Philosophy - Philosophy Course Notes
Proving Invalidity in Sentential Logic - ie. Propositional Logic
Lecture 11
June 2, 2007
A. Proving Invalidity in SL
Use a Characteristic Truth Table:
| A | B | Not A | A & B | A => B | A v B |
| T | T | F | T | T | T |
| T | F | F | F | F | T |
| F | T | T | F | T | T |
| F | F | T | F | T | F |
B. Using Dead Reckoning To Prove Invalidity
1. List all premises and the conclusion across the page horizontally. Indicate all premises are true and the conclusion is false.
2. Use the truth table above to 'break out' the example.
3. Repeat step 2 as often as needed, number them 1-X to show the steps you are taking. If you entirely fill in the truth values for all sentences, the argument is invalid. If you run into a scenario where a sentence is both true and false, then you have shown validity in SL.
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