derivations

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Skills to be acquired in this tutorial:

a) Learning further sentential rules of inference. Carrying out simple sentential derivations using some of the Rules of Inference.

b) Learning elementary Tactics.

Reading

Hausman[2007] Logic and Philosophy Chapter 4

Why this is useful:

Tactics will help you to do derivations.

The Tutorial:

a)

10/12/26

Skills to be acquired in this tutorial:

Learning further sentential rules of inference. Carrying out simple sentential derivations using some of the Rules of Inference.

Reading

Hausman[2007] Logic and Philosophy Chapter 4

The Tutorial:

Thus far we have encountered 3 sentential rules of inference: Simplification, Conjunction, and Addition. If we write these out as forms or patterns, these are the kinds of inferences they permit.

Simplication (Simp)

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Skills to be acquired in this tutorial:

Proving an argument to be valid by displaying a derivation. Carrying out simple sentential derivations using some of the Rules of Inference.

Reading

Hausman[2007] Logic and Philosophy Chapter 4

The Tutorial:

If you suspect that an symbolized argument might be valid, you should attempt to give a derivation of it.

A derivation is a proof of validity.

Tutorials 11 to 25: predicate logic, using the Hausman syntax.

10/12/26 under construction

You now have to tools to appraise arguments to the level of detail offered by predicate logic.

Let us run through how these might be used with a long and difficult example.

Consider the argument

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The material explained here is conceptually at a higher level than the earlier tutorials. It also covers relatively rare cases.

Skills to be acquired:

To understand the concepts of scope, free, bound, and free for. To learn of the restrictions on the quantificational rules

Why this is useful:

The new predicate rules of inference using quantifiers have restrictions on them which are expressed in terms of these concepts. And, in turn, the restrictions on the rules allow them to be used properly.

The Tutorial

Existential Instantiation permits you to remove an existential quantifier from a formula which has an existential quantifier as its main connective.

The circumstance that Existential Instantiation gets invoked looks like this.

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The Tutorial

There is a rule for adding a Existential Quantifier. This permits the step illustrated by the following proof fragments.

5	Fa
6	(∃x)Fx	5 EG

 

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The Tutorial

There also is a rule for adding a Universal Quantifier. This permits the step illustrated by the following proof fragments.

5	Fx
6	(x)Fx	5 UG

 

10/12/26

Skill to be acquired:

To understand the concepts of scope, free, bound. To meet substitution and a simplified version of the rule for removing a Universal Quantifier.