Chapter 5, Tutorial 1

Derivations with MP, MT, and DS

Derivations are a kind of step-by-step deduction of a *series* of conclusions, each leading to the next.

Suppose you know that Chris will get an 'A' or a 'B'. And you also know that if he's to get an 'A', he must turn in proof exercises.

Then you find out he that he does NOT turn in the proofs. What would you conclude?
(a) that he won't get an 'A' and so will get a 'B', (b) nothing, I'm sick of clicking.

You could set out the thinking this way.

If he's to get an 'A', he must turn in the proofs.

__But he doesn't turn in the proofs.__

So, he won't get an 'A'.

So far, that is just MT. Its a valid argument. And we now know Chris didn't get an 'A' (provided we know the premises are true).

But we can continue on in a familiar, valid way.

Because the first fact we premised about Chris was that he will get an 'A' or a 'B', we can now finish our thinking this way:

Chris will get either an 'A' or a 'B'.

__We just concluded that he won't get an 'A'.__

So, we can further conclude, he *will* get a 'B'.

Done!
That's step by step reasoning.

We can symbolize this in SL:

A>P

__ ~P
__ So, ~A

AvB

So, B

And we need to see how this will work in our formal derivations.