This is not a proof (of money having value per se). Though I was hoping that you would address the issue that I raised in my post (since that would be a proof). I mean, the compliance (or lack thereof) between the notion of money having value as such and the law of diminishing marginal utility...
It is proof. Value is somebody prefering one thing over the other.
We could go on discussing the two types of value again, but this time I wanted to stress that money is value.
So you don't want to address the issue of the discrepancy that I pointed out, okay then. Would money have value to you if you could buy with it only things that you don't need (and couldn't barter with) and, consequently, couldn't that you do? I guess that it wouldn't. Therefore it is not money per se that has value but the value of things that you can buy with it, and only through these things that actually satisfy your needs money obtains its value...
And this pretty much explains the apparent contradiction between the law of diminishing marginal utility and money not conforming to it. If you still disagree, then you have to explain this non-conformance somehow
The two types of value is intrinsic value and exchange value. If you really hate the names of those two concepts, you can of course choose other names but if so i can not be bothered to follow the discussion anymore.
The intrinsic value is what you are after when you go to a shop and buy something. You need shoes, they sell shoes, and you go and buy a pair. No magic there.
The exchange value is the speculation that you can get something of intrinscic value in exchange. So money has the exchange value, which is fully speculative. So the if's and but's above is completely rational. If I can buy food tomorrow, what if I can not buy food tomorrow, possibly I can get only something that I don't fancy. Anywy, I speculate that I can get what I want tomorrow, therefore I keep some money for tomorrow, in stead of stuffing my refrigerator with something that can degrade, or what I maybe don't fancy tomorrow. Things with intrinsic value is good, but it depends on the circumstances, maybe what is valuable today is not so tomorrow. Therefore I keep something that is not directly useful, but pure value, for tomorrow.