Logical pluralism without the normativity

Logical pluralism is the view that there is more than one logic. Logical normativism is the view that logic is normative. These positions have often been assumed to go hand-in-hand, but we show that one can be a logical pluralist without being a logical normativist. We begin by arguing directly against logical normativism. Then we reformulate one popular version of pluralism—due to Beall and Restall—to avoid a normativist commitment. We give three non-normativist pluralist views, the most promising of which depends not on logic’s normativity but on epistemic goals.

     

Quine’s Substitutional Definition of Logical Truth and the Philosophical Significance of the Löwenheim-Hilbert-Bernays Theorem

The Löwenheim-Hilbert-Bernays theorem states that, for an arithmetical first-order language L, if S is a satisfiable schema, then substitution of open sentences of L for the predicate letters of S results in true sentences of L. For two reasons, this theorem is relevant to issues relative to Quine’s substitutional definition of logical truth. First, it makes it possible for Quine to reply to widespread objections raised against his account (the lexicon-dependence problem and the cardinality-dependence problem). These objections purport to show that Quine’s account overgenerates: it would count as logically true sentences which intuitively or model-theoretically are not so. Second, since this theorem is a crucial premise in Quine’s proof of the equivalence between his substitutional account and the model-theoretic one, it enables him to show that, from a metamathematical point of view, there is no need to favour the model-theoretic account over one in terms of substitutions. The purpose of that essay is thus to explore the philosophical bearings of the Löwenheim-Hilbert-Bernays theorem on Quine’s definition of logical truth. This neglected aspect of Quine’s argumentation in favour of a substitutional definition is shown to be part of a struggle against the model-theoretic prejudice in logic. Such an exploration leads to reassess Quine’s peculiar position in the history of logic.     

Revisiting Quine on Truth by Convention

In “Truth by Convention” W.V. Quine gave an influential argument against logical conventionalism. Even today his argument is often taken to decisively refute logical conventionalism. Here I break Quine’s arguments into two—(i) the super-task argument and (ii) the regress argument—and argue that while these arguments together refute implausible explicit versions of conventionalism, they cannot be successfully mounted against a more plausible implicit version of conventionalism. Unlike some of his modern followers, Quine himself recognized this, but argued that implicit conventionalism was explanatorily idle. Against this I show that pace Quine’s claim that implicit conventionalism has no content beyond the claim that logic is firmly accepted, implicit rules of inference can be used to distinguish the firmly accepted from the conventional. As part of my case, I argue that positing syntactic rules of inference as part of our linguistic competence follows from the same methodology that leads contemporary linguists and cognitive scientists to posit rules of phonology, morphology, and grammar. The upshot of my discussion is a diagnosis of the fallacy in Quine’s master critique of logical conventionalism and a re-opening of possibilities for an attractive conventionalist theory of logic.     

A defense of contingent logical truths

A formula is a contingent logical truth when it is true in every model M but, for some model M, false at some world of M. We argue that there are such truths, given the logic of actuality. Our argument turns on defending Tarski’s definition of truth and logical truth, extended so as to apply to modal languages with an actuality operator. We argue that this extension is the philosophically proper account of validity. We counter recent arguments to the contrary presented in Hanson’s ‘Actuality, Necessity, and Logical Truth’ (Philos Stud 130:437–459, 2006).     

Naturalizing logic: Errors of reasoning vindicated: Logic reapproaches cognitive science

A complete revision of mainstream logic is an urgent task to be achieved. This revision will be able to bring logic into a creative rapprochement with cognitive science. This can be achieved by trying to do for logic what over forty years ago Quine and others attempted for epistemology. It is necessary to propose a “naturalization” of the logic of human inference. This paper deals with an examination of how the naturalization process might go, together with some indication of what might be achieved by it. To assist the reader in understanding the naturalization of logic I will take advantage of my own research on the concept of abduction, which vindicates the positive cognitive value of the fallacy of the affirming the consequent thanks to the so-called EC-model (Eco-Cognitive model), and of the recent book Errors of Reasoning: Naturalizing the Logic of Inference (2013) [86], by John Woods. While this paper certainly aims at promoting the research program on the naturalization of logic, it also further advocates the placement of abduction in the research programmes of logic, and stresses to what extent our contemporary philosophical and logical tradition is indebted towards Charles Sanders Peirce, a thinker often praised for his productivity but whose quality and importance are too often overlooked.     

Radical Interpretation and Logical Pluralism

I examine Quine’s and Davidson’s arguments to the effect that classical logic is the one and only correct logic. This conclusion is drawn from their views on radical translation and interpretation, respectively. I focus on the latter, but I first address, independently, Quine’s argument to the effect that the ‘deviant’ logician, who departs from classical logic, is merely changing the subject. Regarding logical pluralism, the question is whether there is more than one correct logic. I argue that bivalence may be subject matter dependent, but that distribution and the law of excluded middle can probably not be dropped whilst maintaining the standard meanings of the connectives. In discussing the ramifications of the indeterminacy of interpretation, I ask whether it forces Davidsonian interpreters to adopt Dummett’s epistemic conception of truth vis-à-vis their interpretations. And, if so, does this cohere with their attributing a nonepistemic notion of truth to their interpretees? This would be a form of logical pluralism. In addition, I discuss Davidson’s arguments against conceptual schemes. Schemes incommensurable with our own could be construed as wholesale deviant logics, or so I argue. And, if so, their possibility would yield, in turn, the possibility of a radical logical pluralism. I also address Davidson’s application of Tarski’s definition of truth.

     

Can First-Order Logical Truth be Defined in Purely Extensional Terms?

W. V. Quine thinks logical truth can be defined in purely extensional terms, as follows: a logical truth is a true sentence that exemplifies a logical form all of whose instances are true. P. F. Strawson objects that one cannot say what it is for a particular use of a sentence to exemplify a logical form without appealing to intensional notions, and hence that Quine's efforts to define logical truth in purely extensional terms cannot succeed. Quine's reply to this criticism is confused in ways that have not yet been noticed in the literature. This may seem to favour Strawson's side of the debate. In fact, however, a proper analysis of the difficulties that Quine's reply faces suggests a new way to clarify and defend the view that logical truth can be defined in purely extensional terms.     

Is Default Logic a Reinvention of Inductive-Statistical Reasoning?

Currently there is hardly any connection between philosophy of science and Artificial Intelligence research. We argue that both fields can benefit from each other. As an example of this mutual benefit we discuss the relation between Inductive-Statistical Reasoning and Default Logic. One of the main topics in AI research is the study of common-sense reasoning with incomplete information. Default logic is especially developed to formalise this type of reasoning. We show that there is a striking resemblance between inductive-statistical reasoning and default logic. A central theme in the logical positivist study of inductive-statistical reasoning such as Hempels Criterion of Maximal Specificity turns out to be equally important in default logic. We also discuss to what extent the relevance of the results of Logical Positivism to AI research could contribute to a reevaluation of Logical Positivism in general.     

From a Phono-Logical Point of View: Neutralizing Quine’s Argument Against Analyticity

Though largely unnoticed, in “Two Dogmas” Quine (1951, Two Dogmas of Empiricism, Philosophical Review 60, 20–43. Reprinted in From a Logical Point of View, 20–46) himself invokes a distinction: a distinction between logical and analytic truths. Unlike analytic statements equating ‘bachelor’ with ‘unmarried man’, strictly logical tautologies relating two word-tokens of the same word-type, e.g., ‘bachelor’ and ‘bachelor’ are true merely in virtue of basic phonological form, putatively an exclusively non-semantic function of perceptual categorization or brute stimulus behavior. Yet natural language phonemic categorization is not entirely free of interpretive semantic considerations. “Phonemic reductionism” in both its linguistic (Bloch 1953, Contrast, Language 29, 59–61) and behavioral (Quine 1990, The Phoneme’s Long Shadow, Emics and Etics: The Insider/Outsider Debate, T. Headland, K. Pike and M. Harris, (eds.), Newbury Park, CA, Sage Publications, 164–167) guise is false. The semantic basis of phonological equivalence, however, has repercussions vis-à-vis Quine’s critique of analyticity. A consistent rejection of meaning-based equivalencies eliminates not only analyticity, but imposes a form of phonological eliminativism too. Phonological eliminativism is the reductio result of applying Quinean meaning skepticism to the phonological typing of natural language. But unlike analyticity, phonology is presumably not subject to philosophical dismissal. The semantic basis of natural language phonology serves to neutralize Quine’s argument against analyticity: without the semantics of meaning, more than just synonymy is lost; basic phonology must also be forfeited. Let’s begin with the fact that even Quine has to admit that it is possible for two tokens of the same orthographic type to be synonymous, for that much is presupposed by his own account of logical truth. Paul Boghossian (1999, 343)     

Modal structuralism simplified

Since Benacerraf’s ‘What Numbers Could Not Be,’ there has been a growing interest in mathematical structuralism. An influential form of mathematical structuralism, modal structuralism, uses logical possibility and second order logic to provide paraphrases of mathematical statements which don’t quantify over mathematical objects. These modal structuralist paraphrases are a useful tool for nominalists and realists alike. But their use of second order logic and quantification into the logical possibility operator raises concerns. In this paper, I show that the work of both these elements can be done by a single natural generalization of the logical possibility operator.     

What logical pluralism cannot be

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 many-valued 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 wide-ranging pluralist positions are more plausible in both cases, I suggest, but assessment of those positions needs to be undertaken on a case-by-case basis.     

The logic of Quinean revisability

W.V. Quine is committed to the claim that all beliefs are rationally revisable; Jerrold Katz has argued that this commitment is unstable on grounds of self-application. The subsequent discussion of this issue has largely proceeded in terms of the logic of belief revision, but there is also an issue here for the treatment of Quine’s views in a doxastic modal system. In this paper I explore the treatment of Quinean epistemology in modal terms. I argue that a set of formal revisability desiderata can be distilled from Quine’s epistemic writings, and that there are demonstrably coherent and non-trivial systems that meet these conditions.     

Against Logical Realism

This paper argues against Logical Realism, in particular against the view that there are facts of matters of logic that obtain independently of us, our linguistic conventions and inferential practices. The paper challenges logical realists to provide a non-intuition based epistemology, one which would be compatible with the empiricist and naturalist convictions motivating much recent anti-realist philosophy of mathematics.     

Husserl’s Foundation of the Formal Sciences in his “Logical Investigations”

This article is composed of three sections that investigate the epistemological foundations of Husserl’s idea of logic from the Logical Investigations. First, it shows the general structure of this logic. Husserl conceives of logic as a comprehensive, multi-layered theory of possible theories that has its most fundamental level in a doctrine of meaning. This doctrine aims to determine the elementary categories that constitute every possible meaning (meaning-categories). The second section presents the main idea of Husserl’s search for an epistemological foundation for knowledge, science and logic. Their epistemological clarification can only be reached through a detailed analysis of the structure of those intentions that give us what is meant in our intentions. To reveal the intuitive giveness of logical forms is the ultimate aim of Husserl’s epistemology of logic. Logical forms and meaning-categories can only be given in a certain higher-order intuition that Husserl calls categorical intuition. The third section of this article distinguishes different kinds of categorical intuition and shows how the most basic logical categories and concepts are given to us in a categorical abstraction.     

LOGICAL PLURALISM AND SEMANTIC INFORMATION

Up to now theories of semantic information have implicitly relied on logical monism, or the view that there is one true logic. The latter position has been explicitly challenged by logical pluralists. Adopting an unbiased attitude in the philosophy of information, we take a suggestion from Beall and Restall at heart and exploit logical pluralism to recognise another kind of pluralism. The latter is called informational pluralism, a thesis whose implications for a theory of semantic information we explore. Research Assistant of the Fund for Scientific Research – Flanders (Belgium)     

为分析性辩护

自从蒯因在著名的《经验论的两个教条》等一系列文章中对分析性做出批评以后,分析传统内已经很少有哲学家再对分析性概念持肯定态度了;随之受到威胁的是意义以及逻辑必然性的概念。     

The Three Quines

This paper concerns Quine's stance on the issue of meaning normativity. I argue that three distinct and not obviously compatible positions on meaning normativity can be extracted from his philosophy of language - eliminative ]naturalism (Quine I), deflationary pragmatism (Quine II), and (restricted) strong normativism (Quine III) - which result from Quine's failure to separate adequately four different questions that surround the issue: the reality, source, sense, and scope of the normative dimension. In addition to the incompatibility of the views taken together, I argue on the basis of considerations due to Wittgenstein, Dummett, and Davidson that each view taken separately has self-standing problems. The first two fail to appreciate the ineliminability of the strong normativity of logic and so face a dilemma: they either smuggle it in illicitly, or insofar as they do not, fail to give an account of anything like a language. The third position's mixture of a universalism about logical concepts with a thorough-going relativism about non-logical concepts can be challenged once a distinction is drawn between the universalist and contextualist readings of strong normativity, a distinction inspired by Wittgenstein's distinction between grammatical and empirical judgements.     

Projection of a binary criterion into a model of hierarchical classes

A formal analysis is made of how to project an attribute criterion into the hierarchical classes model for object by attribute data proposed by De Boeck and Rosenberg. The projection is conceptualized as the prediction of the attribute criterion by means of a logical rule defined on the basis of attribute combinations from the model. Eliminative and constructive strategies are proposed to find logical rules with maximal predictive power and minimal formula complexity. Logical analyses of a real data set are reported and compared with a logistic regression to demonstrate the usefulness of the logical strategies, and to show the complementarity of logical and probabilistic approaches.The first suthor is Senior Research Assistant of the National Fund for Scientific Research (Belgium). We would like to thank the Editor, the reviewers, Seymour Rosenberg, and Luc Delbeke for their helpful comments on earlier drafts of this article.     

Expressivism and the Layer Cake Picture of Discursive Practice

Robert Brandom defends the intelligibility of the notion of a fully discursive practice that does not include any kind of logical vocabulary. Logical vocabulary, according to his account, should be understood as an optional extra to discursive practice, not as a necessary ingredient. Call this the Layer Cake Picture of the relation of logical to non-logical discursive practices. The aim pursued in this paper is to show, by way of an internal critique, that the Layer Cake Picture is in fact incompatible with the most central claims of Brandom’s philosophy. A way is sketched how to give up the Layer Cake Picture and still hold on to a position that is central to Brandom’s philosophical outlook, namely his expressivism about logic.     

对充分条件句语义关系的概念理解与逻辑理解的相关与分离

实验用大学生被试考察了充分条件句语义关系表达形式（逻辑形式和概念形式）和条件句类型（五种条件句）对充分条件句语义关系理解的影响。实验结果发现,语义关系表达形式影响被试对条件句中必要性的语义关系理解,而不影响被试对条件句中充分性的语义关系理解,在对条件句前后件之间语义关系的逻辑理解成绩和概念理解成绩之间既有相关又有分离：对是否充分的语义关系的两种理解成绩之间存在相关一致,而对是否必要的语义关系的两种理解成绩之间存在分离;五种条件句在对后件对前件的必要性的知觉难易程度受条件句意义内容的影响而存在明显差异,这种差异导致被试对许可句和定义句的后件必要性理解成绩高于对偶然句、义务句和因果句的后件必要性理解成绩。