If and only if

College Confidential Community
1

<p>So this phrase somewhat confuses me.</p>

<p>P if and only if Q is equivalent to Q is necessary, and sufficient, for P.</p>

<p>I can understand P IF Q <=> Q is necessary for P.</p>

<p>But what about P ONLY IF Q <=> Q is sufficient for P?</p>

<p>I’m going to play World of Warcraft ONLY IF I have nothing better to do.</p>

<p>So here, the ONLY IF implies I will ONLY play WoW in the case that I have nothing better to do, and in no other case. In this case, “nothing better to do” is sufficient in order for me to ONLY play WoW, since all other cases causing me to play WoW are excluded. But it also seems to imply an iff statement. It seems to imply ONLY IF I have nothing better to do, then I will play World of Warcraft, even though a sufficient statement does not imply that given the statement, I MUST carry out its implication. If I have nothing better to do, I could also get drunk. Hm. Yet the ONLY IF statement seems to be exclusive to “get bored => play WoW”. </p>

<p>I can see that IF AND ONLY IF carries more meaning than IF. But it seems that ONLY IF seems to carry the same meaning as IF AND ONLY IF. I dunno, the word “only” doesn’t even look like a word to me anymore. >.< it looks like a string of phonemes</p>

<p>i’m confused…</p>

2

<p>Or I think I found a resolution.</p>

<p>P if Q puts STRESS on Q
I’m going to play WoW IF I’m bored puts STRESS on Q. (Q is necessary for P, P can exist independently of P in the case P if (Q OR R))</p>

<p>P only if Q puts STRESS on P
I’m going to play WoW ONLY IF I’m bored puts STRESS on P (Q is sufficient for P, P MUST come with Q, but Q can exist independently of P)</p>

<p>Maybe that explains the confusion, since most logical connectives place stress on ONE phrase or the OTHER, but in this case, one of the logical connectives puts stress on ONE, the other places stress on the OTHER></p>