gentzen

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.

Roll your own derivations

8/12/26

You may have derivations of your own that you wish to try. Just type, paste, or drag and drop, them into the lower 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 ∼ ∧ ∨ ⊃ ≡ ∀ ∃ ∴

Review of Propositional Logic

2013

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

Replacement or Rewrite Rules

6/21/07

Rewrite Rules

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

8/11/2026

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

Or Elimination and Bi-Conditional Introduction

12/23/05

Or Elimination