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I don't know whether the glass is half full or half empty, but I can tell you that it's completely flempty.

There is a mistake in the first sentence on the right, it misses "is".

Thanks, should be fixed now!

I had come up with a more complete, detailed version of the one above the Banach-Tarski response, and posted it on Facebook a while back. Facebook, however, seems to have lost most of it, and I don't really feel like rewriting it.

Are you half stupid or half geek

I think the first one contain a logical fallacy. It seems to say that if P then Q, not P implies not Q. Is this not denying the antecedent?

I thought so to at first, but it's saying that if a glass is half empty then it's empty. It is not empty, therefore it is not half empty. So, p implies q, not q therefore not p.

Use Banach-Tarsky Theorem to break up the emptiness and then put it back together such that the glass is completely empty? (I narrowly avoided saying "fully empty.")

Surely, due to the problem being trivial, it is left as an exercise for the reader?

i hate it when i see this.... -.-

Two of these are Physicist's responses. Don't steal our ideas! ;)

Is the Klein bottle half full or half empty?

I don't think "half full" and "half empty" exclude mutually. For me the glass is "half full"

and"half empty".Of course, we could always consider the glass to be full, 1/2 with Water and 1/2 with air.

Agreed. It's always either neither or both, since half empty and half full are equivalent. Most of the time it's neither.

The half-water, half-air response is in the 'geeky' link above.

On behalf of other physicists I am hereby formally lodging a protest :-) Quantum mechanics is our playground! :-)

The glass is twice as big as it needs to be.

I'm not entirely comfortable with the Banach-Tarski part, because relocating the non-measurable component sets means that every single atom will be broken, and therefore, while the glass will be full, it will not contain water, but some elementary particles of unknown origin. Ziv's opposite argument of filling the glass with emptiness OTOH seems to hold water (ducks for making a bad pun).

It is a superposition of half full and half empty until it is measured. And where is this glass, anyway? Sadly, we don't know, because we know its momentum exactly. Question: would a half empty glass and a half full glass annihilate each other on contact?

I've found a remarkable proof, but there is not enough space in that comment to write it.

The glass is always full, and as such is neither half empty or half full. :)

Since it would be full of both water and air to some degree at all times.

If we had a system of axioms with which we could decide whether a given glass of water is half empty or half full, then it would contratict itself.

which half of the glass full and which half is empty. And, what is the glass made from?

With Yrekthelas, an engineer would respond that the system of the glass has twice the needed hydrological capacity.

Since amount of water in the glass is a continuous variable and the amount corresponding to half full is an exact number, the probability that the glass is (exactly) half full is 0.

We do not know how full the glass is, as we have no measure for our space.

the last statement is only true, if the axiom of choice is true

the glass is fully full, it didn't say it had to be water, cuz it has extremely small gaseous particles in there (im more of a science geek xD)

This echoes my thought based on PChem - above any region of water, there is water vapor.

Prolog: Yes.

Actually, as matter is mostly empty space, I'd have to say the glass is almost completely empty.

Ah, but as we are assuming that it is indeed half full/empty, I would say that it is a glass filled with protons/neutron/electrons in the center - in which case, I would say that for it to be half-full, it is filled with one helluva high-atomic-numbered nucleus (with metric craptons of protons/neutrons) possibly, if you want the electrons to not be orbiting the glass, as a hugely charged cation.

the glass is in static equilibrium.

The glass is twice as big as it needs to be.

Why doesn't anyone ask "what's in the glass"? If that's irrelevant, I can always fill it with BS.

Looks like you've got twice as much gladss as you need there.

As it seen in the picture, the volume of the water is slightly less then the volume of the non-water in the glass, so it cannot be half-full, so the glass is half-empty

It is undecidable in ZFC

its full> Air and Water and that's the correct answer.