The very big problem with this proposition is that as soon as you take all propositions to be true, you have no method for determining the falsity of any propositions. From any contradictorily accepted propositions any statement can be determined true.
To make this work, you would have to start with a small set of unprovable axiomatic negations, and then build from there. In other words, there is no essential difference between “destructive mathematics” and constructive mathematics, and destructive mathematics has to take a useless rigamarole around the concept of truth and falsity and rebuild constructive mathematics. All statements cannot be assumed to be true or false, they are indeterminate. Formal logic takes axioms and derives what is determinably true and false from those parameters.
From any contradictorily accepted propositions any statement can be determined true.
This is true in classical logic, but not in paraconsistent logic systems. They can prove fewer propositions than classical logic, but there are some situations in which you might want to use one.
I still don’t see a point in assuming every statement to be true. It seems more like a gimmick than anything else. Even without the principle of explosion, there must be a distinction between what is proved to be not false and what isn’t. What use is there in assuming everything to be true?
I see no point in this theory. The application to MWI doesn’t really make sense, and even if it did, that’s no reason to give this proposition any credence. The Tegmark hypothesis is also misunderstood; it states that all well-formed mathematical structures complex enough to have self-aware systems subjectively exist to those systems. I am not sure this can be proven, but I see even less of a connection to “destructive mathematics” than MWI.
The very big problem with this proposition is that as soon as you take all propositions to be true, you have no method for determining the falsity of any propositions. From any contradictorily accepted propositions any statement can be determined true.
To make this work, you would have to start with a small set of unprovable axiomatic negations, and then build from there. In other words, there is no essential difference between “destructive mathematics” and constructive mathematics, and destructive mathematics has to take a useless rigamarole around the concept of truth and falsity and rebuild constructive mathematics. All statements cannot be assumed to be true or false, they are indeterminate. Formal logic takes axioms and derives what is determinably true and false from those parameters.
I’m sorry, but this concept is useless.
This is true in classical logic, but not in paraconsistent logic systems. They can prove fewer propositions than classical logic, but there are some situations in which you might want to use one.
I still don’t see a point in assuming every statement to be true. It seems more like a gimmick than anything else. Even without the principle of explosion, there must be a distinction between what is proved to be not false and what isn’t. What use is there in assuming everything to be true?
I see no point in this theory. The application to MWI doesn’t really make sense, and even if it did, that’s no reason to give this proposition any credence. The Tegmark hypothesis is also misunderstood; it states that all well-formed mathematical structures complex enough to have self-aware systems subjectively exist to those systems. I am not sure this can be proven, but I see even less of a connection to “destructive mathematics” than MWI.
How is this useful to logic?
/me shrugs
I don’t know any use, myself.