Papers included:«About Properties of L-Inconsistent Theories» by Vyacheslav Moiseyev «Paraconsistent logic! » by Jean-Yves Béziau «The Logic of Lying» by Moses Òkè «Sparse Parts» by Kristie Miller «Are Functional Properties Causally Potent?» by Peter Alward «Subcontraries and the Meaning of `If…Then’» by Ronald A. Cordero «Does Frege’s Definition of Existence Invalidate the Ontological Argument?» by Piotr Labenz «Why Prisoners’ Dilemma Is Not A Newcomb Problem» by P. A. Woodward «A Paradox Concerning Science and Knowledge» by Margaret Cuonzo «Between Platonism and (...) Pragmatism: An alternative reading of Plato’s Theaetetus» by Paul F. Johnson «Blob Theory: N-adic Properties Do Not Exist» by Jeffrey Grupp. (shrink)

For centuries, the Sorites Paradox has spurred philosophers to think and argue about the problem of vagueness. This volume offers a guide to the paradox which is both an accessible survey and an exposition of the state of the art, with a chapter-by-chapter presentation of all of the main solutions to the paradox and of all its main areas of influence. Each chapter offers a gentle introduction to its topic, gradually building up to a final discussion of some open (...) problems. Students will find a comprehensive guide to the fundamentals of the paradox, together with lucid explanations of the challenges it continues to raise. Researchers will find exciting new ideas and debates on the paradox. (shrink)

I postulate that the extension of a degree adjective is fixed by implicitly accepted non-analytic reference-fixing principles (“preconceptions”) that combine appeals to paradigmatic cases with generic principles designed to expand the extension of the adjective beyond the paradigmatic range. In regular occasions of use, the paradigm and generic preconceptions are jointly satisfied and determine the existence of an extension/anti-extension pair dividing the adjective’s comparison class into two mutually exclusive and jointly exhaustive subclasses. Sorites paradoxical occasions of use are irregular (...) occasions of use in which the paradigm and generic preconceptions are not jointly satisfied. In them, the relevant degree adjective lacks an extension, and utterances of sentences containing it appearing in sorites arguments do not have truth conditions. I also postulate a probable psychology of paradigm intuitions, used in a psychological explanation of the preference for solutions of the sorites paradox on which paradigm preconceptions retain their intuitive truth-values. (shrink)

When Bertrand Russell alerted Gottlob Frege to an inconsistency in his Grundgesetze, Frege relinquished deep commitments. When Edward Evans-Pritchard alerted the Azande to an inconsistency in their beliefs about witchcraft inheritance, they did not revise their beliefs. Nor did they engage in the defensive maneuvers depicted in Plato’s dialogues. Evans-Pritchard characterized their indifference to contradiction as irrational. My historical thesis is that the ensuing anthropological debate mirrors the debate about the sorites paradox. I favor a simple explanation of this (...) parallelism: Evans-Pritchard’s witchcraft inheritance argument is a sorites argument—albeit in a form masked by the different ontologies of the Azande and Evans-Pritchard. Evans-Pritchard failed to recognize his witchcraft inheritance argument as a sorites paradox because he was witchcraft nihilist in a community of witchcraft realists. My general conjecture is that many of the irrationalities that seem distinctive of alien cultures are actually paradoxes that are universal. The irrationality of the aliens is real and profound; it is just not distinctive of those aliens or their cultures. The universality of the irrationality helps to explain Evans-Pritchard’s surprising success at understanding the Azande. Since he shares their core irrationality, Evans-Pritchard could simulate Azande thinking. Although I am attributing an anthropological illusion to Evans-Pritchard, I think it is one that coheres nicely with his compelling account of Azande. I am a conservative follower of Evans-Pritchard, trying to debug his research programme. I endorse all of his central doctrines and I rely on his insights. (shrink)

The first part of the chapter surveys some of the main ways in which the Sorites Paradox has figured in arguments in practical philosophy in recent decades, with special attention to arguments where the paradox is used as a basis for criticism. Not coincidentally, the relevant arguments all involve the transitivity of value in some way. The second part of the chapter is more probative, focusing on two main themes. First, I further address the relationship between the Sorites (...) Paradox and the main arguments discussed in the first part, by elucidating in what sense they rely on (something like) tolerance principles. Second, I briefly discuss the prospect of rejecting the respective principles, aiming to show that we can do so for some of the arguments but not for others. The reason is that in the latter cases the principles do not function as independent premises in the reasoning but, rather, follow from certain fundamental features of the relevant scenarios. I also argue that not even adopting what is arguably the most radical way to block the Sorites Paradox – that of weakening the consequence relation – suffices to invalidate these arguments. (shrink)

This is a discussion of Delia Fara’s theory of vagueness, and of its solution to the Sorites paradox, criticizing some of the details of the account, but agreeing that its central insight will be a part of any solution to the problem. I also consider a wider range of philosophical puzzles that involve arguments that are structurally similar to the argument of the Sorites paradox, and argue that the main ideas of her account of vagueness helps to respond (...) to some of those puzzles. (shrink)

Take any putative ordinary object which is divisible into a finite number of small units and tolerant to the loss of one of them. We can remove these units one at a time, and since our object definitely doesn’t exist when there are zero units, and since we cannot pinpoint which removal brings about this destruction, the Sorites Puzzle threatens common sense. We can rescue ordinary objects from its grip, but since independently motivated linguistic explanations of vagueness depend on (...) there being multiple candidate contents of vague terms, these efforts succeed only if there are multiple candidates that can be meant by ordinary object terms. Thus, many more objects than common sense accepts have to exist. The 'arguments from vagueness' also offer soritical reasons for object proliferation. Problematising the categories composite object and persisting thing (rather than specific object concepts), these show that either there are none of these (except simples) or every candidate for making up one, does. The latter, less revisionary alternative is plenitudinism. I defend Modally Full Plenitude, because it is three-dimensionalist and non-reductivist about de re modality – a distinct persisting object in any region, and for every modal profile satisfied by the matter in that region. (shrink)

Ethics in the tradition of Derek Parfit’s Reasons and Persons is riddled with sorites-like arguments, which lead us by what seem innocent steps to seemingly false conclusions. Take, for example, spectrum arguments for the Repugnant Conclusion that appeal to slight differences in quality of life. Several authors have taken the view that, since spectrum arguments are structurally analogous to sorites arguments, the correct response to spectrum arguments is structurally analogous to the correct response to sorites arguments. This (...) sorites analogy is here argued against. There are potential structural disanalogies between spectrum arguments and sorites arguments. But even if these arguments are relevantly structurally analogous, they differ in their content in ways that show the sorites analogy to be implausible. Two content-based disanalogies are here explored—one is inspired by Parfit’s work on reductionism, and the other involves hypersensitivity. The chapter concludes with a methodological lesson. (shrink)

Is there an interesting relation between the Preface paradox and the Sorites paradox that might be used to illuminate either or both of those paradoxes and the phenomena of rationality and vagueness with which they, respectively, are bound up? In particular, if we consider the analogy alongside a familiar response to the Preface Paradox that employs degrees of belief, does this give any support to the thought that we should adopt some kind of degree-theoretic treatment of vagueness and the (...) sorites? This chapter argues that it does not; indeed exploring the disanalogies contributes to a case against such a treatment of vagueness more generally. Among other views, it considers Edgington’s account of vagueness that employs a probabilistic structure of “verities”. It then contends that appeal to the framework of supervaluationism yields a better guide to reasoning in vague language than the degree-theoretic treatment can sustain. (shrink)

Sorites arguments employ an induction step such as ‘Small numbers have small successors’. People deduce that there must be an exception to the generalization but are reluctant to conclude that the generalization is false. My hypothesis is that the reluctance is due to the "Generic Overgeneralization Effect". Although the propounder of the sorites paradox intends the induction step to be a universal generalization, hearers assimilate universal generalizations to generic generalizations (for instance, ‘All birds fly’ tends to be remembered (...) as ‘Birds fly’). Most generic generalizations tolerate exceptions – especially when those exceptions are rare, abnormal, or difficult to imagine. Any counterexample to the induction step will have all of these features. (shrink)

What I hope to show here is that the costs of taking sorites arguments seriously, in particular the costs with respect to hopes for precise replacement are significantly greater than proponents of sorites arguments have estimated.

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)

This chapter focuses on one of the common fallacies in Western philosophy called 'sorites fallacy (SF)'. One commits the SF when claiming that because a continuum exists between two distinct categories or states of affairs, then those categories cannot truly be asserted as distinct. In addition, the SF helps us to distinguish between vagueness and relativity. Recognizing the SF is helpful in highlighting the vagueness of linguistic constructs and categorical thinking. But it serves to remind that simply because of (...) the vagueness of categories, we shouldn't render these categories as non‐existent or vacuous. While it can apply to more real‐ world issues than heaps of sand, the fallacy is best understood in its original conception. Imagine seeing a collection of sand grains upon which we claim it to not constitute a heap of sand. (shrink)

I sketch the basic problem of vagueness - the sorites paradox and propose a new solution. I try to show that the paradoxical result of the sorites arguments arises from combining different language games or representation systems without sufficient care. I propose two solutions, two types of regimentating the sorites. They do not allow an inheritance of the vague property F in the whole sequence of objects. The first introduces some quantitatively determined predicates (quantitative regimentation) and the (...) second (relational regimentation) replaces the equivalence relation between successive objects with a suitable weaker asymmetrical relation ‘is at least as much F as’ (or ‘is at most as much F as’). (shrink)

This book examines philosophical approaches to linguistic vagueness, a puzzling feature of natural language that gives rise to the ancient Sorites paradox and challenges classical logic and semantics. -/- The Sorites, or Paradox of the Heap, consists in three claims: (1) One grain of sand does not make a heap. (2) One billion grains of sand do make a heap. (3) For any two amounts of sand differing by at most one grain: either both are heaps of sand, (...) or neither one is. The third claim is rendered plausible by an initial conviction that vague predicates like ‘heap’ tolerate small changes. However, the repeated application of a tolerance principle to the second claim yields the further proposition that one grain of sand does make a heap – which contradicts claim number one. Consequently, many philosophers reject or modify tolerance principles for vague predicates. -/- Inga Bones reassesses prominent responses to the Sorites and defends a Wittgensteinian dissolution of the paradox. She argues that vague predicates are, indeed, tolerant and discusses how this finding relates to the paradox itself, to the notion of validity and to the concept of a borderline case . (shrink)

A sorites argument is a symptom of the vagueness of the predicate with which it is constructed. A vague predicate admits of at least one dimension of variation (and typically more than one) in its intended range along which we are at a loss when to say the predicate ceases to apply, though we start out confident that it does. It is this feature of them that the sorites arguments exploit. Exactly how is part of the subject of (...) this paper. The majority of philosophers writing on vagueness take it to be a kind of semantic phenomenon. If we are right, they are correct in this assumption, which is surely the default position, but they have not so far provided a satisfactory account of the implications of this or a satisfactory diagnosis of the sorites arguments. Other philosophers have urged more exotic responses, which range from the view that the fault lies not in our language, but in the world, which they propose to be populated with vague objects which our semantics precisely reflects, to the view that the world and language are both perfectly in order, but that the fault lies with our knowledge of the properties of the words we use (epistemicism). In contrast to the exotica to which some philosophers have found themselves driven in an attempt to respond to the sorites puzzles, we undertake a defense of the commonsense view that vague terms are semantically vague. Our strategy is to take fresh look at the phenomenon of vagueness. Rather than attempting to adjudicate between different extant theories, we begin with certain pre-theoretic intuitions about vague terms, and a default position on classical logic. The aim is to see whether (i) a natural story can be told which will explain the vagueness phenomenon and the puzzling nature of soritical arguments, and, in the course of this, to see whether (ii) there arises any compelling pressure to give up the natural stance. We conclude that there is a simple and natural story to be told, and we tell it, and that there is no good reason to abandon our intuitively compelling starting point. The importance of the strategy lies in its dialectical structure. Not all positions on vagueness are on a par. Some are so incredible that even their defenders think of them as positions of last resort, positions to which we must be driven by the power of philosophical argument. We aim to show that there is no pressure to adopt these incredible positions, obviating the need to respond to them directly. If we are right, semantic vagueness is neither surprising, nor threatening. It provides no reason to suppose that the logic of natural languages is not classical or to give up any independently plausible principle of bivalence. Properly understood, it provides us with a satisfying diagnosis of the sorites argumentation. It would be rash to claim to have any completely novel view about a topic so well worked as vagueness. But we believe that the subject, though ancient, still retains its power to inform and challenge us. In particular, we will argue that taking seriously the central phenomenon of predicate vagueness—the “boundarylessness” of vague predicates—on the commonsense assumption that vagueness is semantic, leads ineluctably to the view that no sentences containing vague expressions (henceforth ‘vague sentences’) are truth-evaluable. This runs counter to much of the literature on vagueness, which commonly assumes that, though some applications of vague predicates to objects fail to be truth-evaluable, in clear positive and negative cases vague sentences are unproblematically true or false. It is clarity on this, and related points, that removes the puzzles associated with vagueness, and helps us to a satisfying diagnosis of why the sorites arguments both seem compelling and yet so obviously a bit of trickery. We give a proof that semantically vague predicates neither apply nor fail-to-apply to anything, and that consequently it is a mistake to diagnose sorites arguments, as is commonly done, by attempting to locate in them a false premise. Sorites arguments are not sound, but not unsound either. We offer an explanation of their appeal, and defend our position against a variety of worries that might arise about it. The plan of the paper is as follows. We first introduce an important distinction in terms of which we characterize what has gone wrong with vague predicates. We characterize what we believe to be our natural starting point in thinking about the phenomenon of vagueness, from which only a powerful argument should move us, and then trace out the consequences of accepting this starting point. We consider the charge that among the consequences of semantic vagueness are that we must give up classical logic and the principle of bivalence, which has figured prominently in arguments for epistemicism. We argue there are no such consequences of our view: neither the view that the logic of natural languages is classical, nor any plausible principle of bivalence, need be given up. Next, we offer a diagnosis of what has gone wrong in sorites arguments on the basis of our account. We then present an argument to show that our account must be accepted on pain of embracing (in one way or another) the epistemic view of “vagueness”, i.e., of denying that there are any semantically vague terms at all. Next, we discuss some worries that may arise about the intelligibility of our linguistic practices if our account is correct. We argue none of these worries should force us from our intuitive starting point. Finally, we cast a quick glance at other forms of semantic incompleteness. (shrink)

Sorites is the paradox which exploits the tolerance of vague language to get an absurd conclusion. The present note argues that, contrary to some other approaches, formalizing the antinomy does not serve the purpose of elucidation.

An abstract mathematical theory is presented for a common variety of soritical arguments, treated here in terms of responses of a system, say, a biological organism, a gadget, or a set of normative linguistic rules, to stimuli. Any characteristic of the system's responses which supervenes on stimuli is called a stimulus effect upon the system. Classificatory sorites is about the identity of or difference between the effects of stimuli that differ 'only microscopically'. We formulate the classificatory sorites on (...) arguably the highest possible level of generality and show that the 'paradox' is dissolved on grounds unrelated to vague predicates or other linguistic issues traditionally associated with it. If stimulus effects are properly defined (i.e., they are uniquely determined by stimuli), and if the space of the stimuli is endowed with appropriate (not necessarily metric) closeness and connectedness properties, then this space must contain points in every vicinity of which, 'however small', the stimulus effect is not constant. The effects can only be 'tolerant' to very small differences between stimuli if the closeness structure that is used to define very close stimuli does not render the space of stimuli appropriately connected: in this case the 'paradox' cannot be formulated. Nor can it be formulated if the response properties considered are not true effects, i.e., if they do not supervene on stimuli. (shrink)

One way in which we might approach the challenge posed by the Sorites Paradox is considering that Sorites-susceptible predicates have several candidate extensions, or several ways in which these expressions can be made precise. For example, a candidate extension for the predicate ‘is a baby’ is the set of humans of less than two years, but also the set of those less than two years and one second, and of those less than two years and two seconds. In (...) this chapter we present and discuss two theories for vague predicates based on this idea: supervaluationism and subvaluationism. The chapter is structured in three parts. The first presents the super- and subvaluationist theories: their similarities and differences in the semantics, the resulting logics with their most characteristic features. The second reviews the super- and subvaluationist solutions to the Sorites Paradox and provides discussion on several controversies surrounding these theories. The third part introduces proof procedures for s’valuationist logics. (shrink)

On some accounts of vagueness, predicates like “is a heap” are tolerant. That is, their correct application tolerates sufficiently small changes in the objects to which they are applied. Of course, such views face the sorites paradox, and various solutions have been proposed. One proposed solution involves banning repeated appeals to tolerance, while affirming tolerance in any individual case. In effect, this solution rejects the reasoning of the sorites argument. This paper discusses a thorny problem afflicting this approach (...) to vagueness. In particular, it is shown that, on the foregoing view, whether an object is a heap will sometimes depend on factors extrinsic to that object, such as whether its components came from other heaps. More generally, the paper raises the issue of how to count heaps in a tolerance-friendly framework. (shrink)

Two philosophical questions arise about rationality in centipede games that are logically prior to attempts to apply the formal tools of game theory to this topic. First, given that the players have common knowledge of mutual rationality and common knowledge that they are each motivated solely to maximize their own profits, is there a backwards-induction argument that employs only familiar non-technical concepts about rationality, leads to the conclusion that the first player is rationally obligated to end the game at the (...) first step, is deductively valid, employs premises all of which are prima facie highly plausible, and is prima facie sound and )? Second, if there is such an argument, then is it actually sound, or is it instead defective somehow despite being prima facie sound? Addressing these two questions is our project. We present a backwards-induction argument that is prima facie sound; we argue that it is an instance of the notorious sorites paradox, and hence that the concepts of rational obligatoriness and rational permissibility are vague; and we briefly address the potential consequences of all this for the foundations of game theory and decision theory. (shrink)

We develop a mathematical theory for comparative sorites, considered in terms of a system mapping pairs of stimuli into a binary response characteristic whose values supervene on stimulus pairs and are interpretable as the complementary relations 'are the same' and 'are not the same' (overall or in some respect). Comparative sorites is about hypothetical sequences of stimuli in which every two successive elements are mapped into the relation 'are the same', while the pair comprised of the first and (...) the last elements of the sequence is mapped into 'are not the same'. Although soritical sequences of this kind are logically possible, we argue that their existence is grounded in no empirical evidence and show that it is excluded by a certain psychophysical principle proposed for human comparative judgements in a context unrelated to soritical issues. We generalize this principle to encompass all conceivable situations for which comparative sorites can be formulated. (shrink)

The sorites as a formal theory. The sorites paradox has been understood as a failure of classical logic and a way out can be found by choosing a non classical logic (fuzzy logic, for instance). We understand the sorites not as a problem of logic but of ontology, so we preserve classical logic and submit the premisses of the argument to a deeper analysis. As a result we obtain two theories for soritical arguments and enlighten the kind (...) of structure requested by these arguments. The former theory has a lattice theoretic flavor and is fitted for paradoxes like “the heap” and “the bald man”; the latter is group theoretic in character and can manage paradoxes based on observational predicates like “tall”, “red” and so on. In both cases the contradiction is derived from a larger set of hypotheses than in usual analysis and some of these hypotheses make assertions whose empirical meaning can be questioned. (shrink)

Neutralism is the broad view that philosophical progress can take place when (and sometimes only when) a thoroughly neutral, non-specific theory, treatment, or methodology is adopted. The broad goal here is to articulate a distinct, specific kind of sorites paradox (The Observational Sorites Paradox) and show that it can be effectively treated via Neutralism.

The presentation of the “dual picture of vagueness” in my earlier work is supplemented here with a number of additional considerations. I emphasize how the picture lends itself naturally to treatments of the contribution of a typical degree adjective to propositional content and to truth conditions. A number of reasonable refinements of the picture are presented, especially concerning occasions of use of a degree adjective in which a class containing a sorites series is somehow involved in content fixing, but (...) in such a way that an extension ultimately gets fixed for the predicate. I also develop the observation that standard theories of the logical and semantic paradoxes rely on the idea that the content-fixing mechanisms for the paradoxical expressions work well in general but fail in some localized cases, and that while standard theories of the sorites paradox are clearly not based on this idea at all, the dual theory is fully based on the idea. Next, I offer a few remarks on some recent theories of vagueness and the sorites that are broadly in the spirit of the dual picture, emphasizing the aspects where the latter compares favorably against those recent theories. Finally, the question whether the dual theory is statable with truth according to the theory itself is considered in more detail than in my earlier presentation. (shrink)

Taking a series of colour patches, starting with one that clearly looks red, and making each so similar in colour to the previous one that it looks the same as it, we appear to be able to show that a yellow patch looks red. I ask whether phenomenal sorites paradoxes, such as this, are subject to a unique kind of solution that is unavailable in relation to other sorites paradoxes. I argue that they do not need such a (...) solution, nor do they succumb to one. In particular, I reject the claim made by Fara and Raffman that looks the same is a transitive relation, which would allow us to solve phenomenal sorites paradoxes by denying the possibility of the required kind of sorites series. (shrink)

This paper responds to Theron Pummer’s distinction between Sorites arguments and repugnant conclusion arguments by presenting a Sorites overpopulation argument. Also I present a Sorites argument in favour of myths of genius.

One thousand stones, suitably arranged, might form a heap. If we remove a single stone from a heap of stones we still have a heap; at no point will the removal of just one stone make sufficient difference to transform a heap into something which is not a heap. But, if this is so, we still have a heap, even when we have removed the last stone composing our original structure. So runs the Sorites paradox. Similar paradoxes can be (...) constructed with any predicate which, like 'heap', displays borderline vagueness. Although I have frequently heard it said that there is no completely credible and satisfying dissolution of the paradoxes of the Sorites family; and although there is no possible approach to dissolution which has not been at least partially explored, philosophers continue glibly to use vague language as though it were entirely unproblematic. Since no argument has ever been produced which would justify our ignoring the para~doxes, this situation is extremely unsatisfactory. (shrink)

The premises that a four foot man is short and that a man one tenth of an inch taller than a short man is also short entail by universal instantiation and "modus ponens" that a seven foot man is short. The negation of the second premise seems to entail there are virtually no borderline cases of short men, While to deny the second premise and its negation conflicts with the principle of bivalence, If not excluded middle. But the paradox can (...) be dissolved without resort to degrees of truth or any non-Classical system of logic. If some true predications can be semantically uncertain in a sense suitable for defining borderline cases, The second premise can be denied without denying the vagueness of "short" or reintroducing a sorites paradox along with higher order borderline cases. (shrink)

Problems for 'precise replacements' as a way out of sorites paradoxes.

When Bertrand Russell alerted Gottlob Frege to an inconsistency in his Grundgesetze, Frege relinquished deep commitments. When Edward Evans-Pritchard alerted the Azande to an inconsistency in their beliefs about witchcraft inheritance, they did not revise their beliefs. Nor did they engage in the defensive maneuvers depicted in Plato’s dialogues. Evans-Pritchard characterized their indifference to contradiction as irrational. My historical thesis is that the ensuing anthropological debate mirrors the debate about the sorites paradox. I favor a simple explanation of this (...) parallelism: Evans-Pritchard’s witchcraft inheritance argument is a sorites argument—albeit in a form masked by the different ontologies of the Azande and Evans-Pritchard. Evans-Pritchard failed to recognize his witchcraft inheritance argument as a sorites paradox because he was witchcraft nihilist in a community of witchcraft realists. My general conjecture is that many of the irrationalities that seem distinctive of alien cultures are actually paradoxes that are universal. The irrationality of the aliens is real and profound; it is just not distinctive of those aliens or their cultures. The universality of the irrationality helps to explain Evans-Pritchard’s surprising success at understanding the Azande. Since he shares their core irrationality, Evans-Pritchard could simulate Azande thinking. Although I am attributing an anthropological illusion to Evans-Pritchard, I think it is one that coheres nicely with his compelling account of Azande. I am a conservative follower of Evans-Pritchard, trying to debug his research programme. I endorse all of his central doctrines and I rely on his insights. (shrink)

In this paper we present two new approaches for dealing with semantic paradoxes and soritical predicates based on fuzzy logic. We show that both of them have conceptual advantages over the more traditional Łukasiewicz approach, and that the second one even avoids standard proofs of ω-nconsistency.

The theory of consciousness proposed by O'Brien & Opie is open to the Sorites paradox, for it defines a consciousness system internally in terms of computationally relevant units which add up to consciousness only if sufficient in number. The Sorites effect applies on the assumed level of features.

The naive theory of vagueness holds that the vagueness of an expression consists in its failure to draw a sharp boundary between positive and negative cases. The naive theory is contrasted with the nowadays dominant approach to vagueness, holding that the vagueness of an expression consists in its presenting borderline cases of application. The two approaches are briefly compared in their respective explanations of a paramount phenomenon of vagueness: our ignorance of any sharp boundary between positive and negative cases. These (...) explanations clearly do not provide any ground for choosing the dominant approach against the naive theory. The decisive advantage of the former over the latter is rather supposed to consist in its immunity to any form of sorites paradox. But another paramount phenomenon of vagueness is higher-order vagueness: the expressions introduced in order to express in the object language the vagueness of the object language are themselves vague. Two highly plausible claims about higher-order vagueness are articulated and defended: the existence of “definitely ω ” positive and negative cases and the “radical” character of higher-order vagueness itself. Using very weak logical principles concerning vague expressions and the ‘definitely’-operator, it is then shown that, in the presence of higher-order vagueness as just described, the dominant approach is subject to higher-order sorites paradoxes analogous to the original ones besetting the naive theory, and therefore that, against the communis opinio, it does not fare substantially better with respect to immunity to any form of sorites paradox. (shrink)

Vagueness does not necessarily come in with vague predicates, nor need it be expressed by them , but undoubtedly 'vague predicates' are traditionally in the focus of main stream discussions of vagueness. In her current modal logic presentation and discussion of the Sorites paradox Susanne Bobzien[1] lists among the properties of a Sorites series a rather weak modal tolerance principle governing the 'grey zone' containing the borderline cases of the Sorites series, which later proves crucial for her (...) solution of the Sorites paradox by use of epistemic interpreted modal operators in 1st order modal logic. We suggest (for different research interest) instead a non-modal description of the switch in the grey zone (respecting tolerance), by resort to similarity sequences, thus getting tangent to two other areas of research in the field. Let's say -any way- the Sorites paradox vanishes, the Sorites series does not. (shrink)

Raúl Orayen's Lógica, significado y ontología Foot note is a profound book, a thorough inquiry into several important issues in the philosophy of logic. Raúl Orayen is one of the outstanding analytical philosophers in the Spanish speaking world. As in his other publications, he displays a masterly reasoning power. No patched up solutions in this book. Orayen is not going to let what he takes to be unsatisfactory treatments off the hook with vague considerations of their being able to cope (...) «somehow or other» with such difficulties as beset them. (shrink)

I propose a novel solution to the Sorites Paradox. The account vindicates the tolerance of vague predicates in a way that properly addresses the normativity of vagueness while avoiding sorites contradiction, by treating sorites reasoning as a type of defeasible reasoning. I show how this can be done within the setting of a nonmonotonic deontic logic. Central to the proposal is its deontic interpretation of tolerance. I draw a key distinction between two types of tolerance, based on (...) different deontic notions, and show how the account captures key differences between these types of sorites reasoning. I compare the resulting theory to various existing contextualist proposals and argue that it better accounts for the normative aspects of sorites reasoning. (shrink)

When you and I seriously argue over whether a man of seventy is old enough to count as an "old man", it seems that we are appealing neither to our own separate standards of oldness nor to a common standard that is already fixed in the language. Instead, it seems that both of us implicitly invoke an ideal, shared standard that has yet to be agreed upon: the place where we ought to draw the line. As with other normative standards, (...) it is hard to know whether such borderlines exist prior to our coming to agree on where they are. But epistemicists plausibly argue that they must exist whether we ever agree on them or not, as this provides the only logically acceptable response to the sorites paradox. This paper argues that such boundaries do typically exist as hypothetical ideals, but not as determinate features of the present actual world. There is in fact no general solution to the paradox, but attention to practice in resolving vague disagreements shows that its instances can be dealt with separately, as they arise, in many reasonable ways. (shrink)

This discusses the kind of paradox that has since become known as "the forced march sorites", here called "the transition question". The question is whether this is really a new kind of paradox, or the familiar sorites in unfamiliar garb. The author argues that resources adequate to deal with ordinary sorites are sufficient to deal with the transition question, and tentatively proposes an affirmative answer.

It is uncontroversial that, on any run through a Sorites series, a subject, at some point, switches from an ‘F’ verdict on one exhibit to a non-‘F’ verdict on the next. (Where this ‘cut-off’ point occurs tend to differ from trial to trial.) It is a fallacy to infer that there must be a cut-off point simpliciter between F items and non-F items. The transition is from firm ground to swamp. In the Sorites reasoning, some conditionals of the (...) form ‘If Item n is F, then Item n + 1 is F’ are not false but nonsensical. This solution respects boundarylessness. (shrink)

In Section 1 we describe the Sorites paradox and lay out options for a solution. In Section 2 we consider approaches which deny that all premises are true, and note that these solutions all seem open to a certain serious objection. In Section 3 we note a problem for the principle of transitivity of the conditional and present a contex- tualist resolution of the problem, according to which the “counterexamples” to transitivity involve the informal fallacy of shifting the context. (...) In Section 4 we consider the possibility of applying the contextualist resolution of the general transitivity puzzle to Sorites arguments in particular, discussing the views of Kamp, Pinkal and Soames. Our negative conclusion, developed in Section 5, is that the paradoxes can be formulated in a way that does not commit the informal fallacy: context is held fixed. In the final section, we suggest a different defense against the objection used in Section 2. (shrink)

Logical form is thought to be discovered by keeping fixed the logical constants and allowing the non-logical content in the sentence to vary. The problem of logical constants is the problem of defining what counts as a logical constant. In this paper, I will argue that the concept ’logical constant’ is vague. I demonstrate the vagueness of logical constancy by providing a sorites argument, thereby showing the sorites-susceptibility of the concept. Many prior papers in the literature on logical (...) constants hint at this vagueness, but do not explore how theories of vagueness apply to logical constants. In the second half of this paper, I do just this. I consider approaches to logical constants that resemble nihilism about vagueness and more recent theories that relativize truth to precisifications. Finally, I argue that approaches that accept the potential indeterminate status of putative logical constants are preferable to nihilism or relativism about logical constancy. (shrink)

The sorites problem often arises for wrongdoing. In cases of substance use, a father has a drink, which, by itself, does not result in alcohol addiction. But he has another drink and another, until he develops an alcoholism that results in severe harm to his wife and children. Such cases present an interesting puzzle for thinking about moral responsibility because although long-term drinking caused harm to his family, the father likely never chose to drink long-term. Instead, typical drinkers are (...) always making short-term decisions about alcohol consumption: whether one wants to have a beer now, whether one goes out with one’s buddies to the bar tonight, etc. That these individually harmless choices added up to a harmful long-term pattern of drinking was, in a sense, accidental. This article develops a framework for analyzing moral responsibility in such cases. (shrink)

Edgington has proposed a degree-theoretic account of vagueness that yields a highly elegant solution to the sorites paradox. This paper applies her account to the paradox of Theseus’ ship, which is generally classified among the paradoxes of material constitution and not as a sorites paradox.