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The Australasian Journal of Logic最新文献

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Countering Justification Holism in the Epistemology of Logic: The Argument from Pre-Theoretic Universality 反对逻辑认识论中的辩护整体主义:来自前理论普遍性的论证
The Australasian Journal of Logic Pub Date : 2023-10-19 DOI: 10.26686/ajl.v20i3.8201
Frederik J. Andersen
{"title":"Countering Justification Holism in the Epistemology of Logic: The Argument from Pre-Theoretic Universality","authors":"Frederik J. Andersen","doi":"10.26686/ajl.v20i3.8201","DOIUrl":"https://doi.org/10.26686/ajl.v20i3.8201","url":null,"abstract":"
 
 
 A key question in the philosophy of logic is how we have epistemic justification for claims about logical entailment (assuming we have such justification at all). Justification holism asserts that claims of logical entailment can only be justified in the context of an entire logical theory, e.g., classical, intuitionistic, paraconsistent, paracomplete etc. According to holism, claims of logical entailment cannot be atomistically justified as isolated statements, independently of theory choice. At present there is a developing interest in—and endorsement of—justification holism due to the revival of an abductivist approach to the epistemology of logic. This paper presents an argument against holism by establishing a foundational entailment-sentence of deduction which is justified independently of theory choice and outside the context of a whole logical theory.
 
 
","PeriodicalId":367849,"journal":{"name":"The Australasian Journal of Logic","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135780543","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}
引用次数: 0
Semantic Incompleteness of Hilbert system for a Combination of Classical and Intuitionistic Propositional Logic 经典与直觉命题逻辑结合的Hilbert系统的语义不完备性
The Australasian Journal of Logic Pub Date : 2023-10-19 DOI: 10.26686/ajl.v20i3.7696
Masanobu Toyooka, Katsuhiko Sano
{"title":"Semantic Incompleteness of Hilbert system for a Combination of Classical and Intuitionistic Propositional Logic","authors":"Masanobu Toyooka, Katsuhiko Sano","doi":"10.26686/ajl.v20i3.7696","DOIUrl":"https://doi.org/10.26686/ajl.v20i3.7696","url":null,"abstract":"This paper shows Hilbert system (C+J)-, given by del Cerro and Herzig (1996) is semantically incomplete. This system is proposed as a proof theory for Kripke semantics for a combination of intuitionistic and classical propositional logic, which is obtained by adding the natural semantic clause of classical implication into intuitionistic Kripke semantics. Although Hilbert system (C+J)- contains intuitionistic modus ponens as a rule, it does not contain classical modus ponens. This paper gives an argument ensuring that the system (C+J)- is semantically incomplete because of the absence of classical modus ponens. Our method is based on the logic of paradox, which is a paraconsistent logic proposed by Priest (1979).","PeriodicalId":367849,"journal":{"name":"The Australasian Journal of Logic","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135779706","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}
引用次数: 0
The Paradox Paradox Non-Paradox and Conjunction Fallacy Non-Fallacy 悖论，悖论，非悖论和连接谬误，非谬误
The Australasian Journal of Logic Pub Date : 2023-10-19 DOI: 10.26686/ajl.v20i3.8195
Noah Greenstein
{"title":"The Paradox Paradox Non-Paradox and Conjunction Fallacy Non-Fallacy","authors":"Noah Greenstein","doi":"10.26686/ajl.v20i3.8195","DOIUrl":"https://doi.org/10.26686/ajl.v20i3.8195","url":null,"abstract":"Brock and Glasgow recently introduced a new definition of paradox and argue that this conception of paradox itself leads to paradox, the so-called Paradox Paradox. I show that they beg the questions during the course of their argument, but, more importantly, do so in a philosophically interesting way: it reveals a counterexample to the equivalence between being a logical truth and having a probability of one. This has consequences regarding norms of rationality, undermining the grounds for the Conjunction Fallacy.","PeriodicalId":367849,"journal":{"name":"The Australasian Journal of Logic","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135780545","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}
引用次数: 0
A Semi-Constructive Approach to the Hyperreal Line 超实线的半构造方法
The Australasian Journal of Logic Pub Date : 2023-10-19 DOI: 10.26686/ajl.v20i3.8254
Guillaume Massas
{"title":"A Semi-Constructive Approach to the Hyperreal Line","authors":"Guillaume Massas","doi":"10.26686/ajl.v20i3.8254","DOIUrl":"https://doi.org/10.26686/ajl.v20i3.8254","url":null,"abstract":"Using an alternative to Tarskian semantics for first-order logic known as possibility semantics, I introduce an approach to nonstandard analysis that remains within the bounds of semiconstructive mathematics, i.e., does not assume any fragment of the Axiom of Choice beyond the Axiom of Dependent Choices. I define the Fr´echet hyperreal line †R as a possibility structure and show that it shares many fundamental properties of the classical hyperreal line, such as a Transfer Principle and a Saturation Principle. I discuss the technical advantages of †R over some other alternative approaches to nonstandard analysis and argue that it is well-suited to address some of the philosophical and methodological concerns that have been raised against the application of nonstandard methods to ordinary mathematics.","PeriodicalId":367849,"journal":{"name":"The Australasian Journal of Logic","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135780405","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}
引用次数: 1
Threshold-Based Belief Change 基于阈值的信念改变
The Australasian Journal of Logic Pub Date : 2023-10-19 DOI: 10.26686/ajl.v20i3.7408
Hans Rott, Eric Raidl
{"title":"Threshold-Based Belief Change","authors":"Hans Rott, Eric Raidl","doi":"10.26686/ajl.v20i3.7408","DOIUrl":"https://doi.org/10.26686/ajl.v20i3.7408","url":null,"abstract":"In this paper we study changes of beliefs in a ranking-theoretic setting using non-extremal implausibility thresholds for belief. We represent implausibilities as ranks and introduce natural rank changes subject to a minimal change criterion. We show that many of the traditional AGM postulates for revision and contraction are preserved, except for the postulate of Preservation which is invalid. The diagnosis for belief contraction is similar, but not exactly the same. We demonstrate that the one-shot versions of both revision and contraction can be represented as revisions based on semiorders, but in two subtly different ways. We provide sets of postulates that are sound and complete in the sense that they allow us to prove representation theorems. We show that, and explain why, the classical duality between revision and contraction, as exhibited by the Levi and Harper identities, is partly broken by threshold-based belief changes. We also study the logic of iterated threshold-based revision and contraction. The traditional Darwiche-Pearl postulates for iterated revision continue to hold, as well as two additional postulates that characterize ranking-based revision as a restricted `improvement' operator. We investigate the dual notion of iterated threshold-based belief contraction and provide a new set of postulates for it, characterizing contraction as a restricted 'degrading' operator.","PeriodicalId":367849,"journal":{"name":"The Australasian Journal of Logic","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135779860","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}
引用次数: 0
What are acceptable reductions? 可接受的减量是多少?
The Australasian Journal of Logic Pub Date : 2023-10-19 DOI: 10.26686/ajl.v20i3.7692
Sara Ayhan
{"title":"What are acceptable reductions?","authors":"Sara Ayhan","doi":"10.26686/ajl.v20i3.7692","DOIUrl":"https://doi.org/10.26686/ajl.v20i3.7692","url":null,"abstract":"It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the same conclusion would have to be identified. In this paper it will be shown that the question, which reductions we accept in our system, is not only important if we see them as generating a theory of proof identity but is also decisive for the more general question whether a proof has meaningful content. There are certain reductions which would not only force us to identify proofs of different arbitrary formulas but which would render derivations in a system allowing them meaningless. To exclude such cases, a minimal criterion is proposed which reductions have to fulfill to be acceptable.","PeriodicalId":367849,"journal":{"name":"The Australasian Journal of Logic","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135779733","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}
引用次数: 0
A Variety of DeMorgan Negations in Relevant Logics 相关逻辑中的各种民主否定
The Australasian Journal of Logic Pub Date : 2023-08-09 DOI: 10.26686/ajl.v20i2.8311
G. Robles, J. Méndez
{"title":"A Variety of DeMorgan Negations in Relevant Logics","authors":"G. Robles, J. Méndez","doi":"10.26686/ajl.v20i2.8311","DOIUrl":"https://doi.org/10.26686/ajl.v20i2.8311","url":null,"abstract":"The present paper is inspired by Sylvan and Plumwood’s logicBM defined in “Non-normal relevant logics” and by their treatmentof negation with the ∗-operator in “The semantics of first-degree en-tailment”. Given a positive logic L including Routley and Meyer’sbasic positive logic and included in either the positive fragment of Eor in that of RW, we investigate the essential De Morgan negation ex-pansions of L and determine all the deductive relations they maintainto each other. A Routley-Meyer semantics is provided for each logicdefined in the paper.","PeriodicalId":367849,"journal":{"name":"The Australasian Journal of Logic","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116539615","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}
引用次数: 0
Introduction to the special issue ‘Valerie Plumwood’s contributions to Logic’ 《瓦莱丽·普拉姆伍德对逻辑学的贡献》特刊简介
The Australasian Journal of Logic Pub Date : 2023-07-13 DOI: 10.26686/ajl.v29i2.8281
A. Tedder, Guillermo Badia
{"title":"Introduction to the special issue ‘Valerie Plumwood’s contributions to Logic’","authors":"A. Tedder, Guillermo Badia","doi":"10.26686/ajl.v29i2.8281","DOIUrl":"https://doi.org/10.26686/ajl.v29i2.8281","url":null,"abstract":"This is an introduction to the special issue of the AJL on Val Plumwood's manuscript \"False Laws of Logic\" and her other work in logic.","PeriodicalId":367849,"journal":{"name":"The Australasian Journal of Logic","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115799514","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}
引用次数: 0
The Liberation Argument for Inconsistent Mathematics 不一致数学的解放论
The Australasian Journal of Logic Pub Date : 2023-07-13 DOI: 10.26686/ajl.v29i2.8289
Franci Mangraviti
{"title":"The Liberation Argument for Inconsistent Mathematics","authors":"Franci Mangraviti","doi":"10.26686/ajl.v29i2.8289","DOIUrl":"https://doi.org/10.26686/ajl.v29i2.8289","url":null,"abstract":"Val Plumwood charged classical logic not only with the invalidity of some of its laws, but also with the support of systemic oppression through naturalization of the logical structure of dualisms. In this paper I show that the latter charge - unlike the former - can be carried over to classical mathematics, and I propose a new conception of inconsistent mathematics - queer incomaths - as a liberatory activity meant to undermine said naturalization.","PeriodicalId":367849,"journal":{"name":"The Australasian Journal of Logic","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114094657","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}
引用次数: 1
In Support of Valerie Plumwood 支持瓦莱丽·普拉姆伍德
The Australasian Journal of Logic Pub Date : 2023-07-13 DOI: 10.26686/ajl.v29i2.8287
R. Brady
{"title":"In Support of Valerie Plumwood","authors":"R. Brady","doi":"10.26686/ajl.v29i2.8287","DOIUrl":"https://doi.org/10.26686/ajl.v29i2.8287","url":null,"abstract":"\u0000 \u0000 \u0000This paper offers general support for what Valerie Plumwood’s paper is trying to achieve by supporting the rejection of each of her four “false laws of logic”: exportation, illegitimate replacement, commutation (aka. permutation) and disjunctive syllogism. We start by considering her general characterizations of entailment, beginning with her stated definition of entailment as the converse of deducibility. However, this applies to a wide range of relevant logics and so is not able to be used as a criterion for deciding what laws to include in a logic. In this context, we examine the two key differences between deduction from premises to conclusion and entailment from antecedent to consequent. We also consider her use of sufficiency as a general characterizing feature. We then discuss Plumwood’s syntactic criteria used to reject the first three of her false laws of logic and add the Relevance Condition in this context. We next consider semantic characterizing criteria for a logic. After making a case against using truth, we introduce Brady’s logic MC of meaning containment. We then examine the content semantics for MC and use it to reject all of Plumwood’s false laws of logic together with some others. We follow with the related Depth Relevance Condition, which is a syntactic cri- terion satisfied by MC. This clearly rejects the first three of these laws and many others, but not the fourth law. We conclude by giving our overall support for her general enterprise. \u0000 \u0000 \u0000","PeriodicalId":367849,"journal":{"name":"The Australasian Journal of Logic","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129783838","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}
引用次数: 0
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