Hello Craig,
I am sorry for the confusion. The atheist stated that he was "testing the excluded middle with symbolic logic." He concluded that his test showed that it was invalid. What he really showed was that he did not understand the law of excluded middle or symbolic logic.
His formula was (A v B v C):(A v C). I am not sure what ':' means, but it seems as if he was using it in the sense of implication '→'. The 'v' means "or" and the '→' means "If..., then...". If this is what he means (and I think this is what he meant), then he is saying that the law of excluded middle is...
If A or B or C, then A or C.
This is wrong. The law of excluded middle looks like this: (A v ¬A) where '¬' means not. In other words...
Either A or not-A.
What your friend "proved" was that "A or B or C" does not imply "A or C". The reason for this is that "A or B or C" is true if B is true and A and C are false. However, in this situation "A or C" is false. Therefore "A or B or C" does not imply "A or C". This is what your friend meant when he said this...
Quote:
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FTF T T F*...The line marked with a * shows that it is invalid.
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Notice, the first 'F' corresponds to A being false. The first 'T' corresponds to B being true. The second 'F' corresponds to C being false, and the last 'F' correponds to "A or C" being false. He says this shows "it" is invalid. Well, what is this "it"? He said it was the law of excluded middle. Well, it was not. "It" was simply the statement: (A v B v C) → (A v C), which is false.
So, I am really not sure what your friend was saying, but he has some misunderstandings regarding logic. I probably should not have commented on this, but I did because logic is sort of a hobby of mine.
Brian