In my opinion, the problem is much more easy than it may look after reading previous posts. Simply, one must distinguish between, so to say, "nothingness from inside" and "nothingness from outside". Inside empty set is nothing, but this does not mean that empty set itself is nothing; it isn't nothing, it is a set, maybe even THE set or maybe even the SET. 

This is an interesting question  with many possible answers.

The notion of nothingness is important in phenomenology (Husserl, Sartre). 

In mathematics, a set containing no objects, the empty set, has absolute character.   The empty set has no thing (nothing) in it.   However, I am unaware of mathematicians who have viewed the empty set as nothingness.

Well, what is nothingness? Is zero nothingness? Is an empty set nothingness? Is there nothingness that is not absolute? 

If you can define nothingness, then probably the answer to your question will be clearer and absolutely something else.

I have tackled the problem on an informal basis (my personal view) by utilizing the notion of "no thing" as James puts it and extending it to imply the absence of x. I leverage the notion of negation and substitute 'thing' for the variable x. This helps me in dealing with any philosophical cunundrum or inconsistencies that might crop up in my subsequent reasoning.

The second part of your question would deal with absolutes which I would then bind the x to a universal quantifier were for all x does not preclude members y from being present since y is not a bound variable.

Just a thought(and open to criticism)

I am trying to define nothingness not "through an assumed position which something could be, but it is not there", like not the value of an specific parameter, but it***  needs to have no parameter to define under absence of a thing which could be there from a point of view, but before defining such parameters.

*** (as i say "it" i am again defining something which is nothingness that i am talking about, and i am putting nothingness as content of "it" and not its absolute form, because i have no other way to talk)

Another example of "nothingness" is the following. Suppose we are observing a region changing in time. In his life-history it may have  periods of existing and periods of non-existing (for instance, a small lake, which during the summer has no water, or some viruses). Then the region in a period of non-existence is a kind of "nothingness". 

Saleh,

The problem with trying to define it as an "it" is that as you elaborate the notion you will  fall again into the notion I described by invoking the notion of "needs to have no parameter" to define it (as a matter of fact you are imposing necessity which I have not done).

The problem with defining the notion of nothingness is that by itself the word invokes "negation of". Trying to avoid this will bring you to a possible reasoning inconsistencies, contradictions or even paradoxes (at least as far as I know and have read about it).

In my opinion, the problem is much more easy than it may look after reading previous posts. Simply, one must distinguish between, so to say, "nothingness from inside" and "nothingness from outside". Inside empty set is nothing, but this does not mean that empty set itself is nothing; it isn't nothing, it is a set, maybe even THE set or maybe even the SET. 

Aslanbek,

Your solution aims at differentiating the set from the element no-thing which is very reasonable, but then it would leave the nature of no-thing still to be resolved by the definition of no-thing as 'absence of' or in terms of "it" as proposed by Saleh.

Thank you Arturo and Aslanbek very much, your answers are very interesting because it makes it clear that where should i focus on, however maybe we can never point at nature of anything and describe it.

Are you familiar with Frege's distinction between "sense" and "reference" (Sinn and Bedeutung)?

I think there's a fallacy in your reasoning:

"that set still is not representing "absolute nothingness" because it is assumed to be a set of answers for a special question, and still it is carries this information in its title"

Take the concept 'square circle'.  Its sense (Sinn) carries information - all its members have four sides, all its members have points equidistant from a centre.  But its reference (Bedeutung) is nothingness, because there are no square circles.

My first remark in this discussion: here a paper of Professor Jerzy A. Janik (he died in March 2012) can be interesting. The title of this paper is "CONSIDERATIONS CONNECTED WITH THE WORDS “IS” AND “EXISTS”  " (published in "The New and Old Concepts of Physics"   vol. II, 44 (2005)). If I have some other remarks, I will write them here.

http://merlin.fic.uni.lodz.pl/concepts/2005_1_2/2005_1_2_39.pdf

Lukasz,

One very personal preference for me though is to isolate the problem from a purely logical perspective as opposed to using the framework of Quantum mechanics to elaborate on the subject. Using such framework brings up other notions such as the observer into the fold and consciousness (which is pointed to in the paper) that complicates what can potentially be a simpler analysis. But again, that is just my preference.

Thank you for sharing the reference

Nothingness is the complement of  [-inf, inf]. i.e [-inf.inf]c = [i,- i ]c

Data New philosophical view merging infinity to the imaginary number