Let's put this common refrain to rest~ something that I hear all the time in arguments concerning religion.  It goes something like this:

" Remember, you can't prove a negative!"

Really people?

This has become much more common, especially in the arguments amongst Atheists and agnostics concerning certainty, and it really puzzles me how people can be skeptical and free-thinkers, yet take to an idea so easily and not question it.  I will elaborate on this a little more once I have the time, but let me start all of those "can't prove a negative" types off with a question~ " I am not sitting at my desk."  Thats a negative claim.  Are you telling me that there is no way to confirm or disprove that?

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I do not agree with the statement; "You can prove a negative." Your description of god is the main reason why I disagree. God is a concept, an idea, a malformed definition, it does not exist outside of the human mind. Having said that, there is no way to prove that god exists nor is there a way to prove that god doesn't exist because you have no way of testing the concept of god. To prove something, you need evidence. Lack of evidence is not proof of a negative because you can always say that the evidence just hasn't been found yet.

Proving a negative claim and proving a negative claim of existence are different.


When negative proof is cited by atheists it's referring to a god's existence, not where in existence god is, like sitting at a specific desk that can be located and subject to empirical testing.

Prove there is no adult T-Rex tooth in my 1 liter bottle of ginger ale that I am currently holding in my right hand =/= prove there is no invisible, matterless, massless, gravityless, Jupiter sized planet in orbit around the sun between Earth and Mars.

I find that this discussion always has a lot of hypothetical threads attached.  I can be more definitive on one point though.  I know of only one "negative" that's provable.  I can prove I'm not Jewish.  OK sorry, not a pretty visual attached to this one.
You are very correct. It should be that "you cannot prove a negative of any real magnitude." Wide open and subjective? Yeah. Just like most of language.

Go ahead and try to prove that there is no gold in China. Even if you look in every place in China I could be following you around and re-hiding the gold. Like those weapons of mass destruction in Iraq. :-)

So proving a statement like "There is no God" would be close to impossible. I have seen some that show that the concept of God is nonsensical or self contradictory, or what have you. But to show there IS a God one simply needs to produce one.
I'm not sure it would actually be that simple, Joshua. How would you know for sure the god produced was, in fact, a god? There have been a lot of false gods (well OK, all of them), which nonetheless managed to fool plenty of people, but there are always skeptics, and anyhow, what sort of test for godhood is there? It's not like they get board certified or come with a holographic certificate of authenticity sticker or anything.

I'm imagining a god survey. They get to the question, "Do you need a spaceship?" If yes, then not a god. XD


...I think that's the thing with modern humans. Even the godlike characters we come up with, in our movies, books, and so on aren't truly gods. If we met a supreme being tomorrow, with all the bells and whistles, would you really think it to be a god? I'd be more likely to think it was a mass hallucination... I don't think our reality really allows for a god. Hard to believe in something that cannot even exist.

Thank you I was just talking about this with someone today, I am glad that this is being brought up. I think it is a response to theists telling us to "prove" there is no god and since fallacies run a muck in religious arguments the logical way people deal with this "straw man" is by replying that you cant prove a negative. However...

"That which can be asserted without evidence, can be dismissed without evidence." 

— Christopher Hitchens

I do sympathise with the idea though after all it is well and good for you to claim you are not sitting at your desk because you know where you are it is easy to find you. claiming for anything not to exist in the whole cosmos is different because the space is bigger and there are more places to look. I could yell there are no spotted elephants in my room and I would be right but saying that there isn't one anywhere in the world is empirically much harder to prove. Thats when it takes a consensus of people to conclude a negative, improbable not impossible. Too many people base their whole lives solely on what they have narrowly observed. But still not enough evidence to prove a positive in the case of god therefore he doesn't exist. PS I don't think there are spotted elephants although a quick search on google gave me some very nice photoshopped ones ;)

"That which can be asserted without evidence, can be dismissed without evidence." 

— Christopher Hitchens

I never heard of that quote. I will be using it quite frequently. Thanks for bringing it to my attention.

When the claim you can't prove a negative is made, an important qualification is left out. It should be: "You can't prove a universal negative". By a universal negative, I mean something that does not exist. The implication is that if something truly does not exist, and you go looking for it, you will find nothing. But it could be that you just haven't looked in the right places - there are so many places to look - the furthest reaches of outer space.


The trick which theism uses is to make 'God' have properties which lead that supposed entity to be beyond our reach so to speak. You don't see 'God' because 'God' is not usually visible. You don't hear 'God' because 'God' is not usually audible. Of course the claim is that a select few have seen and heard 'God', but for the rest of us, we can't have someone else's experience - not unless, (the theist will say), 'God' wills it.


The only way to prove that 'God' does not exist, is to take some well defined property of 'God', one which must be detectable in ordinary human experience, and show that it is false. For example, 'God' answers prayers; or 'God' does miracles. If we can show that prayers are never answered, and miracles never done, then that shows that a god for whom prayer answering and miracle working are properties, such a god does not exist.


I'm sure theists have ways of explaining all that away too. All I can say is that I have never detected anything which is incontrovertible evidence that there is a god in existence, so there might as well not be. And I guess that theists would blame that on me.

There is slight misinterpretation of what a negative implies in the scientific sense going on here.  "The room is not occupied," is not a negative.  Being occupied or not occupied has nothing to do with the state of being a room.  Therefore, being unoccupied says nothing negative about the room.  Let's take a positive statement:  Spiders have 8 legs.  This statement can be proven true by finding one spider with 8 legs.  Having 8 legs is definitely part of the state of being a spider.  In order to have a negative, we must state something that frames a negative state about being a spider, such as, "No spiders have six legs."  No matter how many eight legged spiders you find, you will never prove this statement.  Even if you found every spider in the universe, you could not prove that you had done so since the possibility of one more spider you have not found cannot be ruled out.  You cannot prove a negative.  Of course, a single six legged spider disproves our theory, but we weren't talking about disproving stuff.

Rich made a good clarification that really gets to the root of this topic, but I would like to take it a step further and demonstrate that you it is possible to prove a negative if you address certain underlying conditions properly. First, here is how I would restate the central question:


1. Is it possible to exclude a possibility without an exhaustive search?

2. If not, is it possible to determine if a search has been exhaustive?


The traditional approach is to implicitly answer 1. as No, an exhaustive search is necessary, and then focus on 2. as the primary question. From this point, there are numerous different ways to attempt an answer, but they all boil down to one issue:


Limitation: Given an incomplete set, the contents of the set are not sufficient to determine the scope of the set. 


Or put another way, if you don't know everything, you can't determine how far away you are from knowing everything. Since the potential range of information is infinite, and we can only acquire a finite amount of information, we can never determine if we've been exhaustive when attempting to prove a negative. If we accept that 1. is a No.


I would argue the contrary-- that 1. can be answered Yes, and that accepting an implicit No answer artificially produces the above paradox. The key switch in this line of thinking is to consider the known information as a cohesive range of data rather than an aggregate of unrelated data points. I would present this directly as: 


Constraint: For any set containing dependent associations, each new element must satisfy every such association. 


So to work off of Rich's example, any attributes which must be satisfied to be a spider will necessarily be satisfied by any newly-discovered spider species. That's what makes positive statements easier to (dis)prove, since they match directly against known attributes. The mistake that is often made with negative statements is assuming that these attributes are a random set, rather than a mutually-compatible set. 


Essentially, a spider doesn't just "happen" to have a certain number of legs and the word "spider" isn't a circular definition, both are driven by empirical demonstrations (a real spider) showing that possessing 8 legs is physically compatible with all the other known attributes of spiders. 


So a much better answer to 1. would be Yes, an exhaustive search can be avoided if a possible attribute would be incompatible with already-known attributes. This changes the focus of 2. from an infinite range of possible data points to a finite number of possible combinations. This can still lead to a massive number of possibilities, but it will always be a finite amount.


Back to the spiders again for a simple demonstration of this approach. Let's take the negative statement, "No species of spider can grow only one leg". This is slightly different than Rich's wording because it contains 2 attributes within the statement (to avoid haggling over the meaning of "spider"). These are:


Attribute A: Possesses only one leg.

Attribute B: Survives well-enough to reproduce.


Without exhaustively checking every single species of spider, this statement can be proven by demonstrating that the locomotive function of a spider is compromised by possessing only one leg. This leads to a solid proof:


Answer: No known spider species can survive with only one leg, therefore Attribute A is incompatible with Attribute B. This conclusively excludes any possibility of a species possessing both attributes which also qualifies as a spider (satisfies the control attributes). 


I would consider this to be a fairly simple, efficient way to prove negative statements. It also has the secondary benefit of short-circuiting the ambiguity of most "unknown to science" arguments. You still can't make the generalization "There are no possible gods," but you can say "There are no possible gods which are inifinitely large, yet existing" because the attributes of 'existing' can be logically incompatible with infinite size. This requires both sides of the argument to select at least one solid, foundational attribute to define any entities they reference-- and anyone who can't provide one isn't equipped to have an argument on any grounds.


That's my bit. It's definitely a non-traditional approach, but I don't see any logical flaws in proving a negative statement by this method, and I personally find it extremely useful for a lot of the tougher topics. How does this sit with the rest of you? Do you see any ways it could be refined or expanded to tackle other similar issues?

I contend that you cannot eliminate the possibility with any search unless the search finds the thing searched for. Just because you did a search, no matter how exhaustive, it doesn't mean that you would not have found it if you searched a little more. The possibility is not removed entirely by any kind of search. It may be diminished, but never removed. Therefore, you cannot prove an negative.


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