I show that the central notion of Constructive Empiricism, empirical adequacy, can be expressed syntactically and specifically in the Received View of the logical empiricists. The formalization shows that the Received View is superior to Constructive Empiricism in the treatment of theories involving constants or functions from observable to unobservable objects. It also suggests a formalization of ‘full empirical informativeness’ in Constructive Empiricism.

I provide an explicit formulation of empirical adequacy, the central concept of constructive empiricism, and point out a number of problems. Based on one of the inspirations for empirical adequacy, I generalize the notion of a theory to avoid implausible presumptions about the relation of theoretical concepts and observations, and generalize empirical adequacy with the help of approximation sets to allow for lack of knowledge, approximations, and successive gain of knowledge and precision. As a test case, I (...) provide an application of these generalizations to a simple interference phenomenon. (shrink)

The notion of empirical adequacy has received recent philosophical attention, especially within the framework of the semantic approach. Empirical adequacy, as explicated in the semantic approach, concerns the relationship between empirical substructures and some phenomena. The aim here is to differentiate this notion of empirical adequacy from one concerning the relationship between data and phenomena. Distinguishing each notion of empirical adequacy emphasizes different aspects of scientific practice—one concerning theory-development from the basis of an established theory, (...) the other concerning theory-development from the basis of data-fitting, where established theory may not foster further development. To illustrate this contrast, an example from financial economics is considered. (shrink)

Empirical adequacy is a central notion in van Fraassen's empiricist view of science. I argue that van Fraassen's account of empirical adequacy in terms of a partial isomorphism between certain structures in some model(s) of the theory and certain actual structures (the observables) in the world, is untenable. The empirical adequacy of a theory can only be tested in the context of an accepted practice of observation. But because the theory itself does not determine the correct practice (...) of observation, its failure to pass the test does not show the failure of an isomorphism between the empirical substructure of some model(s) of the theory and observable structures in nature. Further, because the choice of a practice of observation is a pragmatic one grounded in epistemic goals we seek in observation, van Fraassen's anthropocentric view of observability is epistemically unmotivated. (shrink)

Given Hugh Everett III's understanding of the proper cognitive status of physical theories, his relative-state formulation of pure wave mechanics arguably qualifies as an empirically acceptable physical theory. The argument turns on the precise nature of the relationship that Everett requires between the empirical substructure of an empirically faithful physical theory and experience. On this view, Everett provides a weak resolution to both the determinate record and the probability problems encountered by pure wave mechanics, and does so in (...) a way that avoids unnecessary metaphysical complications. Taking Everett's goal to be showing the empirical faithfulness of the relative-state formulation agrees well with his characterization of his project as one of seeking a model for observation in the correlation structure described by pure wave mechanics and seeking a measure of typicality over this empirical substructure that covaries with our empirically warranted expectations. 1 Pure Wave Mechanics and Relative States2 Everett and Frank3 Everett on the Nature of Physical Theories4 Conditions for Empirical Faithfulness5 The Empirical Faithfulness of Pure Wave Mechanics6 Conclusion. (shrink)

This paper empirically investigates the contention that the folk concept of time is a functional concept: a concept according to which time is whatever plays a certain functional role or roles. This hypothesis could explain why, in previous research, surprisingly large percentages of participants judge that there is time at worlds that contain no one-dimensional substructure of ordered instants. If it seems to participants that even in those worlds the relevant functional role is played, then this could explain why (...) they judge that there is time in those worlds. While our experiment supported the finding that participants are reticent to judge that there is no time, actually, we found no evidence that this is because they deploy a functionalist concept, at least of the kind proposed in recent research. Our findings are, however, consistent with the folk deploying a much more minimal functionalist concept according to which time is just whatever it is—regardless of its nature—that plays the role of grounding our temporal phenomenology. (shrink)

Food charity in the United States has grown into a critical appendage of agro-food supply chains. In 2016, 4.5 billion pounds of food waste was diverted through a network of 200 regional food banks, a fivefold increase in just 20 years. Recent global trade disruptions and the COVID-19 pandemic have further reinforced this trend. Economic geographers studying charitable food networks argue that its infrastructure and moral substructure serve to revalue food waste and surplus labor in the capitalist food system. (...) The political–legal framework undergirding this revaluation process however is still poorly understood. Drawing on a 6-year institutional ethnography of the food banking economy in West Virginia, this paper takes a supply-side approach to examine the material and moral values driving the expansion of food waste recovery as hunger relief. Empirically, it focuses on the laws, contracts and fiscal incentives regulating charitable food procurement at the U.S. Department of Agriculture and Feeding America. The assemblage of government agencies, private businesses and non-profit organizations enrolled into this gift economy at different scales I argue, serves to enclose food waste into a public–private governance structure that regulates food surpluses and ensures these will not disrupt the scarcity logics driving profitability along primary food circuits. (shrink)

In this paper I propose clearly to distinguish four fundamental types of intertheoretical relations that may be used to represent different types of theoretical change in empirical science. These four types can be represented formally through a refined version of the set-theoretical apparatus of structuralism. They may be described as: crystallization, theory-evolution, embedding, and replacement with partial incommensurability. They will be first explicated in intuitive, informal terms, and some historical examples will be suggested for each type. In the second (...) part of the paper, the four types are characterized in structuralistic terms; the notions of a partial substructure and of a diachronic theory-net will play a central role. (shrink)

My model-theoretic realist account of science places linguistic systems and the corresponding non-linguistic structures at different stages of the scientific process. It is shown that science and its progress cannot be analysed in terms of only one of these strata. Philosophy of science literature offers mainly two approaches; to the structure of scientific knowledge analysed in terms of theories and their models, the "statement" and the "non-statement" approaches. In opposition to the statement approach's belief that scientific knowledge is embodied in (...) theories symbolic language) with direct interpretative links---via so-called "bridge principles"---to reality, the defenders of the non-statement approach believe in an analysis where the language in which the theory is formulated plays a much smaller role than the structures which satisfy that theory. ;The model-theoretic realism expounded here retains the notion of a scientific theory as a set of sentences, while simultaneously emphasising the interpretative role of the conceptual models of these theories. My criticism against the non-statement approach is based on the fact that merely "giving" the theory "in terms of" its mathematical structures leaves out any real interpretation of the nature and role of general terms in science. Against the statement approach's "direct" linking of general theoretical terms to reality, my approach interpolates models between theories and reality in the interpretative chain. ;The links between the general terms of scientific theories and their interpretations in the various models of the theory regulate the whole referential process. The terms of a theory are "general" in the sense that they are the result of certain abstractive conceptualisations of the object of scientific investigation and subsequent linguistic formulations of these conceptualisations. Their meanings can be "given back" only by interpreting them in the limited context, of the various conceptual models of their theory and, finally, by finding an isomorphic relation between some substructure of the conceptual model in question and some empirical conceptualisation of relevant experimental data. In this sense the notion of scientific "truth" becomes inextricably linked with that of articulated reference, as it---given its model-dependent nature---should be. (shrink)

In order to delimit the field of theoretical biology, the author distinguishes in empirical biology a substructure and a superstructure. Empirical biology cannot be constituted without a minimum of reference to philosophical ideas such as the principle of identity ; having regard to its objective, which is explanation by means of physico-chemical models, it does not easily avoid ontological aspirations. Further, experimental research makes great use of scientific theories. Finally, the elaboration of the empirical data of (...) biology may find its fulfilment in an ontological science, philosophical biology, which is a branch of the philosophy of nature. Philosophical biology, superstructure of experimental biology, is a discipline intermediate between the special sciences of life, defined in an empirical sense, and metaphysics.Um den Bereich der theoretischen Biologie abzugrenzen, unterscheidet der Autor in der positiven Biologie eine “Infrastruktur” und eine “Suprastruktur”. Die positive Biologie kann nicht ohne ein Minimum von Beziehungen zu den philosophischen Begriffen aufgebaut werden, wie z.B. zu dem Prinzip der Identität ; ihrem Ziele nach betrachtet, welches in der Erklärung durch physiko-chemische Grundbegriffe besteht, kann sie sich nicht gut den ontologischen Ansprüchen entziehen. Darüber hinaus bedient sich die experimentelle Forschung weitgehend der wissenschaftlichen Theorien. Zum Schluss kann die Bearbeitung der empirischen Erkenntnisse in der Biologie ihre Vollendung in einer ontologischen Wissenschaft, die philosophische Biologie, welche ein Zweig der Philosophie der Natur ist, finden. Die philosophische Biologie, die der experimentellen übergeordnet ist, steht als Disziplin zwischen den besonderen Wissenschaften vom Leben, verstanden im empirischen Sinne, und der Metaphysik. (shrink)

Preface The status of sovereignty as a highly ambiguous concept is well established. Pointing out or deploring, the ambiguity of the idea has itself become a recurring motif in the literature on sovereignty. As the legal theorist and international lawyer Alf Ross put it, “there is hardly any domain in which the obscurity and confusion is as great as here.” 1 The concept of sovereignty is often seen as a downright obstacle to fruitful conceptual analysis, carried over from its proper (...) setting in history to “plague and befog contemporary thought.” 2 . . . So contested is the concept that, rather than pursuing the contestation, many political theorists think we should give up so protean a notion. Granting that the debate on the relevance of sovereignty frustratingly oscillates between claims that it will either continue to exist or that it is about to disappear, forgetting it altogether, and thereby escaping this seemingly endless argument, can easily appear as the most urgent task for political theory . The following argument makes a case that the “urgent task” is not the abandonment of the concept of sovereignty, but an understanding of its essential philosophical nature as an integrated and evolving expression of practical reason. Sovereignty is neither ambiguous nor obscure once its fundamental presuppositions are laid bare and its many philosophical and historical manifestations shown to be the product, in actuality, of a single, dialectally dynamic but integrated set of metaphysical elements. This is the first of three arguments describing the evolution of international law as a manifestation of practical reason through an application of philosophical method to the source , locus , and scope of the concept of sovereignty. It moves from a dialectic balance favoring utility to a balance dominated by legal right to a dialectic of duty to humanity and nature. All three arguments are meant to be a contribution to the new field of International Legal Philosophy as defined by Phillip Allott. 4 This field combines a sensitivity to legal practice with an effort to understand the underlying philosophical determinants of empirical choice and behavior. One purpose of international legal philosophy is to “remove” from the minds of those who study the law what Diderot defined as “the sophism of the ephemeral,” and what Allott calls “the disempowering idea that what xii Preface happens to exist now is inevitable and permanent.” 5 A core imperative is to “reunderstand what it is to be a thinking being” 6 and to rediscover the dialectic between the private and the public as it determines, and is redetermined by, legal practice. This requires a “revolution in the human mind” 7 so that we may transcend the current dependence on positivist methods and empirical fact as an end-in-itself, and try to understand the underlying and more constant and essential ideas and inherent dialectics that constitute the substructure or “metaphysics” of international law. I will approach this “revolution” with the use of R. G. Collingwood’s philosophical method 8 and the philosophy of David Hume, applied to international law as an expression of practical reason. The goal of philosophical method is the construction of a comprehensive policy argument (CPA) for a public policy or legal issue. In addition to the conventional use of empirical models and their logic of investigation in the study of policy and law, CPA requires that an underlying philosophical logic of concepts be deciphered to identify the ideas within the issue, and their definition, overlap, and systematic interdependence. Philosophical method is a means with which to interpret and understand competing systematic and complete conceptual logics, existing at the core of an issue and pertinent to policy change. Philosophical method is therefore not meant to be a replacement for the empirical investigation of a policy or legal issue, or the use of scientific method in social studies. Rather, it is a complimentary and prerequisite method that seeks to transcend the limitations of positivism and present a more complete understanding of the philosophical presuppositions of positivist ideas like power, interest, or strategic rationality. Philosophical method is meant to be used with the facts of the policy or legal issue to match an illuminating logic of concepts with a pertinent logic of investigation . Within the CPA, the use of philosophical method and the metaphysics of a policy or legal issue is assumed to be critical to the full understanding of the overlapping concepts, dialectics, and scale of forms that determine, and are determined by, the empirical context of the policy or legal topic. Specifically, instead of utilizing bits and pieces of various theoretical arguments to address narrowly focused empirical questions, as positivism prescribes, I will address the evolution of international law as practical reason in three phases. Each will be approached through a single integrated logic of philosophical concepts from a particular philosopher (i.e., David Hume, G. W. F. Hegel, Immanuel Kant). This philosophically holistic approach to the law is based on the assumption that only through the use of a single integrated argument in legal analysis can sovereignty, or any concept, be understood as a truly systematic and logical whole. A complete philosophical paradigm has a dialectic integrity and systematic logic that can more adequately describe the evolving essence of a concept like sovereignty. This approach also has the advantage of generating a number of distinct holistic descriptions of the law through the application of different philosophical systems, one at a time, to its factual structure. 9 Positivism does not seek Preface xiii holism, and rejects the idea that “theory” has such a characteristic. The essential or comprehensive substructure of any idea is therefore ignored in a method that recommends the observation of empirical problems through the use of whatever hodgepodge of theoretical elements is seen fit to frame its superstructure. This failure to deal with metaphysics has retarded both an essential understanding of international law as a species of legal system, and any holistic and dialectical conceptualization of its inherent concepts, like sovereignty. A second positivist convention expects modern theorists to create new theory rather than to refine and apply that of existing philosophy. This predisposition is driven by the positivist goal of discovery that ignores refinement as a possible purpose of philosophical analysis. Collingwood argues that philosophy must take that set of ideas already known and utilize existing systematic philosophical arguments to refine them so that they evolve closer to their essence as concepts. Considering this imperative, the idea of sovereignty can be assumed to have had valid usage for hundreds of years, over which time, the concept has evolved to mean different things, each a refinement of the definition that preceded it. Transcending positivism means that the scholar’s search is not for “new” material, but to decipher the metaphysical essence of a concept as it has been made manifest over time and context. These manifestations are rooted, and refined from, the known terms of that concept’s inherent idea(s). Rather than depending exclusively on positivism and its conventions, my work utilizes, in addition to Collingwood, the intact philosophical systems of Hume, Hegel, and Kant to trace the refinement of international law as a product of human practical reason. These paradigms, or integrated systems of logical concepts, will be applied to legal practice individually, so that each CPA can be deciphered separately. This provides a set of integrated and logically intact paradigms for the evolutionary stages of practical reason in international law. Because each argument is applied systematically, a deeper understanding of the source, locus, and scope in the development of law in general, and international law in particular, is possible where it is not with the application of various disconnected components of many theories. Each CPA based on Hume, Hegel, or Kant can then be used to describe a distinct context that its logic of concepts best illuminates; specifically, the (1) genesis, (2) contemporary dilemmas, and (3) future of the international legal system. By widening the perspective of international lawyers and policymakers, they can more easily perceive the dialectic of ideas that has created, and is refined by, the legal practice in which they participate. We also move toward Allott’s goal of “human self-perfecting.” 10 And, in addition, by providing a more complete knowledge of the origins of legal practice and its evolution, we illuminate the practical possibilities for what we might “choose to be” 11 in the future. To achieve this, the essential metaphysical elements of state sovereignty and its inherent evolutionary scale of forms will be deciphered and described. This will transform what appears to be a multitude of definitions and xiv Preface practical realizations of the concept of sovereignty into a set of interdependent manifestations of a single substructure, made of a single set of dialectic elements. The interpretation of international law through practical reason sorts and integrates a diverse and discordant literature and defines state sovereignty as a single concept evolving on a scale of forms that allows it to exhibit diverse character traits, all arising from different combinations of common and essential metaphysical elements. This approach, compared to positivist methods and legal realism, allows one to transcend current agreement that sovereignty is, at best, a narrowly focused set of empirical characteristics or, at worst, “organized hypocrisy.” 12 This method also encourages the scholar and practitioner to understand the predispositions and pitfalls of the concept of sovereignty, as well as its potential future paths, more effectively. The use of philosophical method to create policy paradigms out of preexisting philosophical systems and apply these to international law will be called Philosophical-Policy & Legal Design . This approach allows the use of preexisting and complete philosophical arguments that provide an adequate logic of concepts to chart the evolution of the idea of sovereignty along its scale of forms. An examination of the source of practical reason in human social convention with the employment of a philosophical-policy drawn from Hume’s logic of concepts about human nature will demonstrate this new approach. Why Hume? Because, up to now, without an adequate substructure we have arguments, like Brunne é’ s and Troope’s, 13 that may correctly identify international law as an “interactional” system, but cannot present any argument as to why it is, where this empirical reality comes from, or what its implications are for the future. Comparatively, Hume provides a logic of philosophical concepts that answers these concerns. First, he fulfills the requirements for a fuller understanding of the origin and evolution of law from social convention and the dependence of social convention on the human imperative for society. Second, he offers a more adequate delineation of the overlapping concepts of the law in terms of the ideas and institutions that deal with norms and justice (e.g., principle, process, practice, rule, power, interest). Third, he provides a fundamental understanding of the essential dialectics at the core of a conceptualization of the law with both unconscious and conscious human participation (i.e., passion. (shrink)

Substructural theories of truth are theories based on logics that do not include the full complement of usual structural rules. Existing substructural approaches fall into two main families: noncontractive approaches and nontransitive approaches. This paper provides a sketch of these families, and argues for two claims: first, that substructural theories are better-positioned than other theories to grapple with the truth-theoretic paradoxes, and second—more tentatively—that nontransitive approaches are in turn better-positioned than noncontractive approaches.

The aim of the present book is to give a comprehensive account of the ‘state of the art’ of substructural logics, focusing both on their proof theory and on their semantics (both algebraic and relational. It is for graduate students in either philosophy, mathematics, theoretical computer science or theoretical linguistics as well as specialists and researchers.

The article introduces substructural epistemic logics of belief supported by evidence. The logics combine normal modal epistemic logics with distributive substructural logics. Pieces of evidence are represented by points in substructural models and availability of evidence is modelled by a function on the point set. The main technical result is a general completeness theorem. Axiomatisations are provided by means of two-sorted Hilbert-style calculi. It is also shown that the framework presents a natural solution to the problem of logical omniscience.

In this paper, we build on earlier work by Standefer (Logic J IGPL 27(4):543–569, 2019) in investigating extensions of substructural logics, particularly relevant logics, with the machinery of justification logics. We strengthen a negative result from the earlier work showing a limitation with the canonical model method of proving completeness. We then show how to enrich the language with an additional operator for implicit commitment to circumvent these problems. We then extend the logics with axioms for D, 4, and 5, (...) which requires additional justification term operators, following the work of Pacuit (in proceedings of the fifth panhellenic logic symposium, 2005) and Rubtsova (in Grigoriev D, Harrison J (eds) Computer science—theory and applications, CSR 2006; J Logic Comput 16(5):671–684, 2006), and present the required modifications to the frame semantics. We present a simplification of the neighborhood frames from the earlier work and we close by investigating the distinctive contribution of the + operator to the logic. (shrink)

When discussing Logical Pluralism several critics argue that such an open-minded position is untenable. The key to this conclusion is that, given a number of widely accepted assumptions, the pluralist view collapses into Logical Monism. In this paper we show that the arguments usually employed to arrive at this conclusion do not work. The main reason for this is the existence of certain substructural logics which have the same set of valid inferences as Classical Logic—although they are, in a clear (...) sense, non-identical to it. We argue that this phenomenon can be generalized, given the existence of logics which coincide with Classical Logic regarding a number of metainferential levels—although they are, again, clearly different systems. We claim this highlights the need to arrive at a more refined version of the Collapse Argument, which we discuss at the end of the paper. (shrink)

Given a Δ1 ultrapower ℱ/[MATHEMATICAL SCRIPT CAPITAL U], let ℒU denote the set of all Π2-correct substructures of ℱ/[MATHEMATICAL SCRIPT CAPITAL U]; i.e., ℒU is the collection of all those subsets of |ℱ/[MATHEMATICAL SCRIPT CAPITAL U]| that are closed under computable functions. Defining in the obvious way the lattice ℒ) with domain ℒU, we obtain some preliminary results about lattice embeddings into – or realization as – an ℒ. The basis for these results, as far as we take the matter, (...) consists of the well-known class of minimal ℱ/[MATHEMATICAL SCRIPT CAPITAL U]'s, which function as atoms, and the class of minimalfree ℱ/[MATHEMATICAL SCRIPT CAPITAL U]'s, to whose nonemptiness a substantial section of the paper is devoted. It is shown that an infinite, convergent monotone sequence together with its limit point is embeddable in an ℒ, and that the initial segment lattices {0, 1,…, n } are not just embeddable in , but in fact realizable as, lattices ℒ. Finally, the diamond is embeddable; and if it is not realizable, then either the 1 - 3 - 1 lattice or the pentagon is at least embeddable. (shrink)

Substructural fuzzy logics are substructural logics that are complete with respect to algebras whose lattice reduct is the real unit interval [0.1]. In this paper, we introduce Uninorm logic UL as Multiplicative additive intuitionistic linear logic MAILL extended with the prelinearity axiom ((A → B) ∧ t) ∨ ((B → A) ∧ t). Axiomatic extensions of UL include known fuzzy logics such as Monoidal t-norm logic MTL and Gödel logic G, and new weakening-free logics. Algebraic semantics for these logics are (...) provided by subvarieties of (representable) pointed bounded commutative residuated lattices. Gentzen systems admitting cut-elimination are given in the framework of hypersequents. Completeness with respect to algebras with lattice reduct [0, 1] is established for UL and several extensions using a two-part strategy. First, completeness is proved for the logic extended with Takeuti and Titani's density rule. A syntactic elimination of the rule is then given using a hypersequent calculus. As an algebraic corollary, it follows that certain varieties of residuated lattices are generated by their members with lattice reduct [0, 1]. (shrink)

The past decades have seen remarkable progress in the study of substructural logics, be it mathematically or philosophically oriented. This progress has a somewhat perplexing effect: the more subst...

ABSTRACT My aim in this paper is to present a pluralist thesis about the inferential role of logical constants, which embraces classical, relevant, linear and ordered logic. That is, I defend that a logical constant c has more than one correct inferential role. The thesis depends on a particular interpretation of substructural logics' vocabulary, according to which classical logic captures the literal meaning of logical constants and substructural logics encode a pragmatically enriched sense of those connectives. The paper is divided (...) into four parts: first, I introduce the motivation for the pluralist thesis of the paper; second I introduce the calculus for the different logics endorsed in the pluralist thesis; third, I motivate how the different behaviors of the logical vocabulary of these logics can be pragmatically interpreted, and fourth, I motivate how the different inferential roles that each substructural logic attribute to logical constants can coexist, and how we should reason with a logical constant c given this plurality. (shrink)

The new area of logic and computation is now undergoing rapid development. This has affected the social pattern of research in the area. A new topic may rise very quickly with a significant body of research around it. The community, however, cannot wait the traditional two years for a book to appear. This has given greater importance to thematic collections of papers, centred around a topic and addressing it from several points of view, usually as a result of a workshop, (...) summer school, or just a scientific initiative. Such a collection may not be as coherent as a book by one or two authors yet it is more focused than a collection of key papers on a certain topic. It is best thought of as a thematic collection, a study in the area of logic and computation. The new series Studies in Logic and Computation is intended to provide a home for such thematic collections. Substructural logics are nonclassical logics, which arose in response to problems in foundations of mathematics and logic, theoretical computer science, mathematical linguistics, and category theory. They include intuitionistic logic, relevant logic, BCK logic, linear logic, and Lambek's calculus of syntactic categories. Substructural logics differ from classical logics, and from each other, in their presuppositions about Gentzen's structural rules, although their presuppositions about the deductive role of logical constants are invariant. Substructural logics have been a subject of study for logicians during the last sixty years. Specialists have often worked in isolation, however, largely unaware of the contributions of others. This book brings together new papers by some of the most eminent authorities in these varioustraditions to produce a unified view of substructural logics. (shrink)

Substructural logics extending the full Lambek calculus FL have largely benefited from a systematical algebraic approach based on the study of their algebraic counterparts: residuated lattices. Recently, a nonassociative generalization of FL has been studied by Galatos and Ono as the logic of lattice-ordered residuated unital groupoids. This paper is based on an alternative Hilbert-style presentation for SL which is almost MP -based. This presentation is then used to obtain, in a uniform way applicable to most substructural logics, a form (...) of local deduction theorem, description of filter generation, and proper forms of generalized disjunctions. A special stress is put on semilinear substructural logics. Axiomatizations of the weakest semilinear logic over SL and other prominent substructural logics are provided and their completeness with respect to chains defined over the real unit interval is proved. (shrink)

We study first-order logic with two variables FO² and establish a small substructure property. Similar to the small model property for FO² we obtain an exponential size bound on embedded substructures, relative to a fixed surrounding structure that may be infinite. We apply this technique to analyse the satisfiability problem for FO² under constraints that require several binary relations to be interpreted as equivalence relations. With a single equivalence relation, FO² has the finite model property and is complete for (...) non-deterministic exponential time, just as for plain FO² With two equivalence relations, FO² does not have the finite model property, but is shown to be decidable via a construction of regular models that admit finite descriptions even though they may necessarily be infinite. For three or more equivalence relations, FO² is undecidable. (shrink)

We introduce a sequent system which is Gentzen algebraisable with orthomodular lattices as equivalent algebraic semantics, and therefore can be viewed as a calculus for orthomodular quantum logic. Its sequents are pairs of non-associative structures, formed via a structural connective whose algebraic interpretation is the Sasaki product on the left-hand side and its De Morgan dual on the right-hand side. It is a substructural calculus, because some of the standard structural sequent rules are restricted—by lifting all such restrictions, one recovers (...) a calculus for classical logic. (shrink)

This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. _An Introduction to Substrucural Logics_ is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both (...) students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading. (shrink)

What is empiricism and what could it be? Bas . van Fraassen, one of the world’s foremost contributors to philosophical logic and the philosophy of science, here undertakes a fresh consideration of these questions and offers a program for renewal of the empiricist tradition. The empiricist tradition is not and could not be defined by common doctrines, but embodies a certain stance in philosophy, van Fraassen says. This stance is displayed first of all in a searing, recurrent critique of metaphysics, (...) and secondly in a focus on experience that requires a voluntarist view of belief and opinion. Van Fraassen focuses on the philosophical problems of scientific and conceptual revolutions and on the not unrelated ruptures between religious and secular ways of seeing or conceiving of ourselves. He explores what it is to be or not be secular and points the way toward a new relationship between secularism and science within philosophy. (shrink)

This paper deals with substructural nuclear (image-based) logics and their algebraic and Kripke-style semantics. More precisely, we first introduce a class of substructural logics with connective N satisfying nucleus property, called here substructural nuclear logics, and its subclass, called here substructural nuclear image-based logics, where N further satisfies homomorphic image property. We then consider their algebraic semantics together with algebraic characterizations of those logics. Finally, we introduce operational Kripke-style semantics for those logics and provide two sorts of completeness results for (...) them, one of which is based on algebraic completeness for all the logics and the other of which is based on set-theoretic one for the nuclear image-based logics. (shrink)

This paper proposes a new topic in substructural logic for use in research joining the fields of relevance and fuzzy logics. For this, we consider old and new relevance principles. We first introduce fuzzy systems satisfying an old relevance principle, that is, Dunn’s weak relevance principle. We present ways to obtain relevant companions of the weakening-free uninorm systems introduced by Metcalfe and Montagna and fuzzy companions of the system R of relevant implication and its neighbors. The algebraic structures corresponding to (...) the systems are then defined, and completeness results are provided. We next consider fuzzy systems satisfying new relevance principles introduced by Yang. We show that the weakening-free uninorm systems and some extensions and neighbors of R satisfy the new relevance principles. (shrink)

This paper deals with various substructural propositional logics, in particular with substructural subsystems of Nelson's constructive propositional logics N– and N. Doen's groupoid semantics is extended to these constructive systems and is provided with an informational interpretation in terms of information pieces and operations on information pieces.

A mechanism for combining any two substructural logics (e.g. linear and intuitionistic logics) is studied from a proof-theoretic point of view. The main results presented are cut-elimination and simulation results for these combined logics called synthesized substructural logics.

We present substructural negations, a family of negations classified in terms of structural rules of an extended kind of sequent calculus, display calculus. In considering the whole picture, we emphasize the duality of negation. Two types of negative modality, impossibility and unnecessity, are discussed and "self-dual" negations like Classical, De Morgan, or Ockham negation are redefined as the fusions of two negative modalities. We also consider how to identify, using intuitionistic and dual intuitionistic negations, two accessibility relations associated with impossibility (...) and unnecessity. (shrink)

We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalisation of Routley–Meyer ternary frames and a simplification of them. The key innovation of this semantics is the use of a single accessibility relation to relate collections of points to points. Different logics are modeled by varying the kinds of collections used: they can be sets, multisets, lists or trees. We show that collection frames on trees are sound and complete for (...) the basic positive distributive substructural logic $\mathsf {B}^+$, that collection frames on multisets are sound and complete for $\mathsf {RW}^+$ (the relevant logic $\mathsf {R}^+$, without contraction, or equivalently, positive multiplicative and additive linear logic with distribution for the additive connectives), and that collection frames on sets are sound for the positive relevant logic $\mathsf {R}^+$. The completeness of set frames for $\mathsf {R}^+$ is, currently, an open question. (shrink)

It is well known that classical propositional logic can be interpreted in intuitionistic propositional logic. In particular Glivenko's theorem states that a formula is provable in the former iff its double negation is provable in the latter. We extend Glivenko's theorem and show that for every involutive substructural logic there exists a minimum substructural logic that contains the first via a double negation interpretation. Our presentation is algebraic and is formulated in the context of residuated lattices. In the last part (...) of the paper, we also discuss some extended forms of the Kolmogorov translation and we compare it to the Glivenko translation. (shrink)

Stasis-theory seeks to classify rhetorical problems acccording to the underlying structure of the dispute that each involves. Such a classification is of interest to the practising rhetor, since it may help him identify an appropriate argumentative strategy; for example, patterns of argument appropriate to a question of fact may be irrelevant in an evaluative dispute.

Stasis-theory seeks to classify rhetorical problems acccording to the underlying structure of the dispute that each involves. Such a classification is of interest to the practising rhetor, since it may help him identify an appropriate argumentative strategy; for example, patterns of argument appropriate to a question of fact may be irrelevant in an evaluative dispute.

Recent empirical work on folk moral objectivism has attempted to examine the extent to which folk morality presumes that moral judgments are objectively true or false. Some researchers report findings that they take to indicate folk commitment to objectivism (Goodwin & Darley, 2008, 2010, 2012; Nichols & Folds-Bennett, 2003; Wainryb et al., 2004), while others report findings that may reveal a more variable commitment to objectivism (Beebe, 2014; Beebe et al., 2015; Beebe & Sackris, 2016; Sarkissian, et al., 2011; (...) Wright, 2018; Wright, Grandjean, & McWhite, 2013; Wright, McWhite, & Grandjean, 2014). However, the various probes that have been used to examine folk moral objectivism almost always fail to be good direct measures of objectivism. Some critics (Beebe, 2015; Pölzler, 2017, 2018) have suggested that the problems with existing probes are serious enough that they should be viewed as largely incapable of shedding any light on folk metaethical commitments. Building upon the work of Justin Khoo and Joshua Knobe (2018), I argue that many of the existing probes can be seen as good measures of the extent to which people think that the truth of one moral judgment excludes the possibility that a judgment made by a disagreeing party is also true and that the best explanation of the findings obtained using these measures is significant folk support for indexical moral relativism—the view that the content of moral judgments is context-sensitive. If my thesis is correct, many contemporary moral philosophers are deeply mistaken about the metaethical contours of folk morality in one very important respect. (shrink)