We present a theory VF of partial truth over Peano arithmetic and we prove that VF and ID 1 have the same arithmetical content. The semantics of VF is inspired by van Fraassen's notion of supervaluation.

We present a theory VF of partial truth over Peano arithmetic and we prove that VF and ID 1 have the same arithmetical content. The semantics of VF is inspired by van Fraassen's notion of supervaluation.

Three leading philosopher-logicians present a clear and concise overview of formal theories of truth, explaining key logical techniques. Truth is as central topic in philosophy: formal theories study the connections between truth and logic, including the intriguing challenges presented by paradoxes like the Liar.

As the title suggests, this paper aims at surveying some recent advances in the theory of formal truth. It contains an account of the debate concerning the deflationist approach to truth, according to which truth is a ‘thin’ notion in that it should involve no assumption of whatsoever nature. We review here the main issues that were comprised by the discussion accompanying the attempts of translating this idea into logical terms. In the second half of the paper, we focus (...) on a recent theory of truth proposed by Hartry Field, a former ‘champion’ of the deflationary approach. We then discuss it both with respect to the previous conceptual account, and to some further observation concerning the truth–as–revision machinery that this theory can be proved to implicitly make use of. (shrink)

This volume is a collection of original contributions about the core knowledge in fundamental domains. It includes work on naive physics, such as formal specifications of intuitive theories of spatial relations, time causality, substance and physical objects, and on naive psychology.

Theory of Computation -- Computation by Abstracts Devices.

The papers collected in this volume exemplify some of the trends in current approaches to logic, language and computation. Written by authors with varied academic backgrounds, the contributions are intended for an interdisciplinary audience. The first part of this volume addresses issues relevant for multi-agent systems: reasoning with incomplete information, reasoning about knowledge and beliefs, and reasoning about games. Proofs as formal objects form the subject of Part II. Topics covered include: contributions on logical frameworks, linear logic, and different approaches (...) to formalized reasoning. Part III focuses on representations and formal methods in linguistic theory, addressing the areas of comparative and temporal expressions, modal subordination, and compositionality. (shrink)

Inspired by impossibility theorems of social choice theory, many democratic theorists have argued that aggregative forms of democracy cannot lend full democratic justification for the collective decisions reached. Hence, democratic theorists have turned their attention to deliberative democracy, according to which “outcomes are democratically legitimate if and only if they could be the object of a free and reasoned agreement among equals” (Cohen 1997a, 73). However, relatively little work has been done to offer a formal theory of democratic (...) deliberation. This article helps fill that gap by offering a formal theory of three different modes of democratic deliberation: myopic discussion, constructive discussion, and debate. We show that myopic discussion suffers from indeterminacy of long run outcomes, while constructive discussion and debate are conclusive. Finally, unlike the other two modes of deliberation, debate is path independent and converges to a unique compromise position, irrespective of the initial status quo. (shrink)

Contemporary philosophers interested in value theory appear to be largely concerned with questions of the following sort:What is value?What is the meaning of the word ‘good’?Does the attribution of value to an object have a cognitive, or merely an emotive, significance?The first question is metaphysical; to ask it is analogous to asking in physics:What is matter?What is electricity?The others are generally treated as semantical questions; to ask them is analogous to asking in statistics:What is the meaning of the word (...) ‘probable’?Does an attribution of probability express an objective fact, or merely a subjective attitude? (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Martin Heidegger and OntologyEmmanuel Levinas (bio)The prestige of Martin Heidegger 1 and the influence of his thought on German philosophy marks both a new phase and one of the high points of the phenomenological movement. Caught unawares, the traditional establishment is obliged to clarify its position on this new teaching which casts a spell over youth and which, overstepping the bounds of permissibility, is already in vogue. For once, (...) Fame has picked one who deserves it and, for that matter, one who is still living. Anyone who has studied philosophy cannot, when confronted by Heidegger’s work, fail to recognize how the originality and force of his achievements, stemming from genius, are combined with an attentive, painstaking, and close working-out of the argument—with that craftsmanship of the patient artisan in which phenomenologists take such pride. In this study, it is important for us to understand, above all, the true intentions of our author, to illuminate what he thinks really needs to be said, and to surmise what is most critical for him.To get to the heart of Heidegger’s system, it seems fitting to begin with a problem that is generally familiar. We choose the problem of knowledge, a deeper understanding of which takes us to the very threshold of Heidegger’s thought. For this problem, central to modern philosophy, is one of the main obstacles of modern philosophy that Heidegger wishes to surmount. Neo-Kantianism, which takes knowledge as the philosophical problem of the first rank, is the movement against which Heidegger rebels with all his strength. We have, thus, every chance of gaining access to his thought by the main door, so to speak. Once inside the system we will try to trace its outlines, 2 reserving, for a second part of our work, the determination of Heidegger’s place in the history of ideas, especially in the phenomenological movement, as well as of his relations with the philosopher to whom he owes so much—Edmund Husserl. 31In its most general form, the problem of the theory of knowledge has a critical significance. It consists in delineating a domain where knowledge can be certain and in determining the criteria for the legitimate scope of knowledge. But this problem, as normal and as simple as it may appear, has deeper roots. That knowledge should need a criterion at all presupposes that truth is not identical to all that is known and that the course [End Page 11] of things can fail to correspond with the course of thought. “How does knowledge correspond to being?” is a more profound formulation of the problem of knowledge.But we are not going to touch anymore on the primordial phenomenon that generates the problem. The problem of correspondence between thing and thought presupposes a free activity of thought and its isolation in relation to the object. It is precisely this presupposition which renders their harmony and even their contact problematic. “How does the subject take leave of itself to attain the object?” is what the problem of knowledge, in the last analysis, boils down to. Its true source is thus the concept of “subject” as elaborated by modern philosophy. The cogito presided over the subject’s birth. The cogito was the affirmation of the privileged nature of the subject’s immanent sphere, of its unique place in existence; hence, the cogito was the specificity of the subject’s connection to the rest of reality, the sui generis nature which opens up the passage from immanence to transcendence, the passage from ideas contained in the thinking substance to 4 their “formal existence.”The concept of the subject, understood as a substance having a specific position in the entire domain of being, presents us with difficulties of two kinds. First, how do we understand this leave-taking from the self which the thinking substance brings about and which displays an entirely original aspect? Indeed, we could say that thought, in reaching out toward objects, does not actually take leave of itself, since its objects—considered as ideas and contents of thought—are, in a certain sense, already within it. In order to make sense of this paradox, Descartes... (shrink)

In formal semantics, structure is treated as the essential ingredient in the creation of sentence meaning from individual word meaning. This book introduces some of the foundational concepts, principles and techniques in the formal semantics of natural language and outlines the mathematical principles that underlie linguistics meaning. Using English examples, Yoad Winter presents the most useful tools and concepts of formal semantics in an accessible style and includes a variety of practical exercises so that readers can learn to utilize these (...) tools effectively. For readers with an elementary background in set theory and linguistics or with an interest in mathematical modelling, this fascinating study is an ideal introduction to natural language semantics. Designed as a quick yet thorough introduction to one of the most vibrant areas of research in modern linguistics today this volume reveals the beauty and elegance of the mathematical study of meaning. (shrink)

"This book is interesting and well-written. The research methods were explained clearly and conclusions were summarized nicely. It is a relatively quick read at only 130 pages. Anyone who has been told, or who has told others, that mathematicians make better thinkers should read this book." MAA Reviews "The authors particularly attend to protecting positive correlations against the self-selection interpretation, merely that logical minds elect studying more mathematics. Here, one finds a stimulating survey of the systemic difficulties people have with (...) basic syllogisms and deductions." CHOICE connect "The authors particularly attend to protecting positive correlations against the self-selection interpretation, merely that logical minds elect studying more mathematics. Here, one finds a stimulating survey of the systemic difficulties people have with basic syllogisms and deductions." CHOICE Connect For centuries, educational policymakers have believed that studying mathematics is important, in part because it develops general thinking skills that are useful throughout life. This 'Theory of Formal Discipline' (TFD) has been used as a justification for mathematics education globally. Despite this, few empirical studies have directly investigated the issue, and those which have showed mixed results. Does Mathematical Study Develop Logical Thinking? describes a rigorous investigation of the TFD. It reviews the theory's history and prior research on the topic, followed by reports on a series of recent empirical studies. It argues that, contrary to the position held by sceptics, advanced mathematical study does develop certain general thinking skills, however these are much more restricted than those typically claimed by TFD proponents. Perfect for students, researchers and policymakers in education, further education and mathematics, this book provides much needed insight into the theory and practice of the foundations of modern educational policy. (shrink)

In this paper, I have two primary goals. First, I show that the causal-based story approach in A hybrid formal theory of arguments, stories and criminal evidence is ill suited to negative causation. In the literature, the causal-based approach requires that hypothetical stories be causally linked to the explanandum. Many take these links to denote physical or psychological causation, or temporal precedence. However, understanding causality in those terms, as I will show, cannot capture cases of negative causation, which are (...) of interest to the Law. In keeping with this, I also discuss some of the difficulties Hybrid Theory invites by remaining silent on the nature of the causal links. In my second aim, I sketch a way for Hybrid Theory to overcome this problem. By replacing the original, underlying causal structure with contrastive causation in the law, Hybrid Theory can represent reasoning in which the evidence that is appealed to is causally linked via negative causation to the explananda. (shrink)

Habermas absorb and integrate the achievements of contemporary philosophy of language, formed their own philosophy of language - in the form of pragmatics. This theory of speech acts by the meaning of the effectiveness of its intrinsic correlation between the demands of the analysis, pointed out the significance of speech acts only in the order presented in communicative action. Interpretation of speech acts in the ultimate source of the problem, Habermas introduces Husserl's "life-world" theory, and it was the (...) transformation of the form of pragmatics. Form pragmatics of life-world theory digestion of Husserl's life-world theory, a priori, while broadening the theory of Weber's rationalization of the behavior of sight. Habermas has absorbed and integrated many kinds of contemporary philosophy of language and constituted his own one, which is named formal linguistics. By analyzing the internal connection between the meaning of speech act and its validity claims, Habermas has emphasized that the meaning of speech act can be only demonstrated in communicative action. In the final analysis to the origin of meaning of speech act, he introduces Husserl's theory of lifeworld and reformulates it from the point of the formal linguistics. Habermas' theory of lifeworld removes the transcendental element existing in Husserl's theory , it enlarges Weber's theoretical horizon on rationalization of action at the same time. (shrink)

A compact overview of the main formal theories of parthood and of their mutual relationships, up to Classical Extensional Mereology. Written as an Appendix to the other essays included in the volume.

This work explores the conceptual and empirical issues of the concept of knowledge and its relation to the pattern of our belief change, from formal and experimental perspectives. Part I gives an analysis of knowledge (called Sustainability) that is formally represented and naturalistically plausible at the same time, which is claimed to be a synthesized view of knowledge, covering not only empirical knowledge, but also knowledge of future, practical knowledge, mathematical knowledge, knowledge of general facts. Part II tries to formalize (...) the natural pattern of belief change assumed in Sustainability in terms of a specific formal theory of belief change, after carefully examining the notions of belief, belief change, and Information, from which the cognitive function F in Chapter 3 is actually constructed, which is later implemented by a computer program and its behavior against random input is demonstrated. In Part III we proceed to examine the analysis empirically. In particular, we will investigate Sustainability from the developmental point of view. We first justify experimental approach in philosophy as a legitimate method of philosophical investigation, and then developmental approach in particular. The specific proposal of experiment here is what we call the Gettier Task, an analogue of the famous false-belief task in developmental psychology, which has been much discussed in philosophy of mind. Two versions of the Gettier Task were tested on children aged from 6 to 12, and we claim that the data obtained empirically supports our analysis of knowledge, or Sustainability. (shrink)

In this paper I develop a theory of 'function' and function as a deontic modal word and phenomenon. Kratzer’s account of the semantics for the deontic modals is invoked and using her approach a formal schema for the semantics of 'function'-sentences is proposed. My account of function is a modalized and extended version of Cummins’ systems-type account of function. In the biological and physical sciences, on this account, function is a complex empirical deontic modal property. It is built on (...) the property of X’s doing Y well enough to enable Z, which is implicitly deontic because of the evaluative but nonetheless empirical in its biological and physical applications. This account of function resolves many of the traditional puzzles about biological and physical function, and extends naturally to include the other types of function. With a variant treatment of the semantics, this account is argued also to apply to mathematical function, where it is shown to be interestingly related to Frege’s account of function. (shrink)

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)

This paper presents a theory of reasoning with evidence in order to determine the facts in a criminal case. The focus is on the process of proof, in which the facts of the case are determined, rather than on related legal issues, such as the admissibility of evidence. In the literature, two approaches to reasoning with evidence can be distinguished, one argument-based and one story-based. In an argument-based approach to reasoning with evidence, the reasons for and against the occurrence (...) of an event, e.g., based on witness testimony, are central. In a story-based approach, evidence is evaluated and interpreted from the perspective of the factual stories as they may have occurred in a case, e.g., as they are defended by the prosecution. In this paper, we argue that both arguments and narratives are relevant and useful in the reasoning with and interpretation of evidence. Therefore, a hybrid approach is proposed and formally developed, doing justice to both the argument-based and the narrative-based perspective. By the formalization of the theory and the associated graphical representations, our proposal is the basis for the design of software developed as a tool to make sense of the evidence in complex cases. (shrink)

This article argues that Habermas’s formal-pragmatics are better understood as a set of weak-universal dispositions susceptible to erosion over the course of a lifetime, if exposed to continual “disappointing” communicative experiences. Habermas’s rational-reconstructive project to explicate the intuitive rule-consciousness held by competent speakers retains immense theoretical value for analyzing both partisan and mass political discourse, if his emphasis on isolated speech situations is supplemented with a logic of communicative memory better accounting for how disagreement antecedes discourse on the formal-pragmatic register. (...) I argue that Habermas’s concept of the “lifeworld” contains untapped theoretical resources for thinking about the formal-pragmatic consequences of accumulated partisan experiences; namely, how such experiences lead inter-partisan actors to jettison mutual imputations of communicative accountability. I conclude by offering revisions to Habermas’s discourse ethics. Rapport-building intended to alleviate the negative effects of prior accumulated partisan experiences is first necessary if a norm is to enjoy real justification. (shrink)