Posted by John Swensen on February 23, 2000 at 14:51:14:
In Reply to: Re: Re: Re: Re: tuba metals posted by TUBAdAMORE on February 22, 2000 at 21:57:19:
No, not all predictions are vacuously true.
The prediction that, someday, I shall clean and jerk 800 pounds, is false.
The prediction that, someday, I shall die, is true.
A statement is vacuously true if it is conditional on something patently false;
for example, all integer multiples of 9 that are not divisible by 3 are prime is vacuously true, because there are no integer multiples of 9 that are not divisible by 3, even though, by definition, any integer multiple of 9 is not prime. [A prime number is divisible only by itself and 1; the first few prime numbers are 2, 3, 5, 7, 11, 13, 17, and most number theorists do not consider the number 1 to be prime.]