a probability theorem I need help proving
Offline so here is the theorem I need to prove:
P1, P2, P3, and P4 are mutually exclusive and jointly exhaustive propositions. Here is the theorem (X represents multiplication):
P(R/N&E) = P(R/N&E&P1) X P(P1/N&E) + P(R/N&E&P2) X P(P2/N&E) + P(R/N&E&P3) X P(P3/N&E) + P(R/N&E&P4) X P(P4/N&E)
I need to prove this for my probability theory class. This is a theorem used by Alvin Plantinga in his Evolutionary Argument Against Naturalism. According to Plantinga, the reliability of our own mind to grasp truths given naturalism and evolution is low (the second part of the course will be devoted to investigating Plantinga's argument). I need to understand the proof for this theorem so I can hopefully refute his nonsense.
Todangst or Philosophos, work your magic 
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
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It seems all he's done is given the basic set up for subjective probability. I cover Phil's lecture here: http://candleinthedark.com/inductive.html
But I'd just as soon send you to a site where they have bayes theorem set up as a set of formulas that you can just plug numbers into...
Anyway, I assume that the formula seeks to get at the probability of rationality/reason (R?) given Naturalism and Evolution?
Well, it seems to me that all that is here is the basic set up.... it's up to us to come up with our initial assements of what the starting point should be..... whatever that starting point is, it's not zero, ergo Plantinga has no argument, unless he can show how 'supernatural' can even make sense, let alone garner a rating of anything other than 0 in a subjective probability. You have to be coherent to even be an equation in probability theory.
Whether or not his position is true seems moot anyway.... low odds are better than no odds. So I see this as an exercise in futility for the theist..... what does subjective probability even matter in this case, when we do know that reason exists, and that naturalism and evolutionary theory are the only explanations that currently work?!
Anyway, sorry I couldn't help more, and glad to to see you around again!
"Hitler burned people like Anne Frank, for that we call him evil.
"God" burns Anne Frank eternally. For that, theists call him 'good.'
I figured it out. It was basically first applying the theorem of total probability and than using conditional probability cuppled with logical equivolencies.
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
What type of probability theory classes are you taking, Chaoslord2004?
I have taken a year of graduate level theoretical statistics, and we never studied anything like what your talking about.
What kind? Just an introductory course. The first half was devoted to the basic ideas behind probability theory. The last half of the semester will be devoted to a particular application of probability theory: Alvin Plantinga's Evolutionary Argument Against Naturalism (EAAN).
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
I'm jealous. My classes weren't nearly that interesting.
I'd left you a private message a few days ago telling you I might have cracked it as well through almost only purely matehmatical means, but it seems that it's not a necessity anymore.
Inquisition - "The flames are all long gone, but the pain lingers on..."
http://rigoromortis.blogspot.com/