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- Ruth Manor (2006). Solving the Heap. Synthese 153 (2):171 - 186.The present offers a pragmatic solution of the Heap Paradox, based on the idea that vague predicates are “indexical” in the sense that their denotation does not only depend on the context of their use, but it is a function of the context. The analysis is based on the following three claims. The borderlines of vague terms are undetermined in the sense that though they may be determined in some contexts, they may differ from one context to the next. Vagueness serves the important communicative function, enabling speakers to identify entities as objects (as things we can talk about) in terms of some quantitative differences between the “object” and its background in the context. Thus, in some contexts we can naturally partition the group of men uniquely so as to distinguish the bald from the not-bald. Whether a man with a given hair number is among the bald in a given context depends not only on his own hair number but also on the hair number of others in that context. This provides the background for the claim that when we assert that John is bald, we presuppose that there is a unique demarcation to the bald in that context. I consider the truth of the Paradox’s statements in contexts where the presupposition is true and in contexts where it is false. The analysis yields that the contradiction is avoided because though each of the statements is often true, never are all the sentences in the Paradox true together.
Similar books and articles
On two standard views of vagueness, vagueness as to whether Harry is bald entails that nobody knows whether Harry is bald—either because vagueness is a type of missing truth, and so there is nothing to know, or because vagueness is a type of ignorance, and so even though there is a truth of the matter, nobody can know what that truth is. Vagueness as to whether Harry is bald does entail that nobody clearly knows that Harry is bald and that nobody clearly knows that Harry is not bald. But it does not entail that nobody knows that Harry is bald or that nobody knows that Harry is not bald. Hence, the two standard views of vagueness are mistaken.
All sorts of things are context-dependent in one way or another. What it is appropriate to wear, to give, or to reveal depends on the context. Whether or not it is all right to lie, harm, or even kill depends on the context. If you google the phrase ‘depends on the context’, you’ll get several hundred million results. This chapter aims to narrow that down. In this context the topic is context dependence in language and its use. It is commonly observed that the same sentence can be used to convey different things in different contexts. That is why people complain when something they say is ‘taken out of context’ and insist that it be ‘put into context’, because ‘context makes it clear’ what they meant. Indeed, it is practically a platitude that what a speaker means in uttering a certain sentence, as well as how her audience understands her, ‘depends on the context’. But just what does that amount to, and to what extent is it true?
Based on the premise that what is relevant, consistent, or true may change from context to context, a formal framework of relevance and context is proposed in which • contexts are mathematical entities • each context has its own language with relevant implication • the languages of distinct contexts are connected by embeddings • inter-context deduction is supported by bridge rules • databases are sets of formulae tagged with deductive histories and the contexts they belong to • abduction and revision are supported by a notion of consistency of formulae and sets of formulae which are relative to a context, and which can, in turn, be seen as constituents of agendas.
Logical AI develops computer programs that represent what they know about the world primarily by logical formulas and decide what to do primarily by logical reasoning--including nonmonotonic logical reasoning. It is convenient to use logical sentences and terms whose meaning depends on context. The reasons for this are similar to what causes human language to use context dependent meanings. This note gives elements of some of the formalisms to which we have been led. Fuller treatments are in [McC93], [Guh91] and [MB94] and the references cited in the Web page [Buv95]. The first main idea is to make contexts first class objects in the logic and use the formula ist(c,p) to assert that the proposition p is true in the context c. A second idea is to formalize how propositions true in one context transform when they are moved to different but related contexts. An ability to transcend the outermost context is needed to give computer programs the ability to reason about the totality of all they have thought about so far [McC96].
On two standard views of vagueness, vagueness as to whether Harry is bald entails that nobody knows whether Harry is bald—either because vagueness is a type of missing truth, and so there is nothing to know, or because vagueness is a type of ignorance, and so even though there is a truth of the matter, nobody can know what that truth is. Vagueness as to whether Harry is bald does entail that nobody clearly knows that Harry is bald and that nobody clearly knows that Harry is not bald. But it does not entail that nobody knows that Harry is bald or that nobody knows that Harry is not bald. Hence, the two standard views of vagueness are mistaken.
A number of philosophers have argued that the key to understanding the semantic paradoxes is to recognize that truth is essentially relative to context. All of these philosophers have been motivated by the idea that once a liar sentence has been uttered we can ‘step back’ and, from the point of view of a different context, judge that the liar sentence is true. This paper argues that this ‘stepping back’ idea is a mistake that results from failing to relativize truth to context in the first place. Moreover, context-relative liar sentences, such as ‘This sentence is not true in any context’ present a paradox even after truth has been relativized to context. Nonetheless, the relativization of truth to context may offer us the means to avoid paradox, if we can justifiably deny that a sentence about a context can be true in the very context it is about.
By the law of excluded middle, either ‘A is B’ or ‘A is not B’ must be true. Hence either ‘the present King of France is bald’ or ‘the present King of France is not bald’ must be true. Yet if we enumerated the things that are bald, and then the things that are not bald, we should not find the present King of France in either list. Hegelians, who love a synthesis, will probably conclude that he wears a wig. (p. 233).
In this work the concept of 'context' is considered in five main points. First, context is seen as always necessary for an adequate explication of the concepts of meaning and understanding. Context always plays a role and is not merely brought into consideration when handling a special class of statements or terms, or when there is doubt and clarification is necessary. Second, context cannot be completely reduced to some system of representation. The reason for this is the presence of humans, which is always an important component of a context. Humans experience situations in ways that are not always reducible to symbolic representation. Third, contexts are in principle open. In normal cases they cannot be determined or described in advance. A context is not to be equated with a set of information. Fourth, we understand the parameters of a context pragmatically, which is why we are not led into doubt or even to meaning skepticism by the open nature of a context. This pragmatic knowledge belongs to the category of an ability. Fifth, contexts are, in principle, accessible. This denies the idea that some contexts are incommensurable. There are a number of pragmatic ways of accessing unfamiliar contexts. Some of these are here examined in light of the so-called 'culture wars' in the U.S.A.
No categories
Standardly, one says that vagueness arises whenever a concept or linguistic expression admits of borderline cases of application. A predicate such as ‘bald’, for example, is vague because there can be situations in which it is indeterminate whether or not it applies to (a name of) a certain object. Some people are clearly bald (Picasso), some are clearly not bald (the count of Montecristo), and some are borderline cases—our concept of baldness and our linguistic practices do not specify any exact number of hairs that marks the boundary between the bald and the non-bald. Similarly, a singular term such as ‘Mount Everest’ is vague because there is no determinate way of tracing the geographical limits of its referent. Some rocks are clearly part of Everest and some are clearly not, but some rocks enjoy a borderline status.
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.
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