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)

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)

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)

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)

ABSTRACT: This paper offers a generic revenge-proof solution to the Sorites paradox that is compatible with several philosophical approaches to vagueness, including epistemicism, supervaluationism, psychological contextualism and intuitionism. The solution is traditional in that it rejects the Sorites conditional and proposes a modally expressed weakened conditional instead. The modalities are defined by the first-order logic QS4M+FIN. (This logic is a modal companion to the intermediate logic QH+KF, which places the solution between intuitionistic and classical logic.) Borderlineness is introduced (...) modally as usual. The solution is innovative in that its modal system brings out the semi-determinability of vagueness. Whether something is borderline and whether a predicate is vague or precise is only semi-determinable: higher-order vagueness is columnar. Finally, the solution is based entirely on two assumptions. (1) It rejects the Sorites conditional. (2) It maintains that if one specifies borderlineness in terms of the ‒suitably interpreted‒ modal logic QS4M+FIN, then one can explain why the Sorites appears paradoxical. From (1)+(2) it results that one can tell neither where exactly in a Sorites series the borderline zone starts and ends nor what its extension is. Accordingly, the solution is also called agnostic. (shrink)

Vagueness demands many boundaries. Each is permissible, in that a thinker may without error use it to distinguish objects, though none is mandatory. This is revealed by a thought experiment—scrambled sorites—in which objects from a sorites series are presented in a random order, and subjects are required to make their judgments without access to any previous objects or their judgments concerning them.

This paper offers the Boolean many-valued solution to the Sorites Paradox. According to the precisification-based Boolean many-valued theory, from which this solution arises, sentences have not only two truth values, truth (or 1) and falsity (or 0), but many Boolean values between 0 and 1. The Boolean value of a sentence is identified with the set of precisifications in which the sentence is true. Unlike degrees fuzzy logic assigns to sentences, Boolean many values are not linearly but only partially (...) ordered; so there are values that are incomparable. Despite this fact, the sentences in a sorites series can be taken as having values in a linear order, and losing (or gaining) value as we move from sentence to sentence in the series. So there is no sharp borderline between 0 and 1. Assigning Boolean many values instead of the two truth values to sentences for their vagueness values is analogous to assigning propositions instead of the truth values to sentences for their semantic values, as propositions are, from our viewpoint, also Boolean many values. (shrink)

ABSTRACT: Recently a bold and admirable interpretation of Chrysippus’ position on the Sorites has been presented, suggesting that Chrysippus offered a solution to the Sorites by (i) taking an epistemicist position1 which (ii) made allowances for higher-order vagueness. In this paper I argue (i) that Chrysippus did not take an epistemicist position, but − if any − a non-epistemic one which denies truth-values to some cases in a Sorites-series, and (ii) that it is uncertain whether and (...) how he made allowances for higher-order vagueness, but if he did, this was not grounded on an epistemicist position. (shrink)

I argue in this paper that the existence of sorites series of color patches – series of color patches arranged so that the patches on each end look different in color though no two adjacent patches do – shows that the relation of same phenomenal charac­ter as is not a transitive relation. I then argue that the intransitivity of same phenomenal character as conflicts with certain versions of intentionalism, the view that an experiences phenomenal character is exhausted, (...) or fully determined by its intentional content. Lastly, I consider various objections to the arguments and reply to them. (shrink)

This paper provides new examples of vagueness phenomena with comparatives. I show that comparatives of the form ‘x is ADJ-er than y’ can be vague due to a fuzziness in how much of some property makes for a difference in ADJ-ness. The sorites examples I provide cannot be assimilated to cases of indiscriminability or fuzziness in relevant dimensions, standards, or measurement procedures. A revised degree-based semantics with semiorders, a well studied threshold structure, is developed. The treatment of equatives captures (...) the truth of the claim that adjacent items in the sorites series are not relevantly distinguishable in ADJ-ness; and it avoids validating transitivities that would yield paradoxical conclusions. (shrink)

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

There is a well-known moral quandary concerning how to account for the rightness or wrongness of acts that clearly contribute to some morally significant outcome – but which each seem too small, individually, to make any meaningful difference. One consequentialist-friendly response to this problem is to deny that there could ever be a case of this type. This paper pursues this general strategy, but in an unusual way. Existing arguments for the consequentialist-friendly position are sorites-style arguments. Such arguments imagine (...) varying a subject’s predicament bit by bit until it is clear that a relevant difference has been achieved. The arguments offered in this paper are structurally different, and do not rely on any sorites series. For this reason, they are not vulnerable to objections that have been leveled against the sorites-style arguments. (shrink)

This paper develops the treatment of vague predicates begun in my "Vagueness Without Paradox" (Philosophical Review 103, 1 [1994]). In particular, I show how my account of vague words dissolves an "eternal" version of the sorites paradox, i.e., a version in which the paradox is generated independently of any particular run of judgments of the items in a sorites series. In so doing I refine the notion of an internal contest, introduced in the earlier paper, and draw (...) a distinction within the class of internal contexts between contexts of judgment and contexts of consideration. (shrink)

In this paper I offer a critique of the recent popular strategy of giving a contextualist account of vagueness. Such accounts maintain that truth-values of vague sentences can change with changes of context induced by confronting different entities (e.g. different pairs through a sorites series). I claim that appealing to context does not help in solving the sorites paradox, nor does it give us new insights into vagueness per se. Furthermore, the contextual variation to which the contextualist (...) is committed is problematic in various ways. For example, it yields the consequence that much of our everyday (non-soritical) reasoning is fallacious, and it renders us ignorant of what we and others have said. (shrink)

Weber, Colyvan, and Priest have advanced glutty approaches to the sorites, on which the truth about the penumbral region of a soritical series is inconsistent. The major benefit of a glut-based approach is maintaining the truth of all sorites premisses while none the less avoiding, in a principled fashion, the absurdity of the sorites conclusion. I agree that this is a major virtue of the target glutty approach; however, I think that it can be had without (...) gluts. If correct, this result weighs heavily against the proposed glutty approach, at least given the default-consistency principle that all target glutty philosophers accept: posit gluts only if there is no consistent theory that enjoys the same virtues as the would-be glutty solution. (shrink)

This paper examines the mind and language of an omniscient being from a supervaluationist perspective. Two questions hall receive special attention. How ought the supervaluationist explicate the concept of omniscience? And what ought the supervaluationist expect an omniscient speaker to say about a Sorites series?

I attempt to accommodate the phenomenon of vagueness with classical logic and bivalence. I hold that for any vague predicate there is a sharp cut-off between the things that satisfy it and the things that do not; I claim that this is due to the greater naturalness of one of the candidate meanings of that predicate. I extend the thought to the problem of the many and Benacerraf cases. I go on to explore the idea that it is ontically indeterminate (...) what the most natural meanings are, and hence ontically indeterminate where the sharp cut-off in a sorites series is. (shrink)

According to the dominant approach in the theory of vagueness, the nature of the vagueness of an expression ‘F’ consists in its presenting borderline cases in an appropriately ordered series: objects which are neither definitely F nor definitely not F (where the notion of definiteness can be semantic, ontic, epistemic, psychological or primitive). In view of the various problems faced by theories of vagueness adopting the dominant approach, the thesis proposes to reconsider the naive theory of vagueness, according to (...) which the nature of the vagueness of an expression consists in its not drawing boundaries between any neighbouring objects in an appropriately ordered series. It is argued that expressions and concepts which do present this feature play an essential role in our cognitive and practical life, allowing us to conceptualize---in a way which would otherwise be impossible---the typically coarse-grained distinctions we encounter in reality. Despite its strong initial plausibility and ability to explain many phenomena of vagueness, the naive theory is widely rejected because thought to be shown inconsistent by the sorites paradox. In reply, it is first argued that accounts of vagueness based on the dominant approach are themselves subject to higher-order sorites paradoxes. The paradox is then solved on behalf of the naive theory by rejecting the unrestricted transitivity of the consequence relation on a vague language; a family of logics apt for reasoning with vague expressions is proposed and studied (using models with partially ordered values). The characteristic philosophical and logical consequences of this novel solution are developed and defended in detail. In particular, it is shown how the analysis of what happens in the attempt of surveying a sorites series and deciding each case allows the naive theory to recover a "thin" notion of a borderline case. (shrink)

accounts in general, contrary to what he seems to think. Stanley’s discussion concerns the dynamic or ‘forced march’ version of the sorites, viz. the version framed in terms of the judgments that would be made by a competent speaker who proceeds step by step along a sorites series for a vague predicate ‘F’. According to Stanley, the contextualist treatment of the paradox is based on the idea that the speaker shifts the content of the predicate whenever necessary (...) to make it the case that each successive pair of adjacent items are category-identical – in other words, either both items satisfy ‘F’ or neither does. These adjustments allow the speaker to progress from a clear case for ‘F’ to a clear case for ‘not-F’ without breaking the seeming continuity of the series. (shrink)

The paper develops a critical dialectic with respect to the nowadays dominant approach in the theory of vagueness, an approach whose main tenet is that it is in the nature of the vagueness of an expression to present borderline cases of application, conceived of as enjoying some kind of distinctive normative status. Borderlineness is used to explain the basic phenomena of vagueness, such as, for example, our ignorance of the location of cut-offs in a soritical series. Every particular theory (...) of vagueness exemplifying the approach makes use, in the vague object language, of a definiteness operator which, however substantially interpreted, unavoidably inherits the vagueness of the expressions on which it operates ('higher-order vagueness'). It is first argued that finite soritical series force a surprising collapse result concerning a particular set of expressions involving the definiteness operator. It is then shown that, under two highly plausible assumptions about higher-order vagueness (the existence of 'absolutely definitely' positive and negative cases and the 'radical' character of higher-order vagueness itself), the collapse result implies the inadequacy of the dominant approach as a theory of vagueness, as its main tenet can be, at best, not absolutely definitely true. (shrink)

It is a commonplace that the extensions of most, perhaps all, vague predicates vary with such features as comparison class and paradigm and contrasting cases. My view proposes another, more pervasive contextual parameter. Vague predicates exhibit what I call open texture: in some circumstances, competent speakers can go either way in the borderline region. The shifting extension and anti-extensions of vague predicates are tracked by what David Lewis calls the “conversational score”, and are regulated by what Kit Fine calls penumbral (...) connections, including a principle of tolerance. As I see it, vague predicates are response-dependent, or, better, judgement-dependent, at least in their borderline regions. This raises questions concerning how one reasons with such predicates. In this paper, I present a model theory for vague predicates, so construed. It is based on an overall supervaluationist-style framework, and it invokes analogues of Kripke structures for intuitionistic logic. I argue that the system captures, or at least nicely models, how one ought to reason with the shifting extensions (and anti-extensions) of vague predicates, as borderline cases are called and retracted in the course of a conversation. The model theory is illustrated with a forced march sorites series, and also with a thought experiment in which vague predicates interact with so-called future contingents. I show how to define various connectives and quantifiers in the language of the system, and how to express various penumbral connections and the principle of tolerance. The project fits into one of the topics of this special issue. In the course of reasoning, even with the external context held fixed, it is uncertain what the future extension of the vague predicates will be. Yet we still manage to reason with them. The system is based on that developed, more fully, in my Vagueness in Context , Oxford, Oxford University Press, 2006, but some criticisms and replies to critics are incorporated. (shrink)

Vagueness manifests itself (among other things) in our inability to find boundaries to the extension of vague predicates. A semantic theory of vagueness plans to justify this inability in terms of the vague semantic rules governing language and thought. According to a supporter of semantic theory, the inability to find such a boundary is not dependent on epistemic limits and an omniscient being like God would be equally unable. Williamson (Vagueness, 1994 ) argued that cooperative omniscient beings adequately instructed would (...) find a precise boundary in a sorites series and that, for this reason, the semantic theory misses its target, while Hawthorne (Philosophical Studies 122:1–25, 2005 ) stood with the semantic theorists and argued that the linguistic behaviour of a cooperative omniscient being like God would clearly demonstrate that he does not find a precise boundary in the sorites series. I argue that Hawthorne’s definition of God’s cooperative behaviour cannot be accepted and that, contrary to what has been assumed by both Williamson and Hawthorne, an omniscient being like God cannot be a cooperative evaluator of a semantic theory of vagueness. (shrink)

It is notoriously difficult to model the range of application of vague predicates relative to a suitable sorites series. In this paper I offer some critical remarks against an interesting view that has received little attention in the literature. According to it, the sharp cut-offs we find in our semantic models are just artifacts of the theory, and, as such, they are harmless. At the end I discuss a contextualist view that, at a cost, may be able to (...) get around the problems related to sharp cut-offs incurred in by other theories of vagueness. Es sumamente difícil modelar el rango de aplicación de predicados vagos relativo a una serie sorites apropiada. En este artículo ofrezco algunos comentarios críticos en contra de una postura interesante que ha recibido poca atención en la literatura. De acuerdo con ella, los cortes precisos que encontramos en modelos semánticos son simplemente artefactos de la teoría, y, como tales, son inofensivos. Al final del artículo discuto una postura contextualista que, no sin sacrificios, podría ser capaz de evadir los problemas relacionados con cortes precisos que otras teorías de la vaguedad poseen. (shrink)

Philosophers disagree about whether vagueness requires us to admit truth-value gaps, about whether there is a gap between the objects of which a given vague predicate is true and those of which it is false on an appropriately constructed sorites series for the predicate---a series involving small increments of change in a relevant respect between adjacent elements, but a large increment of change in that respect between the endpoints. There appears, however, to be widespread agreement that there (...) is some sense in which vague predicates are gappy which may be expressed neutrally by saying that on any appropriately constructed sorites series for a given vague predicate there will be a gap between the objects of which the predicate is denitely true and those of which it is denitely false. Taking as primitive the operator ‘it is denitely the case that’, abbreviated as ‘D’, we may stipulate that a predicate F is denitely true (or denitely false) of an object just in case ‘DF (a)’, where a is a name for the object, is true (or false) simpliciter.1 This yields the following conditional formulation of a ‘gap principle’: (D Φ (x) ∧ D¬ Φ (y)) → ¬R(x, y). Here ‘ Φ ’ is to be replaced with a vague predicate, while ‘R’ is to stand for a sorites relation for that predicate: a relation that can be used to construct a sorites series for the predicate---such as the relation of being just one millimetre shorter than for the predicate ‘is tall’. Disagreements about the sense in which it is correct to say that vague predicates are gappy can then be recast as disagreements about how to understand the denitely operator. One might give it, for example, a pragmatic construal such as ‘it would not be misleading to assert that’; or an epistemic construal such as ‘it is known that’ or ‘it is knowable that’; or a semantic construal such as ‘it is true that’. (shrink)

Of the many families of words that are thought to be vague, so-called observational predicates may be both the most fascinating and the most confounding. Roughly, observational predicates are terms that apply to objects on the basis of how those objects appear to us perceptually speaking. ‘Red’, ‘loud’, ‘sweet’, ‘acrid’, and ‘smooth’ are good examples. Delia Graff explains that a “predicate is observational just in case its applicability to an object (given a fixed context of evaluation) depends only on the (...) way that object appears” (2001, 3). By the same token observational predicates are, as Crispin Wright observes, terms “whose senses are taught entirely by ostension” (1976). Like other vague predicates, observational words appear to generate sorites paradoxes. Consider for example a series of 20 colored patches progressing from a clearly red one to a clearly orange one, so ordered that each patch is just noticeably different in hue from the one before. The following argument then seems forced upon us: (1) Patch #1 is red. (2) Any patch that differs only slightly in hue from a red patch is itself red. (3) Therefore patch #20 is red. Premise (2) expresses what Wright has called the tolerance of ‘red’: the application of the predicate tolerates small changes in a decisive parameter (here, hue). Of course, most vague predicates, hence most versions of the sorites, are not observational. For instance, given a series of. (shrink)

By pooling together exhaustive analyses of certain philosophical paradoxes, we can prove a series of fascinating results regarding philosophical progress, agreement on substantive philosophical claims, knockdown arguments in philosophy, the wisdom of philosophical belief, the epistemic status of metaphysics, and the power of philosophy to refute common sense. As examples, this Element examines the Sorites Paradox, the Liar Paradox, and the Problem of the Many – although many other paradoxes can do the trick too.

In a series of very influential works, Tim Williamson has advanced and defended a much discussed theory of evidence containing, among other claims, the thesis that, if one knows P, P is part of one's evidence. I argue that K ⊆ E is false, and indeed that it is so for a reason that Williamson himself essentially provides in arguing against the thesis that, if one has a justified true belief in P, P is part of one's evidence: together (...) with a very plausible principle governing the acquisition of knowledge by non-deductive inference based on evidence, K ⊆ E leads, in a sorites-like fashion, to what would seem a series of unacceptably bootstrapping expansions of one's evidence. I then develop some considerations about the functions of and conditions for evidence which are suggested by the argument against K ⊆ E. I close by discussing the relationship of the argument with anti-closure arguments of the style exemplified by the preface paradox: I contend that, if closure is assumed, it is extremely plausible to expect that the diagnosis of what goes wrong in the preface-paradox-style argument cannot be used to block my own argument. (shrink)

Paradox Lost covers ten of philosophy’s most fascinating paradoxes, in which seemingly compelling reasoning leads to absurd conclusions. The following paradoxes are included: The Liar Paradox, in which a sentence says of itself that it is false. Is the sentence true or false? The Sorites Paradox, in which we imagine removing grains of sand one at a time from a heap of sand. Is there a particular grain whose removal converts the heap to a non-heap? The Puzzle of the (...) Self-Torturer, in which a series of seemingly rational choices has us accepting a life of excruciating pain, in exchange for millions of dollars. Newcomb’s Problem, in which we seemingly maximize our expected profit by taking an unknown sum of money, rather than taking the same sum plus $1000. The Surprise Quiz Paradox, in which a professor finds that it is impossible to give a surprise quiz on any particular day of the week... but also that if this is so, then a surprise quiz can be given on any day. The Two Envelope Paradox, in which we are asked to choose between two indistinguishable envelopes, and it is seemingly shown that each envelope is preferable to the other. The Ravens Paradox, in which observing a purple shoe provides evidence that all ravens are black. The Shooting Room Paradox, in which a deadly game kills 90% of all who play, yet each individual’s survival turns on the flip of a fair coin. Each paradox is clearly described, common mistakes are explored, and a clear, logical solution offered. Paradox Lost will appeal to professional philosophers, students of philosophy, and all who love intellectual puzzles. (shrink)

Vagueness is a familiar but deeply puzzling aspect of the relation between language and the world. It is highly controversial what the nature of vagueness is -- a feature of the way we represent reality in language, or rather a feature of reality itself? May even relations like identity or parthood be affected by vagueness? Sorites arguments suggest that vague terms are either inconsistent or have a sharp boundary. The account we give of such paradoxes plays a pivotal role (...) for our understanding of natural languages. If our reasoning involves any vague concepts, is it safe from contradiction? Do vague concepts really lack any sharp boundary? If not, why are we reluctant to accept the existence of any sharp boundary for them? And what rules of inference can we validly apply, if we reason in vague terms? Cuts and Clouds presents the latest work towards a clearer understanding of these old puzzles about the nature and logic of vagueness. The collection offers a stimulating series of original essays on these and related issues by some of the world's leading experts. (shrink)

It is widely supposed that one family of sorites paradoxes, perhaps the most perplexing versions of the puzzle, owe at least in part to the nontransitivity of perceptual indiscriminability. To a first approximation, perceptual indiscriminability is the relationship obtaining among objects (stimuli) that appear identical in some perceptual respect—for example hue, or pitch, or texture. Indiscriminable objects look the same, or sound the same, or feel the same. Received wisdom has it that there are or could be series (...) of objects _o__1…_o__n in which _o_₁ and _o_₂ are indiscriminable, _o_₂ and _o_3 are indiscriminable, etc., and _o_n-1 and_ o_n are indiscriminable, but _o_1 and _o_n are discriminably different. For example, there could be a series of colored patches so ordered that each patch looks the same in hue as its immediate neighbors but the whole progresses from a clear case of red to a clear case of orange. On the assumption that an observational word like ‘red’ applies to both if to either of a pair of perceptually indiscriminable items, the absurd conclusion of the sorites comes into view. Crispin Wright explains. (shrink)

The Stoics’ theory of kataleptic impressions looks different once we attend to their analysis of the Sorites paradox. In defending this view, I reject the long-standing assumption that the Stoics develop their theory by focusing on sensory impressions. The Stoic approach to vagueness shows, for example, that non-sensory impressions can be seemingly indistinguishable by belonging to a series. It also draws attention to an understudied dimension of Stoic theory: in aiming to assent only to kataleptic impressions, one aims (...) to avoid not only assent to false impressions but also assent to those that are neither true nor false. (shrink)

One of the few points of agreement between most theists and non-theists working on the problem of evil is that the existence of a perfect God is incompatible with the existence of pointless evil. In a series of influential papers, however, Peter van Inwagen has argued that careful attention to the reasoning behind this claim reveals fatal difficulties related to the Sorites Paradox. In this paper, I explain van Inwagen’s appeal to sorites reasoning, distinguish between two different (...) arguments in his work, and argue that they both commit the same so-far-unnoticed mistake. (shrink)

Slippery slope arguments are commonly thought to be fallacious. But is there a single fallacy which they all commit? A study of applied logic texts reveals competing diagnoses of the supposed error, and several recent authors take slippery slope arguments seriously. Clearly, there is room for comment. I shall give evidence of divergence on the question of what sort of argument constitutes a slippery slope, distinguish four different types of argument which have all been deemed to be slippery slopes, and (...) contend that two of these types need involve no logical error.We find in textbook accounts three quite differently oriented treatments of slippery slope: conceptual — relating to vagueness and the ancient sorites paradox; precedential — relating to the need to treat similar cases consistently; and causal — relating to the avoidance of actions which will, or would be likely to, set off a series of undersirable events. (shrink)

Many philosophic arguments concerned with infinite series depend on the mutual inconsistency of statements of the following five forms: (1) something exists which has R to something; (2) R is asymmetric; (3) R is transitive; (4) for any x which has R to something, there is something which has R to x; (5) only finitely many things are related by R. Such arguments are suspect if the two-place relation R in question involves any conceptual vagueness or inexactness. Traditional (...) class='Hi'>sorites arguments show that a statement of form (4) can fail to be true even though it has no clear counter-example. Conceptual vagueness allows a finite series not to have any definite first member. I consider the speculative possibilities that there have been only finitely many non-overlapping hours although there has been no first hour and that space and time are only finitely divisible even though there are no smallest spatial or temporal intervals. (shrink)

Sorensen has argued that one can exploit the vagueness of an ordinary predicate like ‘small’ to induce a sort of vagueness in ‘vague’, by constructing a series of predicates of the form ‘n-small’, where x is n- small if and only if x is small or x n. The resulting ‘Sorensen’ed’ predicates present a Sorites case for ‘vague’ ; hence the vagueness of ‘vague’. Hyde argues that this demonstrates that all vague predicates are higher-order vague. Others doubt whether (...) Sorensen’s series really delivers such a result, claiming Hyde’s argument to be either: unsound, because it misidentifies the true source of vagueness in Sorensen’s Sorites ; invalid, because it fails to generalize to all vague predicates ; or circular, because it presupposes the very thing it tries to prove, namely, higher-order vagueness. This paper contributes to the Sorensen-Hyde vs. Tye-Deas-Hull-Varzi debate by clarifying the relations between vague vagueness and higher-order vagueness. I show how claims of higher-order vagueness are derivable from claims of vague vagueness. This is the missing piece needed to complete Hyde’s argument and overcome the objections presented by Deas, Hull, Tye, and Varzi. I then show how Sorensen’s considerations, once properly generalized, pose more far-reaching consequences about the vagueness of ‘vague’ than either defenders or critics of Hyde’s argument have appreciated. (shrink)

Humans have only finite discriminatory capacities. This simple fact seems to be incompatible with the existence of appearances. As many authors have noted, the hypothesis that appearances exist seems to be refuted by reductio: Let A, B, C be three uniformly coloured surfaces presented to a subject in optimal viewing conditions, such that A, B, and C resemble one another perfectly except with respect to their colours. Their colours differ slightly in the following way: the difference between A and B (...) and the difference between B and C are below the discrimination threshold, but the difference between A and C is above this threshold. According to an intuitive construal of what an appearance is, given that A and B appear (to the subject) identical in colour, A and B have the same (colour1) appearance P1; likewise, B and C have the same appearance P2. B's appearance is both P1 and P2. This seems to imply that P1=P2. But then, A and C also have the same appearance, which contradicts the hypothesis that A and C are discriminable. If A and C are discriminable with respect to their colour, they do not have the same appearance with respect to colour. The paradox arising from such a series of judgments of sameness or difference between pairs of coloured surfaces seems to belong to the class of sorites paradoxes. I will show that there is a way to construe colours and their appearances in a way that does not fall prey to the reduction just sketched. (shrink)

Michael Dummett presents a modus tollens argument against a Wittgensteinian conception of meaning. In a series of papers, Dummett claims that Wittgensteinian considerations entail strict finitism. However, by a “sorites argument”, Dummett argues that strict finitism is incoherent and therefore questions these Wittgensteinian considerations.In this paper, I will argue that Dummett’s sorites argument fails to undermine strict finitism. I will claim that the argument is based on two questionable assumptions regarding some strict finitist sets of natural numbers. (...) It will be shown that strict finitism entails none of these assumptions. Hence, the argument does not prove that the view is internally incoherent, and consequently, Dummett fails to undermine the Wittgensteinian conception of meaning. (shrink)

Both arguments are based on the breakdown of normal criteria of identity in certain science-fictional circumstances. In one case, normal criteria would support the identity of person A with each of two other persons, B and C; and it is argued that, in the imagined circumstances, A=B and A=C have no truth value. In the other, a series or spectrum of cases is tailored to a sorites argument. At one end of the spectrum, persons A and B are (...) such that A=B is clearly true; at the other end, A and B are such that the identity is clearly false. In between, normal criteria of identity leave the truth or falsehood of A=B undecided, and it is argued that in these circumstances A=B has no truth value.These arguments are to be understood counterfactually. My claim is that, so understood, neither establishes its conclusion. The first involves a pair of counterfactual situations that are equally possible or tied. If A=B and A=C have no truth value, a counterfactual conditional with one of them as consequent and an antecedent that is true in circumstances in which either is true should have no truth value. Intuitively, however, any such counterfactual is false. The second argument can be seen to invite an analogous response. If this is right, however, there is an important disanalogy between this and the classical paradox of the heap. If the disanalogy is only apparent, the argument shows at most that the existence of persons can be indeterminate. (shrink)

ABSTRACT William Hurlbut, a Stanford University bioethicist and member of the President's Council on Bioethics, recently proposed a solution to the current impasse over human embryonic stem cell research in the United States. He suggested that researchers could use genetic engineering and somatic cell nuclear transfer (i.e. cloning) to develop human ‘pseudo‐embryos’ that have no potential to develop fully into human persons. According to Hurlbut, even thinkers who typically ascribe high moral status to human embryos could approve of destroying these (...) ‘pseudo‐embryos’ for the sake of harvesting human embryonic stem cells. This essay argues, first, that an argument based on the ‘paradox of the heap’ (an argument that many ‘pro‐life’ thinkers employ in order to defend the notion that human embryos have high moral value from the moment of conception) challenges the ethical legitimacy of Hurlbut's proposal. Second, the paper argues that this conflict may illustrate a reductio ad absurdum for this ‘pro‐life’ argument itself rather than being a problem for Hurlbut's proposal. As a result, the paper challenges the ‘pro‐life’ strategy of arguing that one should respond to uncertainty about the moral status of developing embryos by being morally ‘cautious’ and granting all human embryos full moral status from the moment of conception. It appears that one is faced with a complex series of choices (about where to draw the moral line between entities that are human persons and entities that are not), and a strict moral ‘cautiousness’ about this series of choices may ultimately lead to absurdity. (shrink)

The goal of this book is to defend a supervaluationist theory of vagueness. Keefe begins by laying out a series of desiderata for an adequate theory of vagueness generally: among other things, such a theory will need to solve the sorites paradox, provide a plausible analysis of borderline cases, preserve so-called penumbral connections among borderline predications, accommodate the phenomenon of higher-order vagueness, and comport with as many of our ordinary linguistic intuitions as possible. She then proceeds to evaluate (...) in turn each of the main competitors to a supervaluationist theory—including epistemic, many-valued, degree-theoretic, and pragmatic accounts—in light of these desiderata, and finds each seriously lacking. Having thus cleared the ground, she advances a version of the supervaluationist approach and replies to a number of potential objections. (shrink)

I argue that though a satisfactory semantics for the logic of inexact reference may assign no truth value to some statements, it should not assign truth (or falsity) of various degrees. Well-formed assertions are simply true or not. Inexactness does not “ramify.” I distinguish inexactness from other sorts of vagueness, including nonspecificity. I show that arguments from (i) use of quantifiers, (ii) the existence of properties which can be construed as a series of properties (as, e. g., red can (...) be construed as a set of shades of red), (iii) the constructability of apparently paradoxical sorites arguments, and (iv) the presence of prototypes in the extension of a predicate do not show that there are degrees of truth.Much of the alleged evidence that inexactness ramifies is, in fact, a misreading of the undeniable evidence that there may be uncertainty about the truth value of a claim. In support of my claims, I discuss how cases of deeming that a predicate applies relate to its actually applying. A distinction between predicates of “pure” and “impure” function is essential to this. (shrink)

Článek se věnuje argumentu kluzkého svahu a otázce, jak jej identifikovat a hodnotit. Argument kluzkého svahu je využíván v rámci praktického uvažování a v dialogu, svou strukturou odpovídá negativnímu argumentu z důsledku, má v zásadě defeasibilní povahu a je často účinný při snaze přenést důkazní břemeno na stranu oponenta. Hodnocení argumentu kluzkého svahu je založeno na kontextu dialogu spíše než na hodnocení jeho deduktivní či induktivní správnosti.V příspěvku jsou představeny čtyři typy argumentu. Zaprvé argument kluzkého svahu typu sorites, jehož (...) označení odkazuje k paradoxu sorites neboli paradoxu hromady. Argument kluzkého svahu typu sorites je ve své podstatě kombinací argumentu ad absurdum a sofismatu polyzeteseos. Zadruhé kauzální argument kluzkého svahu, který se zakládá na předpovědi série událostí. Tento typ argumentu je často označován jako teorie domina či dominový efekt. Nicméně, ať už jej pojmenujeme jakkoli, zásadní pro jeho identifikaci, analýzu a hodnocení je fakt, že se jedná o předpověď budoucího stavu věcí. Předpověď více či méně pravděpodobnou, zakládající se na slabých či silných předpokladech. Zatřetí precedentální argument kluzkého svahu, který se objevuje v diskuzích o možnosti změny současného pravidla či platné normy. Argumenty založené na precedentu obecně souvisí s usuzováním na základě konkrétního případu. Precedentální argument kluzkého svahu využívá podobnosti mezi případy, a je tedy založen na analogii. A posledním, čtvrtým typem argumentu kluzkého svahu, kterému se příspěvek věnuje, je tzv. plný argument kluzkého svahu či kombinovaný argument kluzkého svahu. (shrink)

In this essay review of Megan Quigley's Modern Fiction and Vagueness: Philosophy, Form, and Language, the editor of Common Knowledge comments on the explicit relationship between that book's arguments and those of the journal's six-part series “Fuzzy Studies: A Symposium on the Consequence of Blur,” published in 2011–13. He points out that there are aesthetic forms and concepts of vagueness that are related only tangentially to what analytic philosophers, in treating the “sorites paradox” and its implications, have meant (...) by the term, and he suggests that this book suffers by limiting itself to Anglophone works, when the most relevant work is perhaps in French, and by limiting its reach to fiction, when the most relevant genres of art are perhaps poetry, painting, and music. The review concludes by regretting Quigley's making T. S. Eliot her study's straw man and by observing not only that her interpretation of Eliot's relationship to analytic philosophy is demonstrably incorrect but also that there is no point in valorizing vagueness or “fuzzy studies” if the upshot is not a sort of mutual respect and acceptance that scientistic clarity in the arts and humanities does not foster. (shrink)

REASON AND REVOLUTION, to which Henry F. May has called attention in his noteworthy book, The Enlightenment in America, mentioned in the first article in the present series, marks the period of American colonial history from 1763 to 1776. The Declaration of Independence, I have maintained, is a consummate expression of these Enlightenment features, influenced by the thought of John Locke and others in philosophy. From cautious moderation the American movement of protest against British rule climaxed in a revolution. (...) The dynamic structure of the epoch unfolded as a kind of sorites, of which the major premises are a general philosophy of rights and a particular theory of the British Empire, the minor premises are numerous allegedly factual violations of these theoretical premises, and the conclusion is a decisive act of separation or independence. Since, however, the Enlightenment mode of revolution rested, to reiterate May's statement, on "the belief in the possibility of constructing a new heaven and earth out of the destruction of the old," the moment in history expressed by the Declaration of Independence logically leads to other moments, one of which is the formation of the American republic as both a federal and national union. This singular moment is crystallized in the Constitution of the United States, a document equal in importance to the Declaration of Independence as a symbol of the Enlightenment. (shrink)

Suppose you're unable to discriminate the colors of two objects. According to the triangulation view, their colors might nonetheless look different to you, and that's something you can discover as a result of further comparisons. The primary motivation for this view is its apparent ability to solve a puzzle involving a series of pairwise indiscriminable objects. I argue that, due to visual noise, the triangulation view doesn't really solve the puzzle.

According to anti-atomism, we represent color properties (e.g., red) in virtue of representing color relations (e.g., redder than). I motivate anti-atomism with a puzzle involving a series of pairwise indistinguishable chips. I then develop two versions of anti-atomism.

ABSTRACT This paper deals with the linguistic phenomenon of vagueness. Based on certain observations regarding the intuitions and linguistic practices of the philosophically informed speaker, we make a series of assumptions concerning the nature and characteristics of the phenomenon. Vagueness is treated as an emerging phenomenon, caused, in essence, by the messy way in which linguistic communities reach classificatory equilibria. Any talk of ‘meaning’, ‘truth’, and such is treated as an indirect way of attempting to describe such equilibria, and (...) it is in regard to these that ascriptions of truth are here relativised. Given such assumptions, we then proceed to formulate and study a semantic theory for languages that contain vague predicates. Finally, we describe two proof systems, one based on trees, and a natural deduction system in the style of Fitch, and outline the appropriate proofs of soundness and completeness. (shrink)

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)