In the paper we define a class of languages for representation o knowledge in those application areas when a complete information about a domain is not available. In the languages we introduce modal operators determined by accessibility relations depending on parameters.

Human cognition requires coping with a complex and uncertain world. This suggests that dealing with uncertainty may be the central challenge for human reasoning. In Bayesian Rationality we argue that probability theory, the calculus of uncertainty, is the right framework in which to understand everyday reasoning. We also argue that probability theory explains behavior, even on experimental tasks that have been designed to probe people's logical reasoning abilities. Most commentators agree on the centrality of uncertainty; some suggest that there is (...) a residual role for logic in understanding reasoning; and others put forward alternative formalisms for uncertain reasoning, or raise specific technical, methodological, or empirical challenges. In responding to these points, we aim to clarify the scope and limits of probability and logic in cognitive science; explore the meaning of the explanation of cognition; and re-evaluate the empirical case for Bayesian rationality. (shrink)

This contribution aims at providing an argumentative method to account for epistemic modality and evidentiality. I claim that these two linguistic categories can work as semantic components of defeasible argumentative schemes based on classification processes. This kind of approximate reasoning is, in fact, frequently indicated by appearance verbs which signal that the inferred standpoint is conceived by the speaker as uncertain due to the deceiving nature of perceptual data. Drawing from an analysis at the semantic-argumentative interface, the way in which (...) prototype theory sheds light on the processes of meaning construction underlying defeasible arguments from definition is also shown. (shrink)

This is not an overly ambitious paper. What I would like to do is to take a thesis that most people would regard as wildly implausible, and convince you that it is, in fact, false. What's worse, the argument I shall give is by no means airtight, though I hope it's reasonably convincing. The thesis has to do with the fuzzy boundaries of terms that refer to familiar middle-sized objects, terms like ‘Kilimanjaro’ and ‘the tallest mountain in Africa.’ It is (...) intuitively clear that Kilimanjaro has a fuzzy boundary, so that there are some clods of earth at the base of the mountain for which there isn't anything, either in our practices in using the word ‘Kilimanjaro’ or in the facts of geography, that determines an answer to the question whether the clod is a part of Kilimanjaro. (shrink)

The word ‘true’ shows some evidence of gradability. For instance, there are cases where truth-bearers are described as ‘slightly true’, ‘completely true’ or ‘very true’. Expressions that accept these types of modifiers are analysed in terms of properties that can be possessed to a greater or lesser degree. If ‘true’ is genuinely gradable, then it would follow that there are degrees of truth. It might also follow that ‘true’ is context-sensitive, like other gradable expressions. Such conclusions are difficult to reconcile (...) with most existing theories: deflationists and inflationists alike tend to reject the thesis that one true truth-bearer can have more or less truth than another. Based on work in natural language, I argue that ‘true’ is not a genuinely gradable expression. I also provide an explanation of the apparent evidence for gradability. Hence there is no reason to think that there is a truth property that comes in degrees. (shrink)

In this paper, we provide a macro level analysis of the visibility of philosophy of science in the sciences over the last four decades. Our quantitative analysis of publications and citations of philosophy of science papers, published in 17 main journals representing the discipline, contributes to the longstanding debate on the influence of philosophy of science on the sciences. It reveals the global structure of relationships that philosophy of science maintains with science, technology, engineering and mathematics and social sciences and (...) humanities fields. Explored at the level of disciplines, journals and authors, this analysis of the relations between philosophy of science and a large and diversified array of disciplines allows us to answer several questions: what is the degree of openness of various disciplines to the specialized knowledge produced in philosophy of science? Which STEM and SSH fields and journals have privileged ties with philosophy of science? What are the characteristics, in terms of citation and publication patterns, of authors who get their philosophy of science papers cited outside their field? Complementing existing qualitative inquiries on the influence of specific authors, concepts or topics of philosophy of science, the bibliometric approach proposed in this paper offers a comprehensive portrait of the multiple relationships that links philosophy of science to the sciences. (shrink)

The sorites paradox is the name given to a class of paradoxical arguments, also known as little by little arguments, which arise as a result of the indeterminacy surrounding limits of application of the predicates involved. For example, the concept of a heap appears to lack sharp boundaries and, as a consequence of the subsequent indeterminacy surrounding the extension of the predicate ‘is a heap’, no one grain of wheat can be identified as making the difference between being a heap (...) and not being a heap. Given then that one grain of wheat does not make a heap, it would seem to follow that two do not, thus three do not, and so on. In the end it would appear that no amount of wheat can make a heap. We are faced with paradox since from apparently true premises by seemingly uncontroversial reasoning we arrive at an apparently false conclusion. (shrink)

I argue for two claims: that the ordinary English truth predicate is a gradable adjective and that truth is a property that comes in degrees. The first is a semantic claim, motivated by the linguistic evidence and the similarity of the truth predicate’s behavior to other gradable terms. The second is a claim in natural language metaphysics, motivated by interpreting the best semantic analysis of gradable terms as applied to the truth predicate. In addition to providing arguments for these two (...) claims, I draw out consequences for debates about deflationism and truth-based analyses of notions such as assertion and logical consequence. (shrink)

There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an agent reports that two things are indistinguishable are both carefully modeled, the problems disappear, and indistinguishability can indeed be taken to be an equivalence relation. Moreover, this model also suggests a logic of vagueness that seems (...) to solve many of the problems related to vagueness discussed in the philosophical literature. In particular, it is shown here how the logic can handle the sorites paradox. (shrink)

In 1880, when Oliver Wendell Holmes (later to be a Justice of the U.S. Supreme Court) criticized the logical theology of law articulated by Christopher Columbus Langdell (the first Dean of Harvard Law School), neither Holmes nor Langdell was aware of the revolution in logic that had begun, the year before, with Frege's Begriffsschrift. But there is an important element of truth in Holmes's insistence that a legal system cannot be adequately understood as a system of axioms and corollaries; and (...) this element of truth is not obviated by the more powerful logical techniques that are now available. (shrink)

In 1907 Borel published a remarkable essay on the paradox of the Heap (“Un paradoxe économique: le sophisme du tas de blé et les vérités statistiques”), in which Borel proposes what is likely the first statistical account of vagueness ever written, and where he discusses the practical implications of the sorites paradox, including in economics. Borel’s paper was integrated in his book Le Hasard, published 1914, but has gone mostly unnoticed since its publication. One of the originalities of Borel’s essay (...) is that it puts forward a model of vagueness as imprecision, making particular use of the Gaussian law of measurement errors to model categorization. The aim of our paper is to give a presentation of the historical context of Borel’s essay, to spell out the mathematical details of his model, and to provide a critical assessment of his theory. Three aspects of Borel’s account are particularly discussed: the first concerns the comparison between Borel’s statistical account and posterior degree-theoretic accounts of vagueness. The second concerns the anti-epistemicist flavor of Borel’s approach, whereby the idea of statistical fluctuation is used to undermine the notion of sharp boundary for vague predicates. The third concerns the problematic link between Borel’s model of vagueness as imprecision and the notion of semantic indeterminacy. An English translation of Borel’s original essay is appended to this paper (Erkenntnis, this issue). (shrink)

ABSTRACT In this work the connections between the fuzzy closure operators and the graded consequence relations are examined Namely, as it is well known, in the crisp case there is a complete equivalence between the notion of closure operator and the one of consequence relation. We extend this result by proving that the graded consequence relations are related to a particular class of fuzzy closure operators, namely the class of fuzzy closure operators that can be obtained by a chain of (...) classical closure operators. (shrink)

We show that it is possible to base fuzzy control on fuzzy logic programming. Indeed, we observe that the class of fuzzy Herbrand interpretations gives a semantics for fuzzy programs and we show that the fuzzy function associated with a fuzzy system of IF-THEN rules is the fuzzy Herbrand interpretation associated with a suitable fuzzy program.

Let S be a set, P the class of all subsets of S and F the class of all fuzzy subsets of S. In this paper an “extension principle” for closure operators and, in particular, for deduction systems is proposed and examined. Namely we propose a way to extend any closure operator J defined in P into a fuzzy closure operator J* defined in F. This enables us to give the notion of canonical extension of a deduction system and to (...) give interesting examples of fuzzy logics. In particular, the canonical extension of the classical propositional calculus is defined and it is showed its connection with possibility and necessity measures. Also, the canonical extension of first order logic enables us to extend some basic notions of programming logic, namely to define the fuzzy Herbrand models of a fuzzy program. Finally, we show that the extension principle enables us to obtain fuzzy logics related to fuzzy subalgebra theory and graded consequence relation theory. (shrink)

ABSTRACT In this paper we introduce a set of six logical values, arising in the application of three-valued logics to time intervals, find its algebraic structure, and use it to define a six-valued logic. We then prove, by using algebraic properties of the class of De Morgan algebras, that this semantically defined logic can be axiomatized as Belnap's ?useful? four-valued logic. Other directions of research suggested by the construction of this set of six logical values are described.

A critical view of the alleged significance of Belnap four-valued logic for reasoning under inconsistent and incomplete information is provided. The difficulty lies in the confusion between truth-values and information states, when reasoning about Boolean propositions. So our critique is along the lines of previous debates on the relevance of many-valued logics and especially of the extension of the Boolean truth-tables to more than two values as a tool for reasoning about uncertainty. The critique also questions the significance of partial (...) logic. (shrink)

In this paper, I identify the source of the differences between classical logic and many-valued logics (including fuzzy logics) with respect to the set of valid formulas and the set of inferences sanctioned. In the course of doing so, we find the conditions that are individually necessary and jointly sufficient for any many-valued semantics (again including fuzzy logics) to validate exactly the classically valid formulas, while sanctioning exactly the same set of inferences as classical logic. This in turn shows, contrary (...) to what has sometimes been claimed, that at least one class of infinite-valued semantics is axiomatizable. (shrink)

This volume analyzes and studies how vagueness occurs and matters as a specific problem in the context of theories that are primarily about something else.

The PhD thesis advances a new approach to vagueness as dispersion, comparing it with the main philosophical theories of vagueness in the analytic tradition.

The paper has three objectives: to expound a set-theoretical triplet model of concepts; to introduce some triplet relations (symbolic, logical, and mathematical formalization; equivalence, intersection, disjointness) between object concepts, and to instantiate them by relations between certain physical object concepts.

In recent years, a number of well-known intentional realists have focused their energy on attempts to provide a naturalized theory of mental representation. What tends to be overlooked, however, is that a naturalized theory of mental representation will not, by itself, salvage intentional realism. Since most naturalistic properties play no interesting causal role, intentional realists must also solve the problem of showing how intentional properties , even if naturalized, could be causally efficacious. Because of certain commitments, this problem is especially (...) difficult for intentional realists such as Fodor. In the current paper I focus on the problem as it arises for such realists, and I argue that the best-known solution proposed to date is inadequate. If what I say is correct, then such intentional realists are left with an additional and substantial problem, and one that has generally not been sufficiently appreciated. (shrink)

Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this paradox, it (...) is demonstrated that any formalized system for the Theory of Computation based on Classical Logic and Turing Model of Computation leads us to a contradiction. We conclude that our mathematical frame work is inappropriate for Theory of Computation. Furthermore, the result provides us a reason that many problems in Complexity Theory resist to be solved.(This work is completed in 2017 -5- 2, it is in vixra in 2017-5-14, presented in Unilog 2018, Vichy). (shrink)

Computational complexity is a discipline of computer science and mathematics which classifies computational problems depending on their inherent difficulty, i.e. categorizes algorithms according to their performance, and relates these classes to each other. P problems are a class of computational problems that can be solved in polynomial time using a deterministic Turing machine while solutions to NP problems can be verified in polynomial time, but we still do not know whether they can be solved in polynomial time as well. A (...) solution for the so-called NP-complete problems will also be a solution for any other such problems. Its artificial-intelligence analogue is the class of AI-complete problems, for which a complete mathematical formalization still does not exist. In this chapter we will focus on analysing computational classes to better understand possible formalizations of AI-complete problems, and to see whether a universal algorithm, such as a Turing test, could exist for all AI-complete problems. In order to better observe how modern computer science tries to deal with computational complexity issues, we present several different deep-learning strategies involving optimization methods to see that the inability to exactly solve a problem from a higher order computational class does not mean there is not a satisfactory solution using state-of-the-art machine-learning techniques. Such methods are compared to philosophical issues and psychological research regarding human abilities of solving analogous NP-complete problems, to fortify the claim that we do not need to have an exact and correct way of solving AI-complete problems to nevertheless possibly achieve the notion of strong AI. (shrink)

In a recent paper, Lee Kerckhove and Sara Waller (hereafter K & W) argue that the concept of personhood is irrelevant for the abortion debate.1 Surprisingly, this irrelevance is due merely to the fact that the predicate ‘being a person’ — hereafter ‘personhood’ — is inherently vague. This vagueness, they argue, reduces ‘personhood’ to incoherency and disqualifies the notion from being a useful moral concept. In other words, if ‘personhood’ isn’t a precise notion with well-defined boundaries, then it cannot be (...) of any use in the debate over the permissibility of abortion. This argument is mistaken. While it may be true that ‘personhood’ is irrelevant for the debate over abortion (a substantive issue not dealt with in this paper), it is not true that ‘personhood’ should be disqualified merely because it is vague. Section 2 of the paper is a quick survey in which I briefly review the importance of ‘personhood’ in some of the more recent literature concerning the moral status of abortion. Section 3 is a reconstruction of K & W’s argument against the relevancy of ‘personhood’ and a criticism showing why their argument fails. Section 4 approaches the use of a vague predicate in moral debate and explores the application of ‘personhood’ given three contemporary solutions to vagueness: degree theory, epistemicism and supervaluationism. (shrink)

The purpose of this paper is to open for investigation a range of phenomena familiar from dynamical systems or chaos theory which appear in a simple fuzzy logic with the introduction of self-reference. Within that logic, self-referential sentences exhibit properties of fixed point attractors, fixed point repellers, and full chaos on the [0, 1] interval. Strange attractors and fractals appear in two dimensions in the graphing of pairs of mutually referential sentences and appear in three dimensions in the graphing of (...) mutually referential triples. (shrink)

The goal of inquiry in this essay is to ascertain to what extent the Principle of Compositionality – the thesis that the meaning of a complex expression is determined by the meaning of its parts and its mode of composition – can be justifiably imposed as a constraint on semantic theories, and thereby provide information about what meanings are. Apart from the introduction and the concluding chapter the thesis is divided into five chapters addressing different questions pertaining to the overarching (...) goal of inquiry. Chapter Two is an attempt to determine whether the Principle of Compositionality is a trivial principle. It is argued that this is not the case in the context of providing the semantics of natural languages since it is an open question whether the best theories that respect available syntactic and semantic data are compositional. Chapter Three and Chapter Four ask whether there are reasons to think that the Principle of Compositionality is true. It is argued that the three most commonly cited reasons for thinking that correct semantic theories must be compositional – Linguistic Creativity, Productivity and Systematicity – in fact only give us reasons to think that the meaning of complex expressions depend on the meanings of their parts and their modes of composition, but not that the meaning of complex expressions depend ONLY on those factors. Chapter Five asks whether there are any reasons to think that the Principle of Compositionality is false. It is argued that all the phenomena that have been suggested entail non-compositionality are in fact compatible with some versions of compositionality. Even if this conclusion is reached in this chapter, the conclusion of the previous two chapters entails that we are not justified in imposing the Principle of Compositionality as an adequacy constraint on Semantic theories. Chapter Six explores the ways in which information about what meanings are can be derived by imposing constraints on semantic theories. It is argued that the distinction emphasized in Chapter Three and Chapter Four between depending on and depending ONLY on is of critical importance. It is demonstrated that the informative potential of the Principle of Compositionality goes far beyond that of the principle we are in fact justified in imposing on semantic theories. So not only is it the case that we cannot learn anything about meanings from the justified imposition of the Principle of Compositionality – since we cannot justifiably impose it as a constraint on semantic theories – what we could have learned from it had we been justified in imposing it is very different from what we can learn from the principle that we are justified in imposing. (shrink)

The idea about this special issue came from a paper published as an updated and upridged version of an older memorial lecture given by Brian D. Josephson and Michael Conrad at the Gujarat Vidyapith University in Ahmedabad, India on March 2, 1984. The title of this paper was “Uniting Eastern Philosophy and Western Science” (1992). We thought that this topic deserves to be revisited after 25 years to demonstrate to the scientific community which new insights and achievements were attained in (...) this fairly broad field during this period. (shrink)

Forty-two years ago, Capra published “The Tao of Physics” (Capra, 1975). In this book (page 17) he writes: “The exploration of the atomic and subatomic world in the twentieth century has …. necessitated a radical revision of many of our basic concepts” and that, unlike ‘classical’ physics, the sub-atomic and quantum “modern physics” shows resonances with Eastern thoughts and “leads us to a view of the world which is very similar to the views held by mystics of all ages and (...) traditions.“ This article stresses an analogous situation in biology with respect to a new theoretical approach for studying living systems, Integral Biomathics (IB), which also exhibits some resonances with Eastern thought. Stepping on earlier research in cybernetics1 and theoretical biology,2 IB has been developed since 2011 by over 100 scientists from a number of disciplines who have been exploring a substantial set of theoretical frameworks. From that effort, the need for a robust core model utilizing advanced mathematics and computation adequate for understanding the behavior of organisms as dynamic wholes was identified. At this end, the authors of this article have proposed WLIMES (Ehresmann and Simeonov, 2012), a formal theory for modeling living systems integrating both the Memory Evolutive Systems (Ehresmann and Vanbremeersch, 2007) and the Wandering Logic Intelligence (Simeonov, 2002b). Its principles will be recalled here with respect to their resonances to Eastern thought. (shrink)

This is the editorial to the special edition of Progress in Biophysics and Molecular Biology on the role engagement with Eastern traditions of thought could play in the advancement of science generally and biology and the science of mind in particular.

“And maybe some of this stuff counts as philosophy after all. The form of a philosophical theory, often enough, is: Let’s try looking over here”- Jerry A. Fodor.

We discuss the hypothesis that the debate about the interpretation of the orthodox formalism of quantum mechanics might have been misguided right from the start by a biased metaphysical interpretation of the formalism and its inner mathematical relations. In particular, we focus on the orthodox interpretation of the congruence relation, '=', which relates equivalent classes of different mathematical representations of a vector in Hilbert space, in terms of metaphysical identity. We will argue that this seemingly "common sense" interpretation, at the (...) semantic level, has severe difficulties when considering the syntactic level of the theory. (shrink)