at1with0 wrote:Can you prove that reality is free of contradictions, khan, or that logic applies to everything? In essence you can't prove the laws of thought, meaning something can be a square and a circle. Of course, language breaks down and everything is both true and false (If everything is true then everything is false and vice versa). Perhaps it's the dualistic nature of language that makes it break down.
A first-order formula is called logically valid if it is true in every structure for its language. The completeness theorem shows that if a formula is logically valid then there is a finite deduction (a formal proof) of the formula. The deduction is a finite object that can be verified by hand or computer. This relationship between truth and provability establishes a close link between model theory and proof theory in mathematical logic.
An important consequence of the completeness theorem is that it is possible to enumerate the logical consequences of any effective first-order theory, by enumerating all the correct deductions using axioms from the theory.
at1with0 wrote:Can you prove that reality is free of contradictions, khan, or that logic applies to everything? In essence you can't prove the laws of thought, meaning something can be a square and a circle. Of course, language breaks down and everything is both true and false (If everything is true then everything is false and vice versa). Perhaps it's the dualistic nature of language that makes it break down.
DIss0n80r wrote:As I already said, precise definitions are specific and thus exclusive. It might help if you were to actually read my posts and not just argue with the voices in your head.
I am not arbitrarily "changing the definitions". That is your own delusion. Definitions might necessarily exclude information which allows for more inclusive and equally valid understanding. You are putting a ridiculous amount of faith into language. Language is dynamic and descriptions are not necessarily absolute. That doesn't mean it's useless, only that some referents may not be wholly describable by trivial tautologies based on categorical thinking. eg. "Circles and squares are different."
DIss0n80r wrote:Maybe reality is not absolutely dualistic.
khanster wrote:DIss0n80r wrote:Maybe reality is not absolutely dualistic.
It is true that reality is absolutely dualistic
or
it is not-true that reality is absolutely dualistic
DIss0n80r wrote:khanster wrote:DIss0n80r wrote:Maybe reality is not absolutely dualistic.
It is true that reality is absolutely dualistic
or
it is not-true that reality is absolutely dualistic
Is reality one thing or many things?