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The grammar descriptions of some languages seem to treat words like all and no, as in 'all giraffes are yellow' and 'no pigs have wings' simply as adjectives, because the words they determine are the nouns.

However, there most certainly is a difference between saying 'no pigs have wings' and 'green pigs have wings'.

This becomes obvious when turning the adjectives into equivalent relative clauses. This works: 'pigs which are green have wings'. This does not: 'pigs which are *no have wings'.

The way I understand these adjectives is they are somewhat like articles or quantifiers in that they help to fix the scope of the noun they determine. A 'mathematical' explanation would be that saying some pigs makes it clear you are talking about a subset of the set of all pigs and the subset is small. And saying the pigs implies that you are referencing a subset you defined earlier or will define in the near future. It doesn't say anything about the pigs in the subset (such as their being green), but gives you some context information. [In prepositional logic, this would be a function of quantifiers, such as ∀ or ∃.]

Most descriptions of grammars I've read (English and non-English) stick to the traditional parts of speech. So, does it make sense to consider words like no, some or all as a separate part of speech in its own right and is there any linguistic theory out there sharing this view?

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    They are sometimes called determiners. You could say determiners are separate, or you could say determiners and articles are kinds of (special) adjectives. It all depends on your definition of "adjective". You use a certain test in your question that presupposed a certain definition of what an adjective is; you could say a definition is in a way a bundle of tests. But there is no fixed, eternal bundle implicitly known to everyone. – Cerberus Jun 29 '13 at 19:35
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    All is a particular kind of determiner called a Quantifier. Quantifiers are logical operators and have many unusual features; they are not your usual determiner. And any "grammar" that calls them adjectives deserves to be ignored. – jlawler Jun 30 '13 at 3:55
  • @jlawler: Or maybe you should rather not judge what you do not know. The reason to call them adjectives is that they behave like typical adjectives in many ways. As always, it depends on which definitions you choose. Diachronicity and comparative linguistics are two more arguments. – Cerberus Jul 3 '13 at 14:23
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    Actually, in English, determiner/quantifier phrases (which may be quite complex) precede adjective phrases (ditto), e.g, q[Not very many of the fewer than 100]q a[loud, semi-drunken, belligerent, and abusive]a attendees survived the ferryboat explosion. So in fact quantifiers don't "behave like typical adjectives" any better than adverbs do; less, if possible. – jlawler Jul 3 '13 at 16:27
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As @Cerberus has commented, these are often lumped into the category of 'determiners', which in English also includes what you've referred to as articles (the, a), possessive pronouns (my, your), and some demonstratives (this, that). These are different from normal adjectives in the following ways:

  • They can't coexist with other determiners (e.g. *the this hat, *my a car)
  • They seem to be required on all singular non-name nouns (e.g. *car is nice)
  • Some can appear entirely without a noun, though some of the ones that can have a morphological change involved (e.g. no cars are there > none are there, but red cars are there > *red are there)

Some syntacticians have theorised that the determiner, not the noun, is the head (basically the core element) of phrases containing nouns. Adjectives, on the other hand, are just an optional component of a noun phrase.

So, at least according to mainstream syntax, your intuition is right - while they're not 'articles' as the term is typically understood, they are in the same category as articles.

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