Methods for Testing Validity/Invalidty

Logic 102

September 19, 2018

Our Methods So Far

So far, we have two ways of testing for validity and invalidity

These methods have some advantages and some drawbacks

Truth Table (Boole)

Pros

Cons

Tarski’s World (Tarksi’s World)

Pros

Cons

New Technique: Formal Proofs (Fitch)

Pros

Cons

Our approach

From now on, we won’t be using Truth Tables for our exercises. (If you want to use them to help you understand an argument better, you are permitted to do so.)

Instead, when we’re not sure whether an argument is valid or invalid, we’re going to use a pincer attack on an argument to attack it from both sides.

Talk it through and take your best guess: Valid or Invalid?

What is a Formal Proof?

A proof is an ordered sequence of sentences, starting from the premises and ending in the conclusion, where each step after the premises comes from applying a truth-preserving formal rule to earlier steps in the sequence.

“Truth-preserving” means that when the rule is applied to true sentences, it never allows us to write down a sentence that could be false.

“Elim”-rules are applied to a step with that connective as its main connective.

“Intro”-rules are applied to allow us to write down a new step that has that connective as its main connective.