CONNECTIVES
Ceqli connectives are based on the Loglan connectives. They are:
kay - and
va - and/or
fi - if and only if
seya - whether or not
da corn kay xyen. He is black and is a dog.
da corn va xyen. He is black or is a dog, and possibly both.
da corn fi xyen. He is black if and only if is a dog.
da corn seya xyen. He is black whether he is a dog or not.
Now, help me out, Loglanists. Would 'or' as in "You can have coffee or tea, but not both." be "fibu", that is, "if and only if" plus the negator bu? That's by analogy with Loglan 'onoi', but I can't follow the logic.
Would I have:
da corn fibu xyen. He is black if and only if he is not a dog. Or, he is either black or he's a dog, but not both.
Right?
Right.
ReplyDeleteHere's how the logic works. If we assert "He is black if and only if he is a non-dog", that means that either (a) he is both black and a non-dog, or (b) he is neither black nor a non-dog. There are four logical possibilities:
Could he be neither black nor a dog? No; if he is a non-dog, he must be black (the "if" part of "if and only if").
Could he be black and a non-dog? Yes, by (a).
Could he be non-black and a dog? Yes, by (b).
Could he be both black and a dog? No; if he is black, he must be a non-dog (the "only if" part of "if and only if").
That is the truth-value pattern of "exclusive or", so "He is black iff he is a non-dog" means the same as "He is either black or a dog but not both."
Thanks! That's a real tooth-grinder.
ReplyDelete