Square of Opposition
, Barker, pp. 31-36.
***Read the section, then the following additional comments.
Barker’s discussion pivots on the crucial distinction between the
Since the work of the nineteenth-century logician and mathematician
George Boole, the hypothetical viewpoint has usually been adopted.
Up until that time, in
accord with what Aristotle taught, the existential viewpoint was assumed.
The difference in a
nutshell is this:
We cannot assume that everything referred to in our statements
We assume that everything referred to in our statements exists.
Let’s say the baseball season has just started, and I say:
All the players hitting fifty homeruns or more this year are pretty good sluggers.
Now, undoubtedly, this is true as far as it goes, but there’s one problem: We don’t know if there
are going to be any baseball players this year who are going to hit fifty or more homeruns. So,
for right now, this is purely a
statement. Basically what I’m really saying is:
If there should be any players hitting fifty or more homeruns
, then they would be pretty
Now let’s move ahead in time and assume that the baseball season is over, and there have been
several players who hit fifty or more homeruns this season. Now if I make my statement, I’m
referring to individuals who really exist, namely players who hit fifty or more home runs this
year. Thus, in the terminology we are learning here, this is an
statement; it is based on
a category of things (baseball players) that
So, this is the difference between the hypothetical and the existential viewpoints. Under the
hypothetical viewpoint we are saying something about a class of things which would be true if
those things existed, but we don’t necessarily know that they do exist.
Take the sentence:
All hobbits live in middle earth.
Is it true?
Well, yes—that’s the nature of hobbits as J. R. Tolkien created them. But we don’t
know that there are any hobbits. So, the statement can be made only from the hypothetical
Categorical Logic, Part 2