derivations

10/13/26

You may have derivations of your own that you wish to try. Just type, paste, or drag and drop, them into the panel, select your derivation, and click 'Start from selection'

You will need to use the correct logical symbols. Here they are

F ∴ F & G ∼ & ∨ ⊃ ≡ ∃ ∴

And the right syntax (the premises separated by commas and then a 'therefore' followed by the conclusion).

So, a selection needs to have a form similar to this

F⊃G,G⊃H∴F⊃H

10/12/26

You may have derivations of your own that you wish to try. Just type, paste, or drag and drop, them into the panel, select your derivation, and click 'Start from selection'.

You will need to use the correct logical symbols. Here they are

F ∴ F . G ∼ ∨ ⊃ ≡ ∃ ∴

And the right syntax (the premises separated by commas and then a 'therefore' followed by the conclusion).

So, a selection needs to have a form similar to this

F⊃G,G⊃H∴F⊃H

You may have derivations of your own that you wish to try. Just type, paste, or drag and drop, them into the panel, select your derivation, and click 'Start from selection'. 

You will need to use the correct logical symbols. Here they are

F ∴ F . G ∼ & ∨ ⊃ ≡ ∃ ∴ (or use the palette to produce them)

And the right syntax (the premises separated by commas and then a 'therefore' followed by the conclusion).

So, a selection needs to have a form similar to this

F⊃G,G⊃H∴F⊃H

10/13/26

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

10/13/26

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

Reading

Herrick[2000] The Many Worlds of Logic Part IV

Skills to be acquired:

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

10/13/26

Reading

Herrick[2000] The Many Worlds of Logic Chapter 18

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.

10/13/26

Reading

Herrick[2000] The Many Worlds of Logic Chapter 18

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

 

10/13/26

Reading

Herrick[2000] The Many Worlds of Logic Chapter 18

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

 

10/13/26

Reading

Herrick[2000] The Many Worlds of Logic Chapter 18

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.

Reading

Herrick[2000] The Many Worlds of Logic Chapter 18

The Tutorial

The sentential rules of derivation carry over unchanged into Predicate Logic

Exercises to accompany Predicate Tutorial 5

Exercise 1 (of 1).