If you are reading about the rules (section 5.3) you will see that the book has 5 rules. These can be condensed for easy checking of validity by combining rules 3 and 4. Here’s how:

1) The middle term must be distributed

2) If a term is distributed in the conclusion, then it must be distributed in a premise

3) Combining rules 2 and 4: The same number of negative claims as appears in the premises, must also appear in the conclusion.

Ask yourself the following:

How many claims can be in the conclusion of a single argument? Only one of course!

So, the maximum number of negative claims possible in the premises is never more than one claim, right?

If there is a negative premise, you better have a negative conclusion. This renders the equation 1 = 1.

If there are no negative claims in the premises, then you better have zero negative claims in the conclusion. This renders the equation 0 = 0.

Let’s try it:

All canines are mammals.

All dogs are canines

Therefore, All dogs are mammals

Canines is the middle term. It is distributed in the major premise (first one) – passes rule 1

Dogs is distributed in the conclusion, and it is also distributed in the minor premise (second one)- passes rule 2

0 = 0 (Zero negative claims in the premises and zero in the conclusion) – passes rule 3

For your discussion here is an exercise:

1) Contribute items that show how this rule works similar to the one above. Make sure your argument is valid so far (before worrying about existential fallacy- rule 5)

2) What advantage is there to having 4 rules specifically stated, as the book does, instead of condensing them. (Hint: it has to do with understanding the fallacies associated with the rules.

3) Can you name the fallacies associated with the first 4 rules in the book and explain them as they relate to the rule?