I was looking for some material of proof or lack of proof in relation to the universal negative, that is: for all p, p is not r. Before being able to say whether it can be proved, we need to define what p and r are members of. My search uncovered an argument that said that since it was possible to prove that there was no integer such that the integer was the square root of two then it was not true to say that it was not possible to prove the universal negative.
To prove a universal negative, it is necessary to show that for ever p, p is not r. Disproving it is easier since all that is necessary is to show that there exists one p that is r. If I was to claim that there was no integer that was the square root of four then I hope all would agree that I was mistaken since two is the square rot of four.
The difficult comes when we make statements like there is no such thing as aliens or there is no such thing as god. What would it require to prove absolutely that these statements are true. Just because I can prove that there is no integer that is the square root of two does not mean that I can prove either of these statements. I need to do clarify what I mean by alien and god. If I restrict my definition of them appropriately then I can say that based on my conception of god or of an alien, then these things do not exist. The question then becomes one of is my conception of an alien or god reasonable.
From my perspective, our conception of something is based on what we have experienced of that thing. So if I have no experience of an alien or of god then what can I based my conception on? What others say or describe as their experience but how can I prove their experience is accurate? It isn't as if I can just go down the street an meet an alien or to the best of my knowledge I can't and for some people the same seems to apply for god. This leaves us with conflicting statements on the existence or non-existence of these things that seem to be based on personal belief rather than experience of.
What I found interesting was the claim by one person that because of the awful things that happen in the world there could be no god because if god was omnipresent and all-powerful then he wouldn't let these things happen. So what can we say about his conception of god? It would seem on the surface that in his conception of god, god would take control whenever something he didn't like looked like happening. What does that mean for the conception of man? Does this person believe that man is not responsible for his actions?
I am a father and as a loving father, I could step in each time that I saw my children doing things that I thought were dangerous or had some risk. The problem is what would my children learn? Would they learn to take responsibility for their actions? I certainly want them to be independent thinkers and to make good decisions so I allow them to take risks. I may also provide a bit of gentle persuasion in an attempt to change their mind. The only time that I would step in and physically stop them, if I had the opportunity and I could do so, is if I felt they were endangering themselves or others. Children need to learn about responsibility and risk taking. They need to understand where their rights and freewill ends and responsibility takes over. They need to learn that the actions they take have consequences.
A conception of god that sees him stepping in a stopping all evil and disease says to me that he has to remove my freedom to choose. He removes from the me the need to be responsible and to accept that my actions have consequences. The easiest way to achieve that is to remove my freewill. I become a puppet or slave. Do I want a world like that? No, I don't! So I would agree with him that a god that stops all evil and harm doesn't exist and I wouldn't want him to exist.
So maybe, we have proven that a god constrained by the conception that he or she was all-powerful and omnipresent would step in and stop all evil doesn't exist and maybe we wouldn't want to exist then what other conceptions of god are there? If we want to show there is no god then we must prove all possible conceptions of god don't exist unless of course we have some experience of God.