What is G-d, how is G-d defined?
Tanakh (bible) says:
Body or no body? Answer = no body (incorporeal)
Infinite or finite? Answer = infinite (no boundaries/limits) e.g., omniscient (all knowing), omnipotent (all reaching).
E.g., G-d is defined via negativa (by saying what G-d is not).
The scientific method involves:
1) Making a hypothesis (theory),
2) Making measurable predictions based upon that theory,
3) Designing an experiment to test the predictions
4) Measuring the experiment outcomes,
5) Analyzing the data to see if the predictions (extended from the theory) are accurate.
This is where measuring G-d becomes a problem: science can only measure things, and G-d doesn't 'qualify as a thing, because G-d is infinite.
In order for a thing to be measured, it has to have finite attributes.
You can call me a thing because you can define me by the attributes of my body (height, girth, weight, proportions, eye colour, hair colour, skin colour, nose size/shape, ears etc. G-d has no body!
You could also define me by my habits or my beliefs. My beliefs are based upon a finite stock of experiences and the way in which I relate those experiences (my neural network connections). In that way, if you get to know me, after a while, my behavior (to a certain extent) may become predictable. G-d is all knowing (omniscient), which means that G-ds beliefs (if G-d has any) are based upon such large amounts of information, that we as humans have no way to measure them and come to any predictions. This means, if I could take G-d for a drink in the bar every week, I'd never be able to predict what drink G-d might pour into his non-body (for instance).
Things only stand out---to the mind---if they have finite attributes that can be measured: a ball, a tree, a person etc., all have finite attributes. Even though you could probably generate many more attributes about these things than those which you keep in memory, the attributes you associate with these things helps you to relate to those things in a useful way.
Without a body, G-d doesn't stand out. We have no way to measure G-d. G-d is not detectable using any of our senses, nor with any equipment we possess. This is the key point: the Romans had a word for objects that stand out---exsisto (from the prefix ex- "out" + the root -sisto "to stand"). The modern English word "exist" derives from the Latin word exsisto! As G-d cannot be sensed or measured, G-d doesn't stand out, so doesn't exist.
Now, you're going to say to me: "hold on, lots of things that now exist---electrons, the higgs boson etc.---didn't exist before, so maybe one day in the future, science will build a machine that can measure G-d?"
That would be possible if G-d were defined by a set of finite attributes that could be measured in some way. As G-d is a concept without relative value (i.e., because G-d is infinite), there is no hope of ever relating G-d to anything.
People often ask, is there anything bigger than infinity, but this shows that people wrongly think that infinity is a number. Infinity isn't a number, and it has no numerical value whatsoever in math.
We use the word infinity in two senses:
1) no boundaries (i.e., nothing)
and
2) without end (e.g., continuous division, continuous addition, eternal etc.)
The word infinity (Latin) actualy means "not perishable".
The Hebrew phrase for infinity is Ayn Sof, and that means "without clarity/boundary/end".
The Sanskrit word for infinity is ananta (an- "without" + anta "end").
As G-d is a Hebrew concept, we have to cede to the definition of Ayn Sof: "without clarity/boundary/end". In our terms, nothing is without boundary, because all things have boundaries e.g., the shape, the colour, etc. Even subatomic particles can be defined. Therefore, it would be safe to say that "nothing" is Ayn Sof, and therefore G-d is nothing (not a thing).
Does that mean: there is no G-d?
Yes, and No!
There is no "thing" G-d!
Is there anything beyond ''thing''?
Well, maybe, but you'll never ever measure it!