Invalid Argument Forms

Question 1

All Jedi use the Force. Dooku uses the Force. Therefore, Dooku is a Jedi.

Answer 1

A –> B
B
\_\_\_\_\_\_\_\_\_
A
(Affirming the Necessary)
You don’t know what else, in addition to Jedi, also uses the Force. So, just because something is in the B (Force user) category doesn’t make it an A (Jedi). It could be an A, but it doesn’t have to be. Turns out, Dooku is a Sith Lord.

Question 2

All tragedies are sad. I’m not a tragedy. Therefore, I’m not sad.

Answer 2

A –> B
/A
\_\_\_\_\_\_\_\_\_
/B
(Denying the Sufficient)

Question 3

All dogs are cute. Some cute things are lovable. Therefore, some dogs are lovable.

Answer 3

A –> B some C
_________
A some C

So all A’s are B’s and some B’s are C’s. Which B’s are C’s? There could be plenty of B’s that are not A’s and it’s those non-A-B’s that are C’s. So it certainly isn’t a necessity that some A’s are C’s.

That was the abstract explanation. Here’s something more tangible. I always use mental pictures to help me with this. Let’s make the first premise true. So, imagine a bucket containing dogs. Now, take that bucket and drop the whole thing into a larger bucket labeled cute things. We’ve just made the first premise true. Now, let’s make our second premise true. We’re going to reach into the bucket of cute things and grab a handful of what’s in there and toss it into the bucket of lovable things. Isn’t it possible that in our handful, we’ve failed to grab any dogs? In other words, we’ve only grabbed the non-dog cute things? That’s why the argument isn’t valid. Because it could be the case that there are no dogs that are lovable.

Question 4

All A’s are B’s. Most B’s are C’s. Therefore, most A’s are C’s

Answer 4

A –> B -most-> C
_________
A -most-> C

Question 5

Some A’s are B’s. Some B’s are C’s. Therefore, some A’s are C’s

Answer 5

A some B some C
_________
A some C

Say we have some computers that are amazing. There are some amazing things that are edible. Does that mean there must be some computers that are edible? No. In fact, we know that no computers are edible.

Question 6

Most A’s are B’s. Most B’s are C’s. Therefore, some A’s are C’s

Answer 6

A -most-> B -most-> C
_________
A some C

Question 7

Some A’s are B’s. Some A’s are C’s. Therefore, some B’s are C’s

Answer 7

A some B
A some C
_________
B some C