-=Dark_Angel=-, P.I.23 Mar 2005

Let's be formal about this, Dovina.

Def. A closed mind of domain D is a mind that deflects all propostions that are not in D, regardless of whether or not said propositions are true.

Def. An open mind is a mind that accepts a proposition if and only if it can convince itself that the proposition is true.

Dovina's Theorem. There exist true propositions that are picked up by an open mind and deflected by a closed one.

Proof. Let C be the closed mind with the empty domain. C therefore deflects all propositions, so in particular it deflects the true proposition "Dovina has a woman's brain."

Let O be the open mind that thinks Dovina has a woman's brain. By definition, O accepts the proposition "Dovina has a woman's brain" and we have the theorem. QED


-=Dark_Angel=-, P.I.'s Important Theorem. For every open mind, there is an equivalent closed mind that accepts and rejects the same propositions.

Proof. Let O be an arbitrary open mind. Let D be the collection of all propositions that O can convince itself are true. O is clearly equivalent to the closed mind with domain D. QED.

Corollary. All Dovina has said is that different minds can disagree about the validity of a proposition. :(