Recipe

Symbolize a whole argument

Use when: you have an English argument and want to test it with a truth table

Goal: the premises and conclusion as formulas, all written with one shared key

Taught in Symbolizing whole arguments

1. 1

   Find the conclusion, list the premises, and add any missing premise you decided the arguer relies on.

   Example

   "The game is off, because the field is flooded and a flooded field means no game." Conclusion: the game is off. Premises: the field is flooded; if the field is flooded, the game is off.

   Why: the table tests the lines you give it, so the lines must be the argument you mean.

2. 2

   List each atomic claim that appears anywhere, give each one letter, and let denials reuse the letter of the claim they deny.

   Example

   F = the field is flooded, G = the game is on. "The game is off" is \neg G.

   Why: shared letters are the threads that tie the premises to each other and to the conclusion.

3. 3

   Translate each premise and the conclusion with that key.

   Example

   F, F \to \neg G, and the conclusion \neg G.

   Why: each line becomes one formula the table can evaluate on every row.

4. 4

   Write A_1, \dots, A_n \therefore C. Then check that no claim got two letters and no letter stands for two claims.

   Example

   F,\ F \to \neg G\ \therefore\ \neg G. "Flooded" means the same thing in both premises, so one letter is right.

   Why: a split or merged letter makes the table judge a different argument from the one in English.