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Logical Pluralism
 To appear, Special Logic issue of the Australasian Journal of Philosophy
, 2000
"... Abstract: A widespread assumption in contemporary philosophy of logic is that there is one true logic, that there is one and only one correct answer as to whether a given argument is deductively valid. In this paper we propose an alternative view, logical pluralism. According to logical pluralism th ..."
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Abstract: A widespread assumption in contemporary philosophy of logic is that there is one true logic, that there is one and only one correct answer as to whether a given argument is deductively valid. In this paper we propose an alternative view, logical pluralism. According to logical pluralism there is not one true logic; there are many. There is not always a single answer to the question “is this argument valid?” 1 Logic, Logics and Consequence Anyone acquainted with contemporary Logic knows that there are many socalled logics. 1 But are these logics rightly socalled? Are any of the menagerie of nonclassical logics, such as relevant logics, intuitionistic logic, paraconsistent logics or quantum logics, as deserving of the title ‘logic ’ as classical logic? On the other hand, is classical logic really as deserving of the title ‘logic ’ as relevant logic (or any of the other nonclassical logics)? If so, why so? If not, why not? Logic has a chief subject matter: Logical Consequence. The chief aim of
Multiple conclusions
 In 12th International Congress on Logic, Methodology and Philosophy of Science
, 2005
"... Abstract: I argue for the following four theses. (1) Denial is not to be analysed as the assertion of a negation. (2) Given the concepts of assertion and denial, we have the resources to analyse logical consequence as relating arguments with multiple premises and multiple conclusions. Gentzen’s mult ..."
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Abstract: I argue for the following four theses. (1) Denial is not to be analysed as the assertion of a negation. (2) Given the concepts of assertion and denial, we have the resources to analyse logical consequence as relating arguments with multiple premises and multiple conclusions. Gentzen’s multiple conclusion calculus can be understood in a straightforward, motivated, nonquestionbegging way. (3) If a broadly antirealist or inferentialist justification of a logical system works, it works just as well for classical logic as it does for intuitionistic logic. The special case for an antirealist justification of intuitionistic logic over and above a justification of classical logic relies on an unjustified assumption about the shape of proofs. Finally, (4) this picture of logical consequence provides a relatively neutral shared vocabulary which can help us understand and adjudicate debates between proponents of classical and nonclassical logics. Our topic is the notion of logical consequence: the link between premises and conclusions, the glue that holds together deductively valid argument. How can we understand this relation between premises and conclusions? It seems that any account begs questions. Painting with very broad brushtrokes, we can sketch the landscape
The Content and Acquisition of Lexical Concepts
, 2006
"... This thesis aims to develop a psychologically plausible account of concepts by integrating key insights from philosophy (on the metaphysical basis for concept possession) and psychology (on the mechanisms underlying concept acquisition). I adopt an approach known as informational atomism, develope ..."
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This thesis aims to develop a psychologically plausible account of concepts by integrating key insights from philosophy (on the metaphysical basis for concept possession) and psychology (on the mechanisms underlying concept acquisition). I adopt an approach known as informational atomism, developed by Jerry Fodor. Informational atomism is the conjunction of two theses: (i) informational semantics, according to which conceptual content is constituted exhaustively by nomological mind–world relations; and (ii) conceptual atomism, according to which (lexical) concepts have no internal structure. I argue that informational semantics needs to be supplemented by allowing contentconstitutive rules of inference (“meaning postulates”). This is because the content of one important class of concepts, the logical terms, is not plausibly informational. And since, it is argued, no principled distinction can be drawn between logical concepts and the rest, the problem that this raises is a general one.
MSc in Logic
, 2011
"... Twodimensional semantics is a formal framework used to characterize the meaning of sentences and subsentential expressions and distinguished by the view according to which the extension of an expression depends on two dimensions. Contextual philosophical interpretations of that framework intend to ..."
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Twodimensional semantics is a formal framework used to characterize the meaning of sentences and subsentential expressions and distinguished by the view according to which the extension of an expression depends on two dimensions. Contextual philosophical interpretations of that framework intend to capture how the extension of an expression depends on context. These interpretations have been argued to provide insight into questions related to logical consequence. This thesis is concerned with problems having to do with logical consequence and the role of context in the determination of truth – with contextual interpretations of twodimensional semantics constituting theories in which solutions to those problems can be devised. The main problem that will be addressed is the logically possible cases problem, the problem of what are the logically possible cases – that is, what are those things x such that, if the premise of an argument is true relative to x while the conclusion of an argument is false relative to x, an argument is logically invalid. Linked to the logically possible cases problem, and thus also of interest in the present thesis, is the relata problem, the problem of what are the things that the relation of logical consequence relates. In particular, the interest will reside in whether the contexts as cases thesis – the thesis that logically possible cases are just contexts / contextrelated entities – and the contextsensitive relata thesis – the thesis that the relata of logical consequence are contextsensitive,
What is Modeled by Truth in All Models?∗
, 2000
"... John Etchemendy has argued that the modeltheoretic definition of logical truth fails as a conceptual analysis of that notion. I will argue that Etchemendy’s criticism cuts deeper than recent critics have conceded. Properly understood, it is directed against the underlying analysis of logical trut ..."
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John Etchemendy has argued that the modeltheoretic definition of logical truth fails as a conceptual analysis of that notion. I will argue that Etchemendy’s criticism cuts deeper than recent critics have conceded. Properly understood, it is directed against the underlying analysis of logical truth as truth on all possible semantic interpretations of a language’s nonlogical vocabulary, not against any particular mathematical realization of that analysis. The only way to block Etchemendy’s argument is to reject his assumption that the possible semantic values for singular terms in an extensional language are the actually existing objects. In fact, a version of his argument goes through even if we retreat to the weaker assumption that the possible semantic values for singular terms are the possibly existing objects. I defend the modeltheoretic analysis by arguing that there is a sense of “possible semantic value ” for which both these assumptions are false. 1 Logical truth and truth in all models It is commonly thought that the best precise account of logical truth we have is the one given in model theory: a sentence S is logically true just in case it is true in every model.1 A model (for a firstorder extensional language) consists in a nonempty set of objects—the domain—and an interpretation function that assigns
Abstract Logical reasoning
"... In the psychological literature on reasoning it has always been assumed that if there is such a thing as mental logic, it must be a set of inference rules. This prooftheoretic conception of mental logic is compatible with but doesn’t do justice to what, according to most logicians, logic is about. ..."
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In the psychological literature on reasoning it has always been assumed that if there is such a thing as mental logic, it must be a set of inference rules. This prooftheoretic conception of mental logic is compatible with but doesn’t do justice to what, according to most logicians, logic is about. Thus, the ongoing debate over mental logic is based on a too narrow notion of logic. Adopting the broader perspective suggested by the standard (Tarskian) view on logic helps to clarify the debate and also shows that the case for mental logic is much stronger than its critics would have us believe. 1
Logic, the A Priori, and the Empirical
"... ABSTRACT: The timehonored view that logic is a nonempirical enterprise is still widely accepted, but it is not always recognized that there are (at least) two distinct ways in which this view can be made precise. One way focuses on the knowledge we can have of logical matters, the other on the na ..."
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ABSTRACT: The timehonored view that logic is a nonempirical enterprise is still widely accepted, but it is not always recognized that there are (at least) two distinct ways in which this view can be made precise. One way focuses on the knowledge we can have of logical matters, the other on the nature of the logical consequence relation itself. More specifically, the first way embodies the claim that knowledge of whether the logical consequence relation holds in a particular case is knowledge that can be had a priori (if at all). The second way presupposes a distinction between structural and nonstructural properties and relations, and it holds that logical consequence is to be defined exclusively in terms of the former. It is shown that the two ways are not coextensive by giving an example of a logic that is nonempirical in the second way but not in the first.
More reflections on consequence∗
, 2014
"... This special issue collects together nine new essays on logical consequence: the relation obtaining between the premises and the conclusion of a logically valid argument. The present paper is a partial, and opinionated, introduction to the contemporary debate on the topic. We focus on two influenti ..."
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This special issue collects together nine new essays on logical consequence: the relation obtaining between the premises and the conclusion of a logically valid argument. The present paper is a partial, and opinionated, introduction to the contemporary debate on the topic. We focus on two influential accounts of consequence, the modeltheoretic and the prooftheoretic, and on the seeming platitude that valid arguments necessarily preserve truth. We briefly discuss the main objections these accounts face, as well as Hartry Field’s contention that such objections show consequence to be a primitive, indefinable notion, and that we must reject the claim that valid arguments necessarily preserve truth. We suggest that the accounts in question have the resources to meet the objections standardly thought to herald their demise and make two main claims: (i) that consequence, as opposed to logical consequence, is the epistemologically significant relation philosophers should be mainly interested in; and (ii) that consequence is a paradoxical notion if truth is.
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"... He did not discover a planet as he intended, but at least Zalta’s view has the theoretical benefit of respecting Le Verrier’s aims to be noncreative. ..."
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He did not discover a planet as he intended, but at least Zalta’s view has the theoretical benefit of respecting Le Verrier’s aims to be noncreative.