And it looks to me like you've got it backwards.


I'm not sure what I have backwards. A proposition is a sentence that is either true or false. In a conditional sentence, the premise (the if part) can be true or false and the conclusion (the then part) can be true or false. That is, each component (P and Q) is a proposition and the statement P->Q (which can be read as "P implies Q" or "if P then Q") is also a proposition. If you call P the minor premise and P->Q the major premise, it's okay with me. I don't specifically recall seeing that nomenclature, but the terminology doesn't change the underlying logic, so I accept it.


Now. Are you talking about the last Table on the page?



a. I would call the normal AND

b. is the standard inclusive OR

c. looks like P AND NOT Q

d. is the standard exclusive OR (XOR)

The standard colloquial defintion of "or" is d. The conflict between b. and d. is the basis for the joke question, "Did you take the bus or bring your lunch?"


a. yes. this is AND.
b. yes. this is OR.
c. no. this is "P implies Q" that sideways U symbol reads (P implies Q, which can also be written P->Q which can also be written as "not P or Q").
d. yes. equivalence is identical to XOR.

Back to c.

Let's look at the table again, only I'm going to add new fields for "NOT Q" and "P and not Q" (C means conditional, Q' means not Q, and Z means "p and not q"

P Q C Q' Z
T T T F  F
T F F T  T
F T T F  F
F F T T  F


We note Column C (P implies Q) is not the same as column Z ("P and not Q"). This time I add columns P' and W (not P or Q).

P Q C P' Z
T T T F  T
T F F F  F
F T T T  T
F F T T  T


We note that column C is the same as column Z.
You can check out http://www.merriam.uiuc.edu/ps481/lectures/topic6/advancedrules.html
and search for "Material implication" and an little more detailed explanation at http://secure.yournotes.com:81/notes/fall98/cse260/cse260_082898.shtml
(the same thing I've done above, but considerably neater).

k