Quote:
Originally Posted by shadowind  Quote:
Originally Posted by pseudonous Remster
Since 1/xy > 1/xyz, it follows that the arguement based on less assumptions is more likely to be true.
| do you mean that if each axiom had a equal probability of being correct
that the probabilitys of just 2 axioms being correct to make the conculsion correct is greater then having three axioms? |
No, each axiom was assigned its own unknown probability of being correct as follows:
The probability the axioms are true is unknown. The probability of axiom A is 1/x, the probablity of axiom B is 1/y and the probability of axiom C is 1/z.
The probability that two of the three axioms are true is greater than the probability that all three axioms are true.
As Romansh pointed out there may be other unknown axioms which could make the conclusions true even if axioms A, B and C are false. This additional complexity can be taken into account, if the conclusion of the argument based on two of the three axioms is included in the conclusion of the arguement based on all three axioms. On the other hand, if the conclusions of each argument are significantly different there is no way I know of to determine which is more likely.