- Is this statement VALID?
- Is this statement TRUE?
The statement "2 + 2 = 5" IS valid.
Addition is defined as a binary operation, having two operands, the
operation symbol, and the equals sign. All are present. The
statement is valid.
- The statement is obviously false. All valid
arithmetic statements are not true, and this leads to untold grief.
The most common mistake engineers make in "doing statistics" or "doing
probabilistics," is to write down a valid statistical statement that
is false(*), then vociferously argue over the statement's validity, and the
subsequent stream of valid arithmetic operations that lead to the
(erroneous) conclusion, which they fervently believe must be correct since
the original statement was "correct."
But all valid arithmetic statements are not true. We aren't interested
in the statement's VALIDITY; we are interested in the statement's VERACITY.
And the distinction between the two is often ignored.
Just because you can make a statistical statement doesn't make it true, no
matter how much you wish that it were.
We engineers aren't stupid, just statistically inattentive.
We wouldn't write down something that is obviously false, like "2 + 2 = 5"
but we often do write down something false that would be true if certain
conditions in the statistical fine-print were met, which they
aren't, so the statement is false at the outset.