It is often said that you cannot prove nor disprove God. People who bring forward this kind of reasoning often try to persuade you that there is a kind of balance, a truce; you can't prove your point (God does not exist), I can't prove mine (God does exist), nor can we disprove each other - so, we are on the same level. I want to generalize this and turn the argument on its head (and ask you if this can be backed by philosophical reasoning):

My question is: Can you give me an example of another thing in the real world that has this kind of trait (i.e. cannot be proved nor disproved)? Is this kind of trait an indication of all the things that do not exist in reality.

Please note: I am not talking about things that take place only inside our brains (like imagination or emotions like love) nor am I talking about math (e.g. Gödel's incompleteness theorem and all that). I am also assuming that there is a real world and we can ever better comprehend it.

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    "I am also assuming that there is a real world and we can ever better comprehend it." I'm not quite sure if I get what you say here - do you want to state that you assume what your senses perceive is reality? – eWolf Aug 26 '11 at 13:29
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    @eWolf: I just wanted to avoid responses that refer to radical constructivism, solipsism and the like. And: No, I don't assume that, but what I think is that we have the epistemological capacity to comprehend the laws of nature - not perfectly though but ever better. – vonjd Aug 26 '11 at 13:38
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    "Reality is that which, when you stop believing in it, doesn't go away." –Philip K. Dick – stoicfury Aug 26 '11 at 16:27
  • Is there any chance I could persuade you to reformulate this without quite so many assumptions? Or at least provide a little more context on the actual problem you are trying to solve? – Joseph Weissman Aug 26 '11 at 16:49
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    @stoicfury: Thank you - this is the most helpful comment I have seen for a long time! – vonjd Aug 26 '11 at 17:17

Sure, there are lots of things that fit in your category-- there's nothing particularly unique about the case of God (and it's not even one case, as there are many, many different conceptions of God, each of which can be argued separately.)

First of all, any ethical claims are going to be outside the bounds of "proof", because "is" does not imply "ought".

Second, anything that involves interpretation is going to be very difficult to prove, because in order to do so, you need to first agree on an objective standard against which to measure interpretations, and the grounding of this objective standard is open to all kinds of epistemological/ontological problems (the attempted solution of which often leads to onto-theology, bringing us back to the start.)

Third, any problems which are not falsifiable, such as questions regarding eternity, or many cosmological questions (such as what there was prior to the big bang, or what will come after the universe contracts to a point.)

Fourth, any questions regarding why things are, beginning with the classic "Why is there something rather than nothing?"

Fifth, any questions regarding the foundations of logic. (This may be excluded by your mathematical objection, but I'm putting it here just in case.) We cannot use logic to prove that logic is well-founded.

I could go on all day, but in order to cut this short, let's reverse the question: what kind of problems actually are provable? We can start with the notion of falsifiable propositions, but we then have to narrow this down further, as many of these are only falsifiable based upon standards of observation which we may not be able to meet. Further, any proofs are going to be ultimately based upon unproven axioms, and unproven methodological techniques. So, at the end of the day, very little is provable, depending on the strictness of your notion of "proof."

You stipulate that "there is a real world and we can ever better comprehend it", but in doing so, you raise the very question you are claiming to investigate. Just as there are competing arguments for the existence and non-existence of God, none of which are completely probative to an observer unwilling to accept certain axioms, so are there similarly competing arguments for the existence or non-existence of the coffee cup on my desk.

In other words, the fact that the existence of God cannot be conclusively proven or disproven is not an additional claim in support of the non-existence argument. (Sorry to disappoint...)

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  • Excellent answer. double plus +1. Can you elaborate on 'is' vs 'ought'? (that doesn't immediately support non-provable...one can have modal arguments). An objection to some of your other cases could be that some of them are not about the 'real' world (logic/why/non-falsifiable things) – Mitch Aug 26 '11 at 14:57
  • @Mitch: You can find a brief overview here: en.wikipedia.org/wiki/Is%E2%80%93ought_problem – Michael Dorfman Aug 26 '11 at 15:46
  • Yes, I am aware of that. I just thought it'd be nice to elaborate in this answer your inference that because of the is-ought distinction, that renders proof impossible (there are proof theories (modal logics) that -do- allow proofs of 'should'-like things_ – Mitch Aug 26 '11 at 16:01
  • I'm not aware of any modal logics which permit the proof of ethical imperatives, but I'm eager to be enlightened. Where can one find a logical system that can prove something one ought to do (without recourse to a corresponding ethical axiom, of course)? – Michael Dorfman Aug 26 '11 at 16:52
  • Just the usual wikipedia appetizer at Deontic logic (as a kind of Modal logic). – Mitch Aug 26 '11 at 17:37

This problem isn't unique to God, in fact as Michael suggests you would find it quite challenging to prove or disprove with certainty the existence of virtually anything. I think the primary contention here is not whether absolute proof exists for objects/concepts (God) or not, but whether the likelihood of their existence and non-existence is equal given that they can't be proven for sure. Thus, just because you can neither prove or nor disprove the existence of God does not mean the likelihood of his existence is 50/50. If people are suggesting that there is some kind of "truce" or "balance" as you put it, as if it's a coin flip as to whether God exists or not, then they have been seriously misled.

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