Here's my take on it.

Agnosticism is illogical and refutes itself. Agnosticism and agnostics characterize God as unknowable, ineffable, incomprehensible to all attempts to understand him. This doctrine is self-refuting. The agnostic is making a knowledge claim about what he/she claims is unknowable. How do agnostics know that God is unknowable if he is unknowable ? How do they even know that God's existence cannot be disproved if God is unknowable, or that God even exists if he is unknowable ? To claim any attribute for God is knowledge and claims to know this unknowable God possesses certain attributes. That's a logical contradiction, and any being containing two incompatible attributes cannot possibly exist. So one need not resort to agnosticism. He/she would be justified in not believing in that God if the concept of it contradicts itself in any way. One is justified in accepting and adopting the atheist position.

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If there is an unseen world that never impinges on the seen world in any way, then its existence or non-existence is of no interest or concern to us—we are perfectly justified in ignoring the idea altogether. That we cannot disprove its existence doesn't matter.

true, the question then becomes whether it impinges on our world in a scientifically measurable way or not. The methods of science aren't good at detecting something that is sporadic or actively avoids rigorous detection. 

I keep wondering in these kinds of discussions, what one means by existence of something, if the existence wouldn't have different effects from non-existence. 

There certainly is a metaphysical reality - mathematics.

From Goedel's theorem, perhaps we can deduce the existence of something mysterious.  If humans are Turing machines, then there are truths that we can't prove.  If we aren't Turing machines, then humans have mystery. 

The guarantee of true, but unprovable statements in certain kinds of axiomatic systems does not provide a guarantee that those statements are interesting or valuable. Gödel's constructions depend on a trick of self-reference. In any logical system self-reference seems to be the easiest, if not the only path to paradox.

If it proves true that there are parallel universes, and if cosmology and physics finally determine the nature of dark energy and dark matter, these phenomena will be completely unguided natural things, and not supernatural or paranormal manifestations of a supernatural intelligence. Two main candidates for the cause of the universe from nothing without God are the nothingness of empty space, through which quantum effects turn nothing into something. The other candidate is actual and literal nothingness void of even space itself, which can cause through quantum effects the appearance of space from out of literally nothing. Neither theory is 100 % certain, but neither theory violates any of our observations of the way nature works that we have formulated into the laws of physics.

Insisting that the existence of God cannot be disproved is the last refuge of the theist. Atheists and agnostics don't disbelieve because they have absolute proofs, but because their understanding of how the world works has advanced beyond the need for supernatural explanations—they simply no longer give them the credence they enjoyed throughout much of history.

Religious beliefs never die, but like MacArthur's old soldiers, just fade away.

Not at all. Agnosticism is not the withholding of judgment in all cases where absolute and definitive evidence is lacking, it is rather withholding the claim of knowledge where it is not warranted and apportioning the degree of belief to the amount of evidence.

Conjectures are often a useful tool in science, outlining fruitful paths for research, but even with conjectures, a degree of plausibility is required so that time and effort are not wasted.

.but no scientist puts the conjecture out there as something that must then be disproved.

Nor does he claim he knows it to be true. It is honestly labeled a conjecture and remains so until evidence supports it or shows it false. (Unfortunately popular articles on science gain popularity through speculations that tickle the fancy of readers, who are often ill equipped to distinguish them from established science.)

The fundamentalist with little or no objective evidence makes assertions designed to be irrefutable and challenges the unbeliever to show he is wrong, which does nothing to establish the truth of his claims.

I think agnostics simply want to hedge their bets...have it both ways, just in case. I once was there no matter how illogical the position is.

That's an old and familiar criticism of agnosticism based on a misunderstanding of what it is.

Agnosticism and agnostics characterize God as unknowable, ineffable, incomprehensible to all attempts to understand him.

Ineffable - too great or extreme to be expressed or described in words.

So if something is not that great or extreme, it's effable?

Ain't English a fun language?

During twelve years in Catholic schools, most nuns delivered the usual absolutist claim. A few said faith is a gift  that some people weren't given. In college, quitting Catholicism, I went to two meetings of the student atheist club and heard people claiming to know what they had no evidence to support.

I was studying science and chose agnosticism.

Claim as you wish, Anthony. Present your evidence. A ten thousand word limit, please.

Agnosticism and agnostics characterize God as unknowable, ineffable, incomprehensible to all attempts to understand him.

No, they don't. It's Christian theologians who make that characterization of God. Here are the words of Dionysius the Areopagite in The Divine Names:

Indeed the inscrutable One is out of the reach of every rational process. Nor can any words come up to the inexpressible Good, this One, this Source of all unity, this supra-existent Being. Mind beyond mind, word beyond speech, it is gathered up by no discourse, by no intuition, by no name. It is and it is as no other being is. Cause of all existence, and therefore itself transcending existence, it alone could give an authoritative account of what it really is.

And here is St. Thomas Aquinas describing the via negativa:

 "Since we cannot know what God is, but only what God is not, we cannot consider how God is but only how He is not."

And before him, Saint Augustine:

What then, brethren, shall we say of God? For if thou hast been
able to understand what thou wouldest say, it is not God. If thou
hast been able to comprehend it, thou hast comprehended
something else instead of God. If thou hast been able to
comprehend him as thou thinkest, by so thinking thou hast
deceived thyself. This then is not God, if thou hast
comprehended it; but if this be God, thou has not comprehended

Sermon II Of the Words of Saint Matthew's Gospel, §16

However, they still insist that they know God exists through internal knowledge placed by God in each soul. In their view the atheist denies what he knows and is in rebellion against his own soul.

Kind of like being agnostic about Santa Claus, the Easter bunny, the summer garden divas, the Halloween Witch, or the Aztec Huitzilopochtli; or Egyptian Ra, or Mayan Itzamna, or Norse Frigg, or Roman God Apollo, or Greek god Zeus, or Celtic god Lugh, etc., etc. etc. 


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