Hi everybody,
I would like to take a moment to comment on some statements made in this thread. I haven't taken the time to read all of the posts here, so forgive me if I end up repeating what somebody else said or haven't addressed a good point that somebody else has said. Well, here it goes:
Stephen John Gault said this:
"If you can't prove god exists, you have to allow for the possibility/probability."
tetrapod.sapien said that:
"because pure proof is not forthcoming in deciding the HIGHEST LIKELIHOOD of truth."
I'd like to comment on these statements since they seem to imply that a proposition's being highly likely is a sufficient condition for being justified in believing that a proposition is true. Here I will argue that this assumption is demonstrated to be false by what is known as the Lottery Paradox. Lets assume the following:
p1= a proposition stating "ticket #1 will lose"
n= the number of tickets being between say, 100 and several million.
So the probability of p1 being false is 1/n and the probability of p1 being true is 1-1/n. With this knowledge, I will propose the following argument:
(a1) The probability for p1 being true is 1-1/n.
(a2) If the probability for p1 being true is 1-1/n, then I am justified in believing that p1 is true.
Therefore,
(a4) I am justified in believing that p1 is true.
The conclusion is problematic, since all other propositions claiming a ticket will lose (p2,p3,...pn) have the same probability of being true (1-1/n). For instance, my ticket #1 has the same probability of losing as Grumby's ticket #3 and Blondie's ticket #n. So everybody can be justified for believing that their ticket will lose. Now things get worse when we conjoin all of our propositions:
(p1&p2&p3&...&pn)
Now for those of you who are unfamiliar with formal logic, conjunction is a truth function between propositions (statements that are either true or false). Observe the following argument structure:
1. P
2. Q
Therefore,
3. P&Q
That's what I'm doing when I'm conjoining propositions. All I'm stating is that if I assume P is true and if I assume Q is true, then P&Q is true. Each proposition which is about a ticket (i.e. p1,p2,etc.) and I am now conjoining each of these propositions into one large proposition, (p1&p2&p3&...&pn). But this large proposition has it's own probability just as each of it's conjuncts do.
Lets suppose that P has a probability of .99 (very high) and suppose that Q also has this probability. If we conjoin these propositions and get P&Q, then we multiply their probabilities to get the probability of the conjunction.
P&Q= 0.99 x 0.99 = 0.9801
As you can see, the probability of this conjunction being true is less than it's conjuncts! It does not matter how highly probable its conjuncts are as long as they're below 1.00. As we can recall, our lottery propositions are extremely low to begin with, being 1-1/n. So if I have a lottery with 100 tickets then the probability each individual ticket has of winning is 1/100. If we subtract this fraction from 1, then we get a very large number, which is the probability it has of losing. So this large proposition, (p1&p2&p3&...&pn), has a high probability of losing.
But if we are justified in believing that this large proposition is true, then we're justified in believing that no ticket will win. But we know that some ticket will win. We cannot be justified in believing that both a ticket will win and no ticket will win. So it seems that premise a2 of my argument is false and being highly probable is not a sufficient condition for me to believe that a proposition is true.
What does this mean? It means that arguments that conclude the likelihood or unlikelihood of a hypothesis being true are irrelevent (assuming that there is nothing else wrong with the argument) since we cannot be justified in believing or disbelieving based on that likelihood. Does any of what I say make sense? Sorry if my response is too long.