Farrell Till's First Error
Farrell Till made a serious error in his misunderstanding of mathematical probability. Mr. Till failed to recognize that there are two kinds of probability. First, there is the probability of unrelated events. Second, there is the probability of related events. In order to illustrate the difference between these two types of probability we will assume that we have six balls with the numbers 1 through 6 on them. These six balls are inserted into a hat and drawn out at random. The probability of an event occurring is p = s/(s + f) where p is the probability of the event, s is the number of ways the event can successfully occur, and f is the number of ways the event can fail to occur. The probability of pulling out the number three ball on the first attempt is p = 1(1 + 5) = 1/6 (one chance in six).
If the first ball drawn is not a three ball and it is placed back into the hat the probability of drawing a three ball on the second draw is p = 1/(1 + 5) = 1/6 (one chance in six again). If this is repeated until it has been attempted six times the probability of drawing the three ball on the sixth attempt is 1/6 (the same as on the first attempt). No matter how many times this procedure is repeated the probability will always be 1/6 (one chance in six). This illustrates the probability of unrelated events (the second event is unrelated to the outcome of the first event).
If the first ball drawn is not the number three ball and it is not placed back into the hat the probability of pulling out the number three ball on the second attempt is p = 1/(1 + 4) = 1/5 (one chance in five). If the number three ball is not drawn on the second attempt and the ball drawn is not put back into the hat the probability of drawing the number 3 ball on the third attempt is p = 1/(1 + 3) = 1/4 (one chance in four). If the process is repeated until five balls have been removed from the hat without drawing the number 3 ball the probability of drawing the number 3 ball on the sixth attempt is p = 1/1 = 1 ((one chance in one or a 100% chance of drawing the ball). This illustrates the probability of related events (the second event is related to the outcome of the first event).
Farrell Till's Second Error
Farrell Till made the same argument that was long ago refuted when he argued for pseudogenes being useless. This argument is essentially the same as the vestigial organ argument which has been proven to be unsound. For a number of years atheists argued that the tonsils, appendix, thyroid, etc. were vestigial organs. The presence of vestigial organs was used as an argument to prove that organic evolution occurred. All biologists know that these "vestigial organs" have been proven to be fully functional in the last few years. Physicians once, routinely, removed these organs when they performed surgery.
This argument is based upon the fallacy of "denying the antecedent" which was discussed in my first article. Mr. Till's argument is:
Second Premise: Christians cannot give a reason for the existence of pseudo-genes.
Conclusion: Pseudo-genes have no purpose (they are vestigial).
(Marion R. Fox, 4004 Twisted Trail Road SE, Oklahoma City,
OK 73150-1910.)
