This dissertation explores several accounts of the intuitions speakers have concerning the truth values of utterances of sentences containing vague nouns and adjectives. While some semanticists have attempted to account for these intuitions with multi-valued logics and supervaluation theories of truth, I focus on how utterances of vague sentences affect hearers' beliefs. ;Following a critique of the major semantical accounts of vagueness, I propose a formal theory of how beliefs are revised following utterances of sentences of the form X is (...) A, X is A and B, and X is A and not A, where A and B are vague scalar adjectives. Formally, a hearer's beliefs are represented as a set of weighted sentences, and the information conveyed by a speaker's utterance is represented as a set of weighted conditionals. When a speaker utters a sentence, a function on these sets yields the hearer's revised beliefs. I derive from this theory a criterion for proper assertability: a sentence is properly assertable in a given context if the maximum information loss that could obtain between competent discourse participants is less than some threshold. I argue that this criterion often predicts the truth-value judgements competent speakers make which violate the basic rules of logic. I extend these theories to utterances of sentences containing vague non-scalar nouns. ;In the second half of the dissertation, I propose two semantic accounts of vagueness. One incorporates the assertability criterion into its definition of truth. The other is independent of it. The former accounts for a large set of intuitions concerning the truth values of utterances of vague sentences. The latter accounts for only a subset of those intuitions, leaving the rest to be explained independently by the theory of proper assertability. ;I conclude with brief discussions of the Sorites Paradox and the experimental data obtained by Tversky and Kahneman which purport to demonstrate people's poor intuitions concerning the probabilities of conjunctions. (shrink)

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)

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)

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)

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)

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)

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)

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)

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)

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.

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 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)

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)

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)

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.

A recent article by Jeff Kochan contains a discussion of modus ponens that among other thing alleges that the paradox of the heap is a counterexample to it. In this note I show that it is the conditional major premise of a modus ponens inference, rather than the rule itself, that is impugned. This premise is the contrapositive of the inductive step in the principle of mathematical induction, confirming the widely accepted view that it is the vagueness of natural language (...) predicates, not modus ponens , that is challenged by Sorites. (shrink)

The sorites paradox receives its most sophisticated early modem discussion in Leibniz’s writings. In an important early document Leibniz holds that vague terms have sharp boundaries of application, but soon thereafter he comes to adopt a form of nihilism aboutvagueness: and it later proves to be his settled view that vagueness results from semantical indeterminacy. The reason for this change of mind is unclear, and Leibniz does not appear to have any grounds for it. I suggest that his various (...) treatments of the sorites do notspring from a single integrated view of vagueness, and that his early position reflects a mercenary interest in the sorites paradox---an interest to use the sorites to reach a conclusion in metaphysics rather than to examine vagueness as a subject to be understood in itsown right. The later nihilist stance reflects Leibniz’s own (if undefended) attitude towards vagueness. (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)

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)

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)

I argue that, contrary to widespread philosophical opinion, phenomenal indiscriminability is transitive. For if it were not transitive, we would be precluded from accepting the truisms that if two things look the same then the way they look is the same and that if two things look the same then if one looks red, so does the other. Nevertheless, it has seemed obvious to many philosophers (e.g. Goodman, Armstrong and Dummett) that phenomenal indiscriminability is not transitive; and, moreover, that this (...) non-transitivity is straightforwardly revealed to us in experience. I show this thought to be wrong. All inferences from the character of our experience to the non-transitivity of indiscriminability involve either a misunderstanding of continuity, a mistaken interpretation of the idea that we have limited powers of discrimination, or tendentious claims about what our experience is really like; or such inferences are based on inadequately supported premisses, which though individually plausible are jointly implausible. (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)

I defend contextualist solutions to the sorites paradox (according to which solutions vague terms are indexicals) from a recent objection raised by Jason Stanley. Stanley's argument depends on the claim that indexical expressions always have invariant interpretations in "Verb Phrase" ellipsis. I argue that this claim is false.

In 1987, Crispin Wright argued that degree-theoretic solutions to the Sorites paradox fail because the solutions do not work when the paradox is restated using a conjunctive major premise. I show that Wright is incorrect: degree-theoretic solutions also work when the paradox is stated with a conjunctive major premise.

Rationing is an unavoidable mechanism for reining in healthcare costs. It entails establishing cutoff points that distinguish between what is and is not offered or available to patients. When the resource to be distributed is defined by vague and indeterminate terms such as “beneficial,” “effective,” or even “futile,” the ability to draw meaningful boundary lines that are both ethically and medically sound is problematic. In this article, I draw a parallel between the challenges posed by this problem and the ancient (...) Greek philosophical conundrum known as the “sorites paradox.” I argue, like the paradox, that the dilemma is unsolvable by conventional means of logical analysis. However, I propose another approach that may offer a practical solution that could be applicable to real-life situations in which cutoffs must be decided (such as rationing). (shrink)

I develop a solution to the Sorites Paradox, according to which a concatenation of valid arguments need not itself be valid. I specify which chains of valid arguments are those that do not preserve validity: those that pass the vague boundary between cases where the relevant concept applies and cases where that concept does not apply. I also develop various criticisms of this solution and show why they fail; basically, they all involve a petitio at some stage. I criticise (...) the conviction that if every short argument in a long concatenated argument is valid, so is the long argument: it is, I argue, the result of an unjustified generalisation from the case of arguments that do not employ vague concepts (as in mathematics) to arguments that do employ them. My approach is Wittgensteinian in its “leaving everything as it is,” in its claiming that the “beginning” has been searched too far back (see paper's epigraph) and in its claim that the paradox was generated by a misapplication of a partial picture of the behaviour of arguments. I conclude my paper by comparing and contrasting my approach to the few precedents found in the vagueness literature and by answering a few additional objections that were raised there. (shrink)

In this paper I examine some difficulties with the argument presented as a topological sorites in Z. Weber and M. Colyvan, ‘A topological sorites’, Journal of Philosophy 107, 311–325. In particular, I suggest that the argument may be used to support the claim that sorites-type paradoxes cannot arise in a cohesive environment.

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)

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.

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 non-transitivity of the relation looks the same as has been used to argue that the relation has the same phenomenal character as is non-transitive—a result that jeopardizes certain theories of consciousness. In this paper, I argue against this conclusion while granting the premise by dissociating lookings and phenomenology; an idea that some might find counter-intuitive. However, such an intuition is left unsupported once phenomenology and cognitive access are distinguished from each other; a distinction that is conceptually and empirically grounded.

Since Nelson Goodman 1951, the assumption that phenomenal indiscriminability is non-transitive is taken generally for granted. Moreover, this assumption was used (by Goodman 1951, Travis 1985, Dummett 1975 and others) to argue against the existence or coherence of subjective and/or observational properties. Recently, however, the assumption has been questioned [Fara 2001] and I agree with Fara that the assumption is much more problematic than was thought, partly because it is not clear what is meant by the relation of phenomenal indiscriminability, (...) and partly because it is not clear how to interpret ideas such as continuous change, and the limitations of our power of perceptual discrimination. In this paper I will bypass the question of the transitivity of phenomenal indiscriminability. I will use only the assumption about the existence (or even the possibility of existence) of a phenomenal sorites. This assumption is less controversial, and accepted (at least the version I will use) by opponents and defenders of transitivity alike. I will argue that the incoherence of 'red' (as response-dependent or purely observational) can be derived without committing ourselves to a view on the question of transitivity, and I will use this incoherence, to argue against the account of 'red' as a response-dependent concept. (shrink)

Agent relativists about vagueness (henceforth ‘agent relativists’) hold that whether or not an object x falls in the extension of a vague predicate ‘P’ at a time t depends on the judgemental dispositions of a particular competent agent at t. My aim in this paper is to critically examine arguments that purport to support agent relativism by appealing to data from forced-march Sorites experiments. The most simple and direct versions of such forced-march Sorites arguments rest on the following (...) (implicit) premise: If competent speakers' judgements vary in a certain way, then the extensions of ‘P’ as used by these speakers must vary in the same way. This premise is in need of independent support, since otherwise opponents of agent relativism can simply reject it. In this paper, I focus on the idea that one cannot plausibly reject this premise, as that would commit one to implausible claims about linguistic competence. Against this, I argue that one can accommodate the data from forced-march Sorites experiments in a way that is compatible with a plausible picture of linguistic competence, without going agent relativist. Thus, there is reason to be sceptical of the idea that such data paired with considerations about linguistic competence can be invoked in order to lend any solid support to agent relativism. Forced-march Sorites arguments of this kind can, and should be, resisted. (shrink)

In 1987, Crispin Wright argued that degree-theoretic (fuzzy) solutions to the Sorites paradox fail because the solutions do not work when the paradox is restated using a conjunctive major premise. I show that Wright is incorrect: degree-theoretic solutions also work when the paradox is stated with a conjunctive major premise.

A person with one dollar is poor. If a person with n dollars is poor, then so is a person with n + 1 dollars. Therefore, a person with a billion dollars is poor. True premises, valid reasoning, a false a conclusion. This is an instance of the Sorites-paradox. (There are infinitely many such paradoxes. A man with an IQ of 1 is unintelligent. If a man with an IQ of n is unintelligent, so is a man with an (...) IQ of n+1. Therefore a man with an IQ of 200 is unintelligent.) Most attempts to solve this paradox reject some law of classical logic, usually the law of bivalence. I show that this paradox can be solved while holding on to all the laws of classical logic. Given any predicate that generates a Sorites-paradox, significant use of that predicate is actually elliptical for a relational statement: a significant token of "Bob is poor" means that Bob is poor compared to x, for some value of x. Once a value of x is supplied, a definite cutoff line between having and not having the paradox-generating predicate is supplied. This neutralizes the inductive step in the associated Sorites argument, and the would-be paradox is avoided. (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)

Das Hauptanliegen dieses Artikels ist, dem Argument der Kontinuität nachzugehen, weil es eines der einflussreichsten Argumente ist, auf denen die moralische Verwerfung von wissenschaftlichen und methodischen Praxen beruht. Zu diesen werden z.B. die Embryonenforschung, Experimente an Embryonen, die assistierte Reproduktion, die Abtreibung, das Klonen zu therapeutischen Zwecken u.a. gezählt. Zunächst wird eine sehr kurze Erklärung des Ansatzes gegeben, der der Fertilisation den Status eines einschneidenden Ereignisses einräumt, indem das Argument der Kontinuität als eines unter vielen identifiziert wird. Weiterhin wird versucht, (...) die drei möglichen Auslegungen des Kontinuitätsbegriffs, die im Kontinuitätsargument enthalten sind, auseinander zu halten. Es wird auch versucht, die überzeugendste philosophische und wissenschaftliche Auslegung der Postfertilisationskontinuität zu widerlegen. Denn letztlich folgt aus der philosophisch und wissenschaftlich naheliegendsten Interpretation nicht: 1) dass die Fertilisation eine notwendige Determinante des moralischen Status ist; 2) dass die Fertilisation die sinnvollste Determinante des moralischen Status ist. Kurzum, der Artikel hat sich zwei Ziele gesetzt: I. zu beweisen, dass gerade aus diesem Argument nicht folgt, dass die oben erwähnten Praxen moralisch unzulässig seien; II. nahezulegen, dass einige pragmatische Strategien, die sich der Sorites-Paradoxa bedienen, einen philosophisch und wissenschaftlich adäquaten Rahmen für alternative Ansätze bereitstellen könnten. (shrink)

Call an argument a ‘happy sorites’ if it is a sorites argument with true premises and a false conclusion. It is a striking fact that although most philosophers working on the sorites paradox find it at prima facie highly compelling that the premises of the sorites paradox are true and its conclusion false, few (if any) of the standard theories on the issue ultimately allow for happy sorites arguments. There is one philosophical view, however, that (...) appears to allow for at least some happy sorites arguments: strict finitism in the philosophy of mathematics. My aim in this paper is to explore to what extent this appearance is accurate. As we shall see, this question is far from trivial. In particular, I will discuss two arguments that threaten to show that strict finitism cannot consistently accept happy sorites arguments, but I will argue that (given reasonable assumptions on strict finitistic logic) these arguments can ultimately be avoided, and the view can indeed allow for happy sorites arguments. (shrink)

I argue against unqualified acceptance of the principle of deductive closure (DC): that, if p follows deductively from premises that are already known, we are in a position to know p. DC, I claim, is a sorites premise; it seems intuitively irresistible, but indiscriminate application of it leads to absurd conclusions. Furthermore, a theory on which the application of DC is restricted explains our practice of deriving new knowledge from old knowledge better than a theory on which our application (...) of DC is unrestricted. This restriction on the application of DC allows contextualists to meet an argument of Hawthorne’s that contextualism must lead either to absurd knowledge attributions or to constant shifting of the standards for knowledge. Even if the standard of knowledge remains constant, the absurd knowledge attribution is the conclusion of a sorites argument and should be rejected. (shrink)

A requirement on any theory of vagueness is that it solve the sorites paradox. It is generally agreed that there are two aspects to such a solution: one task is to locate the error in the sorites argument; the second task is to explain why the sorites reasoning is a paradox rather than a simple mistake. I argue for a further constraint on approaches to the second task: they should conform to the standard modus operandi in formal (...) semantics, in which the semantic theory one develops is taken to be implicit in the ordinary usage of competent speakers. Thus it should not turn out that one's explanation of why ordinary speakers react to the sorites reasoning in the way they do depends on speakers not thinking that the semantics of vague language is governed by the theory one is advocating. I then argue that, out of the current main contenders for a theory of vagueness, only theories that posit degrees of truth can meet this further constraint. (shrink)

According to what I will call a contextualist solution to the sorites paradox, vague terms are context-sensitive, and one can give a convincing dissolution of the sorites paradox in terms of this context-dependency. The reason, according to the contextualist, that precise boundaries for expressions like “heap” or “tall for a basketball player” are so difficult to detect is that when two entities are sufficiently similar (or saliently similar), we tend to shift the interpretation of the vague expression so (...) that if one counts as falling in the extension of the property expressed by that expression, so does the other. As a consequence, when we look for the boundary of the extension of a vague expression in its penumbra, our very looking has the effect of changing the interpretation of the vague expression so that the boundary is not where we are looking. This accounts for the persuasive force of sorites arguments. (shrink)

I argue that the Ruth Chang’s Chaining Argument for her parity view of value incomparability trades illicitly on the vagueness of the predicate ‘is comparable with’. Chang is alert to this danger and argues that the predicate is not vague, but this defense does not succeed. The Chaining Argument also faces a dilemma. The predicate is either vague or precise. If it is vague, then the argument is most plausibly a sorites. If it is precise, then the argument is (...) either question begging or dialectically ineffective. I argue that no chaining-type argument can succeed. (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)

Sergio Tenenbaum and Diana Raffman contend that ‘vague projects’ motivate radical revisions to orthodox, utility-maximising rational choice theory. Their argument cannot succeed if such projects merely ground instances of the paradox of the sorites, or heap. Tenenbaum and Raffman are not blind to this, and argue that Warren Quinn’s Puzzle of the Self-Torturer does not rest on the sorites. I argue that their argument both fails to generalise to most vague projects, and is ineffective in the case of (...) the Self-Torturer itself. (shrink)

The principle of stability now says that if sentence ϕ is true/false in a model M, then ϕ has to stay true/false if M is getting more precise. Formally, let M = D, I be a refinement of M = D, I . Then it has to be the case that for all ϕ: (i) If VM(ϕ) = 1, then VM (ϕ) = 1. (ii) If VM(ϕ) = 0, then VM (ϕ) = 0.

I distinguish two broad approaches to vagueness that I call "robust" and "wimpy". Wimpy construals explain vagueness as robust (i.e., does not manifest arbitrary precision); that standard approaches to vagueness, like supervaluationism or appeals to degrees of truth, wrongly treat vagueness as wimpy; that vagueness harbors an underlying logical incoherence; that vagueness in the world is therefore impossible; and that the kind of logical incoherence nascent in vague terms and concepts is benign rather than malignant. I describe some implications for (...) logic, semantics, and metaphysics. (shrink)

In my paper I argue that a successful theory of vagueness should be able to account for faultless disagreement concerning borderline cases.Firstly, I claim that out of the traditional conceptions of vagueness the best equipped to account for faultless disagreement areparaconsistent solutions. One worry concerning dialetheism is that it seems to allow not only for faultless disagreements between different speakers, but also for such ‘disagreements’ between the given speaker and himself. Another worry, at least for some people, is that subvaluationism (...) and dialetheism account for faultless disagreements by allowing contradictions. Next, I go on to argue that contextual conceptions, which are free from this latter worry, are equally well able to account for such disagreements. To this aim I offer a new account of the usage of personal taste predicates and suggest that we model the usage of all vague predicates on them. The idea is that in clear cases “a is F” means “a is F simpliciter”, whereas in borderline cases it means “a is F-to-me”. Since the boundary between borderline and nonborderline cases depends on context, my solution weds content-contextualism with truth-contextualism. (shrink)

I begin by highlighting the importance of the step size in the induction step of the sorites paradox. A careful analysis reveals that the step size can be characterised as a proper instance of the concept very small . After having accurately described the structure of sorites-susceptible predicates, I argue that the structure of the induction step in the Sorites Paradox is inherently circular. This circularity emerges in the structure of Wang's paradox and also of the classical (...) variations of the paradox with the young, bald, etc. predicates. (shrink)

The past twenty or so years have seen the sorites paradox receive a good deal of philosophical air-time. Yet, in what is surely a sign of a good puzzle, no consensus has emerged. It is perhaps a good time to stop and take stock of the current status of the sorites paradox. My main contention is that the proposals offered to date as ways of blocking the paradox are seriously deficient, and hence there is, at present, no acceptable (...) solution to the sorites. In the final section I argue that, although vagueness is the source of the threat to modus ponens engendered by the sorites, it is also vagueness that protects modus ponens from clear counterexample. (shrink)