p = "Ed is a horse" and q = "Ed has four legs". (p implies q) works out to: "Ed is a horse" implies "Ed has four legs". So far, so good.
Now, what if Ed is a dog? p is false, yet q is true. However, the conditional statement is still true, because it is not claiming he is a horse. It's just claiming that if he were, he'd have four legs.
Another example: p = "All science-fiction fans go to Virginia Tech" and q = "Virginia Tech is crowded". p isn't true, and q is (by the accounts I've heard), yet the statement only claims that Tech would be crowded is all science-fiction fans were there, and is therefore true.
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Oh, shut up, Data
Date: 2003-08-28 12:51 am (UTC)p = "Ed is a horse" and q = "Ed has four legs". (p implies q) works out to: "Ed is a horse" implies "Ed has four legs". So far, so good.
Now, what if Ed is a dog? p is false, yet q is true. However, the conditional statement is still true, because it is not claiming he is a horse. It's just claiming that if he were, he'd have four legs.
Another example: p = "All science-fiction fans go to Virginia Tech" and q = "Virginia Tech is crowded". p isn't true, and q is (by the accounts I've heard), yet the statement only claims that Tech would be crowded is all science-fiction fans were there, and is therefore true.