This paper investigates the question of characterizing first-order LFIs (logics of formal inconsistency) by means of two-valued semantics. LFIs are powerful paraconsistent logics that encode classical logic and permit a finer distinction between contradictions and inconsistencies, with a deep involvement in philosophical and foundational questions. Although focused on just one particular case, namely, the quantified logic QmbC, the method proposed here is completely general for this kind of logics, and can be easily extended to a large (...) family of quantified paraconsistent logics, supplying a sound and complete semantical interpretation for such logics. However, certain subtleties involving term substitution and replacement, that are hidden in classical structures, have to be taken into account when one ventures into the realm of nonclassical reasoning. This paper shows how such difficulties can be overcome, and offers detailed proofs showing that a smooth treatment of semantical characterization can be given to all such logics. Although the paper is well-endowed in technical details and results, it has a significant philosophical aside: it shows how slight extensions of classical methods can be used to construct the basic model theory of logics that are weaker than traditional logic due to the absence of certain rules present in classical logic. Several such logics, however, as in the case of the LFIs treated here, are notorious for their wealth of models precisely because they do not make indiscriminate use of certain rules; these models thus require new methods. In the case of this paper, by just appealing to a refined version of the Principle of Explosion, or Pseudo-Scotus, some new constructions and crafty solutions to certain non-obvious subtleties are proposed. The result is that a richer extension of model theory can be inaugurated, with interest not only for paraconsistency, but hopefully to other enlargements of traditional logic. (shrink)

We explore some topics in the model theory of sheaves of modules. First we describe the formal language that we use. Then we present some examples of sheaves obtained from quivers. These, and other examples, will serve as illustrations and as counterexamples. Then we investigate the notion of strong minimality from model theory to see what it means in this context. We also look briefly at the relation between global, local and pointwise versions of properties (...) related to acyclicity. (shrink)

We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of (...) constructing nonclassical structures, namely, Priest's Collapsing Lemma and Dunn's Theorem in 3-Valued Logic. (shrink)

I defend a conception of Logic as normative for the sort of activities in which inferences super-vene, namely, reasoning and arguing. Toulmin’s criticism of formal logic will be our framework to shape the idea that in order to make sense of Logic as normative, we should con-ceive it as a discipline devoted to the layout of arguments, understood as the representations of the semantic, truth relevant, properties of the inferences that we make in arguing and reason-ing.

Tagmemic theory as a semiotic theory can be used to analyze multiple systems of logic and to assess their strengths and weaknesses. This analysis constitutes an application of semiotics and also a contribution to understanding of the nature of logic within the context of human meaning. Each system of logic is best adapted to represent one portion of human rationality. Acknowledging this correlation between systems and their targets helps explain the usefulness of more than one system. Among these (...) systems, the two-valued system of classical logic takes its place. All the systems of logic can be incorporated into a complex mathematical model that has a place for each system and that represents a larger whole in human reasoning. The model can represent why tight formal systems of logic can be applied in some contexts with great success, but in other contexts are not directly applicable. The result suggests that human reasoning is innately richer than any one formal system of logic. (shrink)

Logical reconstruction is a fundamental philosophical method for achieving clarity concerning the prerequisites, presuppositions and the logical structure of natural language arguments. The scope and limits of this method have become visible not least through its intense application to Anselm of Canterbury’s notorious proofs for the existence of God. This volume collects, on the one hand, reconstructions of Anselmian arguments that take account of the problems of reconstruction and, on the other hand, theoretical reflections on reconstruction with a view to (...) Anselm. We hope that this will allow the reader to critically assess the merits of the theoretical accounts in the light of the reconstructions and the merits of the reconstructions in the light of the theoretical accounts. In general, by considering the example of an outstanding thinker in one or the other way, this volume aims at advancing the methodology and the practice of logical reconstruction. The following remarks explain and motivate this undertaking: What purposes does logical reconstruction serve? What purposes does the reflection on logical reconstruction serve? In which ways can the practice and theory of reconstruction profit particularly from studying Anselm’s reasoning? How can the resulting problems be addressed? – Finally, a short overview over the contributions to this volume is offered. (shrink)

This volume brings together papers on the theory of reconstruction that pay attention to the humdrum exercise of everyday reconstruction and papers that develop reconstructions of Anselmian arguments with a view to the theoretical problems of reconstruction. We hope that this will provide the readers with an opportunity to assess the merits of the theoretical accounts in the light of the reconstructions and the merits of the latter in the light of the former.

Tarskian model theory is almost universally understood as a formal counterpart of the preformal notion of semantics, of the “linkage between words and things”. The wide-spread opinion is that to account for the semantics of natural language is to furnish its settheoretic interpretation in a suitable model structure; as exemplified by Montague 1974.

Logic: Techniques of Formal Reasoning, 2/e is an introductory volume that teaches students to recognize and construct correct deductions. It takes students through all logical steps--from premise to conclusion--and presents appropriate symbols and terms, while giving examples to clarify principles. Logic, 2/e uses models to establish the invalidity of arguments, and includes exercise sets throughout, ranging from easy to challenging. Solutions are provided to selected exercises, and historical remarks discuss major contributions to the theories covered.

This chapter provides broad coverage of the notion of logical consequence, exploring its modal, semantic, and epistemic aspects. It develops the contrast between proof-theoretic notion of consequence, in terms of deduction, and a model-theoretic approach, in terms of truth-conditions. The main purpose is to relate the formal, technical work in logic to the philosophical concepts that underlie reasoning.

Logical consequence in first-order predicate logic is defined substitutionally in set theory augmented with a primitive satisfaction predicate: an argument is defined to be logically valid if and only if there is no substitution instance with true premises and a false conclusion. Substitution instances are permitted to contain parameters. Variants of this definition of logical consequence are given: logical validity can be defined with or without identity as a logical constant, and quantifiers can be relativized in substitution instances or (...) not. It is shown that the resulting notions of logical consequence are extensionally equivalent to versions of first-order provability and model-theoretic consequence. Every model-theoretic interpretation has a substitutional counterpart, but not vice versa. In particular, in contrast to the model-theoretic account, there is a trivial intended interpretation on the substitutional account, namely, the homophonic interpretation that does not substitute anything. Applications to free logic, and theories and languages other than set theory are sketched. (shrink)

In the current paper, we re-examine how abstract argumentation can be formulated in terms of labellings, and how the resulting theory can be applied in the field of modal logic. In particular, we are able to express the (complete) extensions of an argumentation framework as models of a set of modal logic formulas that represents the argumentation framework. Using this approach, it becomes possible to define the grounded extension in terms of modal logic entailment.

Khemlani et al. (2018) mischaracterize logic in the course of seeking to show that mental model theory (MMT) can accommodate a form of inference (, let us label it) they find in a high percentage of their subjects. We reveal their mischaracterization and, in so doing, lay a landscape for future modeling by cognitive scientists who may wonder whether human reasoning is consistent with, or perhaps even capturable by, reasoning in a logic or family thereof. Along the way, (...) we note that the properties touted by Khemlani et al. as innovative aspects of MMT‐based modeling (e.g., nonmonotonicity) have for decades been, in logic, acknowledged and rigorously specified by families of (implemented) logics. Khemlani et al. (2018) further declare that is “invalid in any modal logic.” We demonstrate this to be false by our introduction (Appendix A) of a new propositional modal logic (within a family of such logics) in which is provably valid, and by the implementation of this logic. A second appendix, B, partially answers the two‐part question, “What is a formal logic, and what is it for one to capture empirical phenomena?”. (shrink)

In his sociological works Pareto developed a theory of cyclical social change within the general equilibrium framework. Building on an earlier propositional formalization, we translate Pareto's theory into a series of simultaneous equations and simulate the equation system. The dynamic behavior of the simulation is consistent with Pareto's predictions and demonstrates the internal logic of the theory.

A system of logic usually comprises a language for which a model-theory and a proof-theory are defined. The model-theory defines the semantic notion of model-theoretic logical consequence (⊨), while the proof-theory defines the proof- theoretic notion of logical consequence (or logical derivability, ⊢). If the system in question is sound and complete, then the two notions of logical consequence are extensionally equivalent. The concept of full formalization is a more restrictive one and requires (...) in addition the preservation of the standard meanings of the logical terms in all the admissible interpretations of the logical calculus, as it is proof-theoretically defined. Although classical first-order logic is sound and complete, its standard formalizations fall short to be full formalizations since they allow non-intended interpretations. This fact poses a challenge for the logical inferentialism program, whose main tenet is that the meanings of the logical terms are uniquely determined by the formal axioms or rules of inference that govern their use in a logical calculus, i.e., logical inferentialism requires a categorical calculus. This paper is the first part of a more elaborated study which will analyze the categoricity problem from its beginning until the most recent approaches. I will first start by describing the problem of a full formalization in the general framework in which Carnap (1934/1937, 1943) formulated it for classical logic. Then, in sections IV and V, I shall discuss the way in which the mathematicians B.A. Bernstein (1932) and E.V. Huntington (1933) have previously formulated and analyzed it in algebraic terms for propositional logic and, finally, I shall discuss some critical reactions Nagel (1943), Hempel (1943), Fitch (1944), and Church (1944) formulated to these approaches. (shrink)

Logic and philosophy of science share a long history, though contacts have gone through ups and downs. This paper is a brief survey of some major themes in logical studies of empirical theories, including links to computer science and current studies of rational agency. The survey has no new results: we just try to make some things into common knowledge.

In the multi-agent setting, it is relevant to model group dynamics of agents, and logic has proved a good tool to do so. We propose an epistemic logic, L-DINF-E, that allows one to formalize what are the beliefs formed by a group of agents, where several groups exist and agents can pass from a group to another one. We introduce a new modality which allows an agent to reason about the beliefs of other agents. This allows us to (...) class='Hi'>model aspects of the “Theory of Mind”, understood as the set of social-cognitive skills involving the ability to attribute and reason about mental states, desires, beliefs, and knowledge of agents. In this paper, we present the logic L-DINF-E and illustrate how it can be used to solve “false-belief tasks”, i.e., tests in which an agent should understand that some other agent may develop, under some circumstances, false beliefs. (shrink)

The present paper analyses the topic of scientific discovery and the problem of the existence of a logical framework involved in such endeavour. We inquire how several non-monotonic logic frameworks and other formalisms can account for such a task. In the same vein, we analyse some key aspects of the historical and theoretical debate surrounding scientific discovery, in particular, the context of discovery and context of justification context distinction. We present an argument concerning the weakening of the discovery/justification context dichotomy (...) based on the descriptive accent contained in the non-monotonic logic perspective together with its epistemological concerns. (shrink)

The essay is dedicated to the memory of Jaakko Hintikka and Hilary Putnam, two logically inventive philosophers who, nonetheless, showed deep judgment in bringing to the fore the limits of reducing natural languages to formal languages, via the use of logical forms and model theory. Writing in parallel ecologies, the two proposed rather similar “limitative” theses about the popular logical-form-cum-model theory methodology.

Finite model theory is currently not one of the hot topics in the philosophy and history of mathematics, not even in the philosophy and history of mathematical logic. The philosophy of mathematics and mathematical logic has concentrated on infinite structures, closely related to foundational issues. In that context, finite models deserved only marginal attention because it was taken for granted that the study of finite structures is trivial compared to the study of infinite structures. In retrospect, research on (...) finite structures turned out to be neither trivial nor irrelevant but had an important impact on theoretical computer science. A closer look at the early history of the spectrum problem shows that the birth of finite model theory has roots in formal logic, at a time when computer science did not yet exist. (shrink)

The current paper studies the formal properties of the Global Reflection Principle, to wit the assertion “All theorems of$\mathrm {Th}$are true,” where$\mathrm {Th}$is a theory in the language of arithmetic and the truth predicate satisfies the usual Tarskian inductive conditions for formulae in the language of arithmetic. We fix the gap in Kotlarski’s proof from [15], showing that the Global Reflection Principle for Peano Arithmetic is provable in the theory of compositional truth with bounded induction only ($\mathrm (...) {CT}_0$). Furthermore, we extend the above result showing that$\Sigma _1$-uniform reflection over a theory of uniform Tarski biconditionals ($\mathrm {UTB}^-$) is provable in$\mathrm {CT}_0$, thus answering the question of Beklemishev and Pakhomov [2]. Finally, we introduce the notion of a prolongable satisfaction class and use it to study the structure of models of$\mathrm {CT}_0$. In particular, we provide a new model-theoretical characterization of theories of finite iterations of uniform reflection and present a new proof characterizing the arithmetical consequences of$\mathrm {CT}_0$. (shrink)

Modelling a complex phenomenon such as the mind presents tremendous computational complexity challenges. Modelling field theory addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes more certain, then the evaluation criterion is adjusted dynamically to match that change to the model. This process is called the Dynamic (...) Logic of Phenomena for model construction and it mimics processes of the mind and natural evolution. This paper provides a formal description of DLP by specifying its syntax, semantics, and reasoning system. We also outline links between DLP and other logical approaches. Computational complexity issues that motivate this work are presented using an example of polynomial models. (shrink)

The Logic of Liberal Rights uses basic logic to develop a model of argument presupposed in all disputes about civil rights and liberties. No prior training in logic is required, as each step is explained. This analysis does not merely apply general logic to legal arguments but is also specifically tailored to the issues of civil rights and liberties. It shows that all arguments about civil rights and liberties presuppose one fixed structure and that there can be no original (...) argument in rights disputes, except within the confines of that structure. Concepts arising in disputes about rights, like 'liberal' or 'democratic', are not mere abstractions but have a fixed and precise character. This book integrates themes in legal theory, political science and moral philosophy, as well as the philosophy of logic and language. For the advanced scholar, the book provides a model presupposed by leading theoretical schools . For the student it provides a systematic theory of civil rights and liberties. Examples are drawn from the European Convention in Human Rights but no special knowledge of the Convention is assumed, as the issues analysed arise throughout the world. Such issues include problems of free speech, religious freedom, privacy, torture, unlawful detention and private property. (shrink)

According to the received view formal semantics applies to natural language to some extent only. It is so because natural language is inherently indefinite, in particular, its expressions are ambiguous, vague and admits departures from syntactic rule. Moreover, intensional contexts occur in ordinary language—it results in limitations of the principle of compositionality. The ordinary conversation appeals to various principles, for instance, Grice’s maxims which exceed logical formalism. Thus, ordinary language cannot be fully formalized. On the other hand, if L (...) is a formal language, its metalanguage ML, must be partially informal—for instance, it contains, terms of ordinary mathematics, especially set theory. Even, if, for instance, due to the technique of aritmetization, ML can be represented in L, such a representation is only local. In fact, this view can be derived from some Tarski’s remarks on the role played by natural language. It is usually assumed that the universality of natural language, is the source of troubles associated with antinomies. It is so this circumstance requires a solution, for example by distinguishing levels of language. However, even if antinomies are excluded, what is informal is prior with respect to what is formal. It shows that formal semantics has limitations even with respect to formalized languages. (shrink)

his paper is an excerpt from a larger project that aims to open a new pathway into Spinoza's Ethics by formally reconstructing an initial fragment of this text. The semantic backbone of the project is a custom-made Spinozian model theory that lays out some of the formal prerequisites for more ne-grained investigations into Spinoza's fundamental ontology and modal metaphysics. We implement Spinoza's theory of attributes using many-sorted models with a rich system of identity that allows us (...) to clarify the puzzling status of such logical principles as the Substitution of Identicals and Transitivity of Identity in Spinoza's thought. The intensional structure of our Spinozian models also captures his proposal that states of a airs can be necessitated or excluded by the essences of particular things, an essence-relative modality that should be of interest to philosophers who have sought to rehabilitate the concept of essence in contemporary analytic metaphysics. (shrink)

Written before the impressive collapse of the socialist system in Eastern Europe, this book offers a quite objective and serious systematic analysis of the Marxian labor theory of value, Marx's main scientific legacy. After reconstructing the 'prototype' of this theory - which is the theory as it was left by Marx himself in Capital - the author proceeds to a careful and detailed analysis of its foundational problems, taking into account Bohm-Bawerk's important criticisms. After introducing advanced contemporary (...) formal tools, the author proceeds to a thorough discussion of the dialectical method, just in order to tackle the foundational problems of the theory. He provides a formally precise and well motivated definition of abstract labor, and then proceeds to prove the existence of a measurement of abstract labor - i.e. the existence of numerical labor-values. Using this result, the author provides rigorous axiomatic foundations for the theory of value and then proves the existence of a Marxian competitive equilibrium, which is tantamount to the proof of the possibility of reproduction for a capitalist economy. The author finishes the book by showing in detail how the problems of the prototype are solved, by reconstructing the Leontief model of the labor theory of value on the new logical bases. Written in a very clear style, in the language of contemporary philosophy of science, the book is of interest to philosophers of science and economists, applied logicians and all those interested in the scientific legacy of Karl Marx. (shrink)

A model is said to be -like if but for all , . In this paper, we shall study sentences true in -like models of arithmetic, especially in the cases when is singular. In particular, we identify axiom schemes true in such models which are particularly `natural' from a combinatorial or model-theoretic point of view and investigate the properties of models of these schemes.

We continue the analysis of foundations of positive model theory as introduced by Ben Yaacov and Poizat. The objects of this analysis are $h$-inductive theories and their models, especially the “positively” existentially closed ones. We analyze topological properties of spaces of types, introduce forms of quantifier elimination, and characterize minimal completions of arbitrary $h$-inductive theories. The main technical tools consist of various forms of amalgamations in special classes of structures.

We present here some modifications of tense logic based on intensionally treated game-theoretic concepts. They are intended for construction of formal models with description of intensional acts. Formal characteristic of intensional acts – subject, modus and contents; general scheme – MODUS, where x1, . . . , xm – names of subjects and A1, . . . , An – propositional description. For example: “x1 persuaded x2 that A1 is better than A2”. For the examination of formal (...) structures, making use of time logic, we should notice that an intensional act is an event identical in time with other non-intensional acts. (shrink)

We study the theory of a Hilbert space H as a module for a unital C*-algebra ${\mathcal{A}}$ from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are elementary equivalent to it. Also, we show that this theory has quantifier elimination and we characterize the model companion of the incomplete theory of all non-degenerate representations of ${\mathcal{A}}$ . Finally, we show (...) that there is an homeomorphism between the space of types of norm less than 1 in this model companion, and the space of quasistates of the C*-algebra ${\mathcal{A}}$. (shrink)

In this paper I shall compare two models of concept formation, both inspired by basic convictions of philosophical empiricism. The first, the connectionist model, will be exemplified by Kohonen maps, and the second will be my own dynamic theory of concept formation. Both can be understood in probabilistic terms, both use a notion of convergence or stabilization in modelling how concepts are built up. Both admit destabilization of concepts and conceptual change. Both do not use a notion of (...) representation in some pregiven language, such as a language of thought or some logical language. Representation in a formal language only plays a role on the meta-level, namely within the theory about concept formation. (shrink)

This is a very fine elementary-to-intermediate level text of mathematical logic. The initial chapter of the book consists of a good discussion of standard topics in modern formal logic including arguments and argument forms, logical functors, validity, proof, the axiomatic method, interpretations, and logical systems. The book then proceeds in subsequent chapters to a development of increasingly rich systems of sentential logic, systems of natural deduction, and a chapter on consistency and completeness of formal systems. This takes the (...) student through approximately one half of the book. The second half is devoted to more advanced topics such as non-standard systems of propositional logic, and predicate logic of the first order. Finally, there are chapters on higher functional calculi, the logical paradoxes, and non-standard functional systems. A good deal of attention is paid throughout to completeness and consistency properties, the decision problem for various systems, and algebraic structure. There are no frills or "gimmicks" in this book, but good intelligent discussions of important mathematical issues, and many theorems which are left as exercises to the student. Some items which one wishes had been included are normal forms, and elementary discussions of the theories of recursion and logical models.—H. P. K. (shrink)

The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der Töne. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der Töne in 1990. The conceptual basis has been vastly generalized to topos-theoretic foundations, including a corresponding thoroughly geometric musical logic. The theoretical models and results now include topologies for rhythm, melody, and harmony, as well as a classification theory (...) of musical objects that comprises the topos-theoretic concept framework. Classification also implies techniques of algebraic moduli theory. The classical models of modulation and counterpoint have been extended to exotic scales and counterpoint interval dichotomies. The probably most exciting new field of research deals with musical performance and its implementation on advanced object-oriented software environments. This subject not only uses extensively the existing mathematical music theory, it also opens the language to differential equations and tools of differential geometry, such as Lie derivatives. Mathematical performance theory is the key to inverse performance theory, an advanced new research field which deals with the calculation of varieties of parameters which give rise to a determined performance. This field uses techniques of algebraic geometry and statistics, approaches which have already produced significant results in the understanding of highest-ranked human performances. The book's formal language and models are currently being used by leading researchers in Europe and Northern America and have become a foundation of music software design. This is also testified by the book's nineteen collaborators and the included CD-ROM containing software and music examples. (shrink)

Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap (...) structures are given. Specifically, a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics. (shrink)

Model theory is the branch of mathematical logic looking at the relationship between mathematical structures and logic languages. These formal languages are free from the ambiguities of natural languages, and are becoming increasingly important in areas such as computing, philosophy and linguistics. This book provides a clear introduction to the subject for both mathematicians and the non-specialists now needing to learn some model theory.

BAT is a logic built to capture the inferential behavior of informal provability. Ultimately, the logic is meant to be used in an arithmetical setting. To reach this stage it has to be extended to a first-order version. In this paper we provide such an extension. We do so by constructing non-deterministic three-valued models that interpret quantifiers as some sorts of infinite disjunctions and conjunctions. We also elaborate on the semantical properties of the first-order system and consider a couple of (...) its strengthenings. It turns out that obtaining a sensible strengthening is not straightforward. We prove that most strategies commonly used for strengthening non-deterministic logics fail in our case. Nevertheless, we identify one method of extending the system which does not. (shrink)

Now available in English for the first time, The Visibility of the Image explores the development of an influential aesthetic tradition through the work of six figures. Analysing their contribution to the progress of formal aesthetics, from its origins in Germany in the 1880s to semiotic interpretations in America a century later, the six chapters cover: Robert Zimmermann (1824-1898), the first to separate aesthetics and metaphysics and approach aesthetics along the lines of formal logic, providing a purely syntactic (...) way of using signs, regardless of objective content; Alois Riegl (1858-1905), who went on to further develop aesthetics on the model of formal logic, creating a theory of style in response to Zimmermann's call for an aesthetics oriented toward formal logic; Heinrich Wölfflin (1864-1945), who represents a step toward an understanding of consciousness by using pictures as cognitive tools; Konrad Fiedler (1841-1895), the Saxon philosopher who considered the possibility that some kinds of images are made and viewed not for what they show, but for their visibility's sake alone; Maurice Merleau-Ponty (1908-1961), responsible for taking up the connections between the problems of reducing the range of potential meanings and contexts of a given image down to just the picture surface; Charles William Morris (1901-1979), who set out to establish whether a picture with no objective reference, such as an abstract painting, still counts as a sign, and if so, in what sense. Bringing these thinkers together and interlinking their ideas, Lambert Wiesing presents an engaging history of formal aesthetics, while reconstructing the philosophical foundations for the appearance of new image forms in the 20th century, including the video-clip, abstract collage, digital simulation and virtual reality. Using this original approach, The Visibility of the Image introduces the rise of modern image theory and provides a valuable account of our engagement with pictures in the 21st century. (shrink)

This book addresses the logical aspects of the foundations of scientific theories. Even though the relevance of formal methods in the study of scientific theories is now widely recognized and regaining prominence, the issues covered here are still not generally discussed in philosophy of science. The authors focus mainly on the role played by the underlying formal apparatuses employed in the construction of the models of scientific theories, relating the discussion with the so-called semantic approach to scientific theories. (...) The book describes the role played by this metamathematical framework in three main aspects: considerations of formal languages employed to axiomatize scientific theories, the role of the axiomatic method itself, and the way set-theoretical structures, which play the role of the models of theories, are developed. The authors also discuss the differences and philosophical relevance of the two basic ways of aximoatizing a scientific theory, namely Patrick Suppes’ set theoretical predicates and the "da Costa and Chuaqui" approach. This book engages with important discussions of the nature of scientific theories and will be a useful resource for researchers and upper-level students working in philosophy of science. (shrink)