For instance what would be the status of your Liar sentence in layer logic? You couldn't tell, just for a particular layer which by definition just describes a tiny fraction of the Liar sentence. So the Lair sentence as a whole would be as "paradox" as in classical logic, jumping between true and false. Your logic merely "visualizes" this back-and-forth-jumping.
In layer logic it is not paradox, but an ordinary statement. — Trestone
In layer logic it is not paradox, but an ordinary statement. — Trestone
Or, someone could simply say that a paradox is a statement that has alternating truth values in "layer logic."
And then you've got the same problem you had prior to layer logic.
Is the liar sentence in the layer logic still the "original" liar sentence or something different?
Sometimes this board seems like the philosophy equivalent of a physics board where people mostly present their "free energy" and "time cube" proposals.
What bothers me is the subjective value of "to me". Logic is the last vestige of the absolutists; it is unassailable, much like the flow of a chess game is unassailable. You can't make mistakes, and everything falls into place every time. So if logic is impartial, impersonal, and unbiassed; if it is the ultimate unchanging governing set of rules which can't be applied more than one way, ever, then why is layer logic not that? It is not that, because to you, Testosterone, it must be different than to others; it is different because "to me", that is, to you, it is different than "to someone not me" or to others. And bang, the absolutes of the logic system are crumbled.to me not only the liar sentence is different in layer logic but the whole world:
Like with complex numbers there are more and new possibilities, new dimensions.
Which of those worlds is more "real"?
To me this is an open question. — Trestone
Thanks for the explanation, Testosterone!! It makes sense to me now. I had this sort of pleasure in my life, too, albeit I was a child then: I played with Marklin Toy Trains, and revelled in building complex track structures. I had a lot of track. And as you probably well know, it is a three-track system, so creating track configurations that looped back into themselves was easy, effortless with this design.When I had selected some basic rules for my layer logic it started a life of its own.
And as it is not easy to think consequently in a new logic,
I often add that something is "my personal view or interpretation of layer logic"
especially if it is a conclusion outside logic and mathematics. — Trestone
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