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What you have cited is a pragmatic limit, as you have not seen logic systems with more than 8 or so precepts.

IF there were such a limit to precept quantity,
then YES there would be a limit to the number of different logics.

However, there is no such limit to precept quantity.

Therefore, there are infinite possible logics.

It seems there can be an infinite number of logic rules, but most of them are meaningless, useless or not very relevant to make a solid logic system that can be used for various things. For instance, we can have a rule that says A, B, C, D, ... Z don't have to abide to rule number 1, but that's not really a "primary" rule, or a rule that's going to be used in a logic system in mathematics for example, so is there a limited number of such "primary" rules, and did anyone try to make an accurate estimate of how many of these rules there can be? Most logic systems used in mathematics have less than a dozen of "primary" rules.

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    this isn't really a good question. If there is no precise definition by "pragmatic" or "primary", why are you asking for a limit? Commented Apr 25, 2024 at 0:09

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Pragmatism is a school of thought that holds that the truth of a belief is determined by its practical consequences and usefulness as pushed by philosophers of the likes of William James, John Dewey, and Charles Pierce. In the realm of logic and reasoning, a pragmatic rule would be one that emphasizes useful, real-world reasoning patterns rather than purely formal, abstract rules. Considering there are infinitely many real-world patterns, and pragmatic logic rules are adaptable in the context of real world reasoning and communication it would therefore stem from this that there would be infinitely many pragmatic logic rules depending on the scenario in which you are working. Now there is great utility to having so many pragmatic logic rules as once the situation is defined so too are the pragmatic rules one uses in that situation. Your point of mathematics with "primary" rules, you may need to differentiate the difference between primary rules, pragmatic rules, and axioms. There is a little ambiguity in your question on the nature of these things and it seems that you may be conflating things. Further definitions will help better this answer.

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