Is the Double-Not Arrow the Logical Opposite of 'Either/Or'?

[kitmit2800]

Hi all!

Just like the title, I am wondering if the Double-Not Arrow where 'at least not one of the two, possibly neither' can occur and Either/Or where "at least one of the two, possibly both" can occur are logical opposites.

Thanks so much!

[Dave Killoran]

Hi Kitmit,

Good question!

You are referring to this arrow, right?: A B. That diagram essentially means both can't occur, but anything else can happen.

A statement like "Either A or B must occur" can be diagrammed as: A B. This diagram means both can't be absent, but anything else can occur.

So, on the extreme ends the two are polar opposites, but interestingly they overlap in that two scenarios are possible under each:

• 1. A occurs and B does not occur.
  2. B occurs and A does not occur.

Because they overlap like that and share possibilities, they aren't logical opposites. Logical opposites divide the spectrum into two distinct pieces, and these two don't do that.

Please let me know if that helps. Thanks!

[kitmit2800]

Hi Dave!

Yes, thank you so much; this totally answered my question!

Best,

km