Chapter Five, Tutorial Six

SD Safeguards
and Strategy

Most of the derivations we've done up until this point have not been
very difficult -- we've needed to give relatively easy applications of
the rules and simple presentations of the basic deductive concepts. But
reasoning is often more complicated. In this tutorial we consider *strategy*
for working on more difficult or complicated problems and *safeguards*
against common errors. Let's begin with the latter.

I've noticed that a lot of people make one simple mistake: They look at a line that says something like

Premise 1 A=(B&C)

and then type

1 =E 5 A

This is ** wrong**! The rule

ALSO: the same applies to >E: two inputs are required!

(Moral: You should know your rules very well by now.)

Safeguards

As derivations get more difficult you may sometimes feel the need to
"cheat" on the rules just to do something...*anything...*to
get started on the derivation! Unfortunately, this desperation leads to
misapplication of rules and incorrect derivations. The solution is to
learn strategies for proceeding. We will look to these *strategies*
later in this tutorial. But we begin by looking at **common pitfalls**
to avoid.

Consider the following argument.

[A=(B=L)] & [C=(X&(B>L))]

__ A
__

B>L

A mess! At first, it's hard to even begin to think about this problem. And easy to try to make a "short-cut" not sanctioned by our SD rules. So, let's look at it and see how to avoid these mistakes.

Of course, because you are attempting to show this argument valid by using a derivation of 'B>L' , you will take the two premises as lines one and two of a derivation beginning as follows.

Premise | 1. | [A=(B=L)]&[C=(X&(B>L))] |

Premise | 2. | A |

??? | 3. | ??? |

But line 1 is so complicated, you may want to despair at finding something
to do at line 3. But don't! __Despair is the first pitfall__.
It makes many students

However, there's no need to despair and just start making assumptions. In the pages ahead, we will discover all sorts of strategies for doing derivations. So, hang tough and you will soon be used to complicated derivations.

Now, line 3 needs to be *something*. The *second* pitfall is
__short-cutting a derivation by making up a rule to illicitly
jump to a desired conclusion__. For example...

Premise | 1. | [A=(B=L)]&[C=(X&(B>L))] |

Premise | 2. | A |

1 &E |
3. |
B>L (Mistake!) |

Now, what's the mistake here?