Construct a deductive argument that is valid but not sound.

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pohnpei397 eNotes educator| Certified Educator

A deductive argument is one that takes general concepts and relates them to a specific case.  For example, we know that all human beings are mammals.  We know that I am a human being.  Therefore, we can conclude that I am a mammal.  

Deductive arguments can be evaluated as to whether they are valid and whether they are sound.  They are valid if the are internally consistent.  They are sound if they are valid and also true.  If I make a deductive argument that makes sense internally but is not true, then I have constructed a deductive argument that is valid but not sound.

For example:

All human beings can give birth.  I am a human being.  Therefore, I can give birth.

If the first two statements are true, the third must be true.  Therefore, this is a valid statement.  But not all humans can give birth.  Therefore, this is not a sound statement.

caitlinand | Student

All teachers are fairies 
I am a teacher
Therefore i am a fairy

By using MAV and/or truth trees we can see that this argument is valid by way of its invalidity being false. However, in real terms, we know that teachers are not fairies. Therefore this deductive argument is valid but not true.