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Philosophy

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  • Sure you can only retain, say the set of {and, or} connectives, as functional complete without the need of other connectives. Also in 1st order case you may modify your system's property to not include equality relation symbol whose presence is the default in your classic case. You may even relax the requirement on the domain to go completely free logic way with many more philosophical applications and implications... Commented Jan 7, 2023 at 5:11
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    What you listed are the laws of Boolean algebra, so your logic would have to be Boolean. There are Boolean algebras other than classical 0-1 algebra, trivially, the four valued one whose values are bit pairs of 0s and 1s with bitwise operations. Obviously, it modifies other properties, namely, the number of truth values. Its interpretation as "logic" is also questionable. Commented Jan 7, 2023 at 9:14
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    I don't follow. You define classical logic in terms of these rules, and then you ask if you can have a non-classical logic which validates these rules. This does not make any sense to me, can you clarify what you are asking? (This also does not make any sense to me: "by properties I mean basically anything, even things that aren't properties".) Commented Jan 7, 2023 at 15:00
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    Essentially, I am asking if logical systems are just a collection of logical laws, or there are things outside of logical laws that define them. Commented Jan 7, 2023 at 15:21