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Can You Prove a Negative?

By Bruce Barbour - February 2024 (Version 1.0)

It is sometimes argued that "you can't prove a negative". Another closely related argument form is that "you can't prove a non existence". Often this argument is cited if an atheist is asked to prove that god doesn't exist. (Often after the atheist asks the theist to prove the existence of god.)

This form of argument is a logical fallacy. That the argument form is a fallacy is easy to show.

I will come back to the god example later. As a preliminary example I make the claim to my colleague there is not a six foot high, green, fire breathing, non magical dragon in the next room. To prove it we only need to go into the next room and after a quick (or slow and methodical) look around it will indeed be apparent there is no six foot high, green, fire breathing, non magical dragon in the room. Therefore the negative or non existence - no dragon in the room - has been proved. Easy.

So where did this confusion about the "impossibility" of proving a negative come from?

Let's vary the example. This time my colleague make the simple claim to me that there is not a dragon in the next room. I go into the next room with my colleague. He says to me "see there is no dragon in the room". But then I say to him "the dragon could be invisible, that is why it wasn't found". Unconvinced we bring in some equipment to the room that we think will enable an invisible dragon to be detected. We still finds no evidence of the dragon. But I am still not convinced. I say that, as well as being invisible, the dragon could have magical powers and could put up a veil of deception so my colleague cannot detect it. But it could absolutely still be there. My colleague does not know where to go from that. He cannot prove that there is not an invisible magical dragon with perception masking abilities in the room.

The difference between the first dragon claim and the second? The first dragon was fully defined so what me and the colleague were looking for was known and when it was not found we could say definitively that the dragon did not exist. The second dragon was not defined at all. Consequently we did not know how to detect an undefined dragon.

What is the situation if the positive claim is made. That is (1)
there is a six foot high, green, fire breathing, non magical dragon in the next room. Or (2) there is a dragon in the next room. The first option claim will quickly be shown to be false by going into the room. The second option claim will not be able to be shown to be false - using a line of argument similar to the negative claim.

Whether the claim trying to be proved is a positive or negative claim has little impact on the difficulty of proof or falsity - mostly. What has impact is how well defined what is being looked for is. The challenge to "prove there is no god" is essentially the same as the challenge to "prove there is a god".

There is one proviso. If you are looking to prove a positive claim for something that is undefined, then even if you don't know what you looking for you may still find it - though you may have difficulty in recognising it. This could be through luck. You are looking for something dragon like, you find something and it happens to be what you are looking for. ("Look at what we have stumbled upon. It's a strange phenomenon. That must be a dragon.")

Another scenario is that what you are looking for is so all pervasive that you could not but find it even though you weren't sure of what you were looking for. ("My god. There's dragons everywhere.")

Let's look at the example of god. Can we prove that god doesn't exist? It depends on how well we define god. If we said that god was an old man sitting on a throne just above the clouds that may be able to be disproved. The thousands of airplanes each day have failed to see anything that resembles that definition of god.

For the purposes of this comparison only, god is like our hypothesized undefined dragon. We don't know what we are looking for. God is not sufficiently defined. And even if we can eliminate any particular concept of god it does not eliminate all the other possible concepts of god. And then there is the problem that if god for what ever reason (unfathomable to us) does not want to be found then we will not be able to find god.

The other aspect to keep in mind is, as discussed here, the lack of evidence does not always indicate evidence of lack. To say there is no evidence of, for example, god therefore god does not exist is not logically justified.

The Need for Justification of all Knowledge

My stand as an Agnostic is that all Knowledge needs to be justified. Both:
  • Positive Knowledge – the Knowledge that something exists or that some idea is true; and
  • Negative Knowledge – the Knowledge that something does not exist or that an idea is false,
must be justified for it to be classed as Knowledge. But sometimes this is impossible due to lack of full definition of the thing or idea being considered.


You may be able to prove a negative claim provided it is well defined. You can’t prove a negative that is not sufficiently defined.

You may be able to prove a positive claim provided it is sufficiently defined. You may be able to prove a positive claim that is not sufficiently defined – but this will be due to either luck in finding what you were looking for, or else what you were looking for was so readily apparent that it could not be missed.

All Knowledge - positive or negative - needs to be justified.

The lack of evidence for something is not necessarily the proof of lack of existence.

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