Pub Date : 2017-08-22DOI: 10.2143/LEA.240.0.3254093
Fabrizio Macagno
The reasoning process of analogy is analyzed as a strict interdependence between a process of abstraction of a common feature and the transfer of an attribute of the Analogue to the Primary Subject. The first reasoning step is regarded as an abstraction of a generic characteristic that is relevant for the attribution of the predicate. The abstracted feature can be considered from a logic-semantic perspective as a functional genus, in the sense that it is contextually essential for the attribution of the predicate, i.e. that is pragmatically fundamental (i.e. relevant) for the predication, or rather the achievement of the communicative intention. While the transfer of the predicate from the analogue to the analogical genus and from the genus to the primary subject is guaranteed by the maxims, or rules of inference, governing the genus-species relation, the connection between the genus and the predicate can be complex, characterized by various types of reasoning patterns. The relevance relation can hide an implicit argument from classification, or an evaluation based on values, consequences or rules, or a causal relation, or an argument from practical reasoning.
{"title":"The logical and pragmatic structure of arguments from analogy","authors":"Fabrizio Macagno","doi":"10.2143/LEA.240.0.3254093","DOIUrl":"https://doi.org/10.2143/LEA.240.0.3254093","url":null,"abstract":"The reasoning process of analogy is analyzed as a strict interdependence between a process of abstraction of a common feature and the transfer of an attribute of the Analogue to the Primary Subject. The first reasoning step is regarded as an abstraction of a generic characteristic that is relevant for the attribution of the predicate. The abstracted feature can be considered from a logic-semantic perspective as a functional genus, in the sense that it is contextually essential for the attribution of the predicate, i.e. that is pragmatically fundamental (i.e. relevant) for the predication, or rather the achievement of the communicative intention. While the transfer of the predicate from the analogue to the analogical genus and from the genus to the primary subject is guaranteed by the maxims, or rules of inference, governing the genus-species relation, the connection between the genus and the predicate can be complex, characterized by various types of reasoning patterns. The relevance relation can hide an implicit argument from classification, or an evaluation based on values, consequences or rules, or a causal relation, or an argument from practical reasoning.","PeriodicalId":46471,"journal":{"name":"Logique et Analyse","volume":"87 1","pages":"465-489"},"PeriodicalIF":0.3,"publicationDate":"2017-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76054645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-08-22DOI: 10.2143/LEA.240.0.3254088
Peter W. Milne
We refine the interpolation property of the {&, v, ~, A, E}-fragment of classical first-order logic, showing that if [G is satisfiable] and [D is ot logically true] and G|- D then there is an interpolant c, constructed using only non-logical vocabulary common to both members of G and members of D, such that (i) G entails c in the first-order version of Kleene’s strong three-valued logic (K3), and (ii) c entails D in the first-order version of Priest’s Logic of Paradox (LP). The proof proceeds via a careful analysis of derivations in a cut-free sequent calculus for first-order classical logic. Lyndon’s strengthening falls out of an observation regarding such derivations and the steps involved in the construction of interpolants. The proof is then extended to cover the {&, v, ~, A, E}-fragment of classical first-order logic with identity. Keywords: Craig–Lyndon Interpolation Theorem (for classical first-order logic); Kleene’s strong 3-valued logic;Priest’s Logic of Paradox; Belnap’s four-valued logic
我们改进的插值性质{& v ~一个E}片段经典一阶逻辑,表明如果G是可以满足的,[D ot在逻辑上是真的]和G | - D还有一个interpolant c,构造仅使用non-logical词汇常见G的成员和成员D,这样(我)G需要c的一阶版本克林强劲的三值逻辑(K3),和(2)c需要D的一阶牧师的逻辑悖论(LP)。证明是通过对一阶经典逻辑的无切序演算中的导数的仔细分析进行的。林登的强化来自于对这类推导的观察，以及对构建内插的步骤的观察。然后将证明推广到经典一阶逻辑具有恒等的{&，v， ~， A, E}片段。关键词:Craig-Lyndon插值定理(经典一阶逻辑);Kleene的强三值逻辑;Priest的悖论逻辑;贝尔纳普的四值逻辑
{"title":"A refinement of the Craig-Lyndon Interpolation Theorem for classical first-order logic (with identity)","authors":"Peter W. Milne","doi":"10.2143/LEA.240.0.3254088","DOIUrl":"https://doi.org/10.2143/LEA.240.0.3254088","url":null,"abstract":"We refine the interpolation property of the {&, v, ~, A, E}-fragment of classical first-order logic, showing that if [G is satisfiable] and [D is ot logically true] and G|- D then there is an interpolant c, constructed using only non-logical vocabulary common to both members of G and members of D, such that (i) G entails c in the first-order version of Kleene’s strong three-valued logic (K3), and (ii) c entails D in the first-order version of Priest’s Logic of Paradox (LP). The proof proceeds via a careful analysis of derivations in a cut-free sequent calculus for first-order classical logic. Lyndon’s strengthening falls out of an observation regarding such derivations and the steps involved in the construction of interpolants. The proof is then extended to cover the {&, v, ~, A, E}-fragment of classical first-order logic with identity. Keywords: Craig–Lyndon Interpolation Theorem (for classical first-order logic); Kleene’s strong 3-valued logic;Priest’s Logic of Paradox; Belnap’s four-valued logic","PeriodicalId":46471,"journal":{"name":"Logique et Analyse","volume":"1 1","pages":"389-420"},"PeriodicalIF":0.3,"publicationDate":"2017-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90217293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-03-10DOI: 10.2143/LEA.238.0.3212069
David Atkinson, J. Peijnenburg
Ever since its introduction, the Sleeping Beauty Problem has been fought over by the halfers against the thirders. We distinguish three interpretations of the original problem as described in Adam Elga’s seminal paper on the subject. Elga’s intended interpretation leads to the position of the thirders; but the other readings result in that of the halfers. We show that all three of these results can be obtained by making use of objective probabilities in a four-dimensional rather than a three-dimensional space. Our reasoning avoids various problems, not only of Dutch Book and other subjectivist approaches, but also of earlier treatments in terms of objective probabilities.
{"title":"When Sleeping Beauty First Awakes","authors":"David Atkinson, J. Peijnenburg","doi":"10.2143/LEA.238.0.3212069","DOIUrl":"https://doi.org/10.2143/LEA.238.0.3212069","url":null,"abstract":"Ever since its introduction, the Sleeping Beauty Problem has been fought over by the halfers against the thirders. We distinguish three interpretations of the original problem as described in Adam Elga’s seminal paper on the subject. Elga’s intended interpretation leads to the position of the thirders; but the other readings result in that of the halfers. We show that all three of these results can be obtained by making use of objective probabilities in a four-dimensional rather than a three-dimensional space. Our reasoning avoids various problems, not only of Dutch Book and other subjectivist approaches, but also of earlier treatments in terms of objective probabilities.","PeriodicalId":46471,"journal":{"name":"Logique et Analyse","volume":"31 1","pages":"129-150"},"PeriodicalIF":0.3,"publicationDate":"2017-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73609014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-01-01DOI: 10.15496/publikation-29433
L. Tranchini
{"title":"PROOF ANALYSIS OF GLOBAL CONSEQUENCE","authors":"L. Tranchini","doi":"10.15496/publikation-29433","DOIUrl":"https://doi.org/10.15496/publikation-29433","url":null,"abstract":"","PeriodicalId":46471,"journal":{"name":"Logique et Analyse","volume":"100 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77355583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-12-01DOI: 10.2143/LEA.236.0.3186065
R. Girle
There are several formal systems for persuasive dialogue. Dialogue systems are multi-agent systems, and this contrasts with the general lack of any agency in standard logics other than in the case of epistemic and deontic logics. Dialogue systems have been called logics. A logic usually has a semantics and a proof sys- tem, and questions of soundness and completeness arise. Any dialogue conducted according to the rules of a dialogue logic is a complex process. Dynamic Logic is a logic of processes, with a possible world semantics. This paper is a preliminary exploration of transforming the dialogues of dialogue logic into complex Dynamic Logic processes with emphasis on semantic models. The transformation gives rise to many questions, three of which are discussed. Dialogue logic includes commit- ment sets which behave in a way similar to belief sets and undergo changes during any dialogue. There are issues as to the relationship between belief and commitment, and whether the logics of belief change apply to commitment stores. There is also the issue of the logical nature of the evaluation of dialogues as legal or illegal.
{"title":"Dialogue logic as dynamic logic","authors":"R. Girle","doi":"10.2143/LEA.236.0.3186065","DOIUrl":"https://doi.org/10.2143/LEA.236.0.3186065","url":null,"abstract":"There are several formal systems for persuasive dialogue. Dialogue systems are multi-agent systems, and this contrasts with the general lack of any agency in standard logics other than in the case of epistemic and deontic logics. Dialogue systems have been called logics. A logic usually has a semantics and a proof sys- tem, and questions of soundness and completeness arise. Any dialogue conducted according to the rules of a dialogue logic is a complex process. Dynamic Logic is a logic of processes, with a possible world semantics. This paper is a preliminary exploration of transforming the dialogues of dialogue logic into complex Dynamic Logic processes with emphasis on semantic models. The transformation gives rise to many questions, three of which are discussed. Dialogue logic includes commit- ment sets which behave in a way similar to belief sets and undergo changes during any dialogue. There are issues as to the relationship between belief and commitment, and whether the logics of belief change apply to commitment stores. There is also the issue of the logical nature of the evaluation of dialogues as legal or illegal.","PeriodicalId":46471,"journal":{"name":"Logique et Analyse","volume":"98 1","pages":"427-443"},"PeriodicalIF":0.3,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85333910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-10-26DOI: 10.2143/LEA.236.0.3186062
Luca Incurvati
Mathematical realists have long invoked the categoricity of axiomatizations of arithmetic and analysis to explain how we manage to fix the intended meaning of their respective vocabulary. Can this strategy be extended to set theory? Although traditional wisdom recommends a negative answer to this question, Vann McGee (1997) has offered a proof that purports to show otherwise. I argue that one of the two key assumptions on which the proof rests deprives McGee's result of the significance he and the realist want to attribute to it. I consider two strategies to deal with the problem --- one of which is outlined by McGee himself (2000) --- and argue that both of them fail. I end with some remarks on the prospects for mathematical realism in the light of my discussion.
{"title":"Can the Cumulative Hierarchy Be Categorically Characterized","authors":"Luca Incurvati","doi":"10.2143/LEA.236.0.3186062","DOIUrl":"https://doi.org/10.2143/LEA.236.0.3186062","url":null,"abstract":"Mathematical realists have long invoked the categoricity of axiomatizations of arithmetic and analysis to explain how we manage to fix the intended meaning of their respective vocabulary. Can this strategy be extended to set theory? Although traditional wisdom recommends a negative answer to this question, Vann McGee (1997) has offered a proof that purports to show otherwise. I argue that one of the two key assumptions on which the proof rests deprives McGee's result of the significance he and the realist want to attribute to it. I consider two strategies to deal with the problem --- one of which is outlined by McGee himself (2000) --- and argue that both of them fail. I end with some remarks on the prospects for mathematical realism in the light of my discussion.","PeriodicalId":46471,"journal":{"name":"Logique et Analyse","volume":"4 1","pages":"367-387"},"PeriodicalIF":0.3,"publicationDate":"2016-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90091541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-01-01DOI: 10.2143/LEA.233.0.3149530
R. Stenwall
This paper is an argument against Truthmaker Necessitarianism — the doctrine that the existence of a truthmaker necessitates the truth of the proposition it makes true. Armstrong’s sufficiency argument for necessitarianism is examined and shown to be question begging. It is then argued in detail that truthmaking is a matter of grounding truth and that grounding is a dependency relation that neither entails nor reduces to necessitation.
{"title":"Against Truthmaker Necessitarianism","authors":"R. Stenwall","doi":"10.2143/LEA.233.0.3149530","DOIUrl":"https://doi.org/10.2143/LEA.233.0.3149530","url":null,"abstract":"This paper is an argument against Truthmaker Necessitarianism — the doctrine that the existence of a truthmaker necessitates the truth of the proposition it makes true. Armstrong’s sufficiency argument for necessitarianism is examined and shown to be question begging. It is then argued in detail that truthmaking is a matter of grounding truth and that grounding is a dependency relation that neither entails nor reduces to necessitation.","PeriodicalId":46471,"journal":{"name":"Logique et Analyse","volume":"43 1","pages":"37-54"},"PeriodicalIF":0.3,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81102341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-01-01DOI: 10.2143/LEA.235.0.3170112
Clayton Peterson
The present paper aims to bridge the gap between deontic logic, categorial grammar and category theory. We propose to analyze Forrester's (1984) paradox through the framework of Lambek's (1958) syntactic calculus. We first recall the definition of the syntactic calculus and then explain how Lambek (1988) defines it within the framework of category theory. Then, we briefly present Forrester's paradox in conjunction with standard deontic logic, showing that this paradox contains some features that reflect many problems within the literature. Finally, we analyze Forrester's paradox within the framework of the syntactic calculus and we show how a typed syntax can provide conceptual insight regarding some of the problems that deontic logic faces.
{"title":"From linguistics to deontic logic via category theory","authors":"Clayton Peterson","doi":"10.2143/LEA.235.0.3170112","DOIUrl":"https://doi.org/10.2143/LEA.235.0.3170112","url":null,"abstract":"The present paper aims to bridge the gap between deontic logic, categorial grammar and category theory. We propose to analyze Forrester's (1984) paradox through the framework of Lambek's (1958) syntactic calculus. We first recall the definition of the syntactic calculus and then explain how Lambek (1988) defines it within the framework of category theory. Then, we briefly present Forrester's paradox in conjunction with standard deontic logic, showing that this paradox contains some features that reflect many problems within the literature. Finally, we analyze Forrester's paradox within the framework of the syntactic calculus and we show how a typed syntax can provide conceptual insight regarding some of the problems that deontic logic faces.","PeriodicalId":46471,"journal":{"name":"Logique et Analyse","volume":"1 1","pages":"301-315"},"PeriodicalIF":0.3,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82459921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-01-01DOI: 10.2143/LEA.233.0.3149529
Dany Jaspers, Pieter A. M. Seuren
The present study describes how three now almost forgotten mid-20th-century logicians, the American Paul Jacoby and the Frenchmen Augustin Sesmat and Robert Blanche, all three ardent Catholics, tried to restore traditional predicate logic to a position of respectability by expanding the classic Square of Opposition to a hexagon of logical relations, showing the logical and cognitive advantages of such an expansion. The nature of these advantages is discussed in the context of modern research regarding the relations between logic, language, and cognition. It is desirable to call attention to these attempts, as they are, though almost totally forgotten, highly relevant against the backdrop of the clash between modern and traditional logic. It is argued that this clash was and is unnecessary, as both forms of predicate logic are legitimate, each in its own right. The attempts by Jacoby, Sesmat, and Blanche are, moreover, of interest to the history of logic in a cultural context in that, in their own idiosyncratic ways, they fit into the general pattern of the Catholic cultural revival that took place roughly between the years 1840 and 1960. The Catholic Church had put up stiff resistance to modern mathematical logic, considering it dehumanizing and a threat to Catholic doctrine. Both the wider cultural context and the specific implications for logic are described and analyzed, in conjunction with the more general philosophical and doctrinal issues involved.
{"title":"The Square of Opposition in Catholic hands: a chapter in the history of 20th-century logic","authors":"Dany Jaspers, Pieter A. M. Seuren","doi":"10.2143/LEA.233.0.3149529","DOIUrl":"https://doi.org/10.2143/LEA.233.0.3149529","url":null,"abstract":"The present study describes how three now almost forgotten mid-20th-century logicians, the American Paul Jacoby and the Frenchmen Augustin Sesmat and Robert Blanche, all three ardent Catholics, tried to restore traditional predicate logic to a position of respectability by expanding the classic Square of Opposition to a hexagon of logical relations, showing the logical and cognitive advantages of such an expansion. The nature of these advantages is discussed in the context of modern research regarding the relations between logic, language, and cognition. It is desirable to call attention to these attempts, as they are, though almost totally forgotten, highly relevant against the backdrop of the clash between modern and traditional logic. It is argued that this clash was and is unnecessary, as both forms of predicate logic are legitimate, each in its own right. The attempts by Jacoby, Sesmat, and Blanche are, moreover, of interest to the history of logic in a cultural context in that, in their own idiosyncratic ways, they fit into the general pattern of the Catholic cultural revival that took place roughly between the years 1840 and 1960. The Catholic Church had put up stiff resistance to modern mathematical logic, considering it dehumanizing and a threat to Catholic doctrine. Both the wider cultural context and the specific implications for logic are described and analyzed, in conjunction with the more general philosophical and doctrinal issues involved.","PeriodicalId":46471,"journal":{"name":"Logique et Analyse","volume":"20 1","pages":"1-35"},"PeriodicalIF":0.3,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75796745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-01-01DOI: 10.2143/LEA.234.0.3159740
F. Putte
When our current beliefs face a certain problem – e.g. when we receive new information contradicting them –, then we should not remove beliefs that are not related to this problem. This principle is known as “minimal mutilation” or “conservativity” [21]. To make it formally precise, Rohit Parikh [32] defined a Relevance axiom for (classical) theory revision, which is based on the notion of a language splitting. I show that both concepts can and should be applied in a much broader context than mere revision of theories in the traditional sense. First, I generalize their application to belief change in general, and strengthen the axiom of relevance in order to make it fully syntax-independent. This is done by making use of the least letter-set representation of a set of formulas [27]. Second, I show that the logic underlying both concepts need not be classical logic and establish weak sufficient conditions for both the finest splitting theorem from [25] and the least letter-set theorem from [27]. Both generalizations are illustrated by means of the paraconsistent logic CLuNs and compared to ideas from [14, 36, 24].
{"title":"Splitting and Relevance: Broadening the Scope of Parikh’s Concepts","authors":"F. Putte","doi":"10.2143/LEA.234.0.3159740","DOIUrl":"https://doi.org/10.2143/LEA.234.0.3159740","url":null,"abstract":"When our current beliefs face a certain problem – e.g. when we receive new information contradicting them –, then we should not remove beliefs that are not related to this problem. This principle is known as “minimal mutilation” or “conservativity” [21]. To make it formally precise, Rohit Parikh [32] defined a Relevance axiom for (classical) theory revision, which is based on the notion of a language splitting. I show that both concepts can and should be applied in a much broader context than mere revision of theories in the traditional sense. First, I generalize their application to belief change in general, and strengthen the axiom of relevance in order to make it fully syntax-independent. This is done by making use of the least letter-set representation of a set of formulas [27]. Second, I show that the logic underlying both concepts need not be classical logic and establish weak sufficient conditions for both the finest splitting theorem from [25] and the least letter-set theorem from [27]. Both generalizations are illustrated by means of the paraconsistent logic CLuNs and compared to ideas from [14, 36, 24].","PeriodicalId":46471,"journal":{"name":"Logique et Analyse","volume":"98 1","pages":"173-205"},"PeriodicalIF":0.3,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90381653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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