'Nothing' or 'Nothingness' "has" no properties - not even a definition, how can it be said to "have" no attributes - for to say of 'nothing' that it has no attributes is to attribute the condition of having no attributes to 'nothing.'

It is impossible to "define" nothing as actually existing as an "empty set" or as anything else.

We can usefully dream up the idea of an empty set as a 'let's pretend' mental tool for arriving at certain mathematical results, but it is important to remember that whilst it is OK in the office, or in the classroom, or in ordinary conversation to speak in terms of the existence of an empty set, when one is involved in ontological discussions one is very likely to be challenged as to its actual existence as a real thing, rather than it being a reificational idea in the heads of mathematicians, which dissolves the moment that mathematicians stop thinking about it and finish utilising the theorem for their calculations.

Mathematicians introduce sets into their theories as arbitrary 'inventions' and with them the empty set too merely because it proves expedient for certain purposes.

I have no argument with their practices just as long as they don't start claiming that their useful and laudable fictions actually exist. The pen in their pocket of course doesn't dissolve the moment they stop using it for recording notes about the their calculations. The empty set and its empty "contents" of "nothing" no more exists than the definition of a full set and its imaginary contents.

Mereologically speaking only the singleton denotatum of that which is contained in the set actually exists. [if what are placed in the set are real entities] People who believe that a crowd exists for example, rather than realising that crowds don't really exist and only the individuate men, women and children.

Some people often believe that there is actually something called "nothing" in an empty cupboard, and that this non-existent nothing is necessary and useful for us as an offset for an existential nil mensuration, in order that we may understand that the items which are usually to be found in the full cupboard are not there. This is Platonism gone mad.

There is no such thing as: "all of existence" either - the only things that exist are the individual entities that exist, all else is description of the WAY that things exist - as entitic actions and reactions and interactions, modes, existential states, human brain activity, etc. All this is contrary to Heidegger's so-called "Ontological Difference" of course.

According to the Polish philosopher Lesniewski, it would be correct to say, for example, that the Black Forest is just the set of trees now growing in a certain area, and that this set becomes smaller as trees within it die. Clearly, on this view, there can be no empty set, and a set consisting of just one object as member will be identical with that object, and when that finally disappears there will be no Black Forrest left.

Moreover, sets can change, not least in that they can acquire and lose members over time. Further, there can be no sets of higher type, which means also that there is no way in which the more usual antinomies may be generated. Frege too, as Lesniewski points out, attacks those mathematicians who introduce into their theories such arbitrary 'inventions' as the empty set merely because they prove expedient for certain purposes. There are no general objects, which result when the features common to the particular objects, which are thought of as falling under a given concept and are unified into a whole primitive and old fashioned Platonic template.

I prefer Thadeus Kotarbinski's position, that the set doesn't exist in the first place, to grow or to shrink.

And how do we determine the cause of the impact of an asteroid impacting earth and squashing little Billy Brown? Was it because Billy's mother sent him to visit his grandmother in the next town? Perhaps it was the fact that the train was late when it was in the position on platform 4 when the lump of cosmic rock hit Billy's carriage? Some may say it was Billy's grandmother's fault and she caused it by allowing Billy's mother to go to that High School Dance where she met Billy's Father? Maybe it was caused by an exploding star in the far reaches of space whose detonation caused the asteroid to fly off into another orbit? Maybe the cause was actually in the Big Bang itself, when some of those elements which later came to be the exploding star we call the sun, and the earth, the asteroid, the train, Billy's grandmother, Billy's Father and mother and Billy himself? It must be a queer kind of logic that has such pedestrian and parochial notions about the nature of "events?"

Mathematics - the language of science - encodes logic into a device called an equation which requires its elements to be equivalent on opposite sides of the argument.

But these things - these theories of mathematics do not exist in themselves - maths is a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement, neither mathematics exist or the arguments of the logic of quantity and shape and arrangement which constitute its theorems exist - only the entities which are addressed by the activity of the existing mathematicians exist. In that way the language of math and natural language are similar in that it is only the denotata which the words denote that exist - not the words or significations themselves, which are no more than the existential activity and manners of behaviour of the humans that utter the words.

But what have these "laws" got to do with the subject of my discussion, which is "nothing," and how can the "logical equivalent of "every value in the Universe" include nothing as an equivalent opposite, when nothing doesn't exist to be the "equivalent opposite" of anything? A "value" doesn't exist either, being nothing more than a notional numerical quantity measured or assigned or computed by the embrained human holism..

This is no more than a transcendentalists dreamworld - a reificational wonderland without an Alice and a White Rabbit. The logical equivalent of 'nothing' does not exist any more than nothing exists. "The logical equivalent of Nothing" is just the product of someone's very rich imagination.