From:    # 1 <[log in to unmask]>
> I was asking myself if a language needs a lot of levels of negativity
> [...] "I will can want to have been eaten"
> It's a little weird but it's grammatical (as much I know, and if not
> just follow my toughts it will be ok)

It's not grammatical English, but as a rough thought experiment it's
fine. ("Can" is lexically aberrant in lacking a base form which is
selected by "will", making "will can" impossible.  Instead English
speakers must say "will be able to".)

> to make the sentence negative, each or some of the auxiliaries may be
> negative by adding "not" after it, depending of each tense, aspect, mood, or
> voice you want to say negative
> I will not can want to have been eaten
> I will can not want to have been eaten
> I will can want not to have been eaten
> I will can want to have not been eaten
> I will can want to have been not eaten

This is the phenomenon that semanticists refer to as "scope":
operators such as negation and quantifiers like "many", "some",
etc., provide truth-conditionally different readings
depending on which phrasal constituents fall under the scope of
the operator.  Thus in "many arrows didn't hit the target", there
are at least two readings:  (1) at least one arrow hit the target,
while others did not [where "many" outscopes "not"] (2) in fact no
arrows hit the target, and the cardinality of the arrows not hitting
the target is large [where "not" outscopes "many"].  IIRC, there
should be at least n! readings for n operators, although
usually many or most of the readings will be pragmatically weird or
impossible in the real world.

> So I ask that question: does a language has to have a lot of levels to make
> a sentence negative or may it be possible to make the whole sentence
> negative?

This is actually a somewhat complicated question about which I am
only partially competent.  I think the answer is that it depends on
whether you're speaking about negation as a syntactic process, or
as a semantic process.  E.g. in English, it is commonly assumed that
the negation suffix _n't_ must attach to an auxilliary verb; if there
is none, one must be supplied in the form of "do".

Thomas Wier	       "I find it useful to meet my subjects personally,
Dept. of Linguistics    because our secret police don't get it right
University of Chicago   half the time." -- octogenarian Sheikh Zayed of
1010 E. 59th Street     Abu Dhabi, to a French reporter.
Chicago, IL 60637