It is possible to use logic to prove a negative statement?

Question

I was having an argument with a friend over this. When I say "negative statement", I mean one with the word NO in it, such as "prove that the sky is NOT orange" or "prove that my hand is NOT broken" (I know these are odd exmaples, but they're all I can come up with).

Answer 1

I think it depends on what exactly is being negated. Let's take your two examples:
in the second, yes, it can be prooved. There exists a specific medical definition for a broken hand - you could take the person to a dr, get it x-rayed, and determine whether their hand was broken or not.
In the first, you'd have a hard time of it (in a philosophical discussion, at least). If your opponent is making the arguement that each individual sees colors differently, and that what most people call blue they're seeing as orange, or some such, then you can't really proove that what the sky looks like to them isn't what you see as the color orange.
However, you can make the arguement that regardless of what the color looks like, humans have decided to call the color of the sky blue, and since the naming of things is arbitrary, it's the concensus that matters. Whatever color they're seeing the sky as, it's called blue. It's called blue even if that color is on another object, it's a name to make identification and communication easier. In that sense, since it was started and agreed upon by people in the first place, that's all that matters. The sky is blue.
But you still can't proove that they're not seeing what you call the color orange.

So, it really depends on whether or not the question asked is based on philosopy or fact. "proove I'm not god" versus "proove I'm not 26"

Answer 2

First off if you are going to have an argument with someone remember this ok.
Most of the time you can not win cause they do not know enough about what you are talking about to make a good decision. First thing you end up doing is ttrying to educate them to the point that they can make a decision on what you are talking about. Or even know what you are talking about. Lots of people go by hear say and no nothing of the matter its self except what they have heard someone else tell them at some time or other, then they are experts lol.
You can tell by the eyes when you start talking technical stuff lol you can see they are lost lmao.

Answer 3

Yes.
Starting from any set of axioms for arithmetic, it is possible to prove that there are no even numbers that are equal to one more that another even number.

Certain kinds of negative statements cannot be proved. For instance: "Nowhere swan on Earth was born, red with blue polka dots". To prove that would entail the entire earth being searched. Of course, even without searching the earth, it would be rational to declare that the claim was true, because the chance of it being false was practically zero.

Ask your friend to define exactly what kind of negative statements he is talking about. That will force him to be more precise.

Answer 4

ANY statement may be presented as a negative statement.
For example a statement "the sky is blue" can be formed as "It is NOT the case that the sky is some color other then blue."
So if logic can prove ANY kind of statement then it can prove negative statements.

Answer 5

The responsibility of providing proof and evidence lies with the person making the positive claim. Not with person denying it.

If someone claims there are aliens on mars, it becomes his responsibility to provide evidence for his claim. He cannot say that since no one can prove otherwise, hence aliens exist on mars. That would not make any sense.

However if there is a positive, for which evidence has already been provided then the evidence of disproving lies with the person making the negative claim. It is established that water is hydrogen and oxygen. If a man was to say it is not, then the responsibility of providing evidence lies with him.

Answer 6

Sure, if you have the right evidence to back up your conclusion. Like this:

A) Vegetarians never eat meat.

B) Aaron is a vegetarian.

C) Therefore, Aaron does not eat meat.

Voilà! It's exactly the same process as with a positive statement.

Answer 7

Actually, I think that a lot of mathematicians prove statements by first proving many so-called "negative statements" that would disprove their theorem. So the answer is yes.

Answer 8

Certainly. Cats are not bananas. Zelda is a cat. Zelda is not a banana.

Like many other questions I've seen, a back-and-forth option would help, as I'm not really sure what the question's about. (Not that that stopped me from answering!)

Answer 9

Sure , if you prove a negative then the positive must be erroneous, making it negative and the negative positive.

Answer 10

Of course. Philosophers say
"It is not the case that" blah, blah, blah.
Philosophers do that all the time.