derivations

4/24/06

Tutorial 25 Exercises e

12/14/20

Tutorial 25 Exercises d

4/24/06

12/25/13

Skill to be acquired:

To understand how the various restrictions on the quantificational rules work to exclude certain kinds of invalid inferences

Reading

Bergmann[2004] The Logic Book Section 10.1

The Tutorial

The Rule of Universal Elimination UE

If a derivation contains a line of the form

n (∀<variable>)<scope> <any justification>

then a line of the form

<<scope>[<constant>/<variable>]> 'n ∀E'

2013

Reading

Bergmann[2004] The Logic Book Section 10.1.

The Tutorial

Existential Elimination (often called 'Existential Instantiation') permits you to remove an existential quantifier from a formula which has an existential quantifier as its main connective. It is one of those rules which involves the adoption and dropping of an extra assumption (like ∼I,⊃I,∨E, and ≡I).

The circumstance that Existential Instantiation gets invoked looks like this.

2013

Reading

Bergmann[2004] The Logic Book Section 10.1.

The Tutorial

There is a rule for adding a Existential Quantifier, Existential Introduction (also commonly known as 'Existential Generalization'). This permits the step illustrated by the following proof fragments.

2013

Skill to be acquired:

To learn the rule for adding a Universal Quantifier.

Reading

Bergmann[2004] The Logic Book Section 10.1.

The Tutorial

There also is a rule for adding a Universal Quantifier (often called 'Universal Generalization'). This permits the step illustrated by the following proof fragments.

The rule is

2013

Skill to be acquired:

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

Reading

Bergmann[2004] The Logic Book Section 10.1.

2013

The Tutorial

The sentential rules of derivation carry over unchanged into Predicate Logic

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There are many valid arguments which cannot be shown to be valid using sentential logic alone. For example,

Beryl is a philosopher.
All philosophers are wise.
Therefore
Beryl is wise.