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).

Start the demonstration...

MouseOver the sign to pause
the demonstration

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.

Replay the demonstration.
Next...

How should we think about this problem?