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
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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?