Wittgenstein has shown that that life, in the sense that applies in the first place to human beings, is inherently linguistic. In this paper, I ask what is involved in language, given that it is thus essential to life, answering that language – or concepts – must be both alive and the ground for life. This is explicated by a Wittgensteinian series of entailments of features. According to the first feature, concepts are not intentional engagements. The second feature brings life (...) back to concepts by describing them as inflectible: Attitudes, actions, conversations and other engagements inflect concepts, i.e., concepts take their particular characters in our actual engagements. However, inflections themselves would be reified together with the life they ground unless they could preserve the openness of concepts: hence the third feature of re-inflectibility. Finally, the openness of language must be revealed in actual life. This entails the possibility of conceptual ambivalence. (shrink)

While the past century of neuroscientific research has brought considerable progress in defining the boundaries of the human cerebral cortex, there are cases in which the demarcation of one area from another remains fuzzy. Despite the existence of clearly demarcated areas, examples of gradual transitions between areas are known since early cytoarchitectonic studies. Since multi-modal anatomical approaches and functional connectivity studies brought renewed attention to the topic, a better understanding of the theoretical and methodological implications of fuzzy boundaries in brain (...) science can be conceptually useful. This article provides a preliminary conceptual framework to understand this problem by applying philosophical theories of vagueness to three levels of neuroanatomical research. For the first two levels (cytoarchitectonics and fMRI studies), vagueness will be distinguished from other forms of uncertainty, such as imprecise measurement or ambiguous causal sources of activation. The article proceeds to discuss the implications of these levels for the anatomical study of connectivity between cortical areas. There, vagueness gets imported into connectivity studies since the network structure is dependent on the parcellation scheme and thresholds have to be used to delineate functional boundaries. Functional connectivity may introduce an additional form of vagueness, as it is an organizational principle of the brain. The article concludes by discussing what steps are appropriate to define areal boundaries more precisely. (shrink)

Abstract: Theories of rough sets and fuzzy sets are related and complementary methodologies to handle uncertainty of vagueness and coarseness, respectively. They are generalizations of classical set theory for modeling vagueness and uncertainty. A fundamental question concerning both theories is their connections and differences. There have been many studies on this topic. Topology is a branch of mathematics, whose ideas exist not only in almost all branches of mathematics but also in many real life applications. The topological structure (...) on an abstract set is used as the base, which used to extract knowledge from data. In this paper: topological structure is used to study the relation between rough sets and fuzzy sets. Membership function is used to convert from rough set to fuzzy set and vice versa. This conversion will achieve the advantages of two theories. Some examples and theories are introduced to indicate the importance of using general binary relations in the construction of rough set concepts, and indicate the relation between rough sets and fuzzy sets according to the topological spaces. (shrink)

During the last couple of decades, several attempts have been made to come up with a theory that can handle the various semantic, logical and philosophical problems raised by the vagueness of natural languages. One of the most influential ideas that have come into fashion in recent years is the idea that vagueness should be analysed as a form of context sensitivity. Such contextualist theories of vagueness have gained some popularity, but many philosophers have remained sceptical of the prospects of (...) finding a tenable contextualist solution to the problems of vagueness. This paper provides an introduction to the most popular contextualist accounts, and a discussion of some of the most important arguments for and against them. (shrink)

The ambiguity theory of ‘knows’ is the view that ‘knows’ and its cognates have more than one sense, and that which sense of ‘knows’ is used in a knowledge ascription or denial determines, in part, the meaning (and as a result the truth conditions) of that knowledge ascription or denial. In this paper, I argue that the ambiguity theory of ‘knows’ ought to be taken seriously by those drawn to epistemic contextualism. In doing so I first argue that the ambiguity (...) theory of ‘knows’ is a distinct view from epistemic contextualism. Second, I provide independent philosophical and linguistic considerations to motivate the ambiguity theory. Third, I argue that the ambiguity theory has the same central, generally agreed upon virtues ascribed to epistemic contextualism (namely, the ability to solve certain persistent epistemological problems relating to skeptical arguments and the ability to preserve the truth of most of our everyday, ordinary usages of ‘knows’ and its cognates). Finally, I provide an ambiguity-theory-friendly account of why contextualism may be initially appealing, and why this shouldn’t dissuade us from taking the ambiguity theory seriously nonetheless. (shrink)

Even when they are defined with precision, one can often read and hear judgments about the vagueness of heuristics in debates about heuristic reasoning. This opinion is not just frequent but also quite reasonable. In fact, during the 1990s, there was a certain controversy concerning this topic that confronted two of the leading groups in the field of heuristic reasoning research, each of whom held very different perspectives. In the present text, we will focus on two of the papers published (...) in Psychological Review, wherein the arguments of each of these groups were presented:. (shrink)

The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to the (...) other, each intermediate stage constituting an overlap in certain proportion of both contraries. Hence, degrees in the possession of a property give rise to simple contradictions. The reason why I have chosen those two questions is that they provide the main philosophical motivation for a particular brand of an infinite valued and paraconsistent logic. I will claim that Classical logic (CL) is not adequate to handle fuzzy situations, and, being deficient, is in need of being expanded to make room for degrees of truth and weak contradictions. One can hardly deny the importance of the debate, since what is ultimately at stake is what the limits of truth, rationality, intelligibility and possibility are. The main disciplines within which the research moves are the philosophy of language, philosophy of logic, and ontology. (shrink)

Some have argued that the vagueness exhibited by geographic names and descriptions such as ‘Albuquerque’, ‘the Outback’, or ‘Mount Everest’ is ultimately ontological: these terms are vague because they refer to vague objects, objects with fuzzy boundaries. I take the opposite stand and hold the view that geographic vagueness is exclusively semantic, or conceptual at large. There is no such thing as a vague mountain. Rather, there are many things where we conceive a mountain to be, each with its precise (...) boundary, and when we say ‘Everest’ we are just being vague as to which thing we are referring to. This paper defends this view against some plausible objections. (shrink)

In this article, I present a new interpretation of the pro-life view on the status of early human embryos. In my understanding, this position is based not on presumptions about the ontological status of embryos and their developmental capabilities but on the specific criteria of rational decisions under uncertainty and on a cautious response to the ambiguous status of embryos. This view, which uses the decision theory model of moral reasoning, promises to reconcile the uncertainty about the ontological (...) status of embryos with the certainty about normative obligations. I will demonstrate that my interpretation of the pro-life view, although seeming to be stronger than the standard one, has limited scope and cannot be used to limit destructive research on human embryos. (shrink)

The paper proposes a new formal approach to vagueness and vague sets taking inspirations from Pawlak’s rough set theory. Following a brief introduction to the problem of vagueness, an approach to conceptualization and representation of vague knowledge is presented from a number of different perspectives: those of logic, set theory, algebra, and computer science. The central notion of the vague set, in relation to the rough set, is defined as a family of sets approximated by the so called lower and (...) upper limits. The family is simultaneously considered as a family of all denotations of sharp terms representing a suitable vague term, from the agent’s point of view. Some algebraic operations on vague sets and their properties are defined. Some important conditions concerning the membership relation for vague sets, in connection to Blizard’s multisets and Zadeh’s fuzzy sets, are established as well. A classical outlook on a logic of vague sentences (vague logic) based on vague sets is also discussed. (shrink)

The ambiguity theory of “knows” is the view that knows and its cognates have more than one propositional sense—i.e., more than one sense that can properly be used in “knows that” etc. constructions. The ambiguity theory of “know” has received relatively little attention as an account of the truth-conditions for knowledge ascriptions and denials—especially compared to views like classical, moderate invariantism and epistemic contextualism. In this paper, it is argued that the ambiguity theory of knows has an advantage over both (...) classical, moderate invariantism and epistemic contextualism. This advantage is that it is the only one of these views that can account for “diverging knowledge responses without inconsistency” —i.e., cases in which, for the same subject S and proposition p, one and the same speaker says truly “S knows p” but instead could have truly said “S does not know p” and vice versa. This paper argues both for the existence of DRWI scenarios and the ability of the ambiguity theory of knows to best explain their existence. (shrink)

In this dissertation, I argue that vagueness is a metaphysical phenomenon---that properties and objects can be vague---and propose a trivalent theory of vagueness meant to account for the vagueness in the world. In the first half, I argue against the theories that preserve classical logic. These theories include epistemicism, contextualism, and semantic nihilism. My objections to these theories are independent of considerations of the possibility that vagueness is a metaphysical phenomenon. However, I also argue that these theories are not capable (...) of accommodating metaphysical vagueness. As I move into my positive theory, I first argue for the possibility of metaphysical vagueness and respond to objections that charge that the world cannot be vague. One of these objections is Gareth Evans' much-disputed argument that vague identities are impossible. I then describe what I call the logic of states of affairs. The logic of states of affairs has as its atomic elements states of affairs that can obtain, unobtain, or be indeterminate. Finally, I argue that the logic of states of affairs is a better choice for a theory of vagueness than other logics that could accommodate metaphysical vagueness such as supervaluationism and degree theories. Preference should be given to the logic of states of affairs because it provides a better explanation of higher-order vagueness and does a better job of matching our ordinary understandings of logical operators than supervaluationism does and because it provides a more general account of indeterminacy than the account given by degree theories. Advisor: Reina Hayaki. (shrink)

This essay explores the thesis that for vague predicates, uncertainty over whether a borderline instance x of red/large/tall/good is to be understood as practical uncertainty over whether to treat x as red/large/tall/good. Expressivist and quasi-realist treatments of vague predicates due to John MacFarlane and Daniel Elstein provide the stalking-horse. It examines the notion of treating/counting a thing as F , and links a central question about our attitudes to vague predications to normative evaluation of plans to treat a (...) thing as F . The essay examines how the account applies to normatively defective or contested terms. The final section raises a puzzle about the mechanics of MacFarlane’s detailed implementation for the case of gradable adjectives. (shrink)

We expect the laws of nature that describe the universe to be exact, but what if that isn't true? In this popular science article, I discuss the possibility that some candidate fundamental laws of nature, such as the Past Hypothesis, may be vague. This possibility is in conflict with the idea that the fundamental laws of nature can always and faithfully be described by classical mathematics. -/- [Bibliographic note: this article is featured on the magazine website under a different title (...) as "The fuzzy law that could break the idea of a mathematical universe" and on the magazine cover as "The Flaw at the Heart of Reality: Why precise mathematical laws can never fully explain the universe." It is a popular version of the article "Nomic Vagueness" that can be found on arXiv: 2006.05298.]. (shrink)

Frege supposedly believes that vague predicates have no referent (Bedeutung). But given other things he evidently believes, such a position would seem to commit him to a suspect nihilism according to which assertoric sentences containing vague predicates are neither true nor false. I argue that we have good reason to resist ascribing to Frege the view that vague predicates have no Bedeutung and thus good reason to resist seeing him as committed to the suspect nihilism. In the process, I call (...) attention to several under-appreciated texts in which Frege suggests that a vague predicate, though lacking a Bedeutung of its own, can come to acquire a Bedeutung in certain contexts. The upshot of this suggestion is that vague predicates can serve the purposes of ordinary communication quite well, even if they are useless for logical purposes. (shrink)

In this paper, I will first try to provide a new argument in favour of the contextualist position on the semantics/pragmatics divide. I will argue that many puns, notably multi-stable ones, cannot be dealt with in the non-contextualist way, i.e., as displaying a phenomenon that effectively involves wide context, the concrete situation of discourse, yet only in a pre-, or at least inter-, semantic sense. For, insofar as they involve ambiguous utterances rather than ambiguous sentences, these puns show that the (...) wide context affecting them has a semantic role: it provides many truth-conditions for a single utterance. Moreover, I will try to show that the contextualist can provide a unitary account of the general phenomenon of puns. On the one hand, this account explains multi-stable puns as well as those puns the non-contextualist claims to deal with successfully, i.e., the ones involving a speaker-induced removal of a well-grounded misunderstanding. On the other hand, it also explains zeugmatic puns, i.e., those involving an ‘impossible’ meaning. (shrink)

ABSTRACT: This paper argues that the so-called paradoxes of higher-order vagueness are the result of a confusion between higher-order vagueness and the distribution of the objects of a Sorites series into extensionally non-overlapping non-empty classes.

Recently, research on uncertainty modeling is progressing rapidly and many essential and breakthrough stud ies have already been done. There are various ways such as fuzzy, intuitionistic and neutrosophic sets to handle these uncertainties. Although these concepts can handle incomplete information in various real-world issues, they cannot address all types of uncertainty such as indeterminate and inconsistent information. Also, plithogenic sets as a generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets, which is a set whose elements are (...) characterized by many attributes’ values. In this paper, our aim is to demonstrate and review the history of fuzzy, intuitionistic and neutrosophic sets. For this purpose, we divided the paper as: section 1. History of Fuzzy Sets, section 2. History of Intuitionistic Fuzzy Sets and section 3. History of Neutrosophic Theories and Applications, section 4. History of Plithogenic Sets. (shrink)

A challenge faced by defenders of the precautionary principle is to clarify when the evidence that a harmful event might occur suffices to regard this prospect as a real possibility. Plausible versions of the principle must articulate some epistemic threshold, orde minimisrequirement, which specifies when precautionary measures are justified. Critics have argued that formulating such a threshold is problematic in the context of the precautionary principle. First, this is because the precautionary principle appears to be ambiguous about the distinction between (...) risk and uncertainty: should the principle merely be invoked when evidential probabilities are absent, or also when probabilities have low epistemic credentials? Secondly, defenders of the precautionary principle face an aggregation puzzle: in judging whether or not thede minimisrequirement has been met, how should first-order evidential probabilities and their second-order epistemic standing be aggregated? This article argues that the ambiguity can be resolved, and the epistemological puzzle can be solved. Focusing on decisions in the context of climate uncertainty, I advance a version of the precautionary principle that serves as a plausible decision rule, to be adopted in situations where its main alternative—cost–benefit analysis—does not deliver. (shrink)

Kilimanjaro is an example of what some philosophers would call a ‘vague object’: it is only roughly 5895 m tall, its weight is not precise and its boundaries are fuzzy because some particles are neither determinately part of it nor determinately not part of it. It has been suggested that this vagueness arises as a result of semantic indecision: it is because we didn’t make up our mind what the expression “Kilimanjaro” applies to that we can truthfully say such things (...) as “It is indeterminate whether this particle is part of Kilimanjaro”. After reviewing some of the limitations of this approach, I will propose an alternative account, based on a new semantic relation—multiple reference—capable of holding in a one-many pattern between a term and several objects in the domain. I will explain how multiple reference works, what differentiates it from plural reference and how it might be used to accommodate at least some aspects of our ordinary discourse about vague objects. (shrink)

This paper began life as a short section of a more general paper about non-classical mereologies. In that paper I had a mereological theory that I wanted to show could be applied to all sorts of different metaphysical positions — notably, to those positions that believe in mereological vagueness in re — in “vague individuals”. To do that I felt I first had to dispatch the leading rival theory of vague individuals, which is due to Peter van Inwa-gen, and holds (...) that the part-whole relation admits of degrees. It seemed to me that this theory had a serious technical problem, or at best a serious gap. I sat down to write a paragraph or two highlighting the gap, preferably showing that it couldn’t be filled. This paper is the result. (shrink)

Written as a comment on Crispin Wright's "Vagueness: A Fifth Column Approach", this paper defends a form of supervaluationism against Wright's criticisms. Along the way, however, it takes up the question what is really wrong with Epistemicism, how the appeal of the Sorities ought properly to be understood, and why Contextualist accounts of vagueness won't do.

Ethical vagueness has garnered little attention. This is rather surprising since many philosophers have remarked that the science of ethics lacks the precision that other fields of inquiry have. Of the few philosophers who have discussed ethical vagueness the majority have focused on the implications of vagueness for moral realism. Because the relevance of ethical vagueness for other metaethical positions has been underexplored, my aim in this paper is to investigate the ramifications of ethical vagueness for expressivism. Ultimately, I shall (...) argue that expressivism does not have the resources to adequately account for ethical vagueness, while cognitivism does. This demonstrates an advantage that cognitivism holds over expressivism. (shrink)

Neutrosophy has been introduced some years ago by Florentin Smarandache as a new branch of philosophy dealing with “the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra”. A variety of new theories have been developed on the basic principles of neutrosophy: among them is neutrosophic logics, a family of many-valued systems that can be regarded as a generalization of fuzzy logics. In this paper we present a critical introduction to neutrosophic logics, focusing on (...) the problem of defining suitable neutrosophic propositional connectives and discussing the relationship between neutrosophic logics and other well-known frameworks for reasoning with uncertainty and vagueness, such as (intuitionistic and interval-valued) fuzzy systems and Belnap’s logic. (shrink)

Experimental results on the Ellsberg paradox typically reveal behavior that is commonly interpreted as ambiguity aversion. The experiments reported in the current paper find the objective probabilities for drawing a red ball that make subjects indifferent between various risky and uncertain Ellsberg bets. They allow us to examine the predictive power of alternative principles of choice under uncertainty, including the objective maximin and Hurwicz criteria, the sure-thing principle, and the principle of insufficient reason. Contrary to our expectations, the principle (...) of insufficient reason performed substantially better than rival theories in our experiment, with ambiguity aversion appearing only as a secondary phenomenon. (shrink)

It is common to think that what theory of linguistic vagueness is correct has implications for debates in philosophy of law. I disagree. I argue that the implications of particular theories of vagueness on substantive issues of legal theory and practice are less far-reaching than often thought. I focus on four putative implications discussed in the literature concerning (i) the value of vagueness in the law, (ii) the possibility and value of legal indeterminacy, (iii) the possibility of the rule of (...) law, and (iv) strong discretion. I conclude with some methodological remarks. Delineating questions about conventional meaning, the metaphysics/metasemantics of (legal) content determination, and norms of legal interpretation and judicial practice can motivate clearer answers and a more refined understanding of the space of overall theories of vagueness, interpretation, and law. (shrink)

The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to the (...) other, each intermediate stage constituting an overlap in certain proportion of both contraries. Hence, degrees in the possession of a property give rise to simple contradictions. The reason why I have chosen those two questions is that they provide the main philosophical motivation for a particular brand of an infinite valued and paraconsistent logic. I will claim that Classical logic (CL) is not adequate to handle fuzzy situations, and, being deficient, is in need of being expanded to make room for degrees of truth and weak contradictions. One can hardly deny the importance of the debate, since what is ultimately at stake is what the limits of truth, rationality, intelligibility and possibility are. The main disciplines within which the research moves are the philosophy of language, philosophy of logic, and ontology. (shrink)

Artificial Psychology (AP) is a highly multidisciplinary field of study in psychology. AP tries to solve problems which occur when psychologists do research and need a robust analysis method. Conventional statistical approaches have deep rooted limitations. These approaches are excellent on paper but often fail to model the real world. Mind researchers have been trying to overcome this by simplifying the models being studied. This stance has not received much practical attention recently. Promoting and improving artificial intelligence helps mind researchers (...) to find a holistic model of mental models. This development achieves this goal by using multiple perspectives and multiple data sets together with interactive, and realistic models. In this book, the methodology of approximate inference in psychological research from a theoretical and practical perspective has been considered. Quantitative variable-oriented methodology and qualitative case-oriented methods are both used to explain the set-oriented methodology and this book combines the precision of quantitative methods with information from qualitative methods. This is a book that many researchers can use to expand and deepen their psychological research and is a book which can be useful to postgraduate students. The reader does not need an in-depth knowledge of mathematics or statistics because statistical and mathematical intuitions are key here and they will be learned through practice. What is important is to understand and use the new application of the methods for finding new, dynamic and realistic interpretations. This book incorporates theoretical fuzzy inference and deep machine learning algorithms in practice. This is the kind of book that we wished we had had when we were students. This book covers at least some of the most important issues in mind research including uncertainty, fuzziness, continuity, complexity and high dimensionality which are inherent to mind data. These are elements of artificial psychology. This book implements models using R software. (shrink)

The objective of the paper is to implement and validate diagnosis in the medical field via refined neutrosophic fuzzy logic (RNFL). As such, we have proposed a Max-Min composition (MMC) method in RNFL. This method deals with the diagnosis under certain constraints like uncertainty and indeterminacy. Further, we have considered the diagnosis problems to validate the sensitivity analysis of the novel multi attribute decision-making technique. Finally, we gave the graphical representations and compared the obtained results with other existing measures (...) in refined neutrosophic fuzzy sets. (shrink)

This dissertation looks at a set of interconnected questions concerning the foundations of probability, and gives a series of interconnected answers. At its core is a piece of old-fashioned philosophical analysis, working out what probability is. Or equivalently, investigating the semantic question of what is the meaning of ‘probability’? Like Keynes and Carnap, I say that probability is degree of reasonable belief. This immediately raises an epistemological question, which degrees count as reasonable? To solve that in its full generality would (...) mean the end of human inquiry, so that won’t be attempted here. Rather I will follow tradition and merely investigate which sets of partial beliefs are coherent. -/- The standard answer to this question, what is commonly called the Bayesian answer, says that degrees of belief are coherent iff they form a probability function. I disagree with the way this is usually justified, but subject to an important qualification I accept the answer. The important qualification is that degrees of belief may be imprecise, or vague. Part one of the dissertation, chapters 1 to 6, looks largely at the consequences of this qualification for the semantic and epistemological questions already mentioned. It turns out that when we allow degrees of belief to be imprecise, we can discharge potentially fatal objections to some philosophically attractive theses. Two of these, that probability is degree of reasonable belief and that the probability calculus provides coherence constraints on partial beliefs, have been mentioned. Others include the claim, defended in chapter 4, that chance is probability given total history. -/- As well as these semantic and epistemological questions, studies of the foundations of probability usually include a detailed discussion of decision theory. For reasons set out in chapter 2, I deny we can gain epistemological insights from decision theory. Nevertheless, it is an interesting field to study on its own, and it might be expected that there would be decision theoretic consequences of allowing imprecise degrees of belief. As I show in part two, this expectation seems to be mistaken. Chapter 9 shows that there aren’t interesting consequences of this theory for decision theory proper, and chapters 10 and 11 show that Keynes’s attempt to use imprecision in degrees of belief to derive a distinctive theory of interest rates is unsound. -/- Chapters 7 and 8 provide a link between these two parts. In chapter 7 I look at some previous philosophical investigations into the effects of imprecision. In chapter 8 I develop what I take to be the best competitor to the theory defended here – a constructivist theory of probability. On this view degrees of belief are precise, but the relevant coherence constraint is a constructivist probability calculus. This view is, I think, mistaken, but the calculus has some intrinsic interest, and there are at least enough arguments for it to warrant a chapter-length examination. (shrink)

In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and more sensitive evaluations are made by (...) a decision maker in decision making problems compared to IFVNSs. In other words, such sets enable a decision maker to evaluate the degrees of the truth, the indeterminacy and the falsity as PFVs to model the uncertainty in the evaluations. (shrink)

Symmetry in biological and physical systems is a product of self-organization driven by evolutionary processes, or mechanical systems under constraints. Symmetry-based feature extraction or representation by neural networks may unravel the most informative contents in large image databases. Despite significant achievements of artificial intelligence in recognition and classification of regular patterns, the problem of uncertainty remains a major challenge in ambiguous data. In this study, we present an artificial neural network that detects symmetry uncertainty states in human observers. (...) To this end, we exploit a neural network metric in the output of a biologically inspired Self- Organizing Map Quantization Error (SOM-QE). Shape pairs with perfect geometry mirror symmetry but a non-homogenous appearance, caused by local variations in hue, saturation, or lightness within and/or across the shapes in a given pair produce, as shown here, a longer choice response time (RT) for “yes” responses relative to symmetry. These data are consistently mirrored by the variations in the SOM-QE from unsupervised neural network analysis of the same stimulus images. The neural network metric is thus capable of detecting and scaling human symmetry uncertainty in response to patterns. Such capacity is tightly linked to the metric’s proven selectivity to local contrast and color variations in large and highly complex image data. (shrink)

Kuhn’s view of science is as follows. Science involves two key phases: normal and extraordinary. In normal science, disciplinary matrices (DMs) are large and pervasive. DMs involve “beliefs, values, techniques, and so on shared by the members of a given community” (Kuhn 1996, 175). “And so on” is regrettably vague, but Kuhn (1977, 1996) mentions three other key elements: symbolic generalizations (such as F=dp/dt), models (such as Bohr’s atomic model), and exemplars. These components of DMs overlap somewhat. For instance, symbolic (...) generalizations may feature in techniques and beliefs, and models may exhibit values. To be a (genuine) scientist, in the normal science phase, is to puzzle solve within the boundaries of the DM. It is to buy into the ruling dogma (Kuhn 1963) and to accept that “failure to achieve a solution discredits only the scientist ... ‘It is a poor carpenter who blames his tools’” (Kuhn 1996, 80). Puzzle solving involves a wide variety of activities, including. (shrink)

Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than forcing their unification. In this paper, we introduce nested sequent calculi for propositional standpoint logics---proof systems that manipulate trees whose nodes are multisets of formulae---and show how to automate standpoint reasoning by means of non-deterministic proof-search algorithms. To obtain worst-case complexity-optimal proof-search, we introduce a novel technique in the context (...) of nested sequents, referred to as "coloring," which consists of taking a formula as input, guessing a certain coloring of its subformulae, and then running proof-search in a nested sequent calculus on the colored input. Our technique lets us decide the validity of standpoint formulae in CoNP since proof-search only produces a partial proof relative to each permitted coloring of the input. We show how all partial proofs can be fused together to construct a complete proof when the input is valid, and how certain partial proofs can be transformed into a counter-model when the input is invalid. These "certificates" (i.e. proofs and counter-models) serve as explanations of the (in)validity of the input. (shrink)

This chapter discusses the defence of metaphysical indeterminacy by Elizabeth Barnes and Robert Williams and discusses a classical and bivalent theory of such indeterminacy. Even if metaphysical indeterminacy arguably is intelligible, Barnes and Williams argue in favour of it being so and this faces important problems. As for classical logic and bivalence, the chapter problematizes what exactly is at issue in this debate. Can reality not be adequately described using different languages, some classical and some not? Moreover, it is argued (...) that the classical and bivalent theory of Barnes and Williams does not avoid the problems that arise for rival theories. (shrink)

ABSTRACT: Stewart Shapiro recently argued that there is no higher-order vagueness. More specifically, his thesis is: (ST) ‘So-called second-order vagueness in ‘F’ is nothing but first-order vagueness in the phrase ‘competent speaker of English’ or ‘competent user of “F”’. Shapiro bases (ST) on a description of the phenomenon of higher-order vagueness and two accounts of ‘borderline case’ and provides several arguments in its support. We present the phenomenon (as Shapiro describes it) and the accounts; then discuss Shapiro’s arguments, arguing that (...) none is compelling. Lastly, we introduce the account of vagueness Shapiro would have obtained had he retained compositionality and show that it entails true higher-order vagueness. (shrink)

This article provides an intuitive semantic account of a new logic for comparisons (CL), in which atomic statements are assigned both a classical truth-value and a “how much” value or extension in the range [0, 1]. The truth-value of each comparison is determined by the extensions of its component sentences; the truth-value of each atomic depends on whether its extension matches a separate standard for its predicate; everything else is computed classically. CL is less radical than Casari’s comparative logics, in (...) that it does not allow for the formation of comparative statements out of truth-functional molecules. It is argued that CL provides a better analysis of predicate vagueness than classical logic, fuzzy logic or supervaluation theory. (shrink)

This article argues that resolutions to the sorites paradox offered by epistemic and supervaluation theories fail to adequately account for vagueness. After explaining the paradox, I examine the epistemic theory defended by Timothy Williamson and discuss objections to his semantic argument for vague terms having precise boundaries. I then consider Rosanna Keefe's supervaluationist approach and explain why it fails to accommodate the problem of higher-order vagueness. I conclude by discussing how fuzzy logic may hold the key to resolving the sorites (...) paradox without positing indefensible borders to the correct application of vague terms. (shrink)

At the centenary of Frank H. Knight’s Risk, Uncertainty, and Profit (1921), we explore the continuing relevance of Knightian uncertainty to the theory and practice of entrepreneurship. There are three challenges facing such assessment. First, RUP is complex and difficult to interpret. The key but neglected element of RUP is that Knight’s account is not solely about risk and uncertainty as states of nature, but about how an agent’s beliefs about uncertain outcomes and confidence in those beliefs (...) guide their choices. Second, RUP is Knight’s only effort in this area. His subsequent career led elsewhere, so he did not engage with subsequent interpretations of this work. Third, much of the current literature emphasizes that decisions must be different under the two states of nature with a consequent misunderstanding of entrepreneurial agency. This paper addresses each challenge in sequence. First, we explicate Knight’s (1921) approach and explain why that approach is murky. Second, as a complement to Knight’s interpretation, we examine Frank P. Ramsey’s approach to subjective probabilities to help clarify Knight’s murky approach. What links Knight and Ramsey is a shared pragmatism about entrepreneurial agency under uncertainty that depends upon the beliefs about, and confidence in, their judgments of possible outcomes. This Knight-Ramsey approach does not require actor’s behaviors to be determined by the class of uncertain environment (whether risk, uncertainty, or ambiguity) they face. We focus on the response by the entrepreneur to the existence of uncertainty in all its forms. We argue that this reductive account provides a foundation to examine common problems in management, including managerial hubris, the interaction between entrepreneurs and venture capitalists, and the need for experimentation (such as prototyping and market research) in advance of new product and venture launches. Third, we critique current literature that favors epistemic purism about the ontology of risk and uncertainty and ignores Knight-Ramsey pragmatism in meeting uncertainty, such as using formal and informal institutions for uncertainty mitigation. Our account locates Frank Knight’s subtleties in entrepreneurial behavior firmly in the literature on entrepreneurial agency a century later. (shrink)

It is outlined the possibility to extend the quantum formalism in relation to the requirements of the general systems theory. It can be done by using a quantum semantics arising from the deep logical structure of quantum theory. It is so possible taking into account the logical openness relationship between observer and system. We are going to show how considering the truth-values of quantum propositions within the context of the fuzzy sets is here more useful for systemics. In conclusion we (...) propose an example of formal quantum coherence. (shrink)

In this paper, I will be primarily concerned with moral issues regarding future people and the environment. When it comes to the future, we have deontological and epistemic limitations. The closer to the present, the higher the certainty and the knowledge we have about facts. Thus, when we intend to find moral clarity regarding a future scenario, we deal with an inverse relation between certainty and time. The main problem is that most ways of dealing with moral issues about future (...) scenarios do not address this relation, and rather focus on things that seem to simplify and clarify the uncertainties of the future. In response to this, I propose a different approach, one that operates neutrally and timelessly dealing with the uncertainties of the future while providing moral groundings that can help to clarify the future’s state of moral vagueness. (shrink)

Stewart Shapiro’s book develops a contextualist approach to vagueness. It’s chock-full of ideas and arguments, laid out in wonderfully limpid prose. Anyone working on vagueness (or the other topics it touches on—see below) will want to read it. According to Shapiro, vague terms have borderline cases: there are objects to which the term neither determinately applies nor determinately does not apply. A term determinately applies in a context iff the term’s meaning and the non-linguistic facts determine that they do. The (...) non-linguistic facts include the “external” context: “comparison class, paradigm cases, contrasting cases, etc.” (33) But external-contextsensitivity is not what’s central to Shapiro’s contextualism. Even fixing external context, vague terms’ (anti-)extensions exhibit sensitivity to internal context: the decisions of competent speakers. According to Shapiro’s open texture thesis, for each borderline case, there is some circumstance in which a speaker, consistently with the term’s meaning and the non-linguistic facts, can judge it to fall into the term’s extension and some circumstance in which the speaker can judge it to fall into the term’s anti-extension: she can “go either way.” Moreover, borderline sentences are Euthyphronically judgment- dependent: a competent speaker’s judging a borderline to fall into a term’s (anti- )extension makes it so. For Shapiro, then, a sentence can be true but indeterminate: a case left unsettled by meaning and the non-linguistic facts (and thus indeterminate, or borderline) may be made true by a competent speaker’s judgment. Importantly, among the non-linguistic facts that constrain speakers’ judgments (at least in the cases Shapiro cares about) is a principle of tolerance: for all x and y, if x and y differ marginally in the relevant respect (henceforth, Mxy), then if one competently judges Bx, one cannot competently judge y in any other manner in the same (total) context.1 This does not require that one judge By: one might not consider the matter at all.. (shrink)

Communication facilitates coordination, but coordination might fail if there's too much uncertainty. I discuss a scenario in which vagueness-driven uncertainty undermines the possibility of publicly sharing a belief. I then show that asserting an epistemic modal sentence, 'Might p', can reveal the speaker's uncertainty, and that this may improve the chances of coordination despite the lack of a common epistemic ground. This provides a game-theoretic rationale for epistemic modality. The account draws on a standard relational semantics for (...) epistemic modality, Stalnaker's theory of assertion as informative update, and a Bayesian framework for reasoning under uncertainty. (shrink)

Abstract: We propose a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this semantic view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We provide a new formulation of these ideas in terms of a theory of granular partitions. We show that this (...) theory provides a general framework within which we can understand the relation between vague terms and concepts and the corresponding crisp portions of reality. We also sketch how it might be possible to formulate within this framework a theory of vagueness which dispenses with the notion of truth-value gaps and other artifacts of more familiar approaches. Central to our approach is the idea that judgments about reality involve in every case (1) a separation of reality into foreground and background of attention and (2) the feature of granularity. On this basis we attempt to show that even vague judgments made in naturally occurring contexts are not marked by truth-value indeterminacy. We distinguish, in addition to crisp granular partitions, also vague partitions, and reference partitions, and we explain the role of the latter in the context of judgments that involve vagueness. We conclude by showing how reference partitions provide an effective means by which judging subjects are able to temper the vagueness of their judgments by means of approximations. (shrink)

In ‘Towards a Solution to the Sorites Paradox’, Graham Priest gives us a new account of the sorites based on fuzzy logic. The novelty lies in the suggestion that truth-value assignments should themselves be treated as fuzzy objects, i.e., objects about which we can make fuzzy identity statements. I argue that Priest’s solution does not have the explanatory force that Priest advocates. That is, it does not explain why we find the existence of a cut-off point counter-intuitive. I also argue (...) that this sort of explanation calls for a general theory that goes beyond the special case of linguistic vagueness, for the phenomenon is at bottom not linguistic. (shrink)

I explain in what sense the structure of space and time is probably vague or indefinite, a notion I define. This leads to the mathematical representation of location in space and time by a vague interval. From this, a principle of complementary inaccuracy between spatial location and velocity is derived, and its relation to the Uncertainty Principle discussed. In addition, even if the laws of nature are deterministic, the behaviour of systems will be random to some degree. These and (...) other considerations draw classical physics closer to Quantum Mechanics. An arrow of entropy is also derived, given an arrow of time. Lastly, chaos is given an additional, objective meaning. (shrink)

There has been much debate regarding the 'double-effect' of sedatives and analgesics administered at the end-of-life, and the possibility that health professionals using these drugs are performing 'slow euthanasia.' On the one hand analgesics and sedatives can do much to relieve suffering in the terminally ill. On the other hand, they can hasten death. According to a standard view, the administration of analgesics and sedatives amounts to euthanasia when the drugs are given with an intention to hasten death. In this (...) paper we report a small qualitative study based on interviews with 8 Australian general physicians regarding their understanding of intention in the context of questions about voluntary euthanasia, assisted suicide and particularly the use of analgesic and sedative infusions (including the possibility of voluntary or non-voluntary 'slow euthanasia'). We found a striking ambiguity and uncertainty regarding intentions amongst doctors interviewed. Some were explicit in describing a 'grey' area between palliation and euthanasia, or a continuum between the two. Not one of the respondents was consistent in distinguishing between a foreseen death and an intended death. A major theme was that 'slow euthanasia' may be more psychologically acceptable to doctors than active voluntary euthanasia by bolus injection, partly because the former would usually only result in a small loss of 'time' for patients already very close to death, but also because of the desirable ambiguities surrounding causation and intention when an infusion of analgesics and sedatives is used. The empirical and philosophical implications of these findings are discussed. (shrink)

Like many other philosophical disciplines, ethics is sometimes highly abstract. And many key notions of the discipline are vague, ambiguous or both. Abstractness, vagueness, and ambiguity invite confusion. My objective in this paper is to draw attention to a serious problem that, despite being widespread, has so far remained largely unrecognized: the confusion of different questions in teaching ethics. This confusion occurs, for example, when a philosopher’s viewpoint is presented as an answer to one question, but in fact, the philosopher (...) is addressing a different question with that viewpoint. In the first part of this paper, I will present and clarify several ethical questions that are often confused, and point out damaging consequences that the confusion of such questions entails. In the second part, I will demonstrate the confusion of ethical questions by drawing attention to cases of confused teaching of Schopenhauer’s ethics. Finally, for those interested, I outline how Schopenhauer’s ethics could be taught without confusion. (shrink)

Sentencing outcomes turn on moral and evaluative determinations. For example, a finding of “irreparable corruption” is generally a precondition for juvenile life without parole. A finding that the “aggravating factors outweigh the mitigating factors” determines whether a defendant receives the death penalty. Should such moral determinations that expose defendants to extraordinary penalties be subject to a standard of proof? A broad range of federal and state courts have purported to decide this issue “in the abstract and without reference to our (...) sentencing case law,” as the Supreme Court recently put it. Kansas v. Carr, 577 U.S. 108, 119 (2016). According to these courts, “it would mean nothing” to ask whether the defendant “deserves mercy beyond a reasonable doubt” or “more-likely-than-not deserves it” because moral questions are not “factual.” Instead, moral determinations are highly subjective “value calls” to which concepts of doubt and certainty do not intelligibly apply. -/- Implicit in these rulings is a controversial view of the nature of moral judgment. This Article traces the contours of the view and argues that it is out of step with the way the broader public thinks about morality and fails to address the issues defendants have raised. Courts should avoid wading into such controversial waters for two reasons. First, the judiciary has historically maintained neutrality on issues of significant public concern. Second, even if moral determinations are not factual, applying a standard of proof to at least some moral decisions at sentencing would change the outcome of the sentencer’s deliberations, and improve the legitimacy of the legal system. For the reasonableness of doubt depends on context; and moral questions—"are you certain the defendant deserves death?”—make salient the stakes relative to which a person should decide what to believe about ordinary empirical matters. On the resulting view, reasonable doubt in the final moral analysis is not just intelligible, but essential for correcting a bias in the structure of the bifurcated criminal trial that systematically disadvantages defendants: the tendency for de-contextualized "factual findings” in the guilt phase to control outcomes at sentencing. (shrink)

This volume consists of the invited papers presented at the 23rd International Wittgenstein Conference held in Kirchberg, Austria in August 2000. Among the topics treated are: truth, psychologism, science, the nature of rational discourse, practical reason, contextualism, vagueness, types of rationality, the rationality of religious belief, and Wittgenstein. Questions addressed include: Is rationality tied to special sorts of contexts? ls rationality tied to language? Is scientific rationality the only kind of rationality? Is there something like a Western rationality? and: Could (...) we genetically engineer human beings to be less wicked? (shrink)