Many-valued logics formalize ideas that a realistic characterization of the notion of consequence requires the admissibility of premises which, owing to vagueness, temporal or quantum indeterminacy, or reference-failure, cannot be considered classically bivalent.

To eliminate the inherent vagueness of this notion Jordan in 1887 introduced the following rigorous definition, which has since been adopted as the precise description of the notion of a continuous curve:

* " La vague des passions " ( vagueness, uncertainty of sentiment and passion ): Chateaubriand maintained that while the imagination was rich, the world was cold and empty, and rationalism and civilization had only robbed men of their illusions ; nevertheless, a notion of sentiment and passion continued to haunt men.

It is essential to realize that fuzzy logic uses truth degrees as a mathematical model of the vagueness phenomenon while probability is a mathematical model of ignorance.

Weyl predicted that in the subsequent 20 years, mathematicians would come to realize the total vagueness of notions such as real numbers, sets, and countability, and moreover, that asking about the truth or falsity of the least upper bound property of the real numbers was as meaningful as asking about truth of the basic assertions of Hegel on the philosophy of nature.

In everyday speech, vagueness is an inevitable, often even desired effect of language usage.

The group contends that mandatory motorcycle helmet laws enacted at the state, county, and municipal levels of government against consumers and users are unconstitutional due to vagueness, and this often results in arbitrary and ad hoc enforcement in those states which have enacted mandatory helmet laws.

When the breadth or vagueness of a lexical definition is unacceptable, a precising definition or a stipulative definition is often used.

Because of the vagueness of early symptoms and rapid progression of the disease, diagnosis is often not reached until very late in the course of the disease.

But even without adding this element to the story, the vagueness of the account prohibits one from being objectively clear about which formalization truly captures its essence.

A late start, uncertainty about the direction the Prussians had taken, and the vagueness of the orders given to Grouchy meant that he was too late to prevent the Prussian army reaching Wavre, from where it could march to support Wellington.

In practice, there is a great deal of vagueness about dispositionality ( for example, what exactly constitutes a permutation?

Whitehead contends that the human way of understanding existence as a unity of interlocking and interdependent processes which constitute each other and which cause each other to be and not to be is possible only because the basic form of such an understanding, for all its vagueness and tendency to mistake the detail, is initially given in the way man feels the world.

The vagueness of OBE's conception of a " measurable outcome " is a particular challenge, both in implementing an OBE regime and in testing its effectiveness.

In parecon, it constitutes a replacement for the mainstream economic conception of economic freedom, which Albert and Hahnel argue that by its very vagueness has allowed it to be abused by capitalist ideologues.

In church matters, as in philosophy, the two were opposed — Pletho advocated a partial return to Greek paganism in the form of a syncretic union between Christianity and Zoroastrianism ; while Georgios, more cautious, pressed the necessity for ecclesiastical union with Rome on doctrinal grounds, and was instrumental in drawing up a form which from its vagueness and ambiguity might be accepted by both parties.

Gorin v. United States was cited in many later espionage cases for its discussion of the charge of " vagueness " argument made against the terminology used in certain portions of the law, such as what constitutes " national defense " information.

It also, by its vagueness, is almost as broad as the wording in the 1935 statute.

Naïve realism may accommodate these facts as they stand by virtue of its very vagueness ( or ‘ open-texture ’): it isn ’ t specific or detailed enough to be refuted by such cases.

The New Jersey Superior Court ruled the law was void because of its vagueness.

In Papachristou v. Jacksonville,, the Court held that a traditional vagrancy law was void for vagueness because its “ broad scope and imprecise terms denied proper notice to potential offenders and permitted police officers to exercise unfettered discretion in the enforcement of the law .” In Brown v. Texas,, the Court struck down Texas ’ s stop-and-identify law as violating the Fourth Amendment because it allowed police officers to stop individuals without “ specific, objective facts establishing reasonable suspicion to believe the suspect was involved in criminal activity .” And in Kolender v. Lawson,, the Court struck down a California stop-and-identify law that required a suspect to provide “ credible and reliable identification ” upon request.

Some attacked it for its apparent discontinuity with Utilitarianism, while others criticized its vagueness.

Critics of the concept argue that its vagueness undermines its effectiveness ; that it has become little more than a vehicle for activists wishing to promote certain causes ; and that it does not help the research community understand what security means or help decision makers to formulate good policies.

The Latin term does not a have a legal definition and possibly was deliberately was chosen for its vagueness.

Many organizations criticised this clause for its vagueness.

Conversely, others have criticized the new test for its apparent vagueness, contending that it permits financially powerful organizations such as the RIAA and MPAA to effectively hinder development of new technology by active pursuit of litigation against the developers and distributors.

Jon Pareles of The New York Times described it as " inspirational ", and felt that due to its vagueness, the song is would be applicable to all listeners, not just Carey.

According to Aronowitz, the vagueness of Luxembourgian democracy is one reason for its initial difficulty in gaining widespread support.

Aoun's main objection to the Taif Agreement was its vagueness as to Syrian withdrawal from the country.

The detection, with its emphasis on who-was-where-and-when, is a little too like Ngaio Marsh of the period, and there is some vagueness in the motivation, but this is as taut and atmospheric as any she wrote.

The clear differences between these two periods explains the variety and vagueness of meaning attaching to the term " Alexandrian School.

An alternative was found in the vagueness of state law as to whether the offending order had in fact been authorized.

A certain vagueness may also be caused by tactical appreciation of the fact that the present council meeting is a semipublic affair, with no fewer than six Soviet correspondents accredited.

It is generally contrasted with vagueness, in that specific and distinct interpretations are permitted ( although some may not be immediately apparent ), whereas with information that is vague it is difficult to form any interpretation at the desired level of specificity.

This form of ambiguity is closely related to vagueness.

Although the description sitting-on ( graph 1 ) is more abstract than the graphic image of a cat sitting on a mat ( picture 1 ), the delineation of abstract things from concrete things is somewhat ambiguous ; this ambiguity or vagueness is characteristic of abstraction.

This difficult transition combined with political vagueness, unpreparedness of people for the social and economic changes led to seriously worsen economic conditions during early 1990s.

The fifth and sixth paradoxes are also a single paradox and is usually thought to relate to the vagueness of language.

Those who work within the free software community have searched for less ambiguous terms in efforts to refine their definition so there is no confusion, but have struggle to find words that do not yield vagueness.

Both the terms " warm-blooded " and " cold-blooded " have fallen out of favour with scientists because of the vagueness of the terms and an increased understanding of the field.

" Imminent danger " was found to have too much variability throughout Virginia due to vagueness.

Research in NLP evaluation has received considerable attention, because the definition of proper evaluation criteria is one way to specify precisely an NLP problem, going thus beyond the vagueness of tasks defined only as language understanding or language generation.

While this episode did not dissuade fundamentalists from continuing to object to what they regarded as the " teaching of Secular Humanism ", it did point out the vagueness of the claim.

Some of the challenges for the Semantic Web include vastness, vagueness, uncertainty, inconsistency, and deceit.

This arises from the vagueness of user queries, of concepts represented by content providers, of matching query terms to provider terms and of trying to combine different knowledge bases with overlapping but subtly different concepts.

Fuzzy logic is the most common technique for dealing with vagueness.

They state that lack of definition of obscenity in the statutes, coupled with the existence of hypothetical entities and standards as ultimate arbiters within the Miller Test ( hypothetical " reasonable persons " and " contemporary community standards ") proves that federal obscenity laws are in fact not defined, do not satisfy the vagueness doctrine, and thus are unenforceable and legally dubious.

However, in most specialized texts ( e. g., legal documents ), vagueness is distracting and should be avoided whenever possible.

The philosophical question of what the best theoretical treatment of vagueness is-which is closely related to the problem of the paradox of the heap-has been the subject of much philosophical debate.

Still by, for instance, proposing alternative deduction rules involving Leibniz's law or other rules for validity some philosophers are willing to defend vagueness as some kind of metaphysical phenomenon.