A Linguist Attempt at Explaining My Aversion to Logic

Terminology may be difficult for this post, but I will be diligent in attempting to make sense.

Linguistically (through the study of words and their meanings) it is difficult for me to accept logic, particularly Aristotelian logic, because it is based upon a concept of identity naming.

Some Aristotelian laws of logic look like this:
A is A (law of identity)
Everything is either A or not-A (law of the excluded middle)
Nothing is both A and not-A (law of noncontradicition)

so in this sense... we run across a difficulty in that whatever A is, it has a binary (either a affirmative or negative) relationship anything it could be compared to.

example proof:
A cat is a cat.
A cat is not a dog.
Therefore Leroy the cat is not a dog.

However, because many of the names we give to things do not have referents (or direct meaning attached to something in reality, for example 'justice' has a very abstract referent far removed from daily observations) it is difficult to establish the law of the excluded middle. Meaning... not everything is good or not good... bad or not bad... the relationship is not binary, but a spectrum of meaning where "good" has no specific referent and is instead a range of meaning associated with certain qualities that go largely undefined in our thought process.

So logically... no matter how careful we are in defining any certain word, it is still at a level of abstraction because names are symbols, not the actual item. Even in "cat" we cannot know the word without examples, life experiences, extensional cats (cat1, cat2, cat3 and from these similarities I define "cat").

Therefore to put our abstract language into a binary relationship resembling math seems to leave out the equation. For instance 2+2=4, but two quarts of water and two quarts of bread will not fill a 4 quart container because there are properties contained within the object that are not contained in the number or word. Logic is also this way.

There is no logical proof that can be fully deductive because we always inductively categorize the objects or ideas we place within the symbolic meaning of a word, even in symbols such as A or 1 or X or cat. Logic is not a system like mathematics where the complete system is symbols because words do, for the intent in using them, have ties to reality.

Here is a quote from Einstein that applies to both math and logic:
"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

In a sense what this says is that in order to achieve the binary relationship of yes, no or affirmative, negative we must depart from the referent and move farther up the abstraction ladder, move farther away from the meaning in reality of the thing being referred to. We have to abstract reality from its original state in order to be certain about the properties in it. And then when applying those certainties to reality we have to generalize, and lose the certainty when trying to apply the concepts. In short we introduce variable, the malleability of life enters the equation and chaos theory enters and spirituality enters.

Logic does not account for these in the complete sense. Words cannot, because they abstract meaning due to their symbolic nature. However, this isn't to say that logic, and certainly not math are lost causes, only that logic does not apply to life and ideas so much as to rely on it or to believe it achieves "certainty." It is a system that can only achieve certainty by creating it's own sandbox and ignoring the symbol and abstract nature of language itself, the key tool of philosophy even when logic becomes symbolic and attempts to leave words behind in favor of more mathematical looking symbols.

A two value binary system has its time and place, but I personally believe life is too complicated and rich, that our era has so much information and diversity that labeling yes/no or affirmative/negative is a mind trap. Binary relationships simplify, but simplification can lead to prejudices and snap judgements made without understanding all the implications. Logic to me seems like a crutch, trying to escape the mysteries of the world by stepping into a system that hides the mysteries by ignoring the abstract and symbolic nature of its own self and most essential tools.