Is this variation of modus tollens valid?
As I'm sure you all know, modus tollens can be expressed as
If P, then Q.
Not Q.
Therefore, not P.
So, is it equally valid to say
If not P, then not Q.
Q.
Therefore, P.
I think it is, but wanted to double check. Similarly modifying the "Justification via truth table" from wikipedia (differences in bold):
| p | q | ¬p | ¬q | ¬p → ¬q |
|---|---|---|---|---|
| F | F | T | T | T |
| F | T | T | F | F |
| T | F | F | T | T |
| T | T | F | F | T |
In instances of modus tollens we assume as premises that not p → not q is true and q is true. There is only one line of the truth table - the fourth line - which satisfies these two conditions. In this line, p is true. Therefore, in every instance in which not p → not q is true and q is true, p must also be true.
Edit: doesn't look like my table was formatted correctly...looking into this (FIXED)
Posted Dec 28, 2011, 12:09 AM UTC · edited
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