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  1.  27
    The liberation argument for inconsistent mathematics.Franci Mangraviti - 2023 - Australasian Journal of Logic 29 (2):278-315.
    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.
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  2. Countering Justification Holism in the Epistemology of Logic: The Argument from Pre-Theoretic Universality.Frederik J. Andersen - 2023 - Australasian Journal of Logic 20 (3):375-396.
    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 (...)
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  3. What are acceptable reductions? Perspectives from proof-theoretic semantics and type theory.Sara Ayhan - 2023 - Australasian Journal of Logic 20 (3):412-428.
    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 (...)
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  4. The Paradox Paradox Non-Paradox and Conjunction Fallacy Non-Fallacy.Noah Greenstein - 2023 - Australasian Journal of Logic 20 (3):478-489.
    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.
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  5.  12
    A Semi-Constructive Approach to the Hyperreal Line.Guillaume Massas - 2023 - Australasian Journal of Logic 20 (3):490-536.
    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 (...)
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  6.  7
    Threshold-Based Belief Change.Eric Raidl & Hans Rott - 2023 - Australasian Journal of Logic 20 (3):429-477.
    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 (...)
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  7.  8
    Semantic Incompleteness of Hilbert system for a Combination of Classical and Intuitionistic Propositional Logic.Masanobu Toyooka & Katsuhiko Sano - 2023 - Australasian Journal of Logic 20 (3):397-411.
    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 (...)
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  8.  5
    The class of all 3-valued natural conditional variants of RM3 that are Plumwood Algebras.Jose Miguel Blanco, Sandra M. Lopez & Marcos M. Recio - 2023 - Australasian Journal of Logic 20 (2):188-218.
    Valerie Plumwood introduced in "Some false laws of logic" a series of arguments on how the rules Exported Syllogism, Disjunctive Syllogism, Commutation, and Exportation are not acceptable. Based on this we define the class of Plumwood algebras - logical matrices that do not verify any of these theses. Afterwards we provide conditional variants of the characteristic matrix of the logic RM3 that are also Plumwood algebras. These matrices are given an axiomatization based on First Degree Entailment and are endowed with (...)
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  9.  4
    In Support of Valerie Plumwood.Ross Brady - 2023 - Australasian Journal of Logic 20 (2):219-242.
    This 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 (...)
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  10.  11
    From Excluded Middle to Homogenization in Plumwood’s Feminist Critique of Logic.Thomas Macaulay Ferguson - 2023 - Australasian Journal of Logic 20 (2):243-277.
    A key facet of Valerie Plumwood’s feminist critique of logic is her analysis of classical negation. On Plumwood’s reading, the exclusionary features of classical negation generate hierarchical dualisms, i.e., dichotomies in which dominant groups’ primacy is reinforced while underprivileged groups are oppressed. For example, Plumwood identifies the system collapse following from ex contradictione quodlibet—that a theory including both φ and ∼φ trivializes—as a primary source of many of these features. Although Plumwood considers the principle of excluded middle to be compatible (...)
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  11.  3
    Val (Routley) Plumwood: Work in Logic.Dominic Hyde - 2023 - Australasian Journal of Logic 20 (2):138-153.
    Val Plumwood (nee Morrell) is best known in the logic community for her work on relevant logics published jointly with Richard Sylvan. Together, as `"Val and Richard Routley", they worked at the center of the Canberra Logic Group from 1971 to 1981 before they divorced and changed names, whereupon Val shifted her focus to issues in environmental philosophy. Her writing in that latter field drew so much attention, in fact, that most people familiar with her philosophical work know her solely (...)
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  12.  9
    Some False Laws of Logic.Valerie Plumwood - 2023 - Australasian Journal of Logic 20 (2):97-137.
    This paper argues that some widely used laws of implication are false, and arguments based upon them invalid. These laws are Exportation, Commutation, (as well as various restricted forms of these), Exported Syllogism and Disjunctive Syllogism. All these laws are false for the same reason – that they license the suppression or replacement in some position of some class of propositions which cannot legitimately be suppressed or replaced. These laws fail to preserve the property of sufficiency of premiss set for (...)
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  13.  11
    Feminist Logic, Literally.Ivan Restović - 2023 - Australasian Journal of Logic 20 (2):318-347.
    I this paper, I discuss Plumwood’s feminist logic program. I argue both in favor of her general stance in feminist philosophy of logic and her more specific feminist critique of classical logic. Plumwood’s general position is in opposition with (I think it’s safe to say) the prevailing view in analytic philosophy about the relation between formal logic and feminist theory, according to which feminist theory cannot say anything about or against logic proper, since the issues of oppression are external to (...)
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  14.  15
    A Variety of DeMorgan Negations in Relevant Logics.Gemma Robles & José Mendez - 2023 - Australasian Journal of Logic 20 (2):348-374.
    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 (...)
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  15.  8
    Introduction to the special issue ‘Valerie Plumwood’s contributions to Logic’.Andrew Tedder & Guillermo Badia - 2023 - Australasian Journal of Logic 20 (2):95-96.
    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.
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  16.  12
    Relevance through topical unconnectedness.Tore Fjetland Øgaard - 2023 - Australasian Journal of Logic 20 (2):154-187.
    Ackermann’s motivational spin on his theory of rigorous implication is analyzed and it is shown to contain en equivalent idea to Plumwood’s notion of suppression freedom. The formal properties these ideas back turn out to be properly weaker than Belnap’s variable sharing property, but it is shown that they can be strengthen in various ways. Some such strengthenings, it is shown, yield properties which are equivalent to Belnap’s, and thus provide for new ways of motivating Belnap’s fundamental relevance principle.
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  17.  7
    Interpreting mereotopological connection.Nat Gan - 2023 - Australasian Journal of Logic 20 (1):32-46.
    This paper examines ten possible topological interpretations of connection and for each interpretation, identifies sufficient conditions under which a significant class of topological spaces provides models of General Extensional Mereotopology with Closure Conditions (GEMTC) in which some key mereotopological ideas align with their topological analogues. In particular, there is an interpretation under which the non-empty sets of any symmetric topology are a model of GEMTC with alignment between the mereotopological and topological definitions of (self-)connection, open and closed entities, interior, exterior, (...)
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  18.  4
    Modular labelled calculi for relevant logics.Fabio De Martin Polo - 2023 - Australasian Journal of Logic 20 (1):47-87.
    In this article, we perform a detailed proof theoretic investigation of a wide number of relevant logics by employing the well-established methodology of labelled sequent calculi to build our intended systems. At the semantic level, we will characterise relevant logics by employing reduced Routley-Meyer models, namely, relational structures with a ternary relation between worlds along with a unique distinct element considered as the real (or actual) world. This paper realizes the idea of building a variety of modular labelled calculi by (...)
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  19.  31
    From Collapse Theorems to Proof-Theoretic Arguments.Alessandro Rossi - 2023 - Australasian Journal of Logic 20 (1):1-31.
    On some views, we can be sure that parties to a dispute over the logic of ‘exists’ are not talking past each other if they can characterise ‘exists’ as the only monadic predicate up to logical equivalence obeying a certain set of rules of inference. Otherwise, we ought to be suspicious about the reality of their disagreement. This is what we call a proof- theoretic argument. Pace some critics, who have tried to use proof-theoretic arguments to cast doubts about the (...)
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  20.  4
    Geometry of Relevant Implication II.Alasdair Urquhart - 2023 - Australasian Journal of Logic 20 (1):88-94.
    This note extends earlier results on geometrical interpretations of the logic KR to prove some additional results, including a simple undecidability proof for the four-variable fragment of KR.
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