Depending on how you define the schema for your language’s grammar, you can force certain interesting conditions.
Classical logic, various calculi, etc all have particular grammar and usually a few well defined words in a glossary (which can easily be symbols but become words when spoken) and with this constrained grammar and these constrained words, interesting results can follow.
Now, you may not see logic with a purpose of rhetoric. You may see logic as some structural property of the universe. Lots of people do.
So let’s assume you do. Hypothetical universe just got created that may have no relationship to this one.
Logic has immutable rules that must be followed in that Universe. In that Universe, all other languages are built off of Logic, from math to the production rules of grammar for natural language. In the production rules of grammar for language, a noun is a noun.
Both are nouns that can stand for condition.
The constraints do not seem to pre-exist except in this hypothetical Universe I just created.
Yet if they do, and natural language follows logic, rather than logic being a subset of natural language, then what makes substitution ok for everything *except* logic itself?
It has, to me, all the markings of a useful game. A productive game. A game with rules and a glossary and pieces that move in patterns.
But what is it that makes logic special?
More to the point, what makes logic more special than other languages?
I see *pragmatic value in logic.
But I do not see how a language that is dependent upon a set of a priori “fell from the heavens” axioms can not be considered a game with rules and a glossary.
If you can tell me what you are doing is saying, “Play the game right or [some consequence]”, I can do so.
But, if you are saying “Logic is a foundation upon which this Universe rests?” then I must conclude I’ve found your religion.
Game or religion?
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a) What you wrote is beautiful and on that alone I should like and let it stand.
b) But that is not why we are here is it? We are having a discussion. Since I disagree with some points and a simple “like” from me would be unsatisfying to me – and I suspect to you as well after having invested such time/energy/words on this, I shall continue because I enjoy the process as well.
We’re in agreement about uniqueness.
Yet, you also freely use substitution in such a way where the uniqueness is irrelevant. Suddenly it’s all about the system with nouns that can be substituted like Universal Mad Libs.
I love systems. Systems are great. I compare/contrast them frequently. I have whole hierarchies in my head where they fit. Logic is one of those systems. Rhetoric is another system that resides above Logic (for what is logic for but to convince? [ie – change a state / push / move])
Perhaps we have different hierarchies. Logic is not a fundamental property of the Universe to me. It’s useful word games that we’ve been able to encode in various special grammars, complete with production rules. Symbols can be used as representative of words and these symbols can require a very precise glossary in order to be useful for this game.
Or do you consider logic as more than a useful language game (with special grammar and glossary)?
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