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Added by: Berta Grimau, Contributed by: Patricia BlanchetteAbstract: Description: This article is a short overview of philosophical and formal issues in the treatment and analysis of logical consequence. The purpose of the paper is to provide a brief introduction to the central issues surrounding two questions: (1) that of the nature of logical consequence and (2) that of the extension of logical consequence. It puts special emphasis in the role played by formal systems in the investigation of logical consequence.

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Added by: Berta Grimau, Contributed by: Patricia BlanchetteAbstract: This paper examines the connection between modeltheoretic truth and necessary truth. It is argued that though the modeltheoretic truths of some standard languages are demonstrably "necessary" (in a precise sense), the widespread view of modeltheoretic truth as providing a general guarantee of necessity is mistaken. Several arguments to the contrary are criticized.
Comment: This text would be best used as secondary reading in an intermediate or an advanced philosophy of logic course. For example, it can be used as a secondary reading in a section on the connection between modeltheoretic truth and necessary truth.

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Added by: Franci MangravitiAbstract:
Logical Pluralists maintain that there is more than one genuine/true logical consequence relation. This paper seeks to understand what the position could amount to and some of the challenges faced by its formulation and defence. I consider in detail Beall and Restall’s Logical Pluralism—which seeks to accommodate radically different logics by stressing the way that they each ﬁt a general form, the Generalised Tarski Thesis (GTT)—arguing against the claim that different instances of GTT are admissible precisiﬁcations of logical consequence. I then consider what it is to endorse a logic within a pluralist framework and criticise the options Beall and Restall entertain. A case study involving manyvalued logics is examined. I next turn to issues of the applications of different logics and questions of which logic a pluralist should use in particular contexts. A dilemma regarding the applicability of admissible logics is tackled and it is argued that application is a red herring in relation to both understanding and defending a plausible form of logical pluralism. In the ﬁnal section, I consider other ways to be and not to be a logical pluralist by examining analogous positions in debates over religious pluralism: this, I maintain, illustrates further limitations and challenges for a very general logical pluralism. Certain less wideranging pluralist positions are more plausible in both cases, I suggest, but assessment of those positions needs to be undertaken on a casebycase basis.
Comment: Makes for a nice counter in any course discussing Beall and Restall's pluralism. Given that the paper is a direct response, some previous familiarity with the topic is advised.

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Added by: Berta GrimauSummary: This article provides the basics of a typical logic, sometimes called 'classical elementary logic' or 'classical firstorder logic', in a rigorous yet accessible manner. Section 2 develops a formal language, with a syntax and grammar. Section 3 sets up a deductive system for the language, in the spirit of natural deduction. Section 4 provides a modeltheoretic semantics. Section 5 turns to the relationships between the deductive system and the semantics, and in particular, the relationship between derivability and validity. The authors show that an argument is derivable only if it is valid (soundness). Then they establish a converse: that an argument is valid only if it is derivable (completeness). They also briefly indicate other features of the logic, some of which are corollaries to soundness and completeness. The final section, Section 6, is devoted to a brief examination of the philosophical position that classical logic is 'the one right logic'.
Comment: This article introduces all the necessary tools in order to understand both the prooftheoretic and the modeltheoretic aspects of firstorder classical logical consequence. As such it can be used as a main reading in an introductory logic course covering classical firstorder logic (assuming the students will have already looked at classical propositional logic). Moreover, the article covers some metatheoretic results (soundness, completeness, compactness, upward and downward LöwenheimSkolem), which makes it suitable as a reading for a slightly more advanced course in logic. Finally, the article includes a brief incursion into the topic of logical pluralism. This makes it suitable to be used in a course on nonclassical logics with an introduction module on classical logic.

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Added by: Franci MangravitiAbstract:
Being a pragmatic and not a referential approach to semantics, the dialogical formulation of paraconsistency allows the following semantic idea to be expressed within a semiformal system: In an argumentation it sometimes makes sense to distinguish between the contradiction of one of the argumentation partners with himself (internal contradiction) and the contradiction between the partners (external contradiction). The idea is that external contradiction may involve different semantic contexts in which, say A and not A have been asserted. The dialogical approach suggests a way of studying the dynamic process of contradictions through which the two contexts evolve for the sake of argumentation into one system containing both contexts. More technically, we show a new, dialogical, way to build paraconsistent systems for propositional and ﬁrstorder logic with classical and intuitionistic features (i.e. paraconsistency both with and without tertium nondatur) and present their corresponding tableaux.
Comment: This paper would fit well in a course on dialogical formulations of logic (as either main or further reading, depending on the time dedicated to Lorenzstyle approaches), or in a course on paraconsistent logic (as an alternative way of thinking about paraconsistency); both topics are introduced in an accessible enough way. If students have no familiarity with tableaux systems, sections 4 and 5.2 can be skipped.

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Abstract:
From the introduction: "we argue that the semantics of the first degree paradoxfree implication system FD supports the claim it is superior to strict implication as an analysis of entailment at the first degree level. The semantics also reveals that Disjunctive Syllogism, [...] far from being a paradigmatic entailment, is invalid, and allows the illegitimate suppression of tautologies"
Comment: The paper introduces some of the central ideas in the relevance logic literature, e..g the connection between suppression and sufficiency, and the modeling of negation via the Routley star. It is a natural pick for a specialized course on relevance logic, but it can also be used as an introduction to (or further reading about) relevance logic in a general course on nonclassical logics. Some familiarity with classical and modal logic (in particular, the notion of strict implication) is required.

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Added by: Franci MangravitiAbstract:
Some writers object to logical pluralism on the grounds that logic is normative. The rough idea is that the relation of logical consequence has consequences for what we ought to think and how we ought to reason, so that pluralism about the consequence relation would result in an incoherent or unattractive pluralism about those things. In this paper I argue that logic isn’t normative. I distinguish three diﬀerent ways in which a theory – such as a logical theory – can be entangled with the normative and argue that logic is only entangled in the weakest of these ways, one which requires it to have no normativity of its own. I use this view to show what is wrong with three diﬀerent arguments for the conclusion that logic is normative.
Comment: Appropriate for any course touching on the normativity of logic question. Familiarity with the question and with logical pluralism is helpful, but not required. Could be paired with a defense of normativity for discussion.

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Added by: Franci MangravitiAbstract:
Logical nihilism can be understood as the view that there are no laws of logic. This paper presents both a counterexamplebased argument in favor of logical nihilism, and a way to resist it by using Lakatos' method of lemma incorporation. The price to pay is the loss of absolute generality.
Comment: The paper is appropriate for any course discussing the monism vs pluralism vs nihilism debate in logic (or maybe even focusing on varieties of logical nihilism). On a technical level it requires no more than an introduction to formal logic; some familiarity with monist and pluralist positions is helpful for context.

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Added by: Berta GrimauAbstract: This paper deals with the adequacy of the modeltheoretic definition of logical consequence. Logical consequence is commonly described as a necessary relation that can be determined by the form of the sentences involved. In this paper, necessity is assumed to be a metaphysical notion, and formality is viewed as a means to avoid dealing with complex metaphysical questions in logical investigations. Logical terms are an essential part of the form of sentences and thus have a crucial role in determining logical consequence. Gila Sher and Stewart Shapiro each propose a formal criterion for logical terms within a modeltheoretic framework, based on the idea of invariance under isomorphism. The two criteria are formally equivalent, and thus we have a common ground for evaluating and comparing Sher and Shapiro philosophical justification of their criteria. It is argued that Shapiro's blended approach, by which models represent possible worlds under interpretations of the language, is preferable to Sher’s formalstructural view, according to which models represent formal structures. The advantages and disadvantages of both views’ reliance on isomorphism are discussed.
Comment: This paper provides an original view on the debate on the adequacy of the modeltheoretic notion of logical consequence as well as a good overview of the relevant part of the debate. It can be used as standing on its own, but it can also serve as a complement to Sher (1996), also written by a female logician, and Shapiro (1998). Adequate for a general course on philosophy of logic or in a more specialized course on logical consequence. The paper is not technical, although students should've have taken at least an introductory logic course.
Comment: This article can be used as background or overview reading in a course on the notion of logical consequence. It could also be used in a general course on philosophy of logic having a section on this topic. It makes very little use of technical notation, even though familiarity with firstorder logic is required. It closes with a useful list of suggested further readings.