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Answer by Hunan Rostomyan for Can something be nothing?

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I think what has confused you is the usual grammatical role of "nothing." It appears in sentences like:

(1) Nothing is what I got for Christmas.
(2) I gave her everything, asking for nothing in return.

It appears that "nothing" is a subject in these sentences, i.e., a thing about which other things are said. But actually the semantic value of "nothing" (i.e., what "nothing" contributes to the meaning of the entire sentence) is not some object, but a function from sentences to truth-values. "Nothing", like "everything", "no one", "each day", "exactly one", and so on, is a generalized quantifier. Before getting to the particular cases (1–2), let's look at a standard way of giving the semantic value of "nothing":

[[nothing]] = [λf. ¬∃x s.t. f(x)] where f is a function from individuals to {T/F}, and x is an individual.

Here "nothing" is defined as a property of properties, a second-order property. Its arguments are characteristic functions of sets, its values: truth-values. Using it, (1–2) can be analyzed as follows:

(3) There exists no x such that I got x for Christmas.
(4) I gave her everything, and there exists no x such that I asked for x in return.

Each of those x's that these existential quantifiers supply is a thing, a something, an object. Depending on the context, these objects can even be abstract (like numbers, predicates, points in 2D space, etc.). But the negated existential quantifiers ("there exists no x" = "it's not the case that there exists an x") themselves are not, at least in these particular sentences, being talked about, so they're not even treated as objects like those x's are.

In conclusion, I'd like to very briefly de-mystify some of the superficially problematic things you said:

Claim 1. nothing is still something

Understood as: the semantic value of "nothing" is still something, this is true if and only if "nothing" has a semantic value. We know that it does; it's a function from open sentences to truth-values. So yes: the semantic value of "nothing"is something.

Claim 2. something is not nothing

Superficially, this seems to contradict Claim 1. But it doesn't, because from the fact that the semantic value of "nothing" is something , we can't conclude that something is nothing. And lastly:

Claim 3. something can be anything (or everything)

This can happen in worlds where either only one thing exists or everything is identical to every other thing. In either case, the following sentence captures the truth-conditions of this claim: ∃x ∀y (x = y).

For corrections/suggestions/improvements: please leave a comment or simply edit the post.


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