## Modus Tollens

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### Modus Tollens

If A implies B then Not A implies Not B.

Apparently not everyone takes this for granted as I was surprised to find out. After making this claim on another forum, the claim was challenged and I immediately thought that I screwed up.

As a reach, I assumed the challenge was grounded in that fact that there are domains where logic has multiple values - not simply true or false.

My conjecture was and still is that in logic denying the excluded middle (an infinite valued logic) the first sentence, also called Modus Tollens, is no longer valid.

So here are my questions:

1) Is Modus Tollens valid in a logical system denying the excluded middle?
2) If not what is the minimum number of values in a logical system where Modus Tollens is valid?

Thanks Ed
Last edited by Ed3 on Mon Jun 18, 2012 9:42 pm, edited 1 time in total.
"Albert! Stop telling God what to do." - Niels Bohr
Ed3
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### Re: Modus Tollens

What you said in the first line is not Modus Tollens and it's not correct.
Modus Tollens is: If A implies B then not B implies not A.

Flannel Jesus

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### Re: Modus Tollens

Hi FJ,

OH!!! you are right.

Sorry!!!

Thanks Ed

P.S. I am still interested in the anwsers to the questions using the correct statement of Modus Tollens.
"Albert! Stop telling God what to do." - Niels Bohr
Ed3
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Joined: Sun Oct 31, 2004 2:56 pm
Location: Lakeville MN USA