The Universal Affirmative
The universal affirmative states that all members of a particular class
belong to another class. In set theory, we might say that the universal
affirmative tells us that one set of objects is a subset of the other set.
Here are some important things to know about the universal affirmative:
- All politicians are liars.
- All men are mortal.
- All good Web pages are written in html.
- All good men come to the aid of their party.
- All men have what it takes to become a successful salesman.
- The universal affirmative as stated by Aristotle is not two-way.
Consider, for example, example 1 above. It doesn’t mean that all liars
are politicians. In example 2, we are not stating that all mortal things
are men. (This “reverse” of the orignial statement is called the
converse of the statement. More on converses later. For an
interesting exercise, try to find the converse of the examples! Answers here.
- Here's an interesting question: does the universal affirmative say
that anything exists? For instance, if we say "All men are mortal", does
that mean that there is a mortal man out there somewhere? Or are the
statements "All unicorns are white" or "All fleeps are floops" equally
true? Take a look at the existential import of
universal statements to explore this further.
The Universal Negative
The universal negative states that no member of a class is a member
of another specified class. In set theory, this corresponds to saying
that two sets are “disjoint”, or saying that the intersection of the two
sets is the null set. Here are some important things to know about the
- No politician is intelligent.
- No man is immortal.
- No good Web pages contain Java or browser-specific tags.
- No good men will betray their principles.
- No men have what it takes to be a successful mother.
- The universal negative is effectively two-way, unlike the universal
affirmative. In other words, a universal negative statement
does imply its converse. For instance, in Example 1, we
propose that no politicians are intelligent, and therefore imply that no
intelligent people are politicians. In Example 2, we not only say that no
men are immortal, but that no immortal beings are men. This is the most
important distinction between the universal affirmative and the universal
negative, functionally speaking. (Again, try to find the converses of the
statements and see how they relate to the original statement. Answers here.)
- Does the universal negative imply the existence of anything? It
faces the same problem as the universal affirmative in this sense. When
we say "no politicians are honest", are we saying that there are
politicians, honest people, or are we just keeping quiet about the point?
You can check out the debate here if you missed it before.
I want to go back to the Aristotelian
I want to check out the particular
I think I have the hang of it. I want to see
how these fit together into a syllogism.
back to the History of Logic homepage.
Jason Corley --