanied by two other methods that are needed to complete it: descriptive and dialectical method. I will close by presenting the relations between these three methods.
{"title":"Nicolai Hartmann and the Transcendental Method","authors":"A. PIetras","doi":"10.12775/LLP.2021.001","DOIUrl":"https://doi.org/10.12775/LLP.2021.001","url":null,"abstract":"One of the most often explored, repeatedly interpreted, and recognized again and again as a valuable achievement of Kant’s philosophy, is his transcendental philosophy, a new methodological approach that – as Kant believed – will allow philosophy (metaphysics) to enter upon a secure path of science. In this paper, I explore Nicolai Hartmann’s reinterpretation and development of this methodology in both the historical and systematic context of his thought. First, I will deal with the Neo-Kantian’s understanding of the transcendental method as a starting point of Hartmann’s own understanding of it. Then I will analyze in detail his only paper devoted entirely to the problem of the method, (Hartmann, 1912), to present how he understands the necessary development of this methodology. I will claim that despite the fact that Hartmann – following Kant – never denied that the real essence of philosophy is the transcendental method, he tried to show that this methodus philosophandi cannot be reduced to the Neo-Kantian’s understanding of it. He argued that the core of all true philosophical and scientific research is the transcendental method, but only insofar as it is accompanied by two other methods that are needed to complete it: descriptive and dialectical method. I will close by presenting the relations between these three methods.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41996919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The logic BN4 was defined by R.T. Brady as a four-valued extension of Routley and Meyer’s basic logic B. The system EF4 is defined as a companion to BN4 to represent the four-valued system of (relevant) implication. The system Ł was defined by J. Łukasiewicz and it is a four-valued modal logic that validates what is known as strong Łukasiewicz-type modal paradoxes. The systems EF4-M and EF4-Ł are defined as alternatives to Ł without modal paradoxes. This paper aims to define a Belnap-Dunn semantics for EF4, EF4-M and EF4-Ł. It is shown that EF4, EF4-M and EF4-Ł are strongly sound and complete w.r.t. their respective semantics and that EF4-M and EF4-Ł are free from strong Łukasiewicz-type modal paradoxes.
{"title":"EF4, EF4-M and EF4-Ł: A companion to BN4 and two modal four-valued systems without strong Łukasiewicz-type modal paradoxes","authors":"J. Blanco","doi":"10.12775/llp.2021.010","DOIUrl":"https://doi.org/10.12775/llp.2021.010","url":null,"abstract":"The logic BN4 was defined by R.T. Brady as a four-valued extension of Routley and Meyer’s basic logic B. The system EF4 is defined as a companion to BN4 to represent the four-valued system of (relevant) implication. The system Ł was defined by J. Łukasiewicz and it is a four-valued modal logic that validates what is known as strong Łukasiewicz-type modal paradoxes. The systems EF4-M and EF4-Ł are defined as alternatives to Ł without modal paradoxes. This paper aims to define a Belnap-Dunn semantics for EF4, EF4-M and EF4-Ł. It is shown that EF4, EF4-M and EF4-Ł are strongly sound and complete w.r.t. their respective semantics and that EF4-M and EF4-Ł are free from strong Łukasiewicz-type modal paradoxes.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66615860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The search for the extensions of sentences can be guided by Frege’s “principle of compositionality of extension”, according to which the extension of a composed expression depends only on its logical form and the extensions of its parts capable of having extensions. By means of this principle, a strict criterion for the admissibility of objects as extensions of sentences can be derived: every object is admissible as the extension of a sentence that is preserved under the substitution of co-extensional expressions. The question is: what are the extensions of elementary sentences containing empty singular terms, like ‘Vulcan rotates’. It can be demonstrated that in such sentences, states of affairs as structured objects (but not truth-values) are preserved under the substitution of co-extensional expressions. Hence, such states of affairs are admissible (while truth-values are not) as extensions of elementary sentences containing empty singular
{"title":"States of Affairs as Structured Extensions in Free Logic","authors":"H. Leeb","doi":"10.12775/llp.2020.025","DOIUrl":"https://doi.org/10.12775/llp.2020.025","url":null,"abstract":"The search for the extensions of sentences can be guided by Frege’s “principle of compositionality of extension”, according to which the extension of a composed expression depends only on its logical form and the extensions of its parts capable of having extensions. By means of this principle, a strict criterion for the admissibility of objects as extensions of sentences can be derived: every object is admissible as the extension of a sentence that is preserved under the substitution of co-extensional expressions. The question is: what are the extensions of elementary sentences containing empty singular terms, like ‘Vulcan rotates’. It can be demonstrated that in such sentences, states of affairs as structured objects (but not truth-values) are preserved under the substitution of co-extensional expressions. Hence, such states of affairs are admissible (while truth-values are not) as extensions of elementary sentences containing empty singular","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":"1"},"PeriodicalIF":0.5,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44851914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dialogue Games for Minimal Logic","authors":"A. Pavlova","doi":"10.12775/llp.2020.022","DOIUrl":"https://doi.org/10.12775/llp.2020.022","url":null,"abstract":"","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":"1"},"PeriodicalIF":0.5,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44016747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
As the final component of a chain of reasoning intended to take us all the way to logical nihilism, Russell (2018) presents the atomic sentence ‘prem’ which is supposed to be true when featuring as premise in an argument and false when featuring as conclusion in an argument. Such a sentence requires a non-reflexive logic and an endnote by Russell (2018) could easily leave the reader with the impression that going non-reflexive suffices for logical nihilism. This paper shows how one can obtain non-reflexive logics in which ‘prem’ behaves as stipulated by Russell (2018) but which nonetheless has valid inferences supporting uniform substitution of any formula for propositional variables such as modus tollens and modus ponens.
{"title":"Logical Nihilism and the Logic of ‘prem’","authors":"Andreas Fjellstad","doi":"10.12775/llp.2020.023","DOIUrl":"https://doi.org/10.12775/llp.2020.023","url":null,"abstract":"As the final component of a chain of reasoning intended to take us all the way to logical nihilism, Russell (2018) presents the atomic sentence ‘prem’ which is supposed to be true when featuring as premise in an argument and false when featuring as conclusion in an argument. Such a sentence requires a non-reflexive logic and an endnote by Russell (2018) could easily leave the reader with the impression that going non-reflexive suffices for logical nihilism. This paper shows how one can obtain non-reflexive logics in which ‘prem’ behaves as stipulated by Russell (2018) but which nonetheless has valid inferences supporting uniform substitution of any formula for propositional variables such as modus tollens and modus ponens.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47070871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We provide an application of a sequent calculus framework to the formalization of definite descriptions. It is a continuation of research undertaken in [20, 22]. In the present paper a so-called free description theory is examined in the context of different kinds of free logic, including systems applied in computer science and constructive mathematics for dealing with partial functions. It is shown that the same theory in different logics may be formalised by means of different rules and gives results of varying strength. For all presented calculi a constructive cut elimination is provided.
{"title":"Free Definite Description Theory – Sequent Calculi and Cut Elimination","authors":"Andrzej Indrzejczak","doi":"10.12775/llp.2020.020","DOIUrl":"https://doi.org/10.12775/llp.2020.020","url":null,"abstract":"We provide an application of a sequent calculus framework to the formalization of definite descriptions. It is a continuation of research undertaken in [20, 22]. In the present paper a so-called free description theory is examined in the context of different kinds of free logic, including systems applied in computer science and constructive mathematics for dealing with partial functions. It is shown that the same theory in different logics may be formalised by means of different rules and gives results of varying strength. For all presented calculi a constructive cut elimination is provided.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":"29 1","pages":"505-539"},"PeriodicalIF":0.5,"publicationDate":"2020-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46773607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the 1951 Gibbs lecture, Godel asserted his famous dichotomy, where the notion of informal proof is at work. G. Priest developed an argument, grounded on the notion of naive proof, to the effect that Godel’s first incompleteness theorem suggests the presence of dialetheias. In this paper, we adopt a plausible ideal notion of naive proof, in agreement with Godel’s conception, superseding the criticisms against the usual notion of naive proof used by real working mathematicians. We explore the connection between Godel’s theorem and naive proof so understood, both from a classical and a dialetheic perspective.
{"title":"A Note on Gödel, Priest and Naïve Proof","authors":"Massimiliano Carrara, Enrico Martino","doi":"10.12775/llp.2020.017","DOIUrl":"https://doi.org/10.12775/llp.2020.017","url":null,"abstract":"In the 1951 Gibbs lecture, Godel asserted his famous dichotomy, where the notion of informal proof is at work. G. Priest developed an argument, grounded on the notion of naive proof, to the effect that Godel’s first incompleteness theorem suggests the presence of dialetheias. In this paper, we adopt a plausible ideal notion of naive proof, in agreement with Godel’s conception, superseding the criticisms against the usual notion of naive proof used by real working mathematicians. We explore the connection between Godel’s theorem and naive proof so understood, both from a classical and a dialetheic perspective.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41319658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we study a new operator of strong modality ⊞, related to the non-contingency operator ∆. We then provide soundness and completeness theorems for the minimal logic of the ⊞-operator.
本文研究了与非偶然性算子∆相关的一个新的强模态算子。然后给出了最小逻辑的完备性定理和完备性定理。
{"title":"A Non-Standard Kripke Semantics for the Minimal Deontic Logic","authors":"Edson Bezerra, G. Venturi","doi":"10.12775/llp.2020.016","DOIUrl":"https://doi.org/10.12775/llp.2020.016","url":null,"abstract":"In this paper we study a new operator of strong modality ⊞, related to the non-contingency operator ∆. We then provide soundness and completeness theorems for the minimal logic of the ⊞-operator.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":"1"},"PeriodicalIF":0.5,"publicationDate":"2020-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44519051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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