The concept of logical form, as influentially specified by Frege and Bolzano, is accompanied by a paradox: to capture some universal property of discourse, we must specify that property, thereby rendering it particular and thus unsuitable for the universal purpose. Thus, instead of a single form, we have rather a sequence of them, corresponding to the logics of Aristotle, Frege, Brouwer, and others. In this paper, I argue that Hegel’s conception of logical form focuses on this historical aspect of the problem. Thus, he does not create a new logical form, e.g., that of dialectical logic, as Marx, as well as Priest and others, believe, but makes the attitude towards “fixed determinations” of logic part of these determinations themselves. This corresponds to Hegel’s differentiation between three layers of logic: formal, dialectical, and speculative.
{"title":"Hegel and the Logical Form","authors":"Vojtěch Kolman","doi":"10.12775/llp.2023.010","DOIUrl":"https://doi.org/10.12775/llp.2023.010","url":null,"abstract":"The concept of logical form, as influentially specified by Frege and Bolzano, is accompanied by a paradox: to capture some universal property of discourse, we must specify that property, thereby rendering it particular and thus unsuitable for the universal purpose. Thus, instead of a single form, we have rather a sequence of them, corresponding to the logics of Aristotle, Frege, Brouwer, and others. In this paper, I argue that Hegel’s conception of logical form focuses on this historical aspect of the problem. Thus, he does not create a new logical form, e.g., that of dialectical logic, as Marx, as well as Priest and others, believe, but makes the attitude towards “fixed determinations” of logic part of these determinations themselves. This corresponds to Hegel’s differentiation between three layers of logic: formal, dialectical, and speculative.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45448159","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 dominant analyses of the logical form of natural-language conditionals take them to be “suppositional conditionals”. The latter are true or accepted if the consequent is true/accepted on the supposition of the antecedent. But this can happen although the antecedent is completely irrelevant (or even somewhat adverse) to the consequent. In natural-language conditionals, however, the antecedent is typically meant to support or be evidence for the consequent. The logical form of conditionals will thus be more complex than the suppositional theory would have it. Recently some suggestions as to what this logical form might look like have been made. In this paper, I critically discuss Vincenzo Crupi and Andrea Iacona’s account of “evidential conditionals”, including its recent amendments.
{"title":"On the Logical Form of Evidential Conditionals","authors":"H. Rott","doi":"10.12775/llp.2023.009","DOIUrl":"https://doi.org/10.12775/llp.2023.009","url":null,"abstract":"The dominant analyses of the logical form of natural-language conditionals take them to be “suppositional conditionals”. The latter are true or accepted if the consequent is true/accepted on the supposition of the antecedent. But this can happen although the antecedent is completely irrelevant (or even somewhat adverse) to the consequent. In natural-language conditionals, however, the antecedent is typically meant to support or be evidence for the consequent. The logical form of conditionals will thus be more complex than the suppositional theory would have it. Recently some suggestions as to what this logical form might look like have been made. In this paper, I critically discuss Vincenzo Crupi and Andrea Iacona’s account of “evidential conditionals”, including its recent amendments.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43617003","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}
This paper studies some normative relations that hold between actions, their preconditions and their effects, with particular attention to connecting what are often called ‘ought to be’ norms with ‘ought to do’ norms. We use a formal model based on a form of transition system called a ‘coloured labelled transition system’ (coloured LTS) introduced in a series of papers by Sergot and Craven. Those works have variously presented a formalism (an ‘action language’) nC+ for defining and computing with a (coloured) LTS, and another, separate formalism, a modal language interpreted on a (coloured) LTS used to express its properties. We consolidate these two strands. Instead of specifying the obligatory and prohibited states and transitions as part of the construction of a coloured LTS as in nC+, we represent norms in the modal language and use those to construct a coloured LTS from a given regular (uncoloured) one. We also show how connections between norms on states and norms on transitions previously treated as fixed constraints of a coloured LTS can instead be defined within the modal language used for representing norms.
{"title":"A Unified Logical Framework for Reasoning about Deontic Properties of Actions and States","authors":"P. Kulicki, R. Trypuz, R. Craven, M. Sergot","doi":"10.12775/llp.2023.004","DOIUrl":"https://doi.org/10.12775/llp.2023.004","url":null,"abstract":"This paper studies some normative relations that hold between actions, their preconditions and their effects, with particular attention to connecting what are often called ‘ought to be’ norms with ‘ought to do’ norms. We use a formal model based on a form of transition system called a ‘coloured labelled transition system’ (coloured LTS) introduced in a series of papers by Sergot and Craven. Those works have variously presented a formalism (an ‘action language’) nC+ for defining and computing with a (coloured) LTS, and another, separate formalism, a modal language interpreted on a (coloured) LTS used to express its properties. We consolidate these two strands. Instead of specifying the obligatory and prohibited states and transitions as part of the construction of a coloured LTS as in nC+, we represent norms in the modal language and use those to construct a coloured LTS from a given regular (uncoloured) one. We also show how connections between norms on states and norms on transitions previously treated as fixed constraints of a coloured LTS can instead be defined within the modal language used for representing norms.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44367592","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 paper presents a demarcation of a “minimalistic” concept of logical form, which nevertheless largely agrees with the way the term “logical form” is commonly used in contemporary logic and philosophy of logic. We see logical forms as formulas of formal languages assigned to (compounds of) sentences of a natural language (perhaps modulo notational variance). We thus reject the views of logical forms as underlying structures of thoughts or of the material reality that surrounds us. The assignment of the forms, we claim, aims at envisaging the logical (especially inferential) properties of the analyzed sentences, arguments, or other texts, as the analyzing formulas wear them, as it were, on their sleeves. Hence we suggest an “expressivist” and a pragmatic understanding of logical forms - they are used to expose (and fix) logical properties of sentences in textual contexts and the way of their employment is determined by the goals of the particular studies.
{"title":"Establishing Logical Forms","authors":"J. Peregrin, V. Svoboda","doi":"10.12775/llp.2023.008","DOIUrl":"https://doi.org/10.12775/llp.2023.008","url":null,"abstract":"The paper presents a demarcation of a “minimalistic” concept of logical form, which nevertheless largely agrees with the way the term “logical form” is commonly used in contemporary logic and philosophy of logic. We see logical forms as formulas of formal languages assigned to (compounds of) sentences of a natural language (perhaps modulo notational variance). We thus reject the views of logical forms as underlying structures of thoughts or of the material reality that surrounds us. The assignment of the forms, we claim, aims at envisaging the logical (especially inferential) properties of the analyzed sentences, arguments, or other texts, as the analyzing formulas wear them, as it were, on their sleeves. Hence we suggest an “expressivist” and a pragmatic understanding of logical forms - they are used to expose (and fix) logical properties of sentences in textual contexts and the way of their employment is determined by the goals of the particular studies.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46127520","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}
Logical form is thought to be discovered by keeping fixed the logical constants and allowing the non-logical content in the sentence to vary. The problem of logical constants is the problem of defining what counts as a logical constant. In this paper, I will argue that the concept ’logical constant’ is vague. I demonstrate the vagueness of logical constancy by providing a sorites argument, thereby showing the sorites-susceptibility of the concept. Many prior papers in the literature on logical constants hint at this vagueness, but do not explore how theories of vagueness apply to logical constants. In the second half of this paper, I do just this. I consider approaches to logical constants that resemble nihilism about vagueness and more recent theories that relativize truth to precisifications. Finally, I argue that approaches that accept the potential indeterminate status of putative logical constants are preferable to nihilism or relativism about logical constancy.
{"title":"Logical Constants and the Sorites Paradox","authors":"Zack Garrett","doi":"10.12775/llp.2023.007","DOIUrl":"https://doi.org/10.12775/llp.2023.007","url":null,"abstract":"Logical form is thought to be discovered by keeping fixed the logical constants and allowing the non-logical content in the sentence to vary. The problem of logical constants is the problem of defining what counts as a logical constant. In this paper, I will argue that the concept ’logical constant’ is vague. I demonstrate the vagueness of logical constancy by providing a sorites argument, thereby showing the sorites-susceptibility of the concept. Many prior papers in the literature on logical constants hint at this vagueness, but do not explore how theories of vagueness apply to logical constants. In the second half of this paper, I do just this. I consider approaches to logical constants that resemble nihilism about vagueness and more recent theories that relativize truth to precisifications. Finally, I argue that approaches that accept the potential indeterminate status of putative logical constants are preferable to nihilism or relativism about logical constancy.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49610430","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 paper contains a review and a discussion of Robert Trueman's book Properties and Propositions: The Metaphysics of Higher-Order Logic, Cambridge University Press, 2021, pp. xii + 227. ISBN 978-1-108-81410-2. The discussion is focused on the consistency of Truema's language-based ontology and on its value in defending higher-order logic.
{"title":"Robert Trueman’s Defence of Higher-Order Logic","authors":"M. Tkaczyk","doi":"10.12775/llp.2023.006","DOIUrl":"https://doi.org/10.12775/llp.2023.006","url":null,"abstract":"The paper contains a review and a discussion of Robert Trueman's book Properties and Propositions: The Metaphysics of Higher-Order Logic, Cambridge University Press, 2021, pp. xii + 227. ISBN 978-1-108-81410-2. The discussion is focused on the consistency of Truema's language-based ontology and on its value in defending higher-order logic.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45293623","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}
This paper discusses a generalization of logical expressivism. It is shown that, in the wide sense defined here, the expressivist approach is neutral with respect to different theories of inference and offers a natural framework for understanding logical forms and their function. An expressivist strategy for explaining the development of logical forms is then applied to the analysis of Frege’s Begriffsschrift, Gentzen’s sequent calculus and Belnap’s display logic.
{"title":"An Expressivist Strategy to Understand Logical Forms","authors":"Giacomo Turbanti","doi":"10.12775/llp.2023.005","DOIUrl":"https://doi.org/10.12775/llp.2023.005","url":null,"abstract":"This paper discusses a generalization of logical expressivism. It is shown that, in the wide sense defined here, the expressivist approach is neutral with respect to different theories of inference and offers a natural framework for understanding logical forms and their function. An expressivist strategy for explaining the development of logical forms is then applied to the analysis of Frege’s Begriffsschrift, Gentzen’s sequent calculus and Belnap’s display logic.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48555721","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 word ‘logic’ has many senses. Here we will understand it as meaning an account of what follows from what and why. With contemporary methodology, logic in this sense – though it may not always have been thought of in this way – is a branch of applied mathematics. This has various implications for how one understands a number of issues concerning validity. In this paper I will explain this perspective of logic, and explore some of its consequences with respect to the notion of logical form.
{"title":"Logic as applied Mathematics – with Particular Application to the Notion of Logical Form","authors":"G. Priest","doi":"10.12775/llp.2023.003","DOIUrl":"https://doi.org/10.12775/llp.2023.003","url":null,"abstract":"The word ‘logic’ has many senses. Here we will understand it as meaning an account of what follows from what and why. With contemporary methodology, logic in this sense – though it may not always have been thought of in this way – is a branch of applied mathematics. This has various implications for how one understands a number of issues concerning validity. In this paper I will explain this perspective of logic, and explore some of its consequences with respect to the notion of logical form.\u0000 ","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49170687","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}
This paper examines several intended topological features of the Region Connection Calculus (RCC) and argues that they are either underdetermined by the formal theory or given by the complement axiom. Conditions are identified under which the axioms of RCC are satisfied in topological models under various set restrictions. The results generalise previous results in the literature to non-strict topological models and across possible interpretations of connection. It is shown that the intended interpretation of connection and the alignment of self-connection with topological connection are underdetermined by the axioms of RCC, which suggests that additional axioms are necessary to secure these features. It is also argued that the complement axiom gives RCC models much of their topological structure. In particular, the incompatibility of RCC with interiors is argued to be given by the complement axiom.
{"title":"On Some Meta-Theoretic Topological Features of the Region Connection Calculus","authors":"Nathaniel Gan","doi":"10.12775/llp.2023.002","DOIUrl":"https://doi.org/10.12775/llp.2023.002","url":null,"abstract":"This paper examines several intended topological features of the Region Connection Calculus (RCC) and argues that they are either underdetermined by the formal theory or given by the complement axiom. Conditions are identified under which the axioms of RCC are satisfied in topological models under various set restrictions. The results generalise previous results in the literature to non-strict topological models and across possible interpretations of connection. It is shown that the intended interpretation of connection and the alignment of self-connection with topological connection are underdetermined by the axioms of RCC, which suggests that additional axioms are necessary to secure these features. It is also argued that the complement axiom gives RCC models much of their topological structure. In particular, the incompatibility of RCC with interiors is argued to be given by the complement axiom.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47603041","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}
It is shown how the temporal-modal system of events TM (axiomatized in Appendix) allows for the avoidance of the logical determinism without the rejection of the principle of bivalence. The point is that the temporal and the modal parts of TM are so inter-related that modalities are in-the-real-world-inherent modalities independently of whether they concern actual or only possible events. Though formulated in a tenseless language, whose interpretation does not require the assumption of tense facts at the basic level of reality, TM implies an objective, observer-independent difference between tenses based only on the way in which modalities are distributed along the time continuum. The conclusion is that the arrow of time is an intra-model characteristic of any model of TM that describes the non-deterministic real world up to a certain point of its history, while the flow of time is an inter-model characteristic of the continuous transition between these models.
{"title":"Future Contingencies and the Arrow and Flow of Time in a Non-Deterministic World According to the Temporal-Modal System TM","authors":"Miloš Arsenijević, Andrej Jandrić","doi":"10.12775/llp.2023.001","DOIUrl":"https://doi.org/10.12775/llp.2023.001","url":null,"abstract":"It is shown how the temporal-modal system of events TM (axiomatized in Appendix) allows for the avoidance of the logical determinism without the rejection of the principle of bivalence. The point is that the temporal and the modal parts of TM are so inter-related that modalities are in-the-real-world-inherent modalities independently of whether they concern actual or only possible events. Though formulated in a tenseless language, whose interpretation does not require the assumption of tense facts at the basic level of reality, TM implies an objective, observer-independent difference between tenses based only on the way in which modalities are distributed along the time continuum. The conclusion is that the arrow of time is an intra-model characteristic of any model of TM that describes the non-deterministic real world up to a certain point of its history, while the flow of time is an inter-model characteristic of the continuous transition between these models.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42068780","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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