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)

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.

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)

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)

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)

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)

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)

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)

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)

A solution to the sorites paradox is obtained by distinguishing three formats of the sorites argument and appraising them in the light of four fundamental considerations: (i) the appropriate notion of truth for the application of vague predicates to their borderline cases, (ii) a certain construal of borderline cases, (iii) a certain freedom of use of vague terms not enjoyed by non-Vague terms and (iv) the revocation of that freedom by deductive contexts.

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.

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)

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.

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)

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)

Putative resolutions of the sorites paradox in which the major premise is declared false or illegitimate, Including max black's treatment in terms of the alleged illegitimacy of vague attributions to borderline cases, Are rejected on semantical grounds. The resort to a non-Bivalent logic of representational "accuracy" with a continuum of accuracy values is shown to resolve the paradox, And the identification of accuracy values as truth values is defended as compatible with the central insight of the correspondence (...) theory of truth and with the practical legitimacy of most applications of ordinary, Bivalent logic to statements involving vague predicates. (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)

A persistent argument against the transitivity assumption of rational choice theory postulates a repeatable action that generates a significant benefit at the expense of a negligible cost. No matter how many times the action has been taken, it therefore seems reasonable for a decision-maker to take the action one more time. However, matters are so fixed that the costs of taking the action some large number of times outweigh the benefits. In taking the action some large number of times on (...) the grounds that the benefits outweigh the costs every time, the decision-maker therefore reveals intransitive preferences, since once she has taken it this large number of times, she would prefer to return to the situation in which she had never taken the action at all. We defend transitivity against two versions of this argument: one in which it is assumed that taking the action one more time never has any perceptible cost, and one in which it is assumed that the cost of taking the action, though (sometimes) perceptible, is so small as to be outweighed at every step by the significant benefit. We argue that the description of the choice situation in the first version involves a contradiction. We also argue that the reasoning used in the second version is a form of similarity-based decision-making. We argue that when the consequences of using similarity-based decision-making are brought to light, rational decision-makers revise their preferences. We also discuss one method that might be used in performing this revision. (shrink)

Informal accounts of the sorites paradox usually emphasize that the problem is one of vagueness. The paper uses the idea of fuzzy truth values to provide a formal semantics which shows precisely how sorites-Type arguments are formally invalid.

A finite chain of valid arguments can never lead from truth to falsehood. Call this the concatenation principle, or CP. Some propose to reject CP in response to the sorites paradox. I offer...

The ancient sorites paradox has important implications for metaphysics, for logic, and for semantics. Metaphysically, the paradox can be harnessed to produce a powerful argument for the claim that there cannot be vague objects or vague properties. With respect to logic, the paradox forces a choice between the highly counterintuitive ‘epistemic’ account of vagueness and the rejection of classical two-valued logic. Regarding semantics, nonclassical approaches to the logic of vagueness lead naturally to the idea that truth, (...) for vague discourse, is not direct language-world correspondence grounded in referential connections linking a statement’s basic subsentential constituents (names, predicates, the apparatus of quantification) to real objects and real properties; rather, truth is a matter of indirect correspondence between vague language and nonvague reality. (shrink)

This paper aims to establish that Sorites reasoning, a fundamental part of Parfit's work, is more destructive that he intends. I establish the form that Parfit's arguments take and then substitute premises whose acceptability to Parfit I show. The new argument demonstrates an eliminativism or immaterialism concerning persons which Parfit must find repugnant.

Some issues raised by the notion of surveyability and how it is represented mathematically are explored. Wright considers the sense in which the positive integers are surveyable and suggests that their structure will be a weakly finite, but weakly infinite, totality. One way to expose the incoherence of this account is by applying Wittgenstein's distinction between intensional and extensional to it. Criticism of the idea of a surveyable proof shows the notion's lack of clarity. It is suggested that this concept (...) should be replaced by that of a feasible operation, as strict finitism aims to understand the boundaries of legitimate mathematical knowledge. (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 main purpose of this article is an analysis of the Continuity Argument, one of the most influential arguments upon which the moral condemnation of scientific and medical practices such as embryo research and experimentation, assisted reproduction, abortion, therapeutic cloning, etc. are based. I have firstly given a very brief account of the approach that attributes the status of marker event to fertilization, identifying the Continuity Argument between other argumentation. Further, I have tried to distinguish the three possible interpretations of (...) the notion of continuity assumed in the Continuity Argument, and to isolate the most persuasive formulation of Continuity Argument. Finally, I argue that even from the most convincing philosophical and scientific interpretation of the post-fertilization continuity, it does not follow: that fertilization is a necessary determinant of moral status; that fertilization is the most reasonable determinant of moral status. In short, this article has two goals: to show that this very argument does not entail the stance that the above mentioned practices are morally impermissible; to suggest that some pragmatic strategies which treat sorites-infected paradoxes could insure a philosophically and scientifically appropriate framework for an alternative approach. (shrink)

Any discussion regarding the famous Sorites Paradox is incomplete without considering the value of contextual logic and its meta-language of vagueness. Wittgenstein, though he did not write extensively on the Sorites Paradox in particular, is deeply concerned with its supposed implications. The later Wittgenstein's treatment of logical vagueness in natural and formal languages, and his accompanying treatment of logical soundness as it applies to ordinary languages is thus of considerable help when thinking about the Sorites (...) Paradox. In this paper I pair the later Wittgenstein's treatment of meaning in context with the age-old problem, manifest in the Sorites Paradox, of what happens when we apply induction ad infinitum to a seemingly stable item in a specific, meaning-bearing lexicon. (shrink)

Typical approaches to resolving the sorites paradox attempt to show, in one way or another, that the sorites argument is not paradoxical after all. However, if one can show that the sorites is not really paradoxical, the task remains of explaining why it appears to be a paradox. Our approach begins by addressing the appearance of paradox and then explores what this means for the paradox itself. We examine the sorites from the (...) perspective of the various brain systems that are intuitively comfortable with the key features of the premises of the sorites argument. We suggest that the explicit and implicit cognitive systems are separately responsible for the initial plausibility of the categorical and inductive premises. The appearance of paradox is a function of our brain’s architecture and arises from the conflicting interactions of neurologically distinct systems. (shrink)