Universal Propositions

1. All politicians are liars.
2. All men are mortal.
3. All good Web pages are written in html.
4. All good men come to the aid of their party.
5. 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.

1. No politician is intelligent.
2. No man is immortal.
3. No good Web pages contain Java or browser-specific tags.
4. No good men will betray their principles.
5. 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 check out the particular propositions.

I think I have the hang of it. I want to see how these fit together into a syllogism.

Take me back to the History of Logic homepage.