Logic fondly referred to by Logicians as the ‘Laws of Thought’ [the title to an early text], deals exclusively with abstract things.
But first it needs to lay down some ground rules. And the Classes of Logic are part of the ground rules. If you want to apply the rules of Logic, you must agree to abide by the ground rules.
Logic begins with naming three classes: the Universe Class, the Unit Class and the Null [or Empty ] Class.
This roughly corresponds to what the rest of us call: ‘Everything, One, and Nothing’, or : ‘ Infinity, One, and Zero’.
So where did these Classes come from? We’ll were not too sure. They are sort of like the ‘Conservation Principles’ of Physics that are not themselves derivations from Physics but then get to arbiter what falls under ‘Physics’.
Unlike the Universe or Unit Classes, the Null Class of Logic is a very special class. All absurd expressions, words and phrases that don’t make any sense get to see the inside of the Null Class of Logic.
The Empty [‘Null’] Class of Classical Logic is the sole depository, the designated dumping-ground for all things absurd. It is the ugly-duckling, the black-sheep, the squint-eyed baby Mama tries to hide from the neighbors.
For the Logician such absurd expressions do not apply to the ‘Real World’. The abstracted, doubled, referential world where logical operators are designed to function. There really are no such things.
If you say ‘Round Squares’, it gets put in the Null Class. If you say ‘All Words are Meaningless’, it gets put in the Null Class. And if you say, ‘I don’t exist!’ it gets put in the Null Class. And a Doctor is called to the house to check your mental stability.
This must be one of the oldest Posts in my dog-eared file box. I need to update it with some of the new non-linear loopy logic that’s making the rounds. I’ll get around to it at some point.