145 Sentences With "definiteness" | Random Sentence Generator

For that reason, it is unlikely ordinary people can understand, with any definiteness, what sort of conduct is prohibited.

Adjectives follow the nominal heads of noun phrases. They agree in gender, number, case, and definiteness, and carry case and definiteness markers of the same form as nouns.

The indefinite article is -ek for animates and -ak for inanimates. The indefinite article exists only in the singular, where its absence marks definiteness. In the plural, (in)definiteness does not receive special marking.

Nouns in Maldivian inflect for definiteness, number and case. Definiteness may be one of definite, indefinite or unspecified. Number may be singular or plural. Case may be one of nominative, dative, ablative, genitive, locative, instrumental or emphatic.

The main features marked on Sinhala nouns are case, number, definiteness and animacy.

Swedish adjectives are declined according to gender, number, and definiteness of the noun.

Different interpretations of quantum mechanics violate different parts of local realism and/or counterfactual definiteness.

Adjectives (придавки, pridavki) agree with nouns in gender, number and definiteness with their noun and usually appear before it.

Nominal morphology includes a definiteness suffix, whose form depends on the gender of the head noun, and possessive suffixes.

In linguistics, definiteness is a semantic feature of noun phrases (NPs), distinguishing between referents or entities that are identifiable in a given context (definite noun phrases) and entities which are not (indefinite noun phrases). There is considerable variation in the expression of definiteness across languages and some languages do not express it at all. For example, in English definiteness is usually marked by the selection of determiner. Certain determiners, such as a, an, many, any, either, and some, typically mark an NP as indefinite.

Aristotle defines beauty in Metaphysics as having order, symmetry and definiteness which the mathematical sciences exhibit in a special degree.

Definiteness is expressed if the speaker assumes the hearer has background knowledge on the nominal being inserted into the conversation.

Her valuable assistance has contributed very > materially to the definiteness of the conclusions that it has been possible > to arrive at.

Bulgarian nouns have the categories grammatical gender, number, case (only vocative) and definiteness. A noun has one of three specific grammatical genders (masculine, feminine, neuter) and two numbers (singular and plural), With cardinal numbers and some adverbs, masculine nouns use a separate count form. Definiteness is expressed by a definite article which is postfixed to the noun.

The definite article al- is not typically prefixed to nouns that do not inflect for definiteness. Examples include the interrogative man 'who'.

Tayo nouns do not display much internal morphology, with some number and definiteness information encoded in modifiers and clitics outside of the noun.

The definite article spread areally among the Central Semitic languages and it would seem that Proto-Arabic lacked any overt marking of definiteness.

In Norwegian nynorsk, Swedish, Icelandic and Faroese the past participle must agree in gender, number and definiteness when the participle is in an attributive or predicative position. In Icelandic and Faroese, past participles would also have to agree in grammatical case. In Norwegian bokmål and Danish it is only required to decline past participles in number and definiteness when in an attributive position.

Technically, counterfactual definiteness is lacking. A notable consequence of quantum indeterminism is the Heisenberg uncertainty principle, which prevents the simultaneous accurate measurement of all a particle's properties.

In the nominal morphology there is no inflection for case or definiteness, the morphological categories being number, state (absolute vs. construct) and person (of the possessor, with construct state).

Whereas in finite dimensions every inner product is nondegenerate, in infinite dimensions inner products are (at least) weakly nondegenerate (this can be shown using positive-definiteness of inner products).

In some languages definiteness can be seen a morphological category of nouns. For example, in some Scandinavian languages, such as Swedish, definite nouns inflect with a dedicated set of suffixes. This is known in Swedish as the grammatical category of Species. In Semitic languages the category of state is sometimes tied to definiteness, as some Semitic languages are said to distinguish between three morphological states: Indefinite (Absolute) State, Definite (Emphatic) State, and Construct State.

Nouns are classified according to animacy.Leman 2011, p.5. They change according to grammatical number (singular and plural) but are not distinguished according to genderPetter 1905, p.456. or definiteness.

A Bulgarian adjective agrees in gender, number and definiteness with the noun it is appended to and is put usually before it. The comparative and the superlative form are formed analytically.

The major uses of affixation in Jingulu are found in the expression of demonstratives, as well as the nominal features pronouns, case, number, and (in)definiteness discussed in the next section.

Macedonian nouns (именки, imenki) belong to one of three genders (masculine, feminine and neuter) and are inflected for number (singular and plural), and marginally for case. The gender opposition is not distinctively marked in the plural. The Macedonian nominal system distinguishes two numbers (singular and plural), three genders (masculine, feminine and neuter), case and definiteness. Definiteness is expressed by three definite articles pertaining to the position of the object (unspecified, proximal, and distal) which are suffixed to the noun.

Chara is a subject–object–verb language. Adjectives end in /-a/ like nouns, and inflect for number, definiteness, plurality, and case. In noun phrases adjectives precede their nouns, and are not inflected.

Others, including the, this, every, and both, mark the NP as definite. In some other languages, the marker is a clitic that attaches phonologically to the noun (and often to modifying adjectives): the Hebrew definite article ha- or the Arabic definite article al-. In yet other languages, definiteness is indicated by affixes on the noun or on modifying adjectives, much like the expression of grammatical number and grammatical case. In those languages, the inflections indicating definiteness may be quite complex.

Kashmiri nouns are inflected according to gender, number and case. There are no articles, nor is there any grammatical distinction for definiteness, although there is some optional adverbial marking for indefinite or "generic" noun qualities.

Unlike in more conservative Germanic languages (e.g. German), putting a noun into a prepositional phrase doesn't alter its inflection, case, number or definiteness in any way, except in a very small number of set phrases.

Any of the axioms of an inner product may be weakened, yielding generalized notions. The generalizations that are closest to inner products occur where bilinearity and conjugate symmetry are retained, but positive-definiteness is weakened.

The kinds of expressions which can refer are: # a noun phrase of any structure, such as: the taxi in The taxi's waiting outside; the apple on the table in Bring me the apple on the table; and those five boys in Those five boys were off school last week. In those languages which, like English, encode definiteness, REs are typically marked for definiteness. In the examples given, this is done by the definite article the or the demonstrative adjective, here those. # a noun-phrase surrogate, i.e.

There is no definite article. But when necessary, definiteness may be indicated by other means such as demonstratives. Likewise, it may be contraindicated by use of the word for "one", يو; as in "يو روغتون" - "a hospital".

Bulgarian pronouns vary in gender, number, definiteness and case. They, more than any other part of speech, have preserved the proto-Slavic case system. Pronouns are classified as: personal, possessive, interrogative, demonstrative, reflexive, summative, negative, indefinite and relative.

Urtzi Etxeberria, Lilia Schurcks (eds), Series: Studies in Generative Grammar 116, Mouton de Gruyter. . 2009\. Quantification, Definiteness, and Nominalization. Giannakidou Anastasia and Monika Rathert (eds), Series Oxford Studies in Theoretical Linguistics, Oxford University Press. 1998\. Polarity Sensitivity as (Non)veridical Dependency.

Articles are words used with a noun (as a standalone word or a prefix or suffix) to specify the grammatical definiteness of a noun, and, in some languages, to volume or numerical scope. There are three articles 'a', 'an' and 'the'.

The functional motivation for the implementation of differential subject and object marking is to avoid ambiguity as to what is subject and object in transitive clauses. The most natural hierarchy of animacy and definiteness places transitive subjects higher than transitive object.

Associated with propagation of a disturbance are several different velocities. For definiteness, consider an amplitude modulated electromagnetic carrier wave. The phase velocity is the speed of the underlying carrier wave. The group velocity is the speed of the modulation or envelope.

Though in English the possessive determiners indicate definiteness, in other languages the definiteness needs to be added separately for grammatical correctness. In Norwegian the phrase "my book" would be boka mi,In Norwegian bokmål written form, the phrase could alternatively be written as min bok due to bokmål's Danish heritage. where boka is the definite form of the feminine noun bok (book), and mi (my) is the possessive pronoun following feminine singular nouns. In some Romance languages such as French and Italian, the gender of the possessive determiners agrees with the thing(s) owned, not with the owner.

The basic word order is VOS. However, word order varies and VOS is not always grammatical: factors including animacy, definiteness, topicalization and focus contribute to determining which word order is appropriate. Vázquez Álvarez, Juan Jesús. A Grammar of Chol, a Mayan Language.

Amharic has an accusative marker, -(ə)n. Its use is related to the definiteness of the object, thus Amharic shows differential object marking. In general, if the object is definite, possessed, or a proper noun, the accusative must be used (Leslau 1995: pp. 181 ff.).

Relative clauses and genitive phrases precede nouns, whereas markers for demonstratives, definiteness, number, case, and other particles follow the noun. Lepcha is an ergative language, where the ergative case indicates transitivity and completedness of the event. There is no grammatical agreement between different parts of speech (i.e. verb conjugation).

In the Germanic languages and Balto-Slavic languages, for example (as still in modern German and Lithuanian), there are two paradigms for adjectives, one used in definite noun phrases and the other used in indefinite noun phrases. In some languages, such as Hungarian, definiteness is marked on the verb.

Nouns and adjectives have the categories grammatical gender, number, case (only vocative) and definiteness in Bulgarian. Adjectives and adjectival pronouns agree with nouns in number and gender. Pronouns have gender and number and retain (as in nearly all Indo-European languages) a more significant part of the case system.

The Latvian language is a moderately inflected language, with complex nominal and verbal morphology. Word order is relatively free, but the unmarked order is SVO. Latvian has pre-nominal adjectives and both prepositions and postpositions. There are no articles in Latvian, but definiteness can be indicated by the endings of adjectives.

Zhu 2006, pp.59. ::xuqsang-la xeq sir ::“students’ books” There are no articles in Shanghainese,Zhu 2006, pp.59. and thus, no marking for definiteness or indefiniteness of nouns. Certain determiners (a demonstrative pronoun or numeral classifier, for instance) can imply definite or indefinite qualities, as can word order.

The book states that "the production of all thought-forms" is based on three major principles: > # Quality of thought determines colour. # Nature of thought determines form. > # Definiteness of thought determines clearness of outline. The authors define the following three classes of thought-forms: > # That which takes the image of the thinker.

Pronouns may vary in gender, number, and definiteness, and are the only parts of speech that have retained case inflections. Three cases are exhibited by some groups of pronouns – nominative, accusative and dative. The distinguishable types of pronouns include the following: personal, relative, reflexive, interrogative, negative, indefinitive, summative and possessive.

In very early Semitic languages, definiteness was achieved through gemination of the first letter in a word. For example, the word kitāb would be made definite by ak-kitāb. An additional benefit of this construction was to connote "determination". The lām in the Arabic al- was thus a result of a dissimilation process.

The an, on and in declensions constitute a Germanic word derivation, which is also used for adjectives in the weak form marking definiteness. The declension loosely parallels the Latin nouns in -ō, genitive -ōnis/-inis, which shares the same Indo-European declensional origin (the Greek descendant being the more regularized -ōn, -onos class).

Beja nouns and adjectives have two genders: masculine and feminine, two numbers: singular and plural, two cases: nominative and oblique, and may be definite, indefinite, or in construct state. Gender, case, and definiteness are not marked on the noun itself, but on clitics and affixes. Singular-plural pairs in Beja are unpredictable.

Adjectives in Latvian agree in case, number, and gender with the noun they modify. In addition, they express the category of definiteness. Latvian has no definite and indefinite articles, but the form of the adjective chosen can determine the correct interpretation of the noun phrase. For example, consider the following examples: :Viņa nopirka [vecu māju].

Nouns are inflected for number (singular vs. plural) and definiteness, and are classified into two grammatical genders. Only pronouns inflect for case, and the previous genitive case has become an enclitic. A distinctive feature of the Nordic languages, including Danish, is that the definite articles, which also mark noun gender, have developed into suffixes.

The traditional Copenhagen interpretation of quantum mechanics rejects counterfactual definiteness as it does not ascribe any value at all to a measurement that was not performed. When measurements are performed, values result, but these are not considered to be revelations of pre-existing values. In the words of Asher Peres "unperformed experiments have no results".

Albanian has two grammatical genders, feminine and masculine, neuter is not distinct from masculine. Nouns are morphologically altered for number (singular/plural), definiteness (indefinite/definite), and case. The cases are nominative, accusative, dative, ablative and vocative. Many texts include a genitive case, but this is produced using a linking clitic (see below) and is morphologically identical to the dative.

Latvian grammar represents a classic Indo-European (Baltic) system with well-developed inflection and derivation. Primary word stress, with some exceptions in derivation and inflection, is on the first syllable. There are no articles in Latvian; definiteness is expressed by an inflection of adjectives. Basic word order in Latvian is subject–verb–object; however, word order is relatively free.

Alternatively one might use the case form -ndaulum 'from' and u:a 'man' giving Ushuaia-ndaulum-u:a. Subject nouns take no overt case marking (subject coreference is on the verb instead). Nouns can be marked for accusative, genitive, dative, locative, instrumental and other cases. Geographical information can be incorporated into the string, as can information about number, collectivity, definiteness, etc.

Many statistical distances are not metrics, because they lack one or more properties of proper metrics. For example, pseudometrics violate the "positive definiteness" (alternatively, "identity of indescernibles") property (1 & 2 above); quasimetrics violate the symmetry property (3); and semimetrics violate the triangle inequality (4). Statistical distances that satisfy (1) and (2) are referred to as divergences.

In computer science, having value semantics (also value-type semantics or copy-by-value semantics) means for an object that only its value counts, not its identity. If the concept is fully applied, value semantics implies immutability of the object. The concepts that are used to explain this concept are extensionality, definiteness, substitutivity of identity, unfoldability, and referential transparency.

Willem de Muynck describes an "objective- realist" version of the ensemble interpretation featuring counterfactual definiteness and the "possessed values principle", in which values of the quantum mechanical observables may be attributed to the object as objective properties the object possesses independent of observation. He states that there are "strong indications, if not proofs" that neither is a possible assumption.

Such a system exists for instance in Old Aramaic. Yet in other Semitic languages, like Hebrew or Arabic, definiteness is marked by a pro-clitic, and the state category relates only to the question whether a nominal is necessarily modified by a complement (and is thus in the construct state) or not (being in the free state).

Nunation (, ' ), in some Semitic languages such as Literary Arabic, is the addition of one of three vowel diacritics (ḥarakāt) to a noun or adjective. This is used to indicate the word ends in an alveolar nasal without the addition of the letter nūn. The noun phrase is fully declinable and syntactically unmarked for definiteness, identifiable in speech.

The Dual - These nouns denote two of something. They decline very similarly to the sound masculine plurals because they are not marked for definiteness and look the same in both the accusative and genitive cases. For the nominative, the marking is -āni and for the accusative/genitive, -ayni. An example is "parents," which is wālidāni and wālidayni respectively.

These nouns are marked only for definiteness, as morpho-phonotactic processes have resulted in the complete loss of the case distinctions. When indefinite, they take -an, which rests on an alif maqṣūrah or occasionally '. When definite, they are not marked, and they simply retain their long ' or '. An example is "hospital," which is mustashfan and ' respectively.

Linguists today distinguish determiners from adjectives, considering them to be two separate parts of speech (or lexical categories). But formerly determiners were considered to be adjectives in some of their uses. Determiners are words that are neither nouns nor pronouns, yet reference a thing already in context. They generally do this by indicating definiteness (a vs.

The existence of Hismaic and Safaitic varieties without a definite article strongly suggests that their ancestor lacked a morphological means of definiteness. The definite article entered these varieties through contact with Northwest Semitic languages in the southern Levant. Evidence for such contact is given by a possibly bilingual North Arabian-Canaanite inscription containing a prayer to the gods Malkom, Kemōš, and Qaws.

The language has no overt articles and it seems like these two forms are related to definiteness and/or specificity in some way. Derivational and inflectional affixes associated with nouns are always suffixes, with the exception of the prefixes kip – and che:p -, which denote male and female gender respectively. Gender is not expressed in all nouns, and does not participate in agreement.

In Classical Arabic and Modern Standard Arabic (MSA), nouns and adjectives ( ') are declined, according to case ('), state (definiteness), gender and number. In colloquial or spoken Arabic, there are a number of simplifications such as the loss of certain final vowels and the loss of case. A number of derivational processes exist for forming new nouns and adjectives. Adverbs can be formed from adjectives.

Chiquihuitlán Mazatec distinguishes between three person categories (first, second, and third) and two numbers (singular, plural), and for the first person plural, it distinguishes between inclusive and exclusive categories. In the third person, number is not specified but only definiteness (definite or indefinite). Number is not expressed by free pronouns or noun phrases if it is directly retrievable from context.

This is a glossary of properties and concepts in symplectic geometry in mathematics. The terms listed here cover the occurrences of symplectic geometry both in topology as well as in algebraic geometry (over the complex numbers for definiteness). The glossary also includes notions from Hamiltonian geometry, Poisson geometry and geometric quantization. In addition, this glossary also includes some concepts (e.g.

The fact that certain events seem to 'cause' other events is the recognition of a pattern in the structure of spacetime and the mass-energy that exists in spacetime, which is ultimately either due OR an instantiation of the laws of physics. Note: Stating that causality does not exist may be a bit misleading, as one would have to Define what is meant by 'causality' - it may be that causality is dependent upon counterfactual definiteness, that is, A causes B because, if A did NOT occur, then B would not occur (i.e.: A is necessary for B) AND because A is sufficient for B. It may be possible that causality is ultimately a meaningless concept (if one rejects counterfactual definiteness for instance), but that causal chains are still a valid concept (as they would merely be chains of events).

Judge Campbell dissented, arguing that the court's decision renders the CFAA's provisions unconstitutionally vague, since computer use policies are not written "with the definiteness or precision that would be required for a criminal statute" and they can be changed without notice. The ruling, she argued, places an undue burden on employees to stay current on such policies in order to protect themselves against possible criminal prosecution.

3sg düšǘntsü < düšǘntsi (Malakopi), from Turkish düşünmek, patišáxıs < patišáxis 'king' (Delmeso), from Turkish padişah. Cappadocian noun morphology is characterized by the emergence of a generalized agglutinative declension and the progressive loss of grammatical gender distinctions, e.g. to néka 'the (neuter) woman (feminine)', genitive néka-ju, plural nékes, genitive nékez-ju (Uluağaç). Another Turkish feature is the morphological marking of definiteness in the accusative case, e.g.

The name Kjeåsen comes from kje 'kid' and ås 'hill', inflected for definiteness. The farm has been inhabited at least since the 1650s. Until the road up to the farm was built, all transport took place on the steep path from the bottom of the fjord. In the 1930s a cable car was built that could carry food and others material up to the farm.

Tamil has no articles. Definiteness and indefiniteness are either indicated by special grammatical devices, such as using the number "one" as an indefinite article, or by the context. In the first person plural, Tamil makes a distinction between inclusive pronouns that include the listener and exclusive pronouns that do not. Tamil does not distinguish between adjectives and adverbs - both fall under the category uriccol.

According to Jacob Barth, who was lecturer in Hebrew at the Hildesheimer Rabbinical Seminary, al- comes directly from the Arabic negating particle, lā. He conjectures that lā became al- through a process of metathesis. That is to say, the lām and the alif swapped positions. It is noteworthy that the negation denoted by lā and the definiteness denoted by al- are in stark contrast to each other.

Reaction,Time, Form Definiteness, Movement, and Human also scored relatively high in both cultures. However, these aspects test more of the cognitive-perceptual aspects rather than personality characteristics. Rejection, Form Appropriateness, Shading, Pathognomic Verbalization, Barrier, and Penetration had lower stability coefficients while Space, Sex, Abstract and Balance proved to be extremely infrequent in the children's samples. Test results generally became more stable with age.

In the Scandinavian languages, adjectives (both attributive and predicative) are declined according to the gender, number, and definiteness of the noun they modify. In Icelandic and Faroese, adjectives are also declined according to grammatical case, unlike the other Scandinavian languages. In some cases in Swedish, Norwegian and Danish, adjectives and participles as predicates appear to disagree with their subjects. This phenomenon is referred to as pancake sentences.

Uyghur is an agglutinative language with a subject–object–verb word order. Nouns are inflected for number and case, but not gender and definiteness like in many other languages. There are two numbers: singular and plural and six different cases: nominative, accusative, dative, locative, ablative and genitive. Verbs are conjugated for tense: present and past; voice: causative and passive; aspect: continuous and mood: e.g. ability.

Hungarian grammar is the grammar of Hungarian, a Finno-Ugric language that is spoken mainly in Hungary and in parts of its seven neighboring countries. Hungarian, a highly agglutinative language, uses various affixes, mainly suffixes, to change the meaning of words and their grammatical function. These affixes are mostly attached according to vowel harmony. Verbs are conjugated according to definiteness, tense, mood, person and number.

Norn grammar had features very similar to the other Scandinavian languages. There were two numbers, three genders and four cases (nominative, accusative, genitive and dative). The two main conjugations of verbs in present and past tense were also present. Like all other North Germanic languages, it used a suffix instead of a prepositioned article to indicate definiteness as in modern Scandinavian: ' ("man"); ' ("the man").

Evidence for a DP-projection in West Greenlandic Inuit. Canadian Journal of Linguistics/Revue Canadienne De Linguistique 60 (3): 327. Within this tree, which corresponds to the data above, it is evident that the possessor head is intended to host any possessive markers. This tree also shows a functional projection (FP) sharing features such as person and number with the matrix DP. A head is also needed for valuation of definiteness.

Differential marking is known to be affected by a range of semantic and information structure factors. These include semantic properties of the argument such as animacy, definiteness and referentiality. It also includes properties related to the event semantics, such as the affectedness of arguments or the level of volitionality or control. Finally, in many languages, differential marking is related to the status of arguments as either topical or focal.

Finsler's lemma is a mathematical result named after Paul Finsler. It states equivalent ways to express the positive definiteness of a quadratic form Q constrained by a linear form L. Since it is equivalent to another lemmas used in optimization and control theory, such as Yakubovich's S-lemma, Finsler's lemma has been given many proofs and has been widely used, particularly in results related to robust optimization and linear matrix inequalities.

The versatility of the Mach–Zehnder configuration has led to its being used in a wide range of fundamental research topics in quantum mechanics, including studies on counterfactual definiteness, quantum entanglement, quantum computation, quantum cryptography, quantum logic, Elitzur–Vaidman bomb tester, the quantum eraser experiment, the quantum Zeno effect, and neutron diffraction. In optical telecommunications it is used as an electro-optic modulator for phase and amplitude modulation of light.

Positive-definiteness arises naturally in the theory of the Fourier transform; it can be seen directly that to be positive-definite it is sufficient for f to be the Fourier transform of a function g on the real line with g(y) ≥ 0. The converse result is Bochner's theorem, stating that any continuous positive-definite function on the real line is the Fourier transform of a (positive) measure.

Stone adds finiteness of the process, and definiteness (having no ambiguity in the instructions) to this definition. produce, in a "reasonable" time,Knuth, loc. cit output-integer y at a specified place and in a specified format. The concept of algorithm is also used to define the notion of decidability—a notion that is central for explaining how formal systems come into being starting from a small set of axioms and rules.

The subject of a composition can, therefore, not be understood as an object derived from an external source, but as something intrinsically musical; in other words, as the concrete group of sounds in a piece of music. Now, as a composition must comply with the formal laws of beauty, it cannot run on arbitrarily and at random, but must develop gradually with intelligible and organic definiteness, as buds develop into rich blossoms.”Eduard Hanslick.

DEC Systems Research Center (SRC) Research Report 95 (February 1993) This object model has been shown to have well definiteness decidability (a mechanical proof of it isn't known). The inventor of Baby Modula-3 worked at Systems Research Center (SRC) of Digital Equipment Corporation (DEC) in Palo Alto, California. As DEC was bought by Compaq and Compaq itself was bought by Hewlett-Packard the SRC- report 95 was made available to the public by HP.

Noun roots in Nambikwara typically end in a vowel or the consonant n, t, or h. Classifiers indicating things such as the shape of the referent are suffixed to the root. Some examples include the property of being stick-like (kat3) or powder-like (nũn3). Definiteness (indefinite, definite, or conditional) and causality are also reflected by the use of suffixes. Definite nouns also use additional suffixes to indicate “demonstrativeness, spatio-temporality, evidentiality, and causality”.

The many worlds interpretation rejects counterfactual definiteness in a different sense; instead of not assigning a value to measurements that were not performed, it ascribes many values. When measurements are performed each of these values gets realized as the resulting value in a different world of a branching reality. Thus although unperformed experiments have values, they cannot be used in statistical calculations as one would the single value of a performed experiment. As Prof.

Case- marking is one of the formal guises of differential subject marking, along with agreement, inverse systems and voice alterations, which goes hand in hand with differential subject marking. The use of case marking on subject is to differentiate prominence in arguments. It can be used on subjects of transitive verbs and intransitive verbs. The definiteness and animacy scale of differential subject marking has the same hierarchical structure exhibited in the section on differential object marking.

There is no category of definiteness in Greenlandic and so information on whether participants are already known to the listener or they are new to the discourse is encoded by other means. According to some authors, morphology related to transitivity such as the use of the construction sometimes called antipassiveKappel Schmidt (2003)Sadock (2003) or intransitive objectFortescue (1984) p. 92 & p. 249 conveys such meaning, along with strategies of noun incorporation of non-topical noun phrases.

The negative result of the 1980s tests by Alain Aspect ruled such theories out, provided certain assumptions about the experiment hold. Thus any interpretation of quantum mechanics, including deterministic reformulations, must either reject locality or reject counterfactual definiteness altogether. David Bohm's theory is the main example of a non-local deterministic quantum theory. The many-worlds interpretation is said to be deterministic, but experimental results still cannot be predicted: experimenters do not know which 'world' they will end up in.

In many cases, a phrase with an incorporated noun carries a different meaning with respect to the equivalent phrase where the noun is not incorporated into the verb. The difference seems to hang around the generality and definiteness of the statement. The incorporated phrase is usually generic and indefinite, while the non-incorporated one is more specific. In Yucatec Maya, for example, the phrase "I chopped a tree", when the word for "tree" is incorporated, changes its meaning to "I chopped wood".

Orthographically, the standard orthography writes proclitics as separate words, whereas affixes are written joined to their host root. Most affixes are suffixes and with few exceptions occur only on verbs, whereas the proclitics occur both in nominal and verbal paradigms. Proclitics mark the categories of definiteness and number, person, negation, tense and aspect – often fused in a single proclitic. Suffixes mark direct and indirect objects, as well as clusivity (the distinction between inclusive and exclusive we), number, location and affective emphasis.

Wolof does not mark sexual gender as grammatical gender: there is one pronoun encompassing the English 'he', 'she', and 'it'. The descriptors bu góor (male / masculine) or bu jigéen (female / feminine) are often added to words like xarit, 'friend', and rakk, 'younger sibling' to indicate the person's sex. Markers of noun definiteness (usually called "definite articles") agree with the noun they modify. There are at least ten articles in Wolof, some of them indicating a singular noun, others a plural noun.

The Hebrew noun (שֵׁם עֶצֶם ) is inflected for number and state, but not for case and therefore Hebrew nominal structure is normally not considered to be strictly declensional. Nouns are generally related to verbs (by shared roots), but their formation is not as systematic, often due to loanwords from foreign languages. Hebrew nouns are also inflected for definiteness by application of the prefix ַה (ha) before the given noun. Semantically, the prefix "ha" corresponds roughly to the English word "the".

Proclitics mark the categories of definiteness and number, person, negation, tense and aspect - often fused in a single proclitic. Suffixes mark direct and indirect objects as well as clusivity (the distinction between inclusive and exclusive "we"), number, location and affective emphasis. Historically, as in other Oto-Manguean languages, the basic word order is Verb Subject Object, but some dialects tend towards Subject Verb Object word order, probably under the influence of Spanish. Possessive constructions use the order possessed-possessor, but modificational constructions use modifier-head order.

Res extensa and res cogitans are mutually exclusive and this makes it possible to conceptualize the complete intellectual independence from the body. Res cogitans is also referred to as the soul and is related by thinkers such as Aristotle in his De Anima to the indefinite realm of potentiality. On the other hand, res extensa, are entities described by the principles of logic and are considered in terms of definiteness. Due to the polarity of these two concepts, the natural science focused on res extensa.

An article is any member of a class of dedicated words that are used with noun phrases to mark the identifiability of the referents of the noun phrases. In English, both "the" and "a" are articles, which combine with a noun to form a noun phrase. Articles typically specify grammatical definiteness of the noun phrase, but in many languages they carry additional grammatical information such as gender, number, and case. Articles are part of a broader category called determiners, which also include demonstratives, possessive determiners, and quantifiers.

The class of determiners is used to specify the noun they precede in terms of definiteness, where the marks a definite noun and a or an an indefinite one. A definite noun is assumed by the speaker to be already known by the interlocutor, whereas an indefinite noun is not specified as being previously known. Quantifiers, which include one, many, some and all, are used to specify the noun in terms of quantity or number. The noun must agree with the number of the determiner, e.g.

Khuzestani Arabic is a dialect of Gelet (Southern) Mesopotamian Arabic spoken by the Iranian Arabs in Khuzestan Province of Iran. It is also considered by most contemporary scholars to be a mix of Southern Mesopotamian Arabic and Gulf Arabic spoken in places such as Kuwait and Eastern Arabia. It has had a long history of contact with Persian language, leading to several changes.Khuzestani Arabic: a case of convergence The main changes are in word order, noun–noun and noun–adjective attribution constructions, definiteness marking, complement clauses, and discourse markers and connectors.

Verbs may inflect for grammatical categories such as person, number, gender, tense, aspect, mood, voice, case, possession, definiteness, politeness, causativity, clusivity, interrogativity, transitivity, valency, polarity, telicity, volition, mirativity, evidentiality, animacy, associativity, pluractionality, and reciprocity. Verbs may also be affected by agreement, polypersonal agreement, incorporation, noun class, noun classifiers, and verb classifiers. Agglutinative and polysynthetic languages tend to have the most complex conjugations albeit some fusional languages such as Archi can also have extremely complex conjugation. Typically the principal parts are the root and/or several modifications of it (stems).

A metric on a set X is a function (called the distance function or simply distance) d : X × X → R+ (where R+ is the set of non-negative real numbers). For all x, y, z in X, this function is required to satisfy the following conditions: # d(x, y) ≥ 0 (non-negativity) # d(x, y) = 0 if and only if x = y (identity of indiscernibles. Note that condition 1 and 2 together produce positive definiteness) # d(x, y) = d(y, x) (symmetry) # d(x, z) ≤ d(x, y) + d(y, z) (subadditivity / triangle inequality).

I was too fat, or maybe too tall, or maybe just plain too ugly... you can say my definiteness stems from underlying feelings of insecurity and inferiority. I couldn't conquer these feelings by acting indecisive. I found the only way to get the better of them was by adopting a forceful, concentrated drive."Harris, Eleanor. Audrey Hepburn, Good Housekeeping, August 1959 In 1989, she stated that "my look is attainable ... Women can look like Audrey Hepburn by flipping out their hair, buying the large glasses and the little sleeveless dresses.

In modern Bulgarian, definiteness is expressed by a definite article which is postfixed to the noun, much like in the Scandinavian languages or Romanian (indefinite: , 'person'; definite: , "the person") or to the first nominal constituent of definite noun phrases (indefinite: , 'a good person'; definite: , "the good person"). There are four singular definite articles. Again, the choice between them is largely determined by the noun's ending in the singular. Nouns that end in a consonant and are masculine use –ът/–ят, when they are grammatical subjects, and –а/–я elsewhere.

Foreman (2003) does not reject Woodin's argument outright but urges caution. Solomon Feferman (2011) has argued that CH is not a definite mathematical problem. He proposes a theory of "definiteness" using a semi-intuitionistic subsystem of ZF that accepts classical logic for bounded quantifiers but uses intuitionistic logic for unbounded ones, and suggests that a proposition \phi is mathematically "definite" if the semi-intuitionistic theory can prove (\phi \lor eg\phi). He conjectures that CH is not definite according to this notion, and proposes that CH should, therefore, be considered not to have a truth value.

In differential geometry, one considers a metric tensor, which can be thought of as an "infinitesimal" quadratic metric function. This is defined as a nondegenerate symmetric bilinear form on the tangent space of a manifold with an appropriate differentiability requirement. While these are not metric functions as defined in this article, they induce what is called a pseudo-semimetric function by integration of its square root along a path through the manifold. If one imposes the positive-definiteness requirement of an inner product on the metric tensor, this restricts to the case of a Riemannian manifold, and the path integration yields a metric.

Classical Chinese has long been noted for the absence of inflectional morphology: nouns and adjectives do not inflect for case, definiteness, gender, specificity or number; neither do verbs inflect for person, number, tense, aspect, telicity, valency, evidentiality or voice. However, in terms of derivational morphology, it makes use of compounding, reduplication and perhaps affixation, although not in a productive way. There is also an extensive use of zero-derivation. The basic constituent order of Classical Chinese is subject-verb-object (SVO), but is not fully consistent: there are particular situations where the VS and OV word orders appear.

The wave–particle duality relation, often loosely referred to as the Englert–Greenberger–Yasin duality relation, or the Englert–Greenberger relation, relates the visibility, V, of interference fringes with the definiteness, or distinguishability, D, of the photons' paths in quantum optics. As an inequality: :D^2+ V^2\le 1 \, Although it is treated as a single relation, it actually involves two separate relations, which mathematically look very similar. The first relation, derived by Greenberger and Yasin in 1988, is expressed as P^2+ V^2\le 1 \, . It was later extended by Jaeger, Shimony, and Vaidman in 1995.

To put al- into perspective, there are many ways in which Arabic words can be made definite. These include the use of personal pronouns like "me", the use of proper nouns like "Saudi Arabia", demonstrative pronouns like "this man", relative pronouns like "the man who ...", vocation like "O man", possession like "my man", and of course the definite article like "the man". Apart from possession, prefixing a noun with al- is the weakest form of definiteness. That is, saying "the man" does not define the man being referred to as clearly as saying "this man", for example.

There were no other known outbreaks anywhere in the > United States from which someone could have carried the disease to Haskell > and no suggestions of influenza outbreaks in either newspapers or reflected > in vital statistics anywhere else in the region. And unlike the 1916 > outbreak in France, one can trace with perfect definiteness the route of the > virus from Haskell to the outside world. Miner's report was not published until April 1918 and it failed to collect the attention it needed. It was not until after 2000 that historians' research revealed the origin of one of the deadliest epidemics in human history.

Reduplication is used on some (underived) nouns to indicate smallness or definiteness; e.g. the reduplicated form of meñg 'house' is meñg-meñg and means 'small house', reduplication of tày 'cassowary nail' yields tày tày 'finger nail', and the reduplicated form of dúme 'yam house' is dúme-dúme or dúdúme '(this/that) yam house'. Compare this with the reduplication effect on derived (verbal) nouns: fàrdjór 'making noise' > fàfàrdjór 'making much noise'; màryadjór 'walking, going' > màmàryadjór 'strolling around'. Syntactically, nouns can make up an entire NP and they can be marked by a long list of 'postpositional clitics' (Boevé & Boevé, 1999: 53).

Type 1 syntactic categories (also called 'syntactic unit categories') are sets of syntactic units of the idiolect system, and include the syntactic constituent categories as well as word form categories like cases, numbers, tenses, and definiteness categories. The type 1 syntactic categories of an idiolect system are given through a classification system (a system of cross- and sub-classifications) on the set of all syntactic units of the idiolect system, called the 'Syntactic Unit Ordering.' Type 2 syntactic categories (also called 'word categories') are sets of lexical words. They include the 'parts of speech' of the idiolect system and their subcategories.

The consistent histories approach rejects counterfactual definiteness in yet another manner; it ascribes single but hidden values to unperformed measurements and disallows combining values of incompatible measurements (counterfactual or factual) as such combinations do not produce results that would match any obtained purely from performed compatible measurements. When a measurement is performed the hidden value is nevertheless realized as the resulting value. Robert Griffiths likens these to "slips of paper" placed in "opaque envelopes". Thus Consistent Histories does not reject counterfactual results per se, it rejects them only when they are being combined with incompatible results.

In linguistics, determiner spreading (DS), also known as Multiple or Double Determiners Santelmann, L. 1993:1 is the appearance of more than one determiner associated with a noun phrase, usually marking an adjective as well as the noun itself Martinis, T. 2003:165-190 . The extra determiner has been called an adjectival determiner Rivero, M. L., Rallē, A., & MyiLibrary. 2001:165-166, 191-192 because determiner spreading is most commonly found in adjectival phrases. Typical examples involve multiple occurrences of the definite article or definiteness marking, such is found in (but not limited to) the languages listed below.

The following schematic represents the full range of possible elements that may exist in a noun phrase: [Determiner/demonstrative] [numeral (+classifier)] [adjective(s)] [NOUN] [noun-phrase possessor] [relative clause] Determiners and demonstratives: The initial position of the noun phrase may be occupied by either the determiner te (often followed by the final-position clitic, =e), or a demonstrative. They behave like proclitics, phonologically joining the following independent word. Te serves two functions in the noun phrase, as a marker of both definiteness and grammatical topic. In this sense it is similar to the definite articles in French or Spanish.

In his political opinions he was fairly liberal, but in the regulation of purely personal affairs and conduct he was notably conservative. He was a rare combination of force and urbanity. Although unfailingly careful to avoid giving offense to anybody with whom he came in contact, invariably gracious, and charming in manner, his opinions were not lacking in definiteness, and he was not in any way colorless. These qualities should have won him great distinction either in law or diplomacy, but in politics they left him merely a staunch and dependable "party" man, whose mental independence and natural talents were hampered by party platforms.

The determiner head in West Greenlandic also hosts an uninterpretable definiteness feature (uDEF[ ]), which is present on the highest projection of the noun phrase. To explain focus based changes that are apparent in the following, there is a need for a Specifier, DP landing site. :1) qimmi-t qaqurtu-t marluk taakku :dog-PL white-PL two-PL those-PL :‘those (two white dogs)’ :2) qimmi-t qaqurtu-t taakku marluk :dog-PL white-PL those two :‘those two white dogs’ # In tree 1, the full NP moves to [Spec, DemP], from its original position. # In tree 2, the full NumP, containing NP trace, moves to [Spec, FocP].

In metric geometry, the discrete metric takes the value one for distinct points and zero otherwise. When applied coordinate-wise to the elements of a vector space, the discrete distance defines the Hamming distance, which is important in coding and information theory. In the field of real or complex numbers, the distance of the discrete metric from zero is not homogeneous in the non-zero point; indeed, the distance from zero remains one as its non-zero argument approaches zero. However, the discrete distance of a number from zero does satisfy the other properties of a norm, namely the triangle inequality and positive definiteness.

The relative order of a verb and its active and patient arguments, and whether or not a passive construction may be used, can be affected by the definiteness and topicalization of the arguments. When the agent argument is a definite noun (phrase) and the patient argument is indefinite, only the active construction is grammatical. Thus, the Tzeltal equivalent of the phrase "The dog killed a cat" could not be expressed in the passive voice, because the agent "the dog" is definite but the patient "a cat" is indefinite. Inversely, if the patient is definite and the agent indefinite, the passive voice is grammatically required.

Word-final consonant clusters are also rare, again mainly occurring in learned discourse and via foreign loans: (coal – scientific) and (boxing – sport). Indirect object is usually expressed by with the accusative where Ancient Greek had for accusative of motion toward; bare is used without the article to express indefiniteness duration of time, or contracted with the definite article for definiteness especially with regard to place where or motion toward; or with the genitive, especially with regard to means or instrument. Using one noun with an unmarked accusative article-noun phrase followed by contracted with the definite article of a second noun distinguishes between definite direct and indirect objects, whether real or figurative, e.g. «» or «...» (lit.

Also syntactically, the compound word behaves like the main word – the whole compound word (or phrase) inherits the word class and inflection rules of the main word. That is to say, since "fish" and "shape" are nouns, "starfish" and "star shape" must also be nouns, and they must take plural forms as "starfish" and "star shapes", definite singular forms as "the starfish" and "the star shape", and so on. This principle also holds for languages that express definiteness by inflection (as in North Germanic). Because a compound is understood as a word in its own right, it may in turn be used in new compounds, so forming an arbitrarily long word is trivial.

Thus on the basis of the current estimate for the parameters, the conditional probability for a given observation x(t) being generated from state s is determined for each ; N being the sample size. The parameters are then updated such that the new component weights correspond to the average conditional probability and each component mean and covariance is the component specific weighted average of the mean and covariance of the entire sample. Dempster also showed that each successive EM iteration will not decrease the likelihood, a property not shared by other gradient based maximization techniques. Moreover, EM naturally embeds within it constraints on the probability vector, and for sufficiently large sample sizes positive definiteness of the covariance iterates.

Oromo has no indefinite articles (corresponding to English a, some), but (except in the southern dialects) it indicates definiteness (English the) with suffixes on the noun: ' for masculine nouns (the ch is geminated though this is not normally indicated in writing) and ' for feminine nouns. Vowel endings of nouns are dropped before these suffixes: 'road', 'the road', 'man', / 'the man', 'lake', 'the lake'. Note that for animate nouns that can take either gender, the definite suffix may indicate the intended gender: 'priest', 'the priest (m.)', 'the priest (f.)'. The definite suffixes appear to be used less often than the in English, and they seem not to co-occur with the plural suffixes.

TIQM is explicitly non-local and, as a consequence, logically consistent with counterfactual definiteness (CFD), the minimum realist assumption. As such it incorporates the non-locality demonstrated by the Bell test experiments and eliminates the observer- dependent reality that has been criticized as part of the Copenhagen interpretation. Greenberger–Horne–Zeilinger state the key advance over Everett's Relative State Interpretation is to regard the conjugate state vector of the Dirac formalism as ontologically real, incorporating a part of the formalism that, prior to TIQM, had been interpretationally neglected. Having interpreted the conjugate state vector as an advanced wave, it is shown that the origins of the Born rule follow naturally from the description of a transaction.

Aristotle's concept of hyle is the principle that correlates with eidos (form) and this can be demonstrated in the way the philosopher described hyle, saying it is that which receives form or definiteness, that which is formed. Aristotle explained that "By hyle I mean that which in itself is neither a particular thing nor of a certain quantity nor assigned to any other of the categories by which being is determined." This means that hyle is brought into existence not due to its being its agent or its own actuality but only when form attaches to it. It has been described as a plenum or a field, a conceptualization that opposed Democritus' atomistic ontology.

It also aims to be the definitive source for the registration of new tartans (that pass NAS criteria for inclusion). The register itself is made up of the existing registers of the STA and the STWR as they were at the time of the SRT's launch, and new registrations from 5 February 2009 onward. On the Register's website users can register new tartans (for a fee), search for and request the threadcounts of existing tartans and receive notifications of newly registered tartans. One criticism of the SRT and NAS's management of it is that its exclusivity, in both cost and criteria, necessarily means that it cannot actually achieve its goals of definiteness, preservation and open access.

Most determiners have been traditionally classed along with either adjectives or pronouns, and this still occurs in classical grammars: for example, demonstrative and possessive determiners are sometimes described as demonstrative adjectives and possessive adjectives or as (adjectival) demonstrative pronouns and (adjectival) possessive pronouns respectively. These classical interpretations of determiners map to some of the linguistic properties related to determiners in modern syntax theories, such as deictic information, definiteness and genitive case. However, modern theoristsAccording to the OED (Second Edition), the word determiner was first used in its grammatical sense by Leonard Bloomfield in 1933. of grammar prefer to distinguish determiners as a separate word class from adjectives, which are simple modifiers of nouns, expressing attributes of the thing referred to.

Abbott's research in areas of semantics and pragmatics examines topics in reference and noun phrase interpretation, looking at philosophically-influenced aspects of word meaning, presupposition, and conditional sentences. She has been pivotal in both uniting formal semantics—which adapts analytical techniques from logic to natural languages—and analytical pragmatics—which clarifies the workings of definite and indefinite noun phrases in English. Her work surveying the uses of definiteness in different languages shows how it has mainly been seen in terms of familiarity or uniqueness. Her book Reference, focusing on noun phrases as referring expressions, shows that the issue of speakers' use of language forms to refer to entities has been at the heart of debate among linguists and philosophers for centuries.

In two respects Bell's 1964 paper was a step forward compared to the EPR paper: firstly, it considered more hidden variables than merely the element of physical reality in the EPR paper; and Bell's inequality was, in part, experimentally testable, thus raising the possibility of testing the local realism hypothesis. Limitations on such tests to date are noted below. Whereas Bell's paper deals only with deterministic hidden variable theories, Bell's theorem was later generalized to stochastic theories as well, and it was also realised that the theorem is not so much about hidden variables, as about the outcomes of measurements that could have been taken instead of the one actually taken. Existence of these variables is called the assumption of realism, or the assumption of counterfactual definiteness.

For unconstrained problems with twice- differentiable functions, some critical points can be found by finding the points where the gradient of the objective function is zero (that is, the stationary points). More generally, a zero subgradient certifies that a local minimum has been found for minimization problems with convex functions and other locally Lipschitz functions. Further, critical points can be classified using the definiteness of the Hessian matrix: If the Hessian is positive definite at a critical point, then the point is a local minimum; if the Hessian matrix is negative definite, then the point is a local maximum; finally, if indefinite, then the point is some kind of saddle point. Constrained problems can often be transformed into unconstrained problems with the help of Lagrange multipliers.

The BCS formalism is applicable without modifications to the description of quark matter with color group SU(2), where Cooper pairs are colorless. The Nambu-Jona-Lasinio model predicts the existence of the superconducting phase of SU(2) color quark matter at high densities . This physical picture is confirmed in the Polyakov-Nambu-Jona-Lasinio model , and also in lattice QCD models , in which the properties of cold quark matter can be described based on the first principles of quantum chromodynamics. The possibility of modeling on the lattices of two-color QCD at finite chemical potentials for even numbers of the quark flavors is associated with the positive-definiteness of the integral measure and the absence of a sign problem.

Such is the origin of the agglutinating prenominal class markers from erstwhile articles, which are compensated by the rise of postnominal means of expressing definiteness on the noun. With the fulfilment of each cycle of change, a morphologically consistent phonological representation is realized and serves as input to the next cycle of morphological change. Those processes of inflectional renewal have parallels in recent neurolinguistic research, notably in the works by Gabriele Miceli. Wittmann's comparative approach to studying colonial varieties of French from Quebec, the Americas, and the Indian Ocean reveals that the structural gap with written French is inherent in the variety of oral French reflecting the speech of Paris exported from the cities of northern France from the early 17th century onwards.

De Broglie–Bohm theory highlighted the issue of nonlocality: it inspired John Stewart Bell to prove his now-famous theorem, which in turn led to the Bell test experiments. In the Einstein–Podolsky–Rosen paradox, the authors describe a thought experiment that one could perform on a pair of particles that have interacted, the results of which they interpreted as indicating that quantum mechanics is an incomplete theory. Decades later John Bell proved Bell's theorem (see p. 14 in Bell), in which he showed that, if they are to agree with the empirical predictions of quantum mechanics, all such "hidden- variable" completions of quantum mechanics must either be nonlocal (as the Bohm interpretation is) or give up the assumption that experiments produce unique results (see counterfactual definiteness and many-worlds interpretation).

Adjectives accompany nouns and serve to provide additional information about their referents. Macedonian adjectives agree in form with the noun they modify and are thus are thus inflected for gender, number and definiteness and убав changes to убава (убава жена, a beautiful woman) when used to describe a feminine noun, убаво when used to describe a neuter noun (убаво дете, a beautiful child) and убави when used to form the plural (убави мажи, убави жени, убави деца). Adjectives can be analytically inflected for degree of comparison with the prefix по- marking the comparative and the prefix нај- marking the superlative. Both prefixes cannot be written separately from the adjective: Марија е паметна девојка (Marija is a smart girl), Марија е попаметна од Сара (Marija is smarter than Sara), Марија е најпаметната девојка во нејзиниот клас (Marija is the smartest girl in her class).

The Jesuit Luis Molina published De liberi arbitrii cum gratiae donis, divina praescientia, praedestinatione et reprobatione concordia in 1588, which asserted that God offers his grace to all people, and that it was by an act of free will that each one accepted it or rejected it. Molina's theology of a sufficient grace became popular, but the lack of differentiation between sufficient and efficacious grace (along with the assertion of counterfactual definiteness) was opposed by large sectors of the Church who considered it incompatible with God's sovereignty or goodness. In opposition, the Jansenists claimed to espouse Augustinism, which insisted on a separate determining efficacious grace. The Jesuits accepted Augustine's assertion of the necessity of grace, but rejected the notion that there was any substantial difference between sufficient and efficacious grace (both determine man's behaviour to an extent).

Hence "it is evident that wisdom, knowledge and understanding are eternal and self-subsistent things, superior to matter and all sensible beings, and independent upon them"; and so also are moral good and evil. Cudworth does not attempt to give any list of Moral Ideas. It is, indeed, the cardinal weakness of this form of intuitionism that no satisfactory list can be given, and that no moral principles have the "constant and never-failing entity" (or the definiteness) of the concepts of geometry (these attacks are not uncontested — for example, see "Common Sense" tradition from Thomas Reid to James McCosh and the Oxford Realists Harold Prichard and Sir William David Ross). Henry More's Enchiridion ethicum, attempts to enumerate the "noemata moralia"; but, so far from being self- evident, most of his moral axioms are open to serious controversy.

Simon Kuznets, the economist who developed the first comprehensive set of measures of national income, stated in his first report to the US Congress in 1934, in a section titled "Uses and Abuses of National Income Measurements": > The valuable capacity of the human mind to simplify a complex situation in a > compact characterization becomes dangerous when not controlled in terms of > definitely stated criteria. With quantitative measurements especially, the > definiteness of the result suggests, often misleadingly, a precision and > simplicity in the outlines of the object measured. Measurements of national > income are subject to this type of illusion and resulting abuse, especially > since they deal with matters that are the center of conflict of opposing > social groups where the effectiveness of an argument is often contingent > upon oversimplification. [...] > All these qualifications upon estimates of national income as an index of > productivity are just as important when income measurements are interpreted > from the point of view of economic welfare.

Physicists Graeme Mitchison and Richard Jozsa introduced the notion of counterfactual computing as an application of quantum computing, founded on the concepts of counterfactual definiteness, on a re-interpretation of the Elitzur–Vaidman bomb tester thought experiment, and making theoretical use of the phenomenon of interaction-free measurement. As an example of this idea, in 1997, after seeing a talk on Counterfactual Computation by Richard Jozsa at the Isaac Newton Institute, Keith Bowden (based in the Theoretical Physics Research Unit at Birkbeck College, University of London) published a paper Bowden, Keith G, "Classical Computation can be Counterfactual", in Aspects I, Proc ANPA19, Cambridge 1997 (published May 1999), describing a digital computer that could be counterfactually interrogated to calculate whether a light beam would fail to pass through a maze. (Revised version of "Classical Computation can be Counterfactual") More recently the idea of counterfactual quantum communication has been proposed and demonstrated. Liu Y, et al.

Knuth (1968, 1973) has given a list of five properties that are widely accepted as requirements for an algorithm: # Finiteness: "An algorithm must always terminate after a finite number of steps ... a very finite number, a reasonable number" # Definiteness: "Each step of an algorithm must be precisely defined; the actions to be carried out must be rigorously and unambiguously specified for each case" # Input: "...quantities which are given to it initially before the algorithm begins. These inputs are taken from specified sets of objects" # Output: "...quantities which have a specified relation to the inputs" # Effectiveness: "... all of the operations to be performed in the algorithm must be sufficiently basic that they can in principle be done exactly and in a finite length of time by a man using paper and pencil" Knuth offers as an example the Euclidean algorithm for determining the greatest common divisor of two natural numbers (cf. Knuth Vol. 1 p. 2).

" Robert Millikan wrote, "In a research which is destined to rank as one of the dozen most brilliant in conception, skillful in execution, and illuminating in results in the history of science, a young man twenty-six years old threw open the windows through which we can glimpse the sub-atomic world with a definiteness and certainty never dreamed of before. Had the European War had no other result than the snuffing out of this young life, that alone would make it one of the most hideous and most irreparable crimes in history." George Sarton wrote, "His fame was already established on such a secure foundation that his memory will be green forever. He is one of the immortals of science, and though he would have made many other additions to our knowledge if his life had been spared, the contributions already credited to him were of such fundamental significance, that the probability of his surpassing himself was extremely small.

Each (simple) sentence meaning consists of at least (i) a referential part: a set containing exactly one 'referential meaning' for each referential expression of the syntactic unit; (ii) a propositional part: a pair consisting of a directive part (determining a speech act type) and a proposition; and (iii) a propositional background, consisting of what the speaker co-expresses with the proposition. The referential part and the propositional background of a sentence meaning may be empty. Syntactic meaning composition is based on semantic composition functions associated with (i) the syntactic functions in an idiolect system, by the 'syntactic function interpretation,' (ii) with syntactic categories like tense or definiteness categories, by the 'syntactic category interpretation' (both are components of the sentence-semantic part of the idiolect system). Syntactic meaning composition starts from the lexical meanings of the primitive constituents in a syntactic quadruple: 'basic syntactic meanings' are pairs of a concept, assigned to a primitive constituent by the lexical interpretation, and a 'contextual embedding' of the concept that involves potential speakers and utterances.

We can generalize the notion of a metric from a distance between two elements to a distance between two nonempty finite multisets of elements. A multiset is a generalization of the notion of a set such that an element can occur more than once. Define Z=XY if Z is the multiset consisting of the elements of the multisets X and Y, that is, if x occurs once in X and once in Y then it occurs twice in Z. A distance function d on the set of nonempty finite multisets is a metric if # d(X)=0 if all elements of X are equal and d(X) > 0 otherwise (positive definiteness), that is, (non-negativity plus identity of indiscernibles) # d(X) is invariant under all permutations of X (symmetry) # d(XY) \leq d(XZ)+d(ZY) (triangle inequality) Note that the familiar metric between two elements results if the multiset X has two elements in 1 and 2 and the multisets X,Y,Z have one element each in 3. For instance if X consists of two occurrences of x, then d(X)=0 according to 1.