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

[SteveII]

We are rehashing things already discussed. I cannot possibly know what posts you have read. Here is the very first paragraph under the article of Inductive Reasoning:



Just about everything in that paragraph is wrong--starting with your requirements about premises in a syllogism. Read the link above to learn more about an inductive argument. 

As to the percentage question, you do NOT multiply probabilities together to come up with a net probability in a syllogism. The conclusion's probability is equal to the lowest of the premise probabilities. Think about it--the more premises you have that are likely true would reduce the net probability if you multiplied them together. 

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.