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July 2014
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syscoder [userpic]
Easy logic question (Modus ponens affirming the antecedent)

Is

Either A or B
not B
______________
A


the same thing as

Either A or B
not A
________________
B

Comments

What do you mean, is it the same thing?
It's two uses of the same rule, which arguably have no meaningful difference since they're using only propositional variables ... but I really don't like that oversimplified or-elimination rule. A better rule is: (p v q), (p -> r), (q -> r) |- r.

He doesn't need to put in an or elimination rule unless he's going to try and reason:
Either A or B
A
________________
not B


I mean, for his purposes, either and exclusive or inclusive or (where I did logic, inclusive or being the one we used as standard) works for that. Since it says that one of A or B must be true.

(p v q), ~q |- r is an instance of v-elimination ...

And that goes way past the scope of the logic paper I did a couple of years ago. Or at least, way past the scope of what I can remember.

To say "either A or B, A, therefore not B," is to rely on the exclusive or, not the inclusive or. The inclusive or is the standard interpretation of "or" in the context of logic. I get the feeling I might be misreading you somehow.

I was saying he doesn't need to write out any form of extra rules for an or unless he's going to try and use an exclusive or.

ah, what do you mean by "the same thing"? They're both valid inferences. If this is about a homework question, the answer is totally dependent on the specific rules laid out by your text/prof. Hurley's logic texts, for example, recognize only the latter as an instance of "Disjunctive Syllogism", and not the former; on the other hand, the text of Bergmann et al treat both of your inferences as instances of the same rule, "Disjunction Elimination." (Neither is modus ponens, by the way.)

Ah, unnamed525's post reminded me, that my above characterization of Bergmann et all was incorrect; his description of Disjunction Elimination is actually what they use.

Thanks you guys for the responses. I thought they were the same, but I was not sure. My sister and I are taking the same logic class and she thought it was invalid, so I wanted ask someone that knew logic well.

Sorry about that I meant (Disjunctive Syllogism) not (Modus ponens affirming the antecedent)

If you curious, this is the text book problem.

Mr. Smith is the brakeman's next-door neighbor or Mr. Robinsons is the brakeman's next-door neighbor.
Mr. Robinson is not the brake-man's next-door neighbor.
Therefore Mr. Smith is the brakeman's next-door neighbor.

Re: If you curious, this is the text book problem.

if you assume the premises to be true and the conclusion follows necessarily from the premises then the arguement is valid.

yes?

Could you explain what you mean by "yes?" with the question mark?

yes is the answer to 'are they the same' and the question mark is for me not understanding why we would think they're not the same thing

Because the variables are swapped.
I was just affirming my belief that they were the same.

Posted earlier:

Thanks you guys for the responses. I thought they were the same, but I was not sure. My sister and I are taking the same logic class and she thought it was invalid, so I wanted ask someone that knew logic well.

yeah but that's the thing about variables, you don't know what they represent

These kinds of things make me wonder whats logical about logic -.-