History of Logic: Particular Propositions

Particular Propositions

The Particular Affirmative

EXAMPLES:

Some man is mortal.
There is a woman who is a politician.
At least one computer runs Microsoft products.
There is a fun Web site.

The particular affirmative states that there is at least one member of one class that is a member of a second. It doesn't imply that all members of one class are members of the second.

These sentences sound strange: a more natural language might say that "This Web site is fun." or "Socrates is mortal." However, at this stage of the development of our logical language, we want to be able to distinguish between saying that there is at least one fun Web site and that a specific Web site is fun. While it is true that if this Web site is fun then there is at least one Web site that is fun, it doesn't necessarily follow that if there is at least one Web site that is fun, that this one is. You might think this Web site was lame and Yahoo was fun, for instance.

This takes us naturally to the first thing to remember about the particular affirmative:

It isn't exactly right to talk about the particular affirmative having a converse in the same way that it is to say that a universal term has one. However, there is an implication involved in certain natural language statements that forms the basis for most proofs of particular affirmative statements.
It's simple: to prove that some A is B, all you need to do is find one example of when A is B, and bingo! You're done.

The Particular Negative

EXAMPLES:

Some fictional creatures are not mortal.
Some Web sites are not fun.
Some philosophers don't make sense.
Some computers are not expensive.

The connection between the particular affirmative and negative is easy to see. In fact, in our natural language, we often don't make much of a distinction between the two: modern logic doesn't either.

For example, when you think of the negative particular statement "Some woman is not beautiful." it seems equivalent to the affirmative particular statement "Some woman is homely." On further examination, we see that this is only true if every woman is either beautiful or homely.
Similarly to the particular affirmative, the particular negative can be proven by finding a single example. For instance, if we want to prove that some politician is corrupt, all we have to do is find one corrupt politician.

I want to go back to the first Aristotle stuff.

I want to check out the universal statements.

I want to find out how it fits together to form a syllogism.

Take me back to the History of Logic homepage.

Jason Corley -- corleyj@cobweb.scarymonsters.net