derivations

8/12/26

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.

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

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

3/16/06

So that we can show certain arguments to be valid.

The focus of the course lies with the validity and invalidity of arguments. Now, invalidity can be established by counter-example (by producing an interpretation under which all the premises are true and the conclusion false, at the same time). But validity is a different matter. And the usual approach is to have rules of inference and to do derivations.

Replacement or Rewrite Rules

6/21/07

Rewrite Rules

This video uses '&' as the logical symbol for 'and'.

Example of a Harder Propositional Proof: One of De Morgan's Laws

10/23/06

Example

Example of a Harder Propositional Proof

2/27/06

Example

Reductio ad Absurdum

2/24/06

Absurd Introduction and Simple Reductio

9/12/06

Conditional Proof

This video shows the techniques for Conditional Proof using the downloadable application Deriver. But the techniques are exactly the same for the Proof applet running in a web page. So, the video may look slightly different to what you are looking at, but the underlying principles and approach are the same.

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.