Vagueness (Problems of Philosophy)

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One way is to introduce the machinery of acceptable sharpenings, and reinterpret truth as truth-in-all-sharpenings or truth-in-some-sharpenings. A major selling point has been the conservativism of the resulting systems with respect to classical theoremhood and inference. Supervaluationism and subvaluationism possess interesting formal symmetries, a fact that has been used to argue for the subvaluationist approach.

However, the philosophical motivation behind each is a different matter. Subvaluationism comes with a standard story that is difficult to sign up The acceptability intuitions of each member of a linguistic community amount to their voting for one or more acceptable sharpenings, with truth then characterised as truth-in-a--sufficiency-of-sharpenings. This produces a family of logical systems that are close relations of subvaluationism, share its conservatism results, yet have stronger philosophical foundations in the workings of externalist content.

Vagueness: an introduction (sort of)

Stewart Shapiro's aim in Vagueness in Context is to develop both a philosophical and a formal, model-theoretic account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases.

A person can be tall with respect to male accountants and not tall with respect to professional basketball players. The main feature A central thesis is that in some cases, a competent speaker of the language can go either way in the borderline area of a vague predicate without sinning against the meaning of the words and the non-linguistic facts.

Shapiro calls this open texture, borrowing the term from Friedrich Waismann. The formal model theory has a similar structure to the supervaluationist approach, employing the notion of a sharpening of a base interpretation.

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In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity. The ultimate goal of the technical aspects of the work is to delimit a plausible notion of logical consequence, and to explore what happens with the sorites paradox.

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Later chapters deal with what passes for higher-order vagueness - vagueness in the notions of 'determinacy' and 'borderline' - and with vague singular terms, or objects. In each case, the philosophical picture is developed by extending and modifying the original account. This is followed with modifications to the model theory and the central meta-theorems.

As Shapiro sees it, vagueness is a linguistic phenomenon, due to the kinds of languages that humans speak. But vagueness is also due to the world we find ourselves in, as we try to communicate features of it to each other. Vagueness is also due to the kinds of beings we are.


There is no need to blame the phenomenon on any one of those aspects. In the context of classical crisp, precise sets, there is a familiar connection between the notions of counting, ordering and cardinality. When it comes to vague collections, the connection has not been kept in central focus: there have been numerous proposals regarding the cardinality of vague collections, but these proposals have tended to be discussed in isolation from issues of counting and ordering.

My main concern in this paper is to draw focus back onto the connection between these notions. I then discuss the relationships between this process of counting and various notions of ordering and cardinality for vague sets. Some existing views concerning the cardinality of vague collections fit better than others with my proposal about how to count the members of such a collection.

In particular, the idea that we should approach cardinality via certain formulas of a logical language -- which has been prominent in the recent literature -- is less attractive than other existing proposals. 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. 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. 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. Hilary Putnam has suggested that logic and metaphysics are intimately connected so that logic is dependent upon metaphysics. According to Putnam, the validity of classical logic depends upon the truth of metaphysical realism, whereas the truth of metaphysical anti-realism will justify only some alternative to classical logic.

Moreover, if Putnam's suggestion is correct, then even an attempt to defend one semantics of vagueness over another must include a defense of some metaphysical view. Many semantics for vague languages have been offered in the literature. Two such semantics which have received attention are supervaluation semantics, which justifies classical logic and the Lakoff-Zadeh many-valued semantics, which does not.

There has been varied praise and criticism of each of these approaches, yet no consensus has arisen as to which semantics is to be preferred.

Vagueness – Word Philosophy: An Introductory Anthology

I argue that logic is not dependent upon metaphysics in the way Putnam suggests it is. The justification of logic, in fact, depends upon our linguistic practice. I then use this claim to show that supervaluation semantics is preferable to the Lakoff-Zadeh semantics for natural language. That theory is shown to be incompatible with supervaluation semantic.

Vagueness and Law

I also examine some classical many-valued semantics and find them either inadequate for vague natural language or incompatible with the prosentential theory. I conclude that the prosentential theorist is severely limited when it comes to selecting a semantics for natural language.

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Areas of Mathematics in Philosophy of Mathematics. Prosentential Theory of Truth in Philosophy of Language. The current project is to assess the implication of vague predicates for metaphysics, logic and the philosophy of mind. In the area of metaphysics, it is argued that vagueness shows certain types of metaphysical realism to be untenable. With respect to what constitutes the best logic of vagueness, the favored approach is argued to be a form of supervaluation semantics. Finally, it is argued that vague predicates prove problematic for certain stances in the philosophy of mind, most notably, the stance Theories of Vagueness, Misc in Philosophy of Language.

Today, "The Sorites paradox" is used to refer to a class of paradoxical arguments having a similar form. An example is: A man weighing lbs. Therefore, a man weighing lbs. What makes the argument paradoxical is that while it seems both to be valid and to have true premises, it clearly has a false conclusion. Strawson , Robert Brandom, and others. Reference theories of meaning , also known collectively as semantic externalism , view meaning to be equivalent to those things in the world that are actually connected to signs. There are two broad sub-species of externalism: social and environmental.

Verificationist theories of meaning are generally associated with the early twentieth century movement of logical positivism. In this form, the thesis was abandoned after the acceptance by most philosophers of the Duhem-Quine thesis of confirmation holism after the publication of Quine 's Two Dogmas of Empiricism.

In this version, the comprehension and hence meaning of a sentence consists in the hearer's ability to recognize the demonstration mathematical, empirical or other of the truth of the sentence.

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A pragmatist theory of meaning is any theory in which the meaning or understanding of a sentence is determined by the consequences of its application. Dummett attributes such a theory of meaning to C. Peirce and other early twentieth-century American pragmatists. Other theories exist to discuss non-linguistic meaning i.

Investigations into how language interacts with the world are called "theories of reference. Frege divided the semantic content of every expression, including sentences, into two components: Sinn usually translated as "sense" and Bedeutung translated as "meaning," "denotation," "nominatum," and "reference," among others. The sense of a sentence is the thought that it expresses. Such a thought is abstract, universal and objective.

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