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

[polymath257]

Actually, Jenny is more correct that you are here. If a premise is 100% certain, the multiplication (by 1.0) doesn't change the overall probability. If it is less than 100%, it does and should reduce the overall probability from that.
That said,the simple multiplication is only correct when the premises are probabilistically independent of each other. Otherwise, you multiply the *conditional* probabilities of each based on the previous ones to get the overall probability. The conditional probabilities can be very different than the non-conditional probability of each event.

That's simply not true with inductive premises and demonstrably so. 

For example, say you have 2 premises that make it likely that x is the case. 

1. We can't remember a time when Mary did not go to the market on Wednesday (95%)
2. Mary is at the market. (actually, this is not an inductive premise, so there is not probability to assign. However you can assign 100% if you want). 
3. Therefore Today is Wednesday. (95%)

Now say we add premises to that. 

1. We can't remember a time when Mary did not go to the market 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
7. Therefore today is Wednesday. 

According to your reasoning, the probability of today being Wednesday is 95% x 80% x 80% = 61%. What do you think the probability is that it is Wednesday? 

Baynes Theorem is more applicable to this type of reasoning.

Yikes. First of all, the first premise would be of the form

1. If it is Wednesday, Mary will go to the market.

But you are using it to go from

2. Mary went to the Market.
To
3. It is Wednesday.

That is a faulty conclusion, using the converse.

What you need to get a correct conclusion from 1 is
1'. I don't recall a time Mary went to the Market when it is not Wednesday. (95%).

NOW, the conclusion from Mary being at the market is that today is Wednesday with 95% confidence.

The other hypotheses given are not used in your conclusion. So they have no effect on the resulting probability at all.

However, suppose we have the following:

1. I don't recall a time when Mary went to the market that wasn't a Wednesday. (95%)
2. I don't recall a Wednesday when the street cleaners didn't run (80%).
3. Mary went to the market. (100%).

This can now be used to conclude that the street cleaners are running with (.95*.8=) 76% confidence.

In your example, going from
1. Mary generally goes to the market on Wednesday (95%)
2. Mary went to the market.

you need the probability of the converse 1' above, which cannot be derived from the probability of 1 without additional information (how often Mary goes on other days, for example).