Can You Prove A Negative?

[_Moniker]

Burden of proof came up on MAD and I was looking over the thread and proving a negative proposition came up. I see this repeated lots on the board and am quite puzzled, at times.

I did take logic, yet, give me slack 'cause it was a while ago......

I always thought you could prove a negative proposition. I also found this article:

http://www.infidels.org/library/modern/ ... heory.html

I know the myth of "you can't prove a negative" circulates throughout the nontheist community, and it is good to dispel myths whenever we can. As it happens, there really isn't such a thing as a "purely" negative statement, because every negative entails a positive, and vice versa. Thus, "there are no crows in this box" entails "this box contains something other than crows" (in the sense that even "no things" is something, e.g. a vacuum). "Something" is here a set restricted only by excluding crows, such that for every set S there is a set Not-S, and vice versa, so every negative entails a positive and vice versa. And to test the negative proposition one merely has to look in the box: since crows being in the box (p) entails that we would see crows when we look in the box (q), if we find q false, we know that p is false. Thus, we have proved a negative. Of course, we could be mistaken about what we saw, or about what a crow is, or things could have changed after we looked, but within the limits of our knowing anything at all, and given a full understanding of what a proposition means and thus entails, we can easily prove a negative in such a case.

[_cinepro]

Tarski provided some good examples over at MADB:

Consider each of the following negative propositions

1. 6 is not a prime.

2. There does not exist a regular convex polyhedron with more than 20 faces.

3. the function x^2 on the real line has no maximum value.

4. There is no homeomorphism between the sphere and the torus.

5. There does not exist a pearl under any of a given set of five rocks.

1,2, 3 and 4 are provable mathematically and 5 is provable in the ordinary sense (we can just check)

Now consider each of the following positive propositions

A. All Gods are imaginary.

B. Every place is leprechaun free.

C. All intelligent beings are mortal.

D. There exist universes which we cannot know of.

These seem to be unprovable--yet they are positive statements.

The critical issue isn't so much the phrasing as positive or negative, but the scope of the claim.

Which is why so much of LDS apologetics hinges on changing the scope of the original claim to continually move it into the realm of the untestable. As our ability to test claims improves, the scope of certain claims must be reduced to keep them from being tested.

[_asbestosman]

I think it's more of an issue of conveying an idea with misleading words. The idea of being unable to prove a negative is really talking about how it's impossible to prove that I don't have a dragon in my garage. Every test you come up with will entail an excuse by me (the dragon is invisible, tiny, immaterial, is actually the name of my car, etc).

[_Scottie]

Burden of proof came up on MAD and I was looking over the thread and proving a negative proposition came up. I see this repeated lots on the board and am quite puzzled, at times.

I did take logic, yet, give me slack 'cause it was a while ago......

I always thought you could prove a negative proposition. I also found this article:

http://www.infidels.org/library/modern/ ... heory.html

I know the myth of "you can't prove a negative" circulates throughout the nontheist community, and it is good to dispel myths whenever we can. As it happens, there really isn't such a thing as a "purely" negative statement, because every negative entails a positive, and vice versa. Thus, "there are no crows in this box" entails "this box contains something other than crows" (in the sense that even "no things" is something, e.g. a vacuum). "Something" is here a set restricted only by excluding crows, such that for every set S there is a set Not-S, and vice versa, so every negative entails a positive and vice versa. And to test the negative proposition one merely has to look in the box: since crows being in the box (p) entails that we would see crows when we look in the box (q), if we find q false, we know that p is false. Thus, we have proved a negative. Of course, we could be mistaken about what we saw, or about what a crow is, or things could have changed after we looked, but within the limits of our knowing anything at all, and given a full understanding of what a proposition means and thus entails, we can easily prove a negative in such a case.

Ideas are different than proper nouns. Is it possible to have an idea without it's negative counterpart?

[_bcspace]

Which is why so much of LDS apologetics hinges on changing the scope of the original claim to continually move it into the realm of the untestable. As our ability to test claims improves, the scope of certain claims must be reduced to keep them from being tested.

I think it's more like covering all bases rather than changing the scope of anything. The scope is often orginally defined in terms that do not take all things into account.

[_LifeOnaPlate]

I prefer the question "can you not prove a negative" personally.

[_Moniker]

Ideas are different than proper nouns. Is it possible to have an idea without it's negative counterpart?

I don't understand what your point is. Why wouldn't it be possible to have an idea without a negative counterpart? Just negate the idea and wala. Right?

[_Trevor]

The idea of being unable to prove a negative is really talking about how it's impossible to prove that I don't have a dragon in my garage. Every test you come up with will entail an excuse by me (the dragon is invisible, tiny, immaterial, is actually the name of my car, etc).

That is the best analogy for Book of Mormon apologetics I have ever seen.

[_cksalmon]

Ideas are different than proper nouns. Is it possible to have an idea without it's negative counterpart?

I don't understand what your point is. Why wouldn't it be possible to have an idea without a negative counterpart? Just negate the idea and wala. Right?

One can demonstrate the veracity of a negative proposition the observe of which is necessarily false.

To borrow from Tarski:

6 is a prime number.

This proposition is false by definition.

It's like stating, "Married men are not bachelors."

This negative proposition is definitionally true.

"The Book of Mormon is false" is a historico-textual proposition, not a logical one.

The proposition "the Book of Mormon is true" is not necessarily false.

Thus, "the Book of Mormon is false" cannot be logically demonstrated.

Chris

[_Tarski]

Ideas are different than proper nouns. Is it possible to have an idea without it's negative counterpart?

I don't understand what your point is. Why wouldn't it be possible to have an idea without a negative counterpart? Just negate the idea and wala. Right?

One can demonstrate the veracity of a negative proposition the observe of which is necessarily false.

To borrow from Tarski:

6 is a prime number.

This proposition is false by definition.

It's like stating, "Married men are not bachelors."

Grrrrr

Is the following just false by definition
"2^(20996011)-1 is a prime number"
How about the Riemann Hypothesis? Is it true by definition or is it false by definition. Don't trivialize the struggle, search and discovery aspects of math.

"The Book of Mormon is false" is a historico-textual proposition, not a logical one.

The proposition "the Book of Mormon is true" is not necessarily false.

Thus, "the Book of Mormon is false" cannot be logically demonstrated.

Chris

Well, is anything outside of math and logic provable in the sense you intend??

I don't think the issue is whether a statement is positive or negative (whatever that really means- every statement is the negation of its negation).