Chapter Eight, Tutorial Three

PD
Strategy

Strategy for PD is *very* much like that for SD and SD+.

One *first* provides a goal, then *second* considers
"obvious" ways to reasonably proceed toward that goal.

*Third, *when steps are not obvious, one considers the I-rules for the
main connective of the goal at hand and E-rules for the main connective of
any accessible sentences.

If all else fails, the "desperation" step, *fourth*, is to
use ~E: assume the negation of your current goal.

That's basically all that's needed for PD too. But lets look back to a *very*
easy illustration (from the last quiz).

Keep the ** goal**
in mind:

(^x)Tx

We need to think of the I-rule: ^I. This is the third step in our strategy.

This requires *what*
on line 3?

If
one is to use ^I to derive line 4, then one *must*
first have a substitution instance *of* 4.

So, because your
goal has main connective '^', you have a *new*
goal:

T_

(The blank takes an arbitrary name! Let's choose 'a' and 'Ta')

It's the same for
harder problems: To derive an ^-sentence, *first*
derive its substitution instance with an arbitrary name.

Don't forget!

Now
the rest is easy...

This
simple strategy will most always work...make sure you're ready to apply it
to the harder problems.

How should we think about this problem?