(October 10, 2018 at 1:26 pm)Mister Agenda Wrote: You ma
(October 10, 2018 at 12:06 pm)SteveII Wrote: 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.
You make a good point. On consideration, I realize that I was in error on how to arrive at the probability. Thank you for correcting me.
I'm afraid that based on that consideration, I think I still see a critical flaw in your argument. A valid inductive argument can't be built only of evidence that supports the conclusion unless all of the available evidence supports the conclusion. It also has to include evidence (if any) that renders the conclusion less probable. If, as you say, the evidence that supports the conclusion the least determines the probability of the conclusion, then adding one piece of evidence against the conclusion could significantly reduce the probability of the whole argument. I'm not sure about the 'least probable premise determining the probability of the conclusion' though; intuitively it seems like a large mass of strong evidence that supports a conclusion might outweigh one or two items that seem to render it drastically less likely. Maybe the strength of the evidence has to be considered, one disconfirming fact can topple the conclusion, but only if it is very strong.
It also occurs to me that the argument doesn't consider alternatives to the conclusion that you reached.
Inductive reasoning isn't really supposed to be an 'argument', it's essentially basing conclusions on the available facts. Like a doctor inducing your disease from your symptoms, and reasoning that it's most probably one condition, but hopefully ranking the others since they haven't been ruled out. Are there possible alternative conclusions, and is your conclusion more probable than all of them put together.
Again, thanks for prompting me to think more deeply about your argument and induction in general.
I edited my original answer to you as you were typing. I included this:
EDIT: The conclusion's probability cannot be higher than the lowest of the premise's probabilities that must be true for the conclusion. There are many premises that do not have to be true
As far as other evidence against the conclusion, they would fall in two categories: undercutting defeater and opposing defeater. Undercutting would lower the probability of the premise being true. Opposing would make the premise false.
To oppose my argument, you could go two ways.
1. Undercut the premises that are most needed for the conclusion and then all I have left are very low % premises. Fore example, if evidence were found that there were no first century churches, then who was Paul writing to, there was not some early group of people that believed the resurrection story, etc.--leaving several of my premises significantly less probable.
2. Find only one that is needed for the conclusion and prove it false like convincing evidence that Jesus died while in vacation in the south of Gaul.