Christ is risen!
There's this concept in formal logic, which I think I half remember the Fathers speaking similarly with respect to heresy. Maybe someone can refresh my memory.
Mathematicians have known since the Middle Ages of the principle of explosion. In brief: In any sufficiently powerful system of logic, if you assume anything false,* every falsehood logically follows. In fact a proof exists then for every claim, whether true or false. This means that if I genuinely accept that 1+1=5, I could formally "prove" that the twelfth root of zero is pi. Of course this does not prohibit thinking with imperfect information.
My point being that mathematics does not exist purely for its own sake. When using maths we are really using it as a proxy for something else in the real world, which obeys the same rules that we have expressed in mathematical language. The same rules of reason which we apply in other fields, we also apply when speaking of theology. Whatever theological matters we express in terms of logic and mathematics--and I am not dealing with Transcendence here--we apply the same rules to and reach analogous conclusions.
Hence we say in some sense, that every or perhaps nearly every heresy is really the same as every other. I'm sure you have noticed this in the real world as much as I have. False religions have constantly changing doctrines, which each generation clinging to the ideas they grew up with--new ideas viscerally rejected by their fathers, even though they followed logically from their own. They themselves viscerally reject the new ideas of the day which will be the old conservative ideas of their children. In the end they seem to argue themselves into anything and everything. I could list many examples, like Spinozism or hasidism among the Jews, like ultramontanism or Darwinism among the papists, like Arianism or iconoclasm in the reformation, etc. And yes, they often splinter into many groups.
Give the devil one heresy, no matter how small, and given time he can by logical steps turn that into any other. I guess at the end of the day when everything seems reasonable, ecumenism must result.
So I've been thinking of this, and I half remember that there were off-hand references that I heard somewhere to the Fathers speaking of the equivalence of all heresies. Or maybe I'm just misremembering it. Any takers?
*False being used in the strictly formalistic sense, i.e. contradicting your other assumptions/axioms. The contradiction need not be obvious.
