What makes it a heap

Thirdly, the full implications of abandoning the well-understood classical theory in favour of degree theory need spelling out before a proper evaluation of its worth can be made.

On these points see Sainsbury ch. For an extended defense see Smith ch. Furthermore, it is far from clear whether such an approach successfully avoids problems of higher order vagueness. And the assumption of a totally ordered truth-set is overly simple. Not all natural language sentences are comparable as regards their truth.

Due to the multi-dimensional nature of a concept such as redness, we may be unable to say of two reddish patches differing in hue or brightness or colour-saturation, whether one is redder than the other. On the latter points see Williamson a: ch. Smith [ ch. Smith defends the view he calls fuzzy plurivaluationism , blending together elements of degree theories and supervaluationism.

Smith writes:. For the only semantic facts are the facts about what is happening in each acceptable interpretation—and these are entirely classical hence truth-functional. What we have is just a level of talk laid on top of these semantic facts.

The talk sounds non-truth-functional, but it is in fact epiphenomenal…[I]t does not literally describe a non-truth-functional semantic reality.

Dissatisfied with many-valued and supervaluationist approaches, Kamp introduced a contextualist solution to the paradox. Focussing on the inductive form of the sorites, Kamp maintained that every instantiation of the major premise is true in its individual context, where a context consists of the sentences containing the given predicate previously accepted as true.

For Kamp, a context just is a set of sentences. Each instance is true because its antecedent must be added to the operative context before its consequent is evaluated, and the neighboring values referred to in the antecedent and consequent are only incrementally different. In a classical semantics the universal major premise would then be true as well; but Kamp adopts a non-classical definition dictating that the universal premise is true in contexts i where its instances are true and ii that remain coherent when the universal premise itself is added.

Hence the premise is false, despite all of its instances being true. The contextual relativity of this view is intuitively appealing, and it is free of the need to explain why each instance of the universal premise seems true when at least one must be false.

At the same time, the nonstandard semantics for the universal quantifier may seem unintuitive. Inspired by Kamp, a subsequent contextualist approach Raffman has it that the major premise of the paradox is false but seems true for at least two reasons. The pairwise claim, though true, does not license the paradoxical conclusion, which makes reference only to a value considered individually. The second reason is a hypothesis, viz. The major premise seems true because we fail to realize that truth can be secured for all of its instances together only by equivocating on context.

The latter view has been criticized for among other things applying only to the forced march paradox as opposed to the sorites proper; the sorites concerns a series of values properties like colors, heights, ages, etc.

Inasmuch as their solutions often involve a dynamical element, other contextualist treatments of the paradox may be vulnerable to this objection as well.

Soames , maintains that vague terms are context-sensitive in the manner of indexical expressions. Stanley objects that if Soames is right, then a diagnosis of the paradox as equivocating on an implicit contextual parameter is precluded because indexicals do not admit of variable interpretation in verb phrase ellipsis.

As a result of this fixity of interpretation, versions of the sorites paradox that employ such ellipses are not open to contextualist resolution, even in the presence of the relevant sort of contextual variation. Stanley provides the following example:. Defending the contextualist, Raffman responds by denying that vague terms are indexicals. Although Graff Fara defends an epistemic solution to the paradox, she proposes a dynamical contextualist explanation of the intuitive appeal of the conditional premise s.

On her view, vague predicates express properties that are interest-relative in the sense that their extensions are determined by what counts as significant for a speaker at a time.

A discrimination between two cherry trees that are very similar in height will be very costly given my interest in efficiency. But the discrimination will be costlier still when I am actively considering the two trees as live options for my purpose. Fara Soames appeals to context-sensitivity to defend a three-valued logic of vague predicates, postulating boundaries between the determinate exemplars, the determinate non-exemplars, and the borderline cases.

Tappenden [] suggests a similar three-valued approach that appeals to context to explain the apparent truth of the universally quantified premise, but his use of the notion of context here differs subtly from that of Kamp and Soames. The conditional sorites also admits of solution. Accepting the standard three-valued truth-conditions for the universal quantifier, Soames takes the conditional sorites to have some non-true conditional premise.

In a sorites series, the vagueness of a term is reflected in its possession of multiple equally permissible, arbitrarily different places to stop applying it. Any adequate theory of vagueness must acknowledge the existence of permissible stopping places in a sorites series, since competent users of a vague term are required to stop applying it before the end.

Any particular stopping place in the series is arbitrary, hence without legislative force; speakers cannot justifiably charge each other with error when they stop at different places. The distinction between boundaries and permissible stopping places is a cornerstone of the multi—range approach.

A range of application is just an abstract representation, in the semantics, of a permissible way of applying the predicate. More formally: a range is a set of values e. According to the multi—range view, a sentence applying a vague term to a given value is true relative to each of its ranges that contain that value, and false relative to each of the others.

Note that each predicate has some ranges that overlap with some ranges of the other two. Raffman warns against two potential confusions. In contrast, by their nature, precisifications contain no borderline values. Second, a range of e. Therefore a range contains only a permissible stopping place, whereas a precisification contains a sharp boundary. Fourth, the multi—range view contains no analogue of super-truth; ordinary truth is truth relative to a single range.

Among other things, whereas speakers typically are or can be aware of the context they are relativizing to, and can choose a given context for a certain reason, they do not cannot choose the ranges to which they will relativize their applications of a vague term.

Rather, speakers simply choose how they will classify a given value, and that classification is relativized—automatically, as it were, in virtue of the semantics of the term—to each of its ranges that contains the value in question.

Relativization to ranges is not something speakers do. In this connection it is worth noting that whereas contextualist treatments of the sorites are typically coupled with a distinct type of semantics for vague terms, e. And since each range contains a last age—a permissible stopping place—the major premise of the paradox is false relative to each range of the predicate for any context.

The multi-range theorist hypothesizes that the major premise of the paradox seems true because we confuse it with two pragmatic rules for the use of vague words —5 :. Of its aspects discussed here, the multi—range approach has been criticized most prominently for its commitment to an extreme relativism about truth. Opponents object that it is one thing to relativize truth to possible worlds, and to such contextual factors as speakers, times, spatial locations, comparison classes, speaker interests and purposes, stakes, and standards of assessment; and quite another to relativize truth to factors that vary even after all of those contextual parameters have been fixed.

The extremely fine-grained relativity proposed by the multi—range theorist seems to stretch the notion of truth to the breaking point. Several philosophers have endorsed a type 4 response, drawing the radical conclusion that the paradox is unsolvable; we are just stuck with it.

The question then is what the paradox shows. Dummett , for example, maintains that vague observational predicates whose application is supposed to be governed by a nontransitive indiscriminability relation are incoherent.

Such a view appears fatal to the familiar notion of a determinate shade of color see, e. A different type 4 response holds that, contrary to appearances, conditional sorites paradoxes are sound.

For example, it is true, after all, that no number of grains of wheat make a heap. However, such a view immediately runs into trouble because the paradoxes come in pairs.

As observed above, there are negative and positive versions of the puzzle depending on whether the soritical predicate is negated. To accept all sorites arguments as sound requires assent to the additional claim that, since one grain of wheat makes a heap, any number does. A radical incoherence follows since there is a commitment to all and any number both making a heap and not making a heap.

Similarly, everyone is bald and no one is; everyone is rich and no one is, and so on. The problem is that the soundness of any positive conditional sorites undercuts the truth of the unconditional premise of the corresponding negative version, and vice versa.

Unless one is prepared to accept a pandemic of contradictions in natural language, not all sorites can be sound. Unger and Wheeler propose a more restricted embrace. Dissatisfied with responses of types 1 and 3 , one accepts the applicability and validity of classical norms of reasoning. Nonetheless, dissatisfaction with responses of type 2 considered so far—rejecting some conditional premise—leaves open the option of either rejecting the minor unconditional premise or accepting it and, with it, the soundness of the paradox.

What is advocated is the soundness of those sorites which deny heapness, baldness, hirsuteness, richness, poverty, etc. For criticisms, see Williamson a: Ch.

The sorites paradox has traditionally been seen as unrelated in any substantially interesting way to the semantic and set-theoretic paradoxes of self-reference. However, McGee and Tappenden proposed a unified treatment of the liar and sorites paradoxes based on similarities between vague predicates and the truth predicate.

More recently, Field speaks of. Thus Colyvan points to a number of ways in which paradoxes might be thought to be of a kind per se , concluding that the liar and the sorites are examples and thus deserving of a similar solution. On the assumption that this common structure is sufficient to warrant a similar treatment, Priest advocates a paraconsistent response to the sorites having elsewhere defended a paraconsistent response to the paradoxes of self-reference.

In fact, as with paradoxical sentences, some vague sentences involving borderline cases will furnish examples of true contradictions, dialethias. Having considered several major families of responses to the logical and semantic challenges posed by the sorites, it is worth reflecting upon some of the broader philosophical issues that the problem raises. Since the deeply puzzling phenomenon of vagueness manifests itself first and foremost as a linguistic phenomenon, it is unsurprising that the responses variously intersect with problems concerning meaning, truth and reference.

While the margin-for-error principle discussed in Williamson a might serve to explain how we could be ignorant of the postulated sharp boundaries, it might be thought that since our use of vague terms does not draw sharp boundaries, it could not contain them given the generally accepted connection between meaning and use.

It seems that such a view must abandon the idea that our use determines meaning. One obvious response is that the connection between meaning and use is not as strong as might be supposed. Nature might also sometimes play a role in determining meaning, e. Williamson further responds by pointing out that the determination thesis at issue is really a supervenience thesis—meaning supervenes on use—and this thesis can be agreed to by epistemicists. Granted, the epistemicist cannot say exactly how meaning supervenes on use, and so cannot calculate the meaning or truth-conditions of an application of a vague term from facts about use.

However, the response continues, this inability is something which all theorists ought to accept. To suppose that the epistemic theory must make good on this count is to place unreasonable expectations on the theory see Williamson and Burgess for further discussion. The supervenience thesis is also challenged by symmetry considerations. Patterns of dissent are similarly symmetrical with respect to the two claims. If our patterns of use leave the matter equally unsettled either way then how can the truth of the matter be settled without arbitrariness and a severing of the connection between meaning and use?

The answer, Williamson suggests, lies in the fact that truth and falsity are not symmetrical notions. Falsity obtains in the absence of truth, so where there is symmetry at the level of use, falsity reigns. Whether this response succeeds is debated in Burgess and Weatherson The rejection of bivalence in the context of the T-schema is said to lead to absurdity Williamson a: ch.

This charge applies more generally to any non-bivalent theory of vagueness coupled with the T-schema. If validated, the pressure to abandon bivalence in the presence of vagueness would then cast doubt on a deflationary account of truth.

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Definition of heap Entry 1 of 2. Definition of heap Entry 2 of 2. Examples of heap in a Sentence Noun He dumped the grass clippings into the compost heap. He's in a heap of trouble! I can't believe he's still driving that old heap. Verb the critics heaped scorn on the wannabe blockbuster and its implausible plot heaped the stones in a corner of the yard.

Recent Examples on the Web: Noun Across a parking lot, Ida reduced the company's maintenance shop to a crumpled heap of metal. First Known Use of heap Noun before the 12th century, in the meaning defined at sense 1 Verb before the 12th century, in the meaning defined at sense 1a. Learn More About heap. Time Traveler for heap The first known use of heap was before the 12th century See more words from the same century. Style: MLA. More Definitions for heap. English Language Learners Definition of heap Entry 1 of 2.