Chapter Four, Tutorial Five

Complex
Symbolizations

Here's a simple idea with which you are already familiar: The English form,

(1) If P, then Q

is symbolized as

(2) P>Q

But this statement hides an important point about complex symbolizations.
'P' is a metavariable ranging over *all*
sentences of SL; thus P itself may be a
molecular sentence.

So, we have sometimes used the
clearer but more cumbersome

(1') If , then

I use (1') as a variant on (1). But they mean the same thing. The box, oval, and the colored P and Q are just the *placeholders* we've called metavariables.

Here's the point: All these metavariables are just stand-ins or blanks to be filled by statements. Here they
are to be filled by English statments.

So an instance of (1) or equivalently (1') is

(3) If Chile and Argentina are in South America, then so is Bolivia.

You can see it this way:

Which by (2) should be symbolized with main connective horseshoe (not ampersand); something like:

(4) (C&A)>B

This may seem trivial. But the important point is that the words "If" and "then" in (1) work like the parentheses in (4). Or to put the point just a little differently, "If" and "then" in (3) serve to group Chile and Argentina together, just as parentheses do in SL. Either way, the main connective is the conditional.

The secret to doing complex symbolizations is understanding how English groups its simple sentences. We need to think about other means to group. Begin by thinking about the next question.

Which of the following are true? Click on all correct answers.

- "Either Argentina and Bolivia are in South America, or Chile is" can be symbolized as '(A&B)vC'.
- "Either Argentina and Bolivia are in South America, or Chile is" can be symbolized as 'A&(BvC)'.
- "Both it's the case that either Argentina is in South America or Chile is, and Bolivia is in South America" can be symbolized as '(AvC)&B'.