Hi Kooyeen,
I see what you mean. "Application", I suppose, comes from "application software". Although many people understand "application" as a piece of software, many non-technical savvy people may misunderstand it as something else if the context does not make it clear. To avoid the confusion, we can use "application software" but then we come better to the same situation: "an application software" is incorrect. We have to say "a piece of application software", "an application software package" or "an application software product", etc. This is what I found from a Longman website:
Give an example of an application software and an example of a system software. (2 marks)
This is grammatically wrong. But you see, it is not just me who think of "software" as "a piece of software". The next one is from about.com:
The Skype service comes with an application software, which is why many
people think of Skype as being only a software, overlooking the great
service behind.
There are many situtations that we need to tell people something is a software product. I got 76,000 hits from Google on "a software for", 42,600 hits for "a software from". Yes, these people are all wrong until one day a prominent writer use "a software" and a dictionary include this as an acceptable usage.
Back to your silverware example. I think you would call that a plate, a fork or a knife instead of "a piece of silverware" unless you don't recognise what that piece of silverware is. But this is not the case for "software".