But the examples show that the two statements are not equivalent in some situations. This means that they can't be considered to be equivalent generally.Thanks, Penguin. To be honest, my real answer was "both yes and no and neither yes nor no." but that wasn't on the poll. It doesn't do to use examples, since the possible examples are infinite and potentially illustrate yes, no and neither, as you and others have shown.
I think the distinction here is the difference between "if" and "iff"... I know I only ever used the second in high school math.So, doing away with examples, what is the difference between "is X" and "is not X"? IMO, defining what X is automatically defines what it is not, and defining what not X is automatically defines what it is (ie. "other than X")
The distinction we were given is that "if" specifies one set of circumstances leading to a given outcome, but allows for others. "Iff" (short for "if and only if"), OTOH, does not allow for any other possibility. For example:
- "Billy can get a chocolate bar if his parents give him his allowance" is true - the allowance will let him get a chocolate bar.
- "Billy can get a chocolate bar iff his parents give him his allowance" is false - Billy could find some money on the sidewalk, or someone could give him a chocolate bar.
The way the statements in the OP were phrased, they first statement definted only one set of conditions for A & B; it didn't define the relationship for A & B in all cases.
I see your point to a certain extent, but I think it's important to point out that this thread isn't about proving the truth or merit of "B", it's about trying to figure out whether "B"'s truth or merit is dependent only on "A".This is a big flaw in Aristotelian logic. The assumption a statement or concept must be either true or false does not reflect the diversity of human experience or the disordered chaos of human psychology. Unfortunately, the influence of this lame duck form of binary reasoning infuses language to the extent it is next to impossible to shake the habit of pretending we are able to coolly and rationally distinguish truth from falsehood.