[David Sklansky]

1. With few exceptions I make no effort at rigor. I consider rigorous mathemeticians, like the ones who wasted their lives figuring out how to eliminate the use of infintesimals, either obsessive compulsive, or so devoid of cleverness that they know this is the only way for them to contribute anything.

2. Any eight year old can understand Baye's Theorem. I explain it in a few pages in Getting The Best Of It. Anyone who hasn't read that book has no right to have an opinion about anything. Anyway here is an even shorter explanation. If an event may or may not occur, and if it does occur, there could be two or more explanations, then when it does occur you use the following technique to figure out the probability of a particular explanation. You form the fraction where the numerator is the original probability of the event occurring in that specific way and the denominator is the total probability of the event occurring.
If the probability that New York is destroyed is 5% because there is a one percent chance terrorists will do it, a 2% chance that nuclear war will do it and a 2% chance that an earthquake will do it, it means that if you are returning from Mars and see NY in ruins, it is 2/5 that it was an earthquake.

Slightly tougher one. There are ten coins in a jar. One is heavily weighted towards heads. 90%. You pick a coin and flip three heads. The total chances that could happen is 1/10 x .729 plus 9/10 x .125. DUCY .0729 + .1125 = .1854. So the the chances we picked the bad coin is .729/.1854

Notice that this technique works for events that have already happened as long as everyione agrees on the original probabilities.

3. Considering how simple I consider this comparing probability technique is, and the fact it was explained in my book, it is absurd to think I throw out the words Baye's Theorem to try to make my pronouncements seem more authoritive. I throw out those words as a substitute for the longer sentence "as any non moron can see this is simply a case of making the ratio of two probabilities".

4. This ratio of probability technique (ROP from now on) is the underpinning of the expression "extraordinary claims require extraordinary evidence". ROP is also the reason that the expression "Absence of evidence is not evidence of absence" is WRONG.

Many atheists make the horrible mistake of arguing against statements in the bible or comments by theists that do not directly pertain to miracles. This is silly on their part because the theist's evidence for their position is usually strong. Stuff like "does it make any sense the NO ONE would have stepped forward if they saw Jesus's body, (or if they realized that God wasn't talking to them in the desert).
These arguments would win the day if they were using them to persuade you of incidents that sometimes, though rarely occur. They lose only because they are trying to persuade you of the truth of something extraordinary. Something unheard of. Even more than unheard of. Something that there is good reason to believe is impossible. (Thus Pair The Board's comment that I base my probability of a miracle on its non occurence so far, is wrong. I also base it on the strong suspision that it can't occur. A subtle but important difference.)

The reason why the expression is an ROP problem works like this. Suppose I claim that I can see coins as they are flipped and caught and thus can call them with near perfect accuracy. Would you believe me if I did it five times in a row? You shouldn't if you thought that it was a million to one against me having that ability (even after I claimed it). You would need well over twenty accurate consecutive calls. But even that shouldn't suffice. Unless the only two explanations were that I got lucky or I had the ability. I could also be cheating. And even if that was a 1000-1 shot originally, it would still be, due to ROP, much more likely. So I would have to go to extraordinary lenghths to prove I wasn't cheating.

If my claim instead was that I had some gizmo in my shoe that saw the coin, it would be a less extraordinary claim and perhaps ten flips should convince you. See how that works?

BUT WAIT. Guess what. There really is at least one person who had this physical ability. They called him the Flipper. Now deceased. This changes everything. It shows that there is one example AND it shows that it is not an impossibility.
Because I know about this guy I actually would only need to see about six or seven accurate flips from someone else who claimed this ability before I'd bet on him. Just like I'd totally change my thinking about religion if I ever heard of ANY sort of CLEARLY supernatural event.

I don't have time to get to Evolution and Exodus and Absence of Evidence right now but I will shortly.