Two famous negative results about da Costa’s paraconsistent logic ${\mathscr {C}}_1$ (the failure of the Lindenbaum–Tarski process [44] and its non-algebraizability [39]) have placed ${\mathscr {C}}_1$ seemingly as an exception to the scope of Abstract Algebraic Logic (AAL). In this paper we undertake a thorough AAL study of da Costa’s logic ${\mathscr {C}}_1$. On the one hand, we strengthen the negative results about ${\mathscr {C}}_1$ by proving that it does not admit any algebraic semantics whatsoever in the sense of Blok (...) and Pigozzi (a weaker notion than algebraizability also introduced in the monograph [6]). On the other hand, ${\mathscr {C}}_1$ is a protoalgebraic logic satisfying a Deduction-Detachment Theorem (DDT). We then extend our AAL study to some paraconsistent axiomatic extensions of ${\mathscr {C}}_1$ covered in the literature. We prove that for extensions ${\mathcal {S}}$ such as ${\mathcal {C}ilo}$ [26], every algebra in ${\mathsf {Alg}}^*({\mathcal {S}})$ contains a Boolean subalgebra, and for extensions ${\mathcal {S}}$ such as,, or [16, 53], every subdirectly irreducible algebra in ${\mathsf {Alg}}^*({\mathcal {S}})$ has cardinality at most 3. We also characterize the quasivariety ${\mathsf {Alg}}^*({\mathcal {S}})$ and the intrinsic variety $\mathbb {V}({\mathcal {S}})$, with,, and. (shrink)

Abstraction and idealization are the two notions that are most often discussed in the context of assumptions employed in the process of model building. These notions are also routinely used in philosophical debates such as that on the mechanistic account of explanation. Indeed, an objection to the mechanistic account has recently been formulated precisely on these grounds: mechanists cannot account for the common practice of idealizing difference-making factors in models in molecular biology. In this paper I revisit the debate (...) and I argue that the objection does not stand up to scrutiny. This is because it is riddled with a number of conceptual inconsistencies. By attempting to resolve the tensions, I also draw several general lessons regarding the difficulties of applying abstraction and idealization in scientific practice. Finally, I argue that more care is needed only when speaking of abstraction and idealization in a context in which these concepts play an important role in an argument, such as that on mechanistic explanation. (shrink)

This book pursues the question of how and whether natural language allows for reference to abstract objects in a fully systematic way. By making full use of contemporary linguistic semantics, it presents a much greater range of linguistic generalizations than has previously been taken into consideration in philosophical discussions, and it argues for an ontological picture is very different from that generally taken for granted by philosophers and semanticists alike. Reference to abstract objects such as properties, numbers, propositions, and degrees (...) is considerably more marginal than generally held. (shrink)

In this book, Zalta attempts to lay the axiomatic foundations of metaphysics by developing and applying a (formal) theory of abstract objects. The cornerstones include a principle which presents precise conditions under which there are abstract objects and a principle which says when apparently distinct such objects are in fact identical. The principles are constructed out of a basic set of primitive notions, which are identified at the end of the Introduction, just before the theorizing begins. The main reason for (...) producing a theory which defines a logical space of abstract objects is that it may have a great deal of explanatory power. It is hoped that the data explained by means of the theory will be of interest to pure and applied metaphysicians, logicians and linguists, and pure and applied epistemologists. (shrink)

This essay introduces the concept of deictic abstraction , taking as a point of departure Husserl’s prototypical but insufficient description of the act of ideation in which a shade of color comes to givenness as an ideal object, i.e., a non-individual or abstract object, on the basis of a perceived individual object. This concept comprises not only color-ideation and ideations of universalities of the sensuous sphere , but all acts founded in perceptions in which ideal objects are directly referred (...) to by means of demonstrative expressions . This allows various types of deictic ideations or abstractions, corresponding to the degree of universality and the kind of ideal object concerned, to be brought to light through the analysis of particular cases of everyday acts of deictic abstraction, including deictic abstractions of predicative universals of the lowest level of universality ; deictic abstractions of non-predicative universals, especially of universal ways of doing something ; and deictic abstractions of individual styles of doing something . Deictic abstractions not only turn out to be constitutive for the formation of perceptual concepts of the lower and lowest levels, but also prove to be foundational for all kinds of learning in which schemata of actions are acquired from a model. (shrink)

Abstract creationism about fictional characters is the view that fictional characters are abstract objects that authors create. I defend this view against criticisms from Stuart Brock that hitherto have not been adequately countered. The discussion sheds light on how the number of fictional characters depends on authorial intention. I conclude also that we should change how we think intentions are connected to artifacts more generally, both abstract and concrete.

Resumo O autor defenderá, por um lado, a existência dos objectos abstractos e, por outro, o seu papel causal, numa ontologia platónica, tal como enquadrada por Roderick Chisholm. Se plausível, a natureza e o papel dos abstracta sob a forma de estados de coisas, oferecem-nos razões para acreditar em uma descrição bem-sucedida e explicativa da intencionalidade humana e animal que não está encerrada no mundo físico. Palavras-chave : causalidade, encerramento causal, fisicalismo, objectos abstractos, platonismo, Roderick ChisholmA defense of the existence (...) and causal role of abstract objects in a Platonic ontology as influenced by the work of Roderick Chisholm. If plausible, the nature and role of abstracta in the form of states of affairs gives us some reason to believe that a successful description and explanation of human and animal intentionality that is not closed to the physical world. Keywords : abstract objects, causal closure, causation, physicalism, platonism, Roderick Chisholm. (shrink)

Think of a number, any number, or properties like fragility and humanity. These and other abstract entities are radically different from concrete entities like electrons and elbows. While concrete entities are located in space and time, have causes and effects, and are known through empirical means, abstract entities like meanings and possibilities are remarkably different. They seem to be immutable and imperceptible and to exist "outside" of space and time. This book provides a comprehensive critical assessment of the problems raised (...) by abstract entities and the debates about existence, truth, and knowledge that surround them. It sets out the key issues that inform the metaphysical disagreement between platonists who accept abstract entities and nominalists who deny abstract entities exist. Beginning with the essentials of the platonist–nominalist debate, it explores the key arguments and issues informing the contemporary debate over abstract reality: arguments for platonism and their connections to semantics, science, and metaphysical explanation the abstract–concrete distinction and views about the nature of abstract reality epistemological puzzles surrounding our knowledge of mathematical entities and other abstract entities. arguments for nominalism premised upon concerns about paradox, parsimony, infinite regresses, underdetermination, and causal isolation nominalist options that seek to dispense with abstract entities. Including chapter summaries, annotated further reading, and a glossary, _Entities_ is essential reading for anyone seeking a clear and authoritative introduction to the problems raised by abstract entities. (shrink)

solvers are a quite recent method to uniformly describe algorithms in a rigorous formal way via graphs. Compared to traditional methods like pseudo-code descriptions, abstract solvers have...

Purpose – The purpose of this paper is to explain how abstract space of the State – universally and specifically within the context of Middle Eastern cities – aims to homogenise the city and eliminate any anomaly that threatens its power structure. Design/methodology/approach – Through a historical and discourse analysis of these policies and processes in the two case studies, this paper presents a contextualised reading of Lefebvre’s concept of abstract space and process of abstraction in relation to the (...) alienation of political public spaces. Findings – The paper proposes that regardless of these homogenising strategies being applied universally, they fail to respond to contextual particularities and therefore they – in a contradictory manner – may themselves produce a space of resistance and difference. Originality/value – This paper focusses on Iran, the case of Tehran and Turkey, the case of Taksim Square and Gezi Park in Istanbul. Recent policies and strategies have been proposed and implemented to reduce, alienate and possibly neutralise the impacts of urban and political protests in these cities and socio-political contexts. (shrink)

Paolo Mancosu provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. A familiar way of introducing concepts in mathematics rests on so-called definitions by abstraction. An example of this is Hume's Principle, which introduces the concept of number by stating that two concepts have the same number if and only if the objects falling under each one of them can be put in one-one correspondence. This principle is at (...) the core of neo-logicism. In the first two chapters of the book, Mancosu provides a historical analysis of the mathematical uses and foundational discussion of definitions by abstraction up to Frege, Peano, and Russell. Chapter one shows that abstraction principles were quite widespread in the mathematical practice that preceded Frege's discussion of them and the second chapter provides the first contextual analysis of Frege's discussion of abstraction principles in section 64 of the Grundlagen. In the second part of the book, Mancosu discusses a novel approach to measuring the size of infinite sets known as the theory of numerosities and shows how this new development leads to deep mathematical, historical, and philosophical problems. The final chapter of the book explore how this theory of numerosities can be exploited to provide surprisingly novel perspectives on neo-logicism. (shrink)

Abstraction is seen as an active process which both enlightens and obscures. Abstractions are not true or false but relatively enlightening or obscuring according to the problem under study; different abstractions may grasp different aspects of a problem. Abstractions may be useless if they can answer questions only about themselves. A theoretical enterprise explores reality through acluster of abstractions that use different perspectives, temporal and horizontal scales, and assumes different givens.

A number of philosophers have recently suggested that some abstract, plausibly non-causal and/or mathematical, explanations explain in a way that is radically dif- ferent from the way causal explanation explain. Namely, while causal explanations explain by providing information about causal dependence, allegedly some abstract explanations explain in a way tied to the independence of the explanandum from the microdetails, or causal laws, for example. We oppose this recent trend to regard abstractions as explanatory in some sui generis way, and argue (...) that a prominent ac- count of causal explanation can be naturally extended to capture explanations that radically abstract away from microphysical and causal-nomological details. To this end, we distinguish di erent senses in which an explanation can be more or less abstract, and analyse the connection between explanations’ abstractness and their explanatory power. According to our analysis abstract explanations have much in common with counterfactual causal explanations. (shrink)

We characterize abstraction in computer science by first comparing the fundamental nature of computer science with that of its cousin mathematics. We consider their primary products, use of formalism, and abstraction objectives, and find that the two disciplines are sharply distinguished. Mathematics, being primarily concerned with developing inference structures, has information neglect as its abstraction objective. Computer science, being primarily concerned with developing interaction patterns, has information hiding as its abstraction objective. We show that abstraction (...) through information hiding is a primary factor in computer science progress and success through an examination of the ubiquitous role of information hiding in programming languages, operating systems, network architecture, and design patterns. (shrink)

The neo-Fregean program in the philosophy of mathematics seeks a foundation for a substantial part of mathematics in abstraction principles—for example, Hume’s Principle: The number of Fs D the number of Gs iff the Fs and Gs correspond one-one—which can be regarded as implicitly definitional of fundamental mathematical concepts—for example, cardinal number. This paper considers what kind of abstraction principle might serve as the basis for a neo- Fregean set theory. Following a brief review of the main difficulties (...) confronting the most widely discussed proposal to date—replacing Frege’s inconsistent Basic Law V by Boolos’s New V which restricts concepts whose extensions obey the principle of extensionality to those which are small in the sense of being smaller than the universe—the paper canvasses an alternative way of implementing the limitation of size idea and explores the kind of restrictions which would be required for it to avoid collapse. (shrink)

words compose a significant part of speech. Despite this, learning them is complicated. Abstract concepts collect more heterogeneous exemplars and are more detached from sensory modalities than concrete concepts. Recent views propose that, because of their complexity, other people are pivotal for abstract concepts’ acquisition and use, e.g., to explain their meaning. We tested this hypothesis using a combined behavioral and thermal imaging paradigm. Twenty-one Italian children determined whether acoustic stimuli were or not correct Italian words. Concrete terms yielded faster (...) responses than abstract ones: for the first time, this effect appears with response times in very young children. More crucially, the higher increase in temperature of the nasal tip suggests that, with abstract concepts, children might be more socially and cognitively engaged. (shrink)

In view of current scientific knowledge, it seems premature to hypothesize a qualitative distinction between processes, networks, and structures involved in abstract processes from those based on perception, episodic, or procedural memories. Predictive thought and mental travel strongly rely, at different levels of consciousness, on past and ongoing sensory input, bodily information, and the results of perceptual elaboration.

This paper elaborates distinctions between a core and a periphery in the ontological and the conceptual domain associated with natural language. The ontological core-periphery distinction is essential for natural language ontology and is the basis for the central thesis of my 2013 book Abstract Objects and the Semantics of Natural Language, namely that natural language permits reference to abstract objects in its periphery, but not its core.

Philosophy is generally considered to be very abstract. How philosophical and abstract Is ethical thinking In clinical situations? This paper sketches an answer In the form of a case study and offers me the chance for some self-reflection and readers the chance to eavesdrop on that self-reflection. Aside from any Intrinsic worth of the questions and answers, they also have Implications for how clinical ethicists should be educated or trained, i.e., how abstract should one's work in moral philosophy be?

The paper elaborates specific perceptive purposes and structural procedures generated by the various experimental abstract films and shows the ways how abstract film engages spectator’s attention. By “liberating” our visual system from representational experience, the abstract film encourages us to cultivate different sensory and sensual sensibility, explore new associations and alternative paths for moods and emotions. Various streams of abstract film will be analysed, relying primarily on classical abstract films.

We devise imperative programming languages for verified real number computation where real numbers are provided as abstract data types such that the users of the languages can express real number computation by considering real numbers as abstract mathematical entities. Unlike other common approaches toward real number computation, based on an algebraic model that lacks implementability or transcendental computation, or finite-precision approximation such as using double precision computation that lacks a formal foundation, our languages are devised based on computable analysis, a (...) foundation of rigorous computation over continuous data. Consequently, the users of the language can easily program real number computation and reason about the behaviours of their programs, relying on their mathematical knowledge of real numbers without worrying about artificial roundoff errors. As the languages are imperative, we adopt precondition–postcondition-style program specification and Hoare-style program verification methodologies. Consequently, the users of the language can easily program a computation over real numbers, specify the expected behaviour of the program, including termination, and prove the correctness of the specification. Furthermore, we suggest extending the languages with other interesting continuous data, such as matrices, continuous real functions, et cetera.Abstract taken directly from the thesis.E-mail: sewonpark17@gmail.comURL: https://sewonpark.com/thesis. (shrink)

Invariantists argue that the notion of concept in psychology should be reserved for knowledge that is retrieved in a context-insensitive manner. Contextualists argue that concepts are to be understood in terms of context-sensitive ad hoc constructions. I review the central empirical evidence for and against both views and show that their conclusions are based on a common mischaracterization of both theories. When the difference between contextualism and invariantism is properly understood, it becomes apparent that the way the question of stability (...) is currently investigated will not lead to a consensus. Instead of focusing directly on stability, we should turn our attention to other desiderata on a theory of concepts. In particular, I show that invariantism, but not contextualism, fails to account for compositionality and abstract concepts. (shrink)

argumentation has been shown to be a powerful tool within many fields such as artificial intelligence, logic and legal reasoning. In this paper we enhance Dung’s well-known abstract argumentation framework with explanatory capabilities. We show that an explanatory argumentation framework (EAF) obtained in this way is a useful tool for the modeling of scientific debates. On the one hand, EAFs allow for the representation of explanatory and justificatory arguments constituting rivaling scientific views. On the other hand, different procedures for selecting (...) arguments, corresponding to different methodological and epistemic requirements of theory evaluation, can be formulated in view of our framework. (shrink)

An abstract framework for structured arguments is presented, which instantiates Dung's ('On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming, and n- Person Games', Artificial Intelligence , 77, 321-357) abstract argumentation frameworks. Arguments are defined as inference trees formed by applying two kinds of inference rules: strict and defeasible rules. This naturally leads to three ways of attacking an argument: attacking a premise, attacking a conclusion and attacking an inference. To resolve such attacks, preferences may (...) be used, which leads to three corresponding kinds of defeat: undermining, rebutting and undercutting defeats. The nature of the inference rules, the structure of the logical language on which they operate and the origin of the preferences are, apart from some basic assumptions, left unspecified. The resulting framework integrates work of Pollock, Vreeswijk and others on the structure of arguments and the nature of defeat and extends it in several respects. Various rationality postulates are proved to be satisfied by the framework, and several existing approaches are proved to be a special case of the framework, including assumption-based argumentation and DefLog. (shrink)

Theories of explanation need to account for a puzzling feature of our explanatory practices: the fact that we prefer explanations that are relatively abstract but only moderately so. Contra Franklin-Hall ([2016]), I argue that the interventionist account of explanation provides a natural and elegant explanation of this fact. By striking the right balance between specificity and generality, moderately abstract explanations optimally subserve what interventionists regard as the goal of explanation, namely identifying possible interventions that would have changed the explanandum.

La question de l’abstraction chez Marx n’est pas seulement une question de théorie de la connaissance qui exigerait une distinction entre les mauvaises abstractions génériques et indéterminées et les bonnes abstractions spécifiques et déterminées. Les abstractions sont réelles et sont solidaires d’une domination propre aux formes. L’émancipation du travail vivant est celle d’une « energeia » qui fait l’objet d’un concept adéquat en son mouvement d’actualisation inachevée.

The use of “levels of abstraction” in philosophical analysis (levelism) has recently come under attack. In this paper, I argue that a refined version of epistemological levelism should be retained as a fundamental method, called the method of levels of abstraction. After a brief introduction, in section “Some Definitions and Preliminary Examples” the nature and applicability of the epistemological method of levels of abstraction is clarified. In section “A Classic Application of the Method ofion”, the philosophical fruitfulness (...) of the new method is shown by using Kant’s classic discussion of the “antinomies of pure reason” as an example. In section “The Philosophy of the Method of Abstraction”, the method is further specified and supported by distinguishing it from three other forms of “levelism”: (i) levels of organisation; (ii) levels of explanation and (iii) conceptual schemes. In that context, the problems of relativism and antirealism are also briefly addressed. The conclusion discusses some of the work that lies ahead, two potential limitations of the method and some results that have already been obtained by applying the method to some long-standing philosophical problems. (shrink)

Philosophers have often claimed that general ideas or representations have their origin in abstraction, but it remains unclear exactly what abstraction as a psychological process consists in. We argue that the Lockean aspiration of using abstraction to explain the origins of all general representations cannot work and that at least some general representations have to be innate. We then offer an explicit framework for understanding abstraction, one that treats abstraction as a computational process that operates (...) over an innate quality space of fine-grained general representations. We argue that this framework has important philosophical implications for the nativism-empiricism dispute, for questions about the acquisition of unstructured representations, and for questions about the relation between human and animal minds. (shrink)

This paper examines the potential for abstracting propositions – an as yet untested way of defending the realist thesis that propositions as abstract entities exist. I motivate why we should want to abstract propositions and make clear, by basing an account on the neo-Fregean programme in arithmetic, what ontological and epistemological advantages a realist can gain from this. I then raise a series of problems for the abstraction that ultimately have serious repercussions for realism about propositions in general. I (...) first identify problems about the number of entities able to be abstracted using these techniques. I then focus on how issues of language relativity result in problems akin to the Caesar problem in arithmetic by exposing circularity and modal concern over the status of the criterion of identity for propositions. (shrink)

We challenge the arguments of Cohen Kadosh & Walsh (CK&W) on two grounds. First, interactions between number form (e.g., notation, format, modality) and an experimental factor do not show that the notations/formats/modalities are processed separately. Second, we discuss evidence that numbers are coded abstractly, also when not required by task demands and processed unintentionally, thus challenging the authors' dual-code account.

Recent scholarship emphasizes the scaffolding role of language for cognition. Language, it is claimed, is a cognition-enhancing niche ( Clark, 2006 ), a programming tool for cognition ( Lupyan and Bergen, 2016 ), even neuroenhancement ( Dove, 2019 ) and augments cognitive functions such as memory, categorization, cognitive control, and meta-cognitive abilities (“thinking about thinking”). Yet, the notion that language enhances or augments cognition, and in particular, cognitive control does not easily fit in with embodied approaches to language processing, or (...) so we will argue. Accounts aiming to explain how language enhances various cognitive functions often employ a notion of abstract representation. Yet, embodied approaches to language processing have it that language processing crucially, according to some accounts even exclusively, involves embodied, modality-specific, i.e., non-abstract representations. In coming to understand a particular phrase or sentence, a prior experience has to be simulated or reenacted. The representation thus activated is embodied (modality-specific) as sensorimotor regions of the brain are thereby recruited. In this paper, we will first discuss the notion of representation, clarify what it takes for a representation to be embodied or abstract, and distinguish between conceptual and (other) linguistic representations. We will then put forward a characterization of cognitive control and examine its representational infrastructure. The remainder of the paper will be devoted to arguing that language augments cognitive control. To that end, we will draw on two lines of research, which investigate how language augments cognitive control: (i) research on the availability of linguistic labels and (ii) research on the active usage of a linguistic code, specifically, in inner speech. Eventually, we will argue that the cognition-enhancing capacity of language can be explained once we assume that it provides us with (a) abstract, non-embodied representations and with (b) abstract, sparse linguistic representations that may serve as easy-to-manipulate placeholders for fully embodied or otherwise more detailed representations. (shrink)

Modern science relies heavily on Galilean idealization, which establishes ceteris paribus laws—laws about what happens when a factor operates unimpeded. But these laws are of little direct use since factors seldom do operate unimpeded. The follow‐up to Galilean idealization is abstraction—we talk simply of what the factor does. The best way to understand this abstraction is as an ascription of a capacity, not in terms of any kind of laws. Even the process of ‘de‐idealization’ or of ‘concretization’ that (...) results in a concrete phenomenological law inevitably involves further concepts in the capacity family. (shrink)

Gilead et al. offer a thoughtful and much-needed treatment of abstraction. However, it fails to build on an extensive literature on abstraction, representational diversity, neurocognition, and psychopathology that provides important constraints and alternative evidence-based conceptions. We draw on conceptions in software engineering, socio-technical systems engineering, and a neurocognitive theory with abstract representations of gist at its core, fuzzy-trace theory.

Neologicists have sought to ground mathematical knowledge in abstraction. One especially obstinate problem for this account is the bad company problem. The leading neologicist strategy for resolving this problem is to attempt to sift the good abstraction principles from the bad. This response faces a dilemma: the system of ‘good’ abstraction principles either falls foul of the Scylla of inconsistency or the Charybdis of being unable to recover a modest portion of Zermelo–Fraenkel set theory with its intended (...) generality. This article argues that the bad company problem is due to the ‘static’ character of abstraction on the neologicist's account and develops a ‘dynamic’ account of abstraction that avoids both horns of the dilemma. 1 Introduction2ion Reconstructed3 From Bad to Worse4 Abstraction Reconceived5 Bad Company Made GoodA AppendixA.1SemanticsA.2LogicA.3ConsistencyA.4Strength. (shrink)

rationality has increasingly been a target of attack in contemporary educational research and practice and in its place practical reason and situated thinking have become a focus of interest. The argument here is that something is lost in this. In illustrating how we might think about the issue, this paper makes a response to the charge that as a result of his commitment to the ‘Enlightenment project’ Vygotsky holds abstract rationality as the pinnacle of thought. Against this it is argued (...) that Vygotsky had a far more sophisticated appreciation of reason and of its remit. The paper proceeds first by examining the picture of Vygotsky that is presented in the work of James Wertsch, and especially his claim that Vygotsky was an ambivalent rationalist, goes on to provide an account of Vygotsky that corrects this picture, and develops this in the light of the work of Robert Brandom, who shares Vygotsky’s inheritance of Hegel. The conclusion towards which this piece points is that the philosophical underpinnings of Vygotsky’s work provide a radically different idea of rationality and epistemology from that characterised as abstract rationality and that this has significance for education studies. (shrink)

The costs of and returns from actions are varied and individually concrete dimensions, combined in heterogeneous ways. The many needs of the body also fluctuate. Making action selection efficiently track some ultimate goal, whether fitness or another utility function, itself requires representational abstraction. Therefore, predictive brains need abstract value representations.

This section is meant to be a mutual effort. If you find an article you think should be abstracted in this section, do not be bashful—submit it for consideration to Kenneth V. Iserson care of CQ. If you do not like the editorial comments, this will give you an opportunity to respond in the letters section. Your input is desired and anticipated.

Theabstract variable binding calculus (VB-calculus) provides a formal frame-work encompassing such diverse variable-binding phenomena as lambda abstraction, Riemann integration, existential and universal quantification (in both classical and nonclassical logic), and various notions of generalized quantification that have been studied in abstract model theory. All axioms of the VB-calculus are in the form of equations, but like the lambda calculus it is not a true equational theory since substitution of terms for variables is restricted. A similar problem with the standard (...) formalism of the first-order predicate logic led to the development of the theory of cylindric and polyadic Boolean algebras. We take the same course here and introduce the variety of polyadic VB-algebras as a pure equational form of the VB-calculus. In one of the main results of the paper we show that every locally finite polyadic VB-algebra of infinite dimension is isomorphic to a functional polyadic VB-algebra that is obtained from a model of the VB-calculus by a natural coordinatization process. This theorem is a generalization of the functional representation theorem for polyadic Boolean algebras given by P. Halmos. As an application of this theorem we present a strong completeness theorem for the VB-calculus. More precisely, we prove that, for every VB-theory T that is obtained by adjoining new equations to the axioms of the VB-calculus, there exists a model D such that T s=t iff D s=t. This result specializes to a completeness theorem for a number of familiar systems that can be formalized as VB-calculi. For example, the lambda calculus, the classical first-order predicate calculus, the theory of the generalized quantifierexists uncountably many and a fragment of Riemann integration. (shrink)

A co-authored article with Roy T. Cook forthcoming in a special edition on the Caesar Problem of the journal Dialectica. We argue against the appeal to equivalence classes in resolving the Caesar Problem.

Properly speaking, the corporation, considered as an entity distinct from its members, cannot be morally responsible for wrongful corporate acts. Setting aside (in this abstract) acts brought about through negligence or omissions, we may say that moral responsibility for an act attaches to that agent (or agents) in whom the act "originates" in this sense: (1) the agent formed the (mental) intention or plan to bring about that act (possibly with the help of others) and (2) the act was intentionally (...) brought about through bodily movements over which that agent had direct control (i.e. the kind of direct mental control that I have over the body I refer to as "my" body) and through which the agent carried out his (mental) intention or plan. Corporate acts do not thus originate in some corporate entity distinct from its members because the corporation has neither a mind to form intentions nor a body it directly controls: it lacks the proper mind/body unity. Instead, corporate acts originate in individual autonomous human beings who make up the corporation and who intentionally bring about corporate acts through their own bodily movements. Such human individuals, and not "the corporation," are morally responsible for corporate acts. Moreover, to say that an entity is "morally responsible" for a wrongful act is to say that the entity is liable to blame and punishment. But it is not possible to impose blame and punishment on a corporation without inflicting it on corporate members. Thus, to say that a corporation (as an entity distinct from its members) is "morally responsible" for a wrongful corporate act is to imply that a (possibly innocent) corporate member legitimately may be punished for something for which another entity was morally responsible. This violates the moral principles that underlie blame and punishment. To hold that the corporation can be morally responsible for its acts is to adopt a dangerous organicism. (shrink)

This paper contains a joint study of two sentential logics that combine a many-valued character, namely tetravalence, with a modal character; one of them is normal and the other one quasinormal. The method is to study their algebraic counterparts and their abstract models with the tools of Abstract Algebraic Logic, and particularly with those of Brown and Suszko's theory of abstract logics as recently developed by Font and Jansana in their "A General Algebraic Semantics for Sentential Logics". The logics studied (...) here arise from the algebraic and lattice-theoretical properties we review of Tetravalent Modal Algebras, a class of algebras studied mainly by Loureiro, and also by Figallo, Landini and Ziliani, at the suggestion of the late Antonio Monteiro. (shrink)