You assert "it is reasonable to believe in God." All the atheist does is ask you "What REASON do you have?"

You have made several noticeable errors thus far.
1. God is a being. How do you know that? It generally comes from asking the wrong question. If the question is flawed, your answer will be flawed. When you ask "Who made the universe." You are asserting an answer in the question. "Who!" Better questions would be, "How did the universe get here? Was the universe created? How would you support such ideas?"

@"Scientific arguments are fascinating, but I find they are never ending. To put it crudely, the only thing absolute about evidence is our ability to tailor it to our biases."

Wow, that comment is so far out on the limb that it does not see the light of day with the rest of the tree. What do you think SCIENCE is. The whole goal of science is to remove biases and replace them with hard observable facts. If you want to see Biased science you need to look at Creationist claims. Biased science begins with a goal and then cherry picks information to prove a point. Typical examples of this are the UFO inquiries, Big Foot supporters, Missing 411, and Jesus. Science never begins with an assertion and then tries to prove it by choosing facts. It begins with a hypothesis and then does everything it can to disprove it. Only when the information can not be disproved does it become a fact and then lead to a hypothesis. What the general public calls science is not anything scientific at all. NO ONE EVER TAILORS INFORMATION. To do that would get a scientist laughed out of any scientific academy. The only people tailoring information are the conspiracy theories and religion.

@ "Stumping either side doesn’t pose resolution, rather it just leaves the subdued candidate with the feeling that their answer hasn’t been discovered yet."

Either side is not stumped. This is a Religious God of the Gaps position. "You can not prove my god does not exist so it does." BULLSHIT. It is not our job to define or prove your god does not exist. The burden of proof is on the person making the claim. If you assert your god is real or exists, YOU MUST PROVIDE THE EVIDENCE. NO ONE IS STUMPED. Religion has never met their burden of proof and we have tens or thousands of failed gods to prove it. No one is STUMPED by this other than the RELIGIOUS.

@ "Sort of a “my brother can beat up your brother” type of thing. " Of course it is! Scientists have to jump through hoops to prove a theory that does not match what we already know. If you are going to prove a theory, you have to be able to answer all the challenges to that theory. A theory is a body of evidence, FACTS, HARD COLD FACTS, that are interpreted to the best of our ability. If you have another interpretation of a body of facts, that incorporates all the facts and explains them all, but differs from the current scientific theory, you can win yourself a Nobel Prize. Science is extremely competitive, but the FACTS are the same.
Religion on the other hand consists of competing myths. Take the Mormons baptizing Jews for Example. The Jewish community is actually upset about all the dead Jews being converted to Mormonism. HOW FRIGGING STUPID IS THIS. Every Christian denomination asserts their belief systems are more correct than another Church's belief systems and they know this based on FAITH and their interpretation of the ancient iron age book of confusion. RELIGION IS NOT SCIENTIFIC.

@ "“technically, anything is possible” You do not understand "possibility." Show me a round square. "By definition things make themselves impossible." An undefined, invisible god is exactly the same thing as nothing at all. Once you define a god, it is never a god. It is never a god as it can be imagined to be greater or less than its definition. Even that being than which no greater can be imagined is subject to the +1 rule. You can always add another attribute. And finally, as Sheldon stated (I believe) You can not IMAGINE A GOD INTO EXISTENCE. Just because you think it is real, does not make it so. You need facts and evidence. If you agree with the laws of logic, a triangle is a triangle and can not be a square, where is it you are seeing these paradoxes you speak of?

WOW DID YOU STEP OFF THE DEEP END ON THIS ONE... @ The only catch is all claims will be tested by identifying if such a claim can remain consistent within itself. If it cannot then it indicates a paradox.

NO! NO! NO! A claim that is inconsistent can be rejected on that inconsistency or reduced to a probability based on the sample size. If a claim can not remain consistent it remains unproved and can therefore be rejected as a claim. THE BURDEN OF PROOF HAS NOT BEEN MET. No paradox at all. Science calls it simply the "Null Hypothesis." Nothing can be said about the claim to be true. The claim is rejected. It is not a PARADOX by any definition of the word.

@ "It is indisputable, doesn’t require evidence, and can be understood by the most simple of minds."

WRONG - Of course it requires evidence. You can not make wild assertions without evidence. That is what religions do. We know all triangles have three sides because that is the name we have given to all three sided objects in the real world. Language is symbolic and those symbols can be measured, tested, and relied upon to be true based on the way we use them. A non-euclidean triangle has more area than a Euclidean triangle. We discovered a new geometry that expanded our knowledge. As we look deeper and deeper into Plank Time, where our physics breaks down, we may find another new geometry and come up with new ideas of the properties of triangles and squares. But in each and every case, things will be clearly defined. Things are what they are and they are not what they are not. There are no half way points. Something half way is a new thing.

We can not confuse objects with definitions. And isn't that exactly what you have done with your definition of paradox. You are defining perfectly understandable things as paradoxical. You are seeing paradoxes, where none exist and pretending that this is somehow mystical.

(Wiping sweat from his brow, Stretching his fingers. Gazing intently through the noonday sun and straight across home plate into the well worn pitchers mitt.) Cog readies himself for the second pitch. (But somewhere deep in the back of his mind is the idea that the coach could call in a new pitcher at any time. After all, pitching in this situation just looks like good practice.)

@ "The problem I have with this is the notion that, with more evidence, such an unproven claim can be reversed."

And it remains unproven until it is proved. This is the only rational position. You do not believe it first and then hope someone will prove it for you. If you think your position is tenable, prove it. The appropriate response to things we do not yet know is "We do not yet know." The appropriate response to claims that have no evidence, logic or reason supporting them is "There is no reason to believe these claims."

@ "What I propose is there are claims that can be made which will be forever false, " Then it is not a paradox. It is an unsubstantiated claim. A paradox is something that contradicts itself. "God both exists and does not exist at the same time" is a paradox. Nevertheless, it must also be a quality of God as the greatest god that one can imagine is a non-existent god. Surely a god that does not exist and still does all the things that an existent god can do is greater than the existent god.

@ “Paradox” defined as “a self contradictory proposition” There is nothing self contradictory or paradoxical in the propositions you assert. Please show the paradox.

@ "a claim that is not consistent remains unproven" or is relegated to a "PROBABILITY." Probabilities are inconsistent yet prove to be true. To establish a probability you must have a set of something in which the probability occurs. The probability of a god being real is ZERO. Of the hundreds of thousands of gods that we have, we have no instance of a god being real. Probability ZERO. Possibility is whatever you make it? Fantasize all you like. We have not seen the entire universe. It may be possible but it is not probable.

@ To summarize my approach so far is I am not yet focused on aspects of God. I am only focused on aspects of logic.

But you are not following the three basic laws of logic. You do not even appear close.
1. The Law of Identity. X is X. (Things are what they are.)
2. The Law of Non-Contradiction (Things are not what they are not.)
3. The Law of Excluded Middle The law of excluded middle says that a statement is either true or false. For example, my hair is brown. It is either true or false that my hair is brown. (It could be named any shade of brown. Infinite shades of brown, but each shade is its own shade.) Another example: I am pregnant. The statement is either true or false. Since I am a male, it is not possible for me to be pregnant. Therefore, the statement is false. If I were a female, it would be possible for me to be pregnant (given normal bodily conditions). A woman is not "kind-of" pregnant. She either is or is not pregnant - there is no middle position. The law of excluded middle is important because it helps us deal in absolutes. This is particularly important in a society where relativism is promoted and truth statements are denied. A triangle is a triangle and it is not any other shape.

Where are your paradoxes?

@ I suggest evidence can be completely absent for a conclusion to be this solidified (this is a proposition).

Not sure what you mean by solidified but I will assume you are referring to a "Truth" claim. As far as we know, even truth claims can change based on new information. "Gravity Exists." Of this we are quite certain. What is it? This keeps changing. Newton believed it was an "Attraction Force." Einstein came up with a theory of warped or bent space. Now we are discussing Gravitational Waves and that could lead us into a whole new area of exploration. There is still this thing called Gravity that we are trying to understand.

@ What I propose is there are claims that can be made which will be forever false, and no amount of evidence can reverse that.

Agreed. A is A and A is not B. Logical. A will never be B no matter how insistent you are that A is B. An elephant is not a penguin. This statement will be forever false even if we just switch the names. They are not the same thing.

@ such a definite conclusion does not always require evidence (another claim).
How will anyone know what you are talking about without evidence? I can think of no case at all where evidence is not required. It is evidence and exploration that brought us to the Laws of Logic in the first place. Trial and Error. So if you assert you can draw a definite conclusion about something with no evidence at all.... You will have to prove your assertion.

@ This is why I use the example of a triangle with 4 sides. It doesn’t need evidence to disprove,

It absolutely needs evidence to be proved. You need the evidence of what you are calling a triangle. For something to be a triangle it must have the properties of a triangle. You only know a triangle is not a triangle when the properties of the object do not match the properties of a triangle. A is A. A is not B.

@ it just needs an understanding of its definition.
How do you understand the definition of a triangle without knowing what a side is? (A property, observable and measurable.) You can not define a triangle without its properties. You can not understand it without understanding its properties. You only know triangles exist because of the evidence of their properties.

What you are asserting is that PLICKETS are real and have properties. You can understand them without knowing anything at all about them. You can say things about them though you know nothing of their properties. You can formulate conclusions about them without any evidence at all. They are just self evident. No. Furthermore; every conclusion you make about PLICKETS will be evidence. It can be looked for, measured, observed etc...;./

So obviously we completely disagree on the meaning an nature of triangles. You can't even discuss a triangle without knowing its properties (Evidence).

This is the problem with God. As soon as you say "It exists" you are giving it a property that can be looked at. Now you have to justify the statement with "beyond time and space." Now you have to prove that there is something beyond time and space. And it goes on and on and on.

And folks that is an amazing set of pitches from Cognostic. All three balls were over the middle of the plate at high speed and totally bamboozled the batter. The edge of his bat is still smoking with the air friction as they went past . Aaaaand, yes, the catcher is being replaced so he can dunk his hand in iced water.
Is there another batter brave enough or foolish enough to take on this line up....Killens is warming up in the bull pen, Tin Man practising his special drop, curve twist ball, thats always entertaing watching the batter twist himsel into a pretzel trying to see that one....and yes Ol Man is playing wall of death on the back wall on his recently modified trike, waiting his turn at bat. So top of the second it is one nil to the Atheists. Can the Believers come back?