On Mar 9, 7:00 pm, magi...@math.berkeley.edu (Arturo Magidin) wrote: > > >> Proof by contradiction can be formalized as > > >> (P -> (A and not(A))) -> not(P). [...] > The proof in question, in fact, does not even use proof by > contradiction. It has the form > > (P -> not(P)) -> not(P). > > This is not a proof by contradiction.
Does the second one have a name?
Superficially, the two formulas appear similar. Certainly they evoke a similar sense. Is there any sense in which we might consider an antecedent as being in-scope in the consequent, which would allow us to connect the two? Or is the relationship a superficial structural similarity merely?
Does anything interesting happen if we transform them somewhat?
(P -> (A and not(A))) -> not(P) (P -> false) -> not(P). (not(P) or false) -> not(P) not(P) -> not(P)
Well, I seem to have destroyed the formula's essential nature by these manipulations. How did THAT happen? Apparently truth-value-preserving transformations don't preserve some things that aren't truth values.