Introducing Symbolic Logic by Robert M. Martin

Author:Robert M. Martin [Martin, Robert M.]
Language: eng
Format: epub, pdf
ISBN: 978-1-4604-0115-6
Publisher: Broadview Press
Published: 2004-11-15T00:00:00+00:00

Learning the Derivation System

Exercise 2.13. As a review of the functions of our rules, lets begin by filling in the justifications in these derivations

2.13.1

2.13.2

2.13.3

2.13.4

2.13.5. Would 4,R be a correct justification for step 8 in question 2.13.4? Explain.

But your main job will be to construct your own derivations. This is not a mechanical matter (like constructing truth tables was). It sometimes takes some ingenuity and strategic thought.

Strategies

Here are some hints regarding strategies for constructing derivations.

There are two basic varieties of thought-processes used in constructing derivations: top-down thinking, and bottom-up thinking. When you use top-down thinking, you look at what you have, and consider what you can get from it using various rules. Often you’ll be able to see this by identifying the main connective in the steps you have, and applying the elimination rule for that sort of sentence.

Suppose, for example, you had these two premises:

B ⊃ D

A & B

and you were supposed to derive (B & D) from them. Then top-down thinking might go as follows:

The first premise is (B ⊃ D). This is a conditional sentence, so ⊃E can be used on this conditional to get D—if I had B. The other premise is (A & B). This premise is a conjunction, so &E can be used on it, to get either A or B.

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