# What is this technique to gain proof called?

I just found out that I always missused the term deduction. I always thought that deduction meant gaining a proof by showing that all the other possible answers are wrong. But deduction is actually something like this:

1. All men are green
2. John is a man
3. RESULT: John is green

But what is my first mentioned method (bold) called?

• In any system of logic that I can think of, that wouldn't count as a proof. Just because everyone else is wrong doesn't mean you are right. You could all very well be wrong. Consider inductive reasoning, a form of reasoning which shares the same lack of conclusive power (albeit for not the same reasons). – stoicfury Feb 19 '12 at 11:16
• Im no philosopher, nor a mathematician or a physicist. Im an artist and a programmer and I dont really care much for the meaning of the word "proof". I was actually afraid that this would be the first reaction :) But an example of my reasoning, that can at least give a correct answer, if not a proof: A question on a test has three possible answers. The question is: what color is this? Answers: blue, yellow, taupe. I dont know the color taupe, but I can see that the color is NOT blue and NOT yellow: hence the color must be taupe. I got the answer by knowing that the other answers were false. – Hans Wassink Feb 19 '12 at 11:51
• I see what you're saying now. I misinterpreted what you meant by "all other possible answers" as "all those that may be the case" (i.e., some answers), rather than the theoretical complete set of all answers. In the event that you know at least 1 answer is true, and you have ruled out the complete set of all other "possible" answers, then yes Disjunctive Syllogism is correct, as Tom points out below. – stoicfury Feb 19 '12 at 15:32
• Thanks Stoic, I shouldve mentioned that it was known that exactly one answer was correct :) – Hans Wassink Feb 21 '12 at 7:47

## 2 Answers

This is known as "the process of elimination."

• That is exactly what I was looking for Michael! Thanks – Hans Wassink Feb 21 '12 at 7:44

In formal logic this is called a Disjunctive Syllogism (sometimes called 'the process of elimination' in informal logic) - grandchild of the syllogism a la Aristotle you've got going on with the green man. As logically valid as they come, this one!

Formally if one knows: 'X or Y' and 'not X', one may conclude 'Y'

It's often difficult to find the premises in practice for anything non-trivial (it's easy with different colours of paint, but try listing different theories of electron behaviour!), but as with all logic the conclusions follow irrefutably from the premises if they are there. (Unless of course the propositions under investigation, like certain quantum properties, are not governed by standard logic: but that is another story...)