Disproving Odin - An Experiment in arguing with a theist with Theist logic

[polymath257]

Yes, and the probability of the conclusion is the product of the (relative) probabilities for the premises involved in the conclusion.

In your addition of other premises, you are providing alternative ways to get to the conclusion, not additional premises for a deduction of that conclusion.

So, for example, suppose we have

A and B implies Z

and also

C and D implies Z

and also

E and F implies Z.

We first multiply the probabilities of A and B to get the probability of going *that* route to Z. Then we multiply the probabilities of C and D for *that* route to Z. Finally, we multiply the probabilities of E and F for the probability that *that* route to Z works.

Then, to find the *overall* probability of Z, we multiply the probabilities that *all* routes fail and subtract that from 1.

Of course, at each stage we should use relative probabilities.

Yes. So the example of these observations:


1. Mary usually goes to the market only on Wednesday (95%)
2. Mary is at the market. 
3. The street cleaners usually run on Wednesday (80%)
4. The street cleaner just went around the corner 
5. The garbage is picked up on Tuesday evening (80%)
6. The garbage cans in the alley are empty
yields the probability that today is Wednesday 1-(5% x 20% x 20%) at 99.8%

OK, you added a bit from previous premises: that Mary usually *only* goes to the market on Wednesday. That is important for the deduction. You should also have the word *only* in 3 and 5 for this to be a correct computation. This is crucial for the computation.

I want to point out that these are NOT the same as your previous premises. And the differences are relevant in the computations.

In particular, the previous ways you stated your premises allowed for Mary to go to the market on a day other than Wednesday with an undermined probability. The same is true of the street washers and the garbage collection.

But, and this is also important. The deduction scheme in each branch of this computed probability are single steps. If the branches had more steps, then along each branch, the probabilities would be multiplied. And *that* is relevant to how this discussion started.

If we have the following:

A implies B (with 70% probability)
A (with 80% probability)

and we want to conclude B, the probability of a correct conclusion (assuming independence of the first and second premises) would be .7*.8=.56, or 56%. This is NOT analogous to the scheme above where several different branches apply.

In particular, you have been dishonest a couple of times:
1. In changing the premises used in the discussion.
2. In suggesting that the *original* scheme is similar to the scheme you just introduced.