Proving Negatives

It is possible to prove negatives. A simple example is a deductive proof: given A, and A => ¬B, then you can prove ¬B.

However, proofs are not the mechanism for validating scientific theories. Consider Kepler's First Law: The way to validate this theory, is not by means of proof, but rather by empirical observations. Once the theory is considered validated empirically, you may then use it as an axiom in a proof. For example, from Kepler's law you can prove "The earth's orbit is an ellipse".

Once you distinguish between logical proofs and invalidating/validating theories with evidence, then everything becomes quite obvious:

Consider the theory (A) "god exists".
It trivial to write a proof for both A, and a different proof for ¬A. It just depends on which axioms you start with.

As a scientific theory, it becomes pretty easy to invalidate. If god's existence implies answering prayers, then you could compare predominantly atheist countries with religious ones, comparing infant mortality rates or various metrics. In Sweden 23% believe in god, and the infant mortality rate is 3.18 deaths/1000 live births. In USA, 76-80% identify as christian, and the infant mortality rate is 7.07. You could however argue that god does not answer prayers, or christians are not praying for healthy children, or that god is punishing christians but not atheists, etc (Statistics from http://en.wikipedia.org/wiki/List_of_countries_by_infant_mortality_rate,
http://en.wikipedia.org/wiki/Religion_in_the_United_States,
http://en.wikipedia.org/wiki/Demographics_of_atheism).

Lastly consider the theory "god does not exist". This is where people say you can't prove a negative. To understand what is happening here, we need to look at simpler theories first:

Consider the theory (A) "God answers only 25% of all prayers". This can easily be validated/invalidated as shown earlier. Now consider the theory (B) "NOT 'God only answers 25% of all prayers'", this is also easily validated/invalidated, by just measuring what percentage of prayers are answered. E.g. If it's 26%, then that's invalidating the theory.

It gets trickier when your theories are more complex. Let's assume that (A) "God exists" implies all of the following: (B) "God answers at least 0.1% of prayers", and (C) "God does occasional miracles", and (D-Z) a whole host of other claims about the powers of God. Demonstrating contrary evidence for any ONE of the implicated theories B-Z, would be invalidating for theory A. (axioms {A=>B^C^D^...^Z}, with contrary evidence for B we get proof {¬B, ¬(B^C^D^...^Z), ¬A (modus tollens) }, conclusion {¬A}) Here, I've just demonstrated the non-existence of God by contrary evidence.

What I think people mean by "you can't prove a negative" is theories which make weak claims are extremely difficult validate/invalidate.

If theory "god exists" implies that god has -some- power, and his power is answering prayers, AND/OR miracles AND/OR a whole host of over things. Then you would have to find contrary evidence for ALL super powers to disprove that "god exists". Since god is said to have many super powers, but nobody wants to assert any particular condition that he'll use any particular power, it becomes almost impossible to work with this theory. Theories like this are a dime a dozen, hence the flying spaghetti monster. This is why God debates sometimes reach fix-point with "Well you can't prove god's existence", retort "Well you can't prove god's non-existence".

So in summary, you can prove negatives/positive, you can invalidate/validate theories stated in the negative or positive provided they make claims that can actually be investigated in a reasonable amount of time. (axioms {A=>B^CD}

(please upvote)

What is meant by negative? It really doesn't have to do with grammatical negative. "Not this." There are positive and negative claims. What is a positive claim? A positive claim is the assertion of some claim as true. A negative claim is the rejection of the positive assertion. A positive claim may be "I am male.". The negative response can be, "I don't believe you are male." The burden of proof lies on the one making the assertion. Now, if I stated,"I am not female". Despite having a grammatical negative or even stating what I am not,it is positive assertion of something (what I am not) The negative response could be "I don't accept that you are not female." Now that we went over positves and negatives let's get to the meat of the question. Can a negative be proven? Well, by these defitions one need have to. Let's look at this example of a positive claim, "I am a woman."and the negative is "The claim that you are a woman is false." Then I provide a sample of my male DNA,and a negative was proven.

What is meant by negative? It really doesn't have to do with grammatical negative. "Not this." There are positive and negative claims. What is a positive claim? A positive claim is the assertion of some claim as true. A negative claim is the rejection of the positive assertion. A positive claim may be "I am male.". The negative response can be, "I don't believe you are male." The burden of proof lies on the one making the assertion. Now, if I stated,"I am not female". Despite having a grammatical negative or even stating what I am not,it is positive assertion of something (what I am not) The negative response could be "I don't accept that you are not female." Now that we went over positves and negatives let's get to the meat of the question. Can a negative be proven? Well, by these defitions one need not have to. Let's look at this example of a positive claim, "I am a woman."and the negative is "The claim that you are a woman is false." Then I provide a sample of my male DNA,and a negative was "proven".

That's a terrible stutter you've got there . . . and rather elaborate, too . . .

Possible objection to you can prove a negative. Nothing is really proven. It meets a certain point when it's high degree of certainty. That's when most people accept it true. However, no-one can say that there is no possibility that it was proven. Take the claims "I am a woman" and "The claim you are a woman is false."Now, I can be said I look, dress, act, and can provide DNA to say the positive claim is false. However, someone can question the validity of DNA testing and outwardly behaviors,and say "Well, you are a woman to your self-image.Your statement tells as much." I can say well, I was lying,and they could say I can't be trusted.Blah blah although doubter has to cast some dount. So, the claim that said clain was not proven false.

My bad.

You must be a newcomer. It's been resolved.

Thanks for the comedy. Atheist takes on "science" - what a hoot!

Anyone else find absurdity amusing? Just think where we'd be if Newton, Mendel, the Wright Bros. and so on played superficially with statistics that have no bearing on the logical issues involved.

Amusing choice in this era and location.

...still you would need to establish a better time parameter to disprove the existence of X as the term "occasionally" is very vague concerning the frame by which existence of anything can or not manifest itself...not questioning the proof structure here which is sound, but merely its informative meaningfulness...oh by the way just to make it clear I don´t believe in a "God" (Conscious all powerful entity) at least as normally people conceive of it....at best stretching the limits of the word intended meaning I can concede to a mathematical all encompassing abstract algorithm or something similar...