Wednesday, December 21, 2005

Logic Lesson: The Four Forms of Propositions

In Aristotelian logic, there are four forms of propositions: universal affirmative, universal negative, particular affirmative, and particular negative. All declarative sentences can be properly characterized as one of these four forms.

For brevity, we may refer to each of these forms by a system of abbreviation, which was codified during the Middle Ages. The abbreviations are as follows: A = universal affirmative, E = universal negative, I = particular affirmative, and O = particular negative.*

If we use the letter "S" to stand for the logical subject and the letter "P" to stand for the logical predicate, the forms of the four propositions can be given as follows:
A: All S is P.
E: No S is P.
I: Some S is P.
O: Some S is not P.

Some examples: "All men are mortal" is in A form; that is, it is a universal affirmative proposition. "No ravens are white" is in E form. "Some politicians are corrupt" is in I form. And "Some politicians are not corrupt" is in O form.**

When we say a proposition is universal or particular, we are describing its quantity; when we say it is affirmative or negative, we refer to its quality. So, for example, how do we know that "All men are mortal" is a universal affirmative proposition? It is universal because it refers to all men, and it is affirmative because it says that all men are such and such, as opposed to saying that all men are not such and such. "Some politicians are not corrupt" is in O form because it talks about some politicians and says that they are not corrupt.

There are other finer details to go into, but we will put them off until later. Try your hand at some exercises given in the post below. Answers to the exercises appear when you click "Read more."

* The reasoning behind the abbreviations is that the Latin affirmo has as its first two vowels "a" and "i", and the Latin nego has as its first two vowels "e" and "o".

** More on the O in the answer to exercise 12.

No comments: