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

Question 8

If the sufficient condition is failed, it yields ____ (what)?

Answer 8

DENYING THE SUFFICIENT CONDITION

If the sufficient condition is failed, it yields no information about the necessary condition.

The necessary condition could be true or could be false.

Question 9

In general, affirming the necessary condition yields ____(what)?

Answer 9

AFFIRMING THE NECESSARY CONDITION

In general, affirming the necessary condition yields no information about the sufficient condition.

If the necessary condition is satisfied, it yields no information about the sufficient condition. The sufficient condition could be true or could be false.

Question 10

If the “ALL” arrow shows up first in the chain and then you see the “MOST” arrow, there ____ (what)?

Answer 10

ALL BEFORE MOST

If the ALL arrow shows up first in the chain and then you see the MOST arrow, there are NO VALID conclusions to be drawn via the chain.

Question 11

When you see an “ALL” arrow before a “SOME” arrow, there _____(what)?

Answer 11

ALL BEFORE SOME

When you see an ALL arrow before a SOME arrow, there are NO VALID conclusions to be drawn.

From the lesson on the relationships between the quantifiers, you know that the “most” arrow implies the “some” arrow which means that “A —m→ B” implies “A ←s→ B.”

Question 12

When two most statements are chained together AND they do NOT emanate from the same set, there _____(what)?

Answer 12

MOST BEFORE MOST

When two most statements are chained together and they do NOT emanate from the same set, there are no valid conclusions to draw via the chain.

Question 13

When you see a logic chain with two some arrows, there _____(what)?

Answer 13

SOME BEFORE SOME

When you see a logic chain with two some arrows, there are no valid conclusions to be drawn.

Question 14

Are Sufficient Conditions equal to Necessary Conditions?

Answer 14

CONFUSING SUFFICIENCY FOR NECESSITY

NO, Sufficient conditions are not necessary conditions and necessary conditions are not sufficient conditions.

Question 15

Are “MOST” statements Reversible?

Answer 15

Most Statements are Not Reversible

FALSE, they are not.