Proof that using only logical form is valid?

Question

I'm studying logic. One of the fundamental things that I find everywhere is the claim and I'm quoting wikipedia:

"The concept of logical form is central to logic, it being held that the validity of an argument is determined by its logical form, not by its content."

And a logical form is defined (on Wikipedia) as follows:

"The logical form of a sentence (or proposition or statement or truthbearer) or set of sentences is the form obtained by abstracting from the subject matter of its content terms or by regarding the content terms as mere placeholders or blanks on a form."

And they go on to say that:

"The importance of the concept of form to logic was already recognized in ancient times. Aristotle, in the Prior Analytics, was probably the first to employ variable letters to represent valid inferences."

But why does it work? Why is only the form important and not the subject matter? I mean, is it a fact? Is there a proof that shows conclusively that this is the case? Or is it just something that we found to work? Let me give an informal example. Say we have something like the following (a logical form):

X is better than Y.
Y is better than Z.
=> X is better than Z.

So we can make the following inference:

iOS is better than Android.
Android is better than Blackberry.
=> iOS is better than Blackberry.

(Please don't mind if you don't agree with the phone preferences. It's just an example)

Above inference is valid. So far so good. But a weird inference would be:

Bad food is better than nothing.
Nothing is better than good food.
=> Bad food is better than good food.

This is obviously an invalid inference. So does the subject matter? Or is it because of natural language issues? "Nothing" perhaps isn't an object and has an implicit negation.

Edit: Thanks guys. I understand the reasoning behind the incorrectness of the example. I would still like to know the answer to my actual question. Can we prove that using logical form alone is enough and it's okay to abstract away the subject matter?

Edit 2: I got very interesting views about this on Philosophy Stack exchange. Here's the link if you're interested: https://philosophy.stackexchange.com/questions/26459/proof-that-using-only-logical-form-is-valid

Answer 1

When you say "nothing", you use two different meanings of the word. The first time, it means "the lack of anything"; the second time, it means "there does not exist anything that..." .

Another explanation: Let G be good food, B be bad food, and N be nothing.

Your phrases are "B is better than N" and "there is no X so that X is better than G". We just happen to say the italicized part above in English as the word "nothing".

As for the actual question: If a supposedly logical proof didn't work, then one of the statements must be logically invalid. If something can be transformed into logical form, the original statements don't matter because the transformation into pure logical form by definition keeps qualities the same.