derivations

2/5/08 10Software

Reading

Hausman[2007] Logic and Philosophy Chapter 9

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.

2/5/08 10Software

Reading

Hausman[2007] Logic and Philosophy Chapter 9

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

 

Tutorial 19 Simplified Universal Generalization.

2/5/08 10Software

Reading

Hausman[2007] Logic and Philosophy Chapter 9

The Tutorial

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

2/5/08 10Software

Reading

Hausman[2007] Logic and Philosophy Chapter 9

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.

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.

12/22/05

Introduction to Tactics

This video is set in the context of the downloadable program, but it applies equally well in the setting of a proof applet. [It is also using a different logical system. However it will convey the principles, The video will be replaced with one suitable for this setting.]

9/4/06

Tutorial 5 Example: Doing a derivation

This movie shows the downloadable application being used, but the manipulations are so similar to those of the web page applet that it really covers both.

This video is also using a different logical system, but it is close enough for now to illustrate the important points. [The video will be revised and replaced.]

Roll your own derivations

6/21/07 10 Software

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'.

[Often copy-and-paste won't work directly from a Web Page; however, usually drag-and-drop will work!]

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

F ∴ F . G ∼ ∧ ∨ ⊃ ≡ ∃ ∴