Thank you for addressing specifically the example I raised!
This doesn’t go through, what you have are two separate propositions “H → (T → [insert absurdity here]” and “T → (H → [insert absurdity here]” [1], and actually deriving a contradiction from the consequent requires proving which antecedent obtains, which you can’t do since neither is a theorem.
So what changes if H and T are theorems? Let O mean “googolth digit of pi is odd” and E mean “googolth digit of pi is even”. I have two separate propositions:
O → ( E → Absurdity )
E → (O → Absurdity)
Now its possible to prove either E or O. How does it allow me to derive a contradition?
Thank you for addressing specifically the example I raised!
So what changes if H and T are theorems? Let O mean “googolth digit of pi is odd” and E mean “googolth digit of pi is even”. I have two separate propositions:
O → ( E → Absurdity )
E → (O → Absurdity)
Now its possible to prove either E or O. How does it allow me to derive a contradition?