Gila Sher

The question motivating my investigation is: Are the basic philosophical principles underlying the "core" system of contemporary logic exhausted by the standard version? In particular, is the accepted narrow construal of the notion "logical term" justified? ;As a point of comparison I refer to systems of 1st-order logic with generalized quantifiers developed by mathematicians and linguists . Based on an analysis of the Tarskian conception of the role of logic I show that the standard division of terms into logical and extra-logical is partly arbitrary. I argue that the semantic principles of Tarskian logic allow any higher order mathematical predicate or relation to function as a logical term in a 1st-order system, provided it is introduced in the right way into the syntactic-semantic apparatus. ;Formally, I propose a new, "constructive", semantic characterization of logical terms. A logical term is defined by a function which, given a model, "shows" how to construct relations, sets, or n-tuples of individuals which satisfy it. I discuss the linguistic applicability of the extended logic and bring numerous examples. ;One chapter is devoted to branching quantification--a non-standard logico-linguistic construction obtained by affixing a non-linear, partially-ordered quantifier-prefix to a well-formed formula. Although standard branching quantifiers were given a complete account by Henkin and Walkoe, it is not altogether clear what the meaning of branching generalized quantifiers is. I propose a new analysis of the generalized branching prefix which extends the existent, partial, definitions due to Barwise, and I develop a generalization leading to a "family" of branching structures. ;In conclusion I discuss the philosophical impact of the generalized conception of logic on such issues as the logicist thesis, the interaction between mathematics and logic, ontological commitment via logic, metaphysics and logical semantics

In this paper I develop a new conception of Tarskian logic based on Tarski’s intuitive characterization of logical consequence as formal and necessary in his 1936 paper. Special emphasis is placed on the role of logic in our system of knowledge, the origins of semantics, the semantic definition of logical consequence, and the role of logical and non-logical terms in a logical system. The paper offers a new definition of logical terms based on the question: what division of terms into logical and extra-logical would yield a logical system that satisfies Tarski’s intuitive characterization of logical consequence in complete generality? I discuss the consequences of the new conception for revision in logic, the logicist thesis, and the relation between logic and mathematics. I offer a proof-theoretic perspective on the semantic conception delineated in this paper. And I conclude with a postscript on Tarski’s lecture, “What are Logical Notions?”, which was published shortly after the present conception of logic was developed.

Substantivism is a general philosophical methodology advocating a substantive approach to philosophical theorizing. In this article, I present an overview of this methodology with a special emphasis on the field of truth. I begin with a framework for understanding what is at stake in the substantivist–deflationist debate and describe the substantivist critique of deflationism. I then proceed to discuss contemporary substantivism as a positive methodology, present examples of recent substantivist theories of truth, delineate several principles of philosophical substantivism, and connect it to contemporary thought about the nature and methods of philosophy. Due to limitations of space, I am unable to discuss all the forms contemporary substantivism has taken. But I try to give a clear sense of the central principles, challenges, and promise of this methodology.

Gila Sher approaches knowledge from the perspective of the basic human epistemic situation—the situation of limited yet resourceful beings, living in a complex world and aspiring to know it in its full complexity. What principles should guide them? Two fundamental principles of knowledge are epistemic friction and freedom. Knowledge must be substantially constrained by the world (friction), but without active participation of the knower in accessing the world (freedom) theoretical knowledge is impossible. This requires a grounding of all knowledge, empirical and abstract, in both mind and world, but the fall of traditional foundationalism has led many to doubt the viability of this ‘classical’ project. Sher challenges this skepticism, charting a new foundational methodology, foundational holism, that differs from others in being holistic, world-oriented, and universal (i.e., applicable to all fields of knowledge). Using this methodology, Epistemic Friction develops an integrated theory of knowledge, truth, and logic. This includes (i) a dynamic model of knowledge, incorporating some of Quine’s revolutionary ideas while rejecting his narrow empiricism, (ii) a substantivist, non-traditional correspondence theory of truth, and (iii) an outline of a joint grounding of logic in mind and world. The model of knowledge subjects all disciplines to demanding norms of both veridicality and conceptualization. The correspondence theory is robust and universal yet not simplistic or naive, admitting diverse forms of correspondence. Logic’s grounding in the world brings it in line with other disciplines while preserving, and explaining, its strong formality, necessity, generality, and normativity.

Branching quantifiers were first introduced by L. Henkin in his 1959 paper ‘Some Remarks on Infmitely Long Formulas’. By ‘branching quantifiers’ Henkin meant a new, non-linearly structured quantiiier-prefix whose discovery was triggered by the problem of interpreting infinitistic formulas of a certain form} The branching (or partially-ordered) quantifier-prefix is, however, not essentially infinitistic, and the issues it raises have largely been discussed in the literature in the context of finitistic logic, as they will be here. Our discussion transcends, however, the resources of standard lst-order languages and we will consider the new form in the context of 1st-order logic with 1- and 2-place ‘Mostowskian` generalized quantifiers.2..

In this paper I reconstruct David Foster Wallace’s argument against fatalism in his undergraduate honors thesis, “Richard Taylor’s ‘Fatalism’ and the Semantics of Physical Modality”. My goal is to present the argument in a clear and concise way, so that it is easy to see its main line of reasoning and potential power. A secondary goal is to offer clarificatory and critical notes on some of the issues at stake. The reconstruction reveals interesting connections between Wallace’s argument and John MacFarlane’s recent work on relative truth.

This chapter offers a logical, linguistic, and philosophical account of modern quantification theory. Contrasting the standard approach to quantifiers (according to which logical quantifiers are defined by enumeration) with the generalized approach (according to which quantifiers are defined systematically), the chapter begins with a brief history of standard quantifier theory and identifies some of its logical, linguistic, and philosophical strengths and weaknesses. It then proceeds to a brief history of generalized quantifier theory and explains how it overcomes the weaknesses of the standard theory. One of the main philosophical advantages of the generalized theory is its philosophically informative criterion of logicality. The chapter describes the work done so far in this theory, highlights some of its central logical results, offers an overview of its main linguistic contributions, and discusses its philosophical significance.

The problem that motivates me arises from a constellation of factors pulling in different, sometimes opposing directions. Simplifying, they are: (1) The complexity of the world; (2) Humans’ ambitious project of theoretical knowledge of the world; (3) The severe limitations of humans’ cognitive capacities; (4) The considerable intricacy of humans’ cognitive capacities . Given these circumstances, the question arises whether a serious notion of truth is applicable to human theories of the world. In particular, I am interested in the questions: (a) Is a substantive standard of truth for human theories of the world possible? (b) What kind of standard would that be?

The paper offers a new analysis of the difficulties involved in the construction of a general and substantive correspondence theory of truth and delineates a solution to these difficulties in the form of a new methodology. The central argument is inspired by Kant, and the proposed methodology is explained and justified both in general philosophical terms and by reference to a particular variant of Tarski's theory. The paper begins with general considerations on truth and correspondence and concludes with a brief outlook on the "family" of theories of truth generated by the new methodology.

Logic and mathematics are abstract disciplines par excellence. What is the nature of truth and knowledge in these disciplines? In this paper I investigate the possibility of a new approach to this question. The underlying idea is that knowledge qua knowledge, including logical and mathematical knowledge, has a dual grounding in mind and reality, and the standard of truth applicable to all knowledge is a correspondence standard. This applies to logic and mathematics as much as to other disciplines; i.e., logical and mathematical truth are based on correspondence. But the view that logical and mathematical truth are (i) based on correspondence and (ii) require a grounding in reality demands a change in the common conception of both correspondence and epistemic grounding.

In the early part of the 20th century the logical positivists launched a powerful attack on traditional philosophy, rejecting the very idea of philosophy as a substantive discipline and replacing it with a practical, conventionalist, meta-theoretical view of philosophy. The positivist critique was based on a series of dichotomies: the analytic vs. the synthetic, the external vs. the internal, the apriori vs. the empirical, the meta-theoretical vs. the object- theoretical, the conventional vs. the factual. Quine's attack on the positivists' dichotomies was, by extension (if not by intention), also an attack on their critique of philosophy. Quine's own theory, however, in time took an extreme naturalistic turn that, if anything, deepened the schism between philosophy and knowledge. In this paper I show that many of Quine's early philosophical ideas - his denial of the analytic-synthetic distinction, his thesis of the interconnectedness of knowledge, his universal revisability thesis, his principle of the inseparability of language and theory, his methodological pragmatism, and his realism - are in fact compatible with a substantive philosophy. Moreover, certain inner tensions in Quine's theory naturally lead to a new model of knowledge in which philosophy plays a substantive role: not as a "first philosophy", or as a "meta-science", or as a "chapter in psychology", but as an independent discipline in its own right, alongside, continuous with, and complementary to, science.

Knowledge requires both freedom and friction . Freedom to set up our epistemic goals, choose the subject matter of our investigations, espouse cognitive norms, design research programs, etc., and friction (constraint) coming from two directions: the object or target of our investigation, i.e., the world in a broad sense, and our mind as the sum total of constraints involving the knower. My goal is to investigate the problem of epistemic friction, the relation between epistemic friction and freedom, the viability of foundationalism as a solution to the problem of friction, an alternative solution in the form of a neo-Quinean model, and the possibility of solving the problem of friction as it applies to logic and the philosophy of logic within that model.