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Existence is a relatively simple concept -- it is defined as that which consists of either matter or energy. Therefore if a god exists, it must be composed of either matter or energy.
The opposite must also be true. If a god is not composed of matter or energy, then that god, by definition, does not exist. Thus to argue that a god exist, despite a total absence of matter or energy, is to argue, existence equals non-existence, which is a complete contradiction.
If a god exists, then physical evidence is really the only methodology by which we can ascertain that a god exists. Of course, this does not require direct physical evidence -- we cannot perceive black holes directly, but we know that they exist due to the effects of their gravity wells on surrounding matter, as well as the flashes of energy that are released as captured matter crosses the event horizon. But since "existence" is defined as that which is composed of matter or energy, the proof of existence must be some evidence of that matter or energy.
Evidence is defined as that which impacts our physical senses in some manner, either directly, or through some translating device such as a spectrograph or an oscilloscope. Since our sensory organs are designed to perceive the effects of matter and energy, it is through the evidence of the senses that we can determine the existence or nonexistence of things.
If I argue that something exists, but then claim there is no way to detect it, my argument contradicts itself. Let's say I tell a deaf man that I hear a deep, loud sound coming from a speaker. If he lays his hand on it and feels no vibrations, he has every right to be skeptical. If I say that this loud sound does not have vibrations, he may then pull out his trusty microphone or other sound wave detector. If this instrument detects no sound in the vicinity, can I still tell him that this loud sound is occurring? At some point, if my definition of "loud sound" basically boils down to "that which is the opposite of any evidence that a loud sound is occurring," then clearly my approach to truth needs a little work.
This approach helps clarify the truth value of the proposition that a god does not exist. If a god exists, then sensual evidence of some sort is required to determine the existence of that god. If a god is not made up of matter or energy, then that god does not exist, since that which is not composed of matter or energy -- does not exist.
If a god is made up of matter and energy, then it is subject to physical laws. Since it is bound by physical laws, miracles are impossible, because miracles are, by definition, violations of physical laws. Likewise, a god cannot be all knowing and all-powerful, since both attributes would violate the basic tenets of physical laws. All knowing would require instantaneous knowledge of all matter, past, present and future, which is clearly impossible, while all powerful would require the ability to break the bounds of physical laws, which brings us back to the realm of nonexistence.
If a god is subject to physical laws, then praying to a god makes about as much sense as worshiping a black hole, begging the Sun to grant you favors, or circumcising your son to appease the moon. If a god is not subject to physical laws, then the concept of a god is synonymous with the concept of non-existence.
Why is there such resistance to the fact that a god does not exist? Many people redefine "God" within their own minds as "a potential form of matter or energy that has not been discovered yet," or "that which could exist in an alternate universe," or something to that effect.
However, either a criterion for determining truth exists, or it does not. If such a criterion exists, then it must be objective, and based on the evidence of the senses and reason, which precludes the existence of any deities. If no such criterion exists, then both everything and nothing is true, and agnosticism, atheism, superstition, religion and the belief of the flying spaghetti monster are all equally valid.
If an objective criterion for truth exists, then it cannot logically be applied according to whim, or only in situations that feel emotionally comfortable. Through this logical method we can determine no god exists.
Actions are more important than beliefs.