A thing that does not interact with any instrument that we use for detecting things will, of course, go undetected by us. How immense is the quantity of things in existence that have thus far eluded our detection? What reason do we have to believe that we could - at any stage - know what percentage of all the things in existence we have successfully mapped out?
We may, at a certain stage, conclude that there is something that, while unknown to us, is in existence, because of a mysterious influence that is observed to be exerted upon something that we can detect and is known to exist. But what of all the things that might exist but not be detectable by us, even by the most indirect of inferences? What reason do we have to assume that there is any limit - whatsoever - to the variety of things that exist of which we have no knowledge or even mere suspicion, and that may possibly be present right under our very noses, so to speak, and interwoven into the very fabric of our own existence?
In this day and age, how heretical it would seem to put forward a scientific notion that any thing imaginable should be assumed to exist unless it can be proven to not exist. It seems reasonable - at least at some level - to argue that if something cannot be proven to exist, then it should be assumed to not exist. Perhaps the best - and most appropriate - compromise then, for those things which can neither be proven to exist nor be proven to not exist, would be to conclude that they both exist and do not exist, simultaneously. And in this "realm of existential duality", perhaps there is a place for the human notion of "god".