A point of view was expressed in another thread, and I think that a separate thread will be required to examine that point of view.
“true” isn’t absolute but relative to the rules of the particular system
A theorem is true if it conforms to the axioms:
Link to post:
Is there a materialist explanation of mathematics?
Link to thread:
After a system of deductive logic has been developed, it is possible to ignore what made the development possible, and to try to reduce the potentially difficult-to-analyze concept of a statement being true to the question of how one comes to know or believe that the statement is true. However, I suspect that such an attempt will inevitably fail, as it is founded on self-deception.
To know that a particular statement has been deduced via some assumptions and some system of deductive logic is to know something of no particular significance. For it to be significant, one needs to know or believe that the system of deductive logic that is relied upon does what it is supposed to do: preserve truth. If all of the assumptions are true, and a conclusion is deduced from them, then the conclusion is supposed to also be true.
To relativize truth is to deny the existence of a question until after one has an answer.
I could edit and change what I quoted to get something that I agree with:
#1 “Provable” isn’t absolute, but is relative to the rules of the particular system.
#2 A statement is a theorem if it can be deduced from the axioms.
#3 If all of the axioms are true and there exists at least one valid deduction of the statement from the axioms, then the statement is true.
Request to all readers: please let me know if you see anything controversial there.