Back to Russell's History of Western Philosophy, and he mentions St Anselm's ontological argument for the existence of God.
We define 'God' as the greatest possible object of thought. Now if an object of thought does not exist, another, exactly like it, which does exist is greater. Therefore the greatest of all objects of thought must exist.
According to Russell, "Clearly an argument with such a distinguished history, is to be treated with respect," having mentioned its influence on luminaries such as Liebniz, Descartes and Hegel.
Firstly if God can be meaningfully defined as the greatest possible object of thought, then this God is not God - that which produces all life, and within which all life truly is - but is instead merely an object or creation of human thought, and so does not autonomously exist outside of that thought. What Anselm is really trying to prove is the existence of "the greatest object of thought", which he dignifies with the name "God".
However, this is before even getting to the substance of the argument; it instead being apparently the imagined uncontroversial introduction to the essential matter of whether God exists or not. Unfortunately, as shown, this uncontroversial introduction asserts God's non-existence by declaring God to be meaningfully capable of definition as an object of human thought. Also how could the absolute source of all being exist as an object within that being, and so again be an object of thought? Such an imagined entity may be called God, but is merely another object within existence.
But anyway, to repeat the argument:
Now if an object of thought does not exist, another, exactly like it, which does exist is greater.
So the non-existence of the greatest thing is nothing to be worried at, as there will be something else exactly like it which does exist, thus satisfying the need for the existence of something greater than everything else. So to examine this a little.
If something does not exist, then it is not something but nothing, and so is not an 'it'; an 'it' being necessarily something. And so if something else is exactly like nothing, then it too must obviously be nothing, and so also does not exist.
To go a little further with this argument: if something is exactly like something else, how could it be greater than it or different from it in any way? To be exactly like it is to not differ from it in the slightest. When using language in philosophy as a truth tool, all falls apart if words like "exactly alike" are allowed to mean something other than exactly alike; instead meaning "alot alike", or "superficially alike". So someone might say one mass-produced object- say an empty Heinz beans can - is exactly like another; but if examined through a microscope, obviously enough, they will be revealed to not be exactly alike but very definitely unique and different. The one thing exactly alike something can only be itself, and naturally it's meaningless to go talking of a substance being exactly like itself. Of course it's exactly like itself. It is itself.
As for "the greatest object of thought", I have no idea what kind of parameters one is supposed to use, but what such people think they are dealing with leads back to the void, this apex of pure reason, examined earlier.
Thought can hardly get more dangerous than when discussing God as something that can be enclosed within that thought; a dreadful false energy begins to unroll itself, and this so because this is not logic working itself out antiseptically on a blank page, but in the dynamic living medium of human minds, and with its unfolding repurcussions on into the broader physical environment.
But in fairness to Anselm, if prizes were given for making statements that made no sense whatsover, then his here would be well rewarded, not that such statements seems especially unusual phenomena within Western philosophy.