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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

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  • $\begingroup$ As for your question on whether it is justified and the proof to the justification that abstract the form alone move away from the subject matter I can't seem to find an answer online anywhere but I'm guessing you should look into justification logic(though its probably pretty advanced) and the justification of validity. I found some sites that might address the question indirectly. I hope they help and I hope someone comes around with answer. Im waiting too. Site on Justification Logic: plato.stanford.edu/entries/logic-justification/#MatLogTra basicincome.com/bp/zlogic.htm $\endgroup$ – Red Aug 11 '15 at 23:22
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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.

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  • $\begingroup$ Thanks Deusovi. It was a good explanation for reasoning behind the example. Any comments on my actual question though? $\endgroup$ – shobhu Aug 11 '15 at 22:31
  • $\begingroup$ So this means that logical reasoning can only be applied to something that can be transformed into logical form and not to everything. I mean, then there is a possibility that there can be something(s) that cannot be logically reasoned. Right? $\endgroup$ – shobhu Aug 13 '15 at 7:12
  • $\begingroup$ @shobhu: Well, any statement can be transformed into logical form. You can always replace an entire statement with a variable. Your question is like asking "Is there any time that the number after 47 isn't 48?" There's not, because 48 is defined as the number after 47. Similarly, logical implication (if A then B) is defined as a situation where as long as A is true, then B is necessarily true. If a logical is flawed, then either there is a problem in the translation from English statement to logical form or you've made a logical error. $\endgroup$ – Deusovi Aug 13 '15 at 7:16
  • $\begingroup$ I understand that a logical form doesn't change the meaning and qualities of a statement. But still, why does only the structure matter and not the subject. I'll give an example. For me, Summer is better than Winter. (In summers I get to eat ice creams) Winter is better than Spring (I love the snowfall). Logically, Summer is better than Spring. But for me it is not. I prefer Spring because it's not as hot. So, how can subject (me in this case) not matter when drawing conclusions? It matters that the I (a human) will not always be logical. $\endgroup$ – shobhu Aug 13 '15 at 7:44
  • $\begingroup$ @shobhu: You believe things that contradict each other. This is not an issue with logic, it's an issue with your preferences; when you say "better", you do not mean the transitive comparison that is used in logic. $\endgroup$ – Deusovi Aug 13 '15 at 7:46

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