Friday, December 25, 2009

Proving a Negative

I always thought that proving a negative is impossible. I just learned and read that it is not. It would be difficult though to prove a negative because one must have omniscience to do so. But "proving" in proving a negative does not necessarily mean proving beyond reasonable doubt or a mathematical proof. One must only need reasons or evidence (or maybe the burden of proof) to prove a negative and not necessarily a proof beyond reasonable doubt. There are two (plus one below) ways in which one can prove the nonexistence of something. One is to prove that it cannot exist because it leads to a contradiction (incompatible properties argument) and the other is by carefully looking and seeing (empirical evidence).

Incompatible properties arguments attempt to show a logical contradiction in the concept in question. It shows that an entity (or something) cannot exist because of a certain contradiction. A good example of this is the properties of the Christian God/Theism. One can prove that this god does not exist by showing contradictions in some of its properties. For example, Omniscience and Free Will. A being/entity cannot be omniscient and at the same time free (acquires free will). It shows that that entity can't simply exist because of the two contradictory properties. Another example is the Transcendence and Omnipresence properties of the theist god. The incompatible properties argument can also show that two objects cannot logically exist simultaneously. For example, the god of Islam cannot co-exist with the God of Christians.

Another way to prove a negative is by carefully looking and seeing. The idea is that if a thing exists, one must be able to detect its existence directly or indirectly (not directly observable but the object causes effects which are directly observable). For example, suppose a friend of mine claims that there is a dog in my room but when I went to my room I found no dog. Since I found no dog, then I can conclude that there was no dog in my room. This same method allows us to know that things such as unicorns, Loch Ness Monster, Bigfoot do not exist. Of course one could argue in my example above that that dog may have left when I arrived in my room. But based on the lack of proof/evidence that there was a really dog and that based on the limits of my understanding of anything (I could be mistaken on what I saw) I still proved a negative in such a case. Again, proof here is not the same as mathematical proof.

Lastly, another good way (found also here) to know that a person is justified in believing that a thing, say X, does not exist if all of the conditions below are met:
  1. the area where evidence would appear, if there were any, has been comprehensively examined, and
  2. all of the available evidence that X exists is inadequate, and
  3. X is the sort of entity that, if X exists, then it would show.
So all in all, based on the three ways above one can really prove a negative or that prove that there is no god or Santa Claus or Loch Ness Monster or a planet between Earth and Venus.

12 comments:

innerminds said...

Interesting. I guess it's not impossible to prove a negative after all, although it's more difficult in some cases. For example, proving there is no dog in your room is a lot easier than proving that there is no oil in Davao, because you'd have to dig up every square inch of the entire city in order to support your claim. It's even more difficult to prove that there are no fairies, because you'd then need to have simultaneous 24-hour CCTV survellaince on every patch of land in the entire planet showing no fairies.

Discreet Infidel said...

I think you do not really need to dug up every square inch of DC to prove that there is no oil in Davao. Or you do not really need 24 hour cctv surveillance on every patch of land to prove that there are no fairies. proof here, as ive said above, is not a mathematical proof (which is necessarily true) but it is proof in the scientific sense and in the sense used in law courts and in everyday life.

Also it is not really possible to look in every corner of Davao or of the world to look for oil or fairies respectively. We can just look around within the limits of our ability and our desire to expend time and resources on looking. And based on that I can say that there are no oil in Davao and that there are no fairies.

Discreet Infidel said...

Continuation from first paragraph

...Just like when you prove that there is a creator. You do not have the proof (empirical) to support your claim that there is a creator but you have logical and philosophical proof :)

innerminds said...

I beg to disagree with your first comment. You said that "you do not really need 24 hour cctv surveillance on every patch of land to prove that there are no fairies. proof here, as ive said above, is not a mathematical proof (which is necessarily true) but it is proof in the scientific sense."

What I understand about "scientific statements" is that they are based on observation. How can you say that there are no fairies if you cannot simultaneously observe the entire planet?

Discreet Infidel said...
This comment has been removed by the author.
Discreet Infidel said...

The nonexistence of fairies simply meet the three conditions above. Also, based on our observation (within our limits), there are no evidences that fairies exist anywhere. No one has ever shown nor found any evidences for fairies.

Also, i think that scientific statements do not necessarily need "first hand" or direct observation. We know that macroevolution occurred yet we did not observed it first hand. We know that the universe expanded billions of years ago yet we were not there to observe it and we know that it expanded and is continuously expanding.

Now, i may not be able to observe the entire planet simultaneously to prove beyond reasonable doubt that there are no fairies but I (we) know that there are no fairies simply because of the lack of and inadequate (if there are any evidences) evidence (and that it meets the 3 conditions above).

innerminds said...

You wrote: "The nonexistence of fairies simply meet the three conditions above."

By conditions, you mean:

1. the area where evidence would appear, if there were any, has been comprehensively examined
- How can you say that there are no fairies when you have not comprehensively examined the entire area of Earth?


2. all of the available evidence that X exists is inadequate
- Having no evidence that X exists merely discredits the claim that X exists but does not automatically allow the conclusion that X does not exist.

3. X is the sort of entity that, if X exists, then it would show.
- Agreed. However, fairies are said to appear to only a few selected special people at a certain time...

Discreet Infidel said...

How can you say that there are no fairies when you have not comprehensively examined the entire area of Earth?
-As ive said in my comment it is not possible to do that. We can only look around within the limits of our ability. ANd as far as i know, no one has ever found (within the limit of their ability)any evidence that shows fairies exist. Unless you have one? :D


Having no evidence that X exists merely discredits the claim that X exists but does not automatically allow the conclusion that X does not exist.
-So are you saying that since there are no evidences that X exist, we can't yet safely conclude that X doesnt exist? The lack of evidence already shows that X does not exist.


Agreed. However, fairies are said to appear to only a few selected special people at a certain time...
- But i have never heard any special people that claims they saw fairies.

innerminds said...

I have no evidence that fairies exist.

But even if there is no evidence that fairies exist, this doesn't allow us to conclude (in the scientific sense) that fairies don't exist. Well, you could say that we can "safely" conclude that fairies don't exist (similar to #6 in Dawkins' spectrum - I can't know for sure but I strongly believe that fairies don't exist and I live my on this assumption).

You wrote: "But i have never heard any special people that claims they saw fairies."

- I have. LOL

But seriously, I think we're arguing on mere semantics here, particularly on the word "proof". I don't believe in fairies, but saying that "there are no fairies" is simply not a scientific statement in the strict sense.

Discreet Infidel said...

Agreed :D

BarnStormer said...

Good post, it got me thinking about the nature of positive and negative statements for any future discussions I might have.

@innerminds,
You've met somebody who has claimed they saw fairies? The closest I've gotten to this is people telling me they've seen ghosts.

Discreet Infidel said...

Thanks for the comment. Ive added your blog on my list (but its private:)

Post a Comment