RE: How we determine facts.
January 7, 2015 at 6:52 pm
(This post was last modified: January 7, 2015 at 6:54 pm by 100 Years of Solitude.)
(January 6, 2015 at 8:58 pm)Heywood Wrote: Consider the following.
Suppose you have a bag of marbles. The bag may contain only marbles colored white or it may not. You do not know. What is the probability that the bag contains only white marbles. You don't know, so lets say the probability the bag only contains white marbles is X.
Suppose you draw a marble from the bag and it is white. The result of this draw doesn't tell you the probability of X, but you do learn something from it. You learn the probability of X is closer to 1 than you previously thought. Why? Because each time you draw a marble and find it to be white, you decrease the number of ways a non white marble could be in the bag.
For example, suppose the bag has 3 marbles in it. W stands for a white marble. B stands for a non-white(black) marble. If 3 marbles are in the bag the possible starting conditions are:
WWW (3 white marbles)
WWB (2 white marbles and black marble)
WBB (1 white marbles and 2 black marbles)
BBB (3 black marbles)
Before we start drawing marbles the probability that all the marbles are white is .25. Now suppose we draw a white marble. Now only two marbles are left in the bag and we've eliminated one possible initial starting condition. The remaining possible starting conditions are:
WWW
WWB
WBB.
We now know that the probability all the marbles are white is .33. Suppose we draw another white marble. The remaining possible starting conditions are:
WWW
WWB
We now know that the probability all the marbles are white is .5. Do you see what is going on here? Every time you observe a white marble while never observing a non-white marble confidence in the proposition that all the marbles are white increases.
It is essentially this thinking that we use to determine what is a fact or at least likely to be true of reality and what isn't.
You are admitting that the probability of taking any of the 2 coins is the same ( you are going by the classic definition of probability from Laplace) which might not happen(example: the probability of taking a white coin is 99% while the other 1% or we simply don't know the probability of taking any of the two coins), you are assuming they are equal in terms of probability but ok let's ignore that.
Still the reasoning is flawed.
BWW is different than WBB because you are taking the coins in sucession and not the 3 at once, therefore it acounts for another case.
The probability subject is very trick because most of it is of theory and requires multiple conditions to happen in order to take place in reality.
