propositional

Review of Propositional Logic

12/23/05

You now have to tools to appraise propositional arguments.

Let us run through how these might be used with two examples.

Example 1.

Consider the argument

If no human action is free, then no one is responsible for what they do.
If no one is responsible for what they do, no one should be punished.
Therefore
If no human action is free, no one should be punished.

First it should be symbolized

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.

2013

Skills to be acquired

Becoming familiar with common inference patterns and being able to use them via rewrite rules. This helps with assessing ordinary everyday reasoning such as that found in the law, in newspapers, in advertisements, etc.

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

2013

Skills to be acquired:

Learning the Rules Or Elimination and the Introduction of the Biconditional.

The Tutorial:

Or Elimination, in the guise of Dilemma, also is a form of inference dating from antiquity.

The core idea of it that if a conclusion follows from both disjuncts of a disjunction, then the conclusion follows full stop. As an example in English, if either I am going to eat an ice-cream or I am going to eat some cake, and if I eat ice-cream I break my diet, and if I eat cake I break my diet, then ... I break my diet.

Quiz 6 Applet

This contains an applet, so it will be slow loading and likely it will ask you about security.

2013

Skills to be acquired:

Learning reductio proof, both as plain Negation Introduction and via (double) Negation Elimination (to prove some formulas that do not have negation as their main connective).

The Tutorial:

Reductio ad Absurdum is the second of the classical forms of inference.