A challenge often presented to Atheists by fundamentalist Christians and various Theists is that Atheists have no proof there is no God, therefore Atheism is just another faith. Although Atheists do not have the Burden of Proof, we can still put forth different types of reasoning to give a philosophical justification for an Atheological worldview. There are two main categories of evidence that can be used. I will divide my arguments into different sections for these categories. The first is called evidential arguments. These are arguments that some facts about the world are cited as evidence against God’s existence; for example, the large amount of suffering in the world, or the argument from Biblical defects. These arguments carry the probabilistic conclusion that God does not exist; in other words, on balance of probability it is more likely than not that God does not exist. Therefore, these arguments do not carry conclusive evidence that there is absolutely no God. The second is called logical evidence against God’s existence. These are philosophical evidence which cites that either a) The proposition that God exists is logically incoherent in some way, or, b) the concept of God is incoherent in some way. This type of evidence purports to conclusively demonstrate the fact of Atheism based on logical incompatibility with the cited contingent facts about the world and the proposition that God exists.
Part I: The Evidential Evidence Against God’s Existence
1: The Argument from Evil and Suffering
The Problem of Evil cites the large amount of suffering as evidence against God’s existence. In syllogism form we have:
- If God exists unjustified evil does not exist
- Unjustified evil does exist
- Therefore, God does not exist.
The world is indeed full of unnecessary suffering and evil. When I say the word evil, I do not limit myself to just moral evil such as sin. Rather, I am referring to all types of calamity that can befall humans (i.e., earthquakes, storms, floods, etc.) and the existence of mass suffering (i.e., famines, poverty, oppression, etc). I do not believe that Theists have a good answer for the Problem of Suffering and Evil. As Charles Brandlaugh argues:
The existence of evil is a terrible stumbling block for the theist. Pain, misery, crime, poverty confront the advocate of eternal goodness, and challenge with unanswerable potency his declaration of Deity all-good, all-wise and all-powerful. Evil is either caused by God or it exists independently; but it cannot be caused by God, as in that case he would not be all-good; nor can it exist hostilely, as in that case he would not be all-powerful. If all-good he would desire to annihilate evil, and continued evil contradicts either God’s desire or God’s ability to prevent it. Evil must either have had a beginning or it must have been eternal, but according to the theist it cannot be eternal because God alone is eternal. Nor can it have had a beginning, for if it had a beginning it either must have originated in God or outside God; but according to the theist, it cannot have originated in God for he is all-good, and out of all goodness evil cannot originate; nor can evil have originated outside God, for, according to the theist, God is infinite, and it is impossible to go outside of or beyond infinity.
Examples of disasters include Hurricane Sandy that left billions of dollars in damage and hundreds dead, and the Haitian earthquake that left hundreds of people dead. Thousands more examples could be noted.
William Rowe points out:
Lightning strikes a tree in a forest, causing a forest fire. A fawn is caught in this fire, and suffers intense agony for an extended period of time before finally dying. (This has undoubtedly happened many times in the Earth’s history.)
A five year old girl is, by her mother’s boyfriend, severely beaten, raped and strangled to death. 
Either God wants to abolish evil and cannot, or he can but does not want to, or he cannot and does not want to, or lastly he can and wants to. If he wants to remove evil, and cannot, he is not omnipotent; if he can, but does not want to, he is not benevolent; if he neither can nor wants to, he is neither omnipotent nor benevolent; but if God can abolish evil and wants to, how does evil exists?” 
One final note: This does not disprove the existence of all gods; however, it is strong evidence against a God that is supposedly all loving , all-powerful, and all-knowing.
2: The Argument from Demographics
- If the demographics of Theism are better explained by Atheism than Theism, then the demographics of Theism make Atheism more plausible than Theism.
- The demographics of Theism are better explained by Atheism than Theism.
- Therefore, Atheism is more plausible than Theism.
We can begin by making some simple observations:
- There are many more Muslims than Christians in Saudi Arabia; 
- There are many more Hindus in India than in the rest of the world ; and,
- In the ancient world, every culture had its own mythology. In fact, these mythologies often contradicted each other and varied wildly. 
This pattern is very surprising on the basis of Theism. Why would God let such an important matter depend strongly upon the time and place of one’s birth? In fact, Atheism explains these demographics better. If God does not exist, then religions are but elaborate social constructions. Therefore, we would predict that the demographics would obey the contours of history and geography similar to other beliefs and ideologies. This is, in fact, what we observe.
Part II: Logical Arguments
3. What is God?
Before one can make a rational conclusion on whether or not God exists, we must first create a coherent definition of God (this is called “ignosticism”). Consider the following dialogue:
- Person 1: “A Blorb Exists.”
- Person 2: “Prove it.”
- Person 1: “The universe must have had a cause and that cause was the blorb.”
We can plug and chug any type of evidence for the existence of the blorb. However, we still cannot make a rational basis for the existence of the blorb until person 1 defines it. As W. T. Blackstone argues:
Until the content of a belief is made clear, the appeal to accept the belief on faith is beside the point, for one would not know what one has accepted. The request for the meaning of a religious belief is logically prior to the question of accepting that belief on faith or the question of whether that belief constitutes knowledge. 
Until Theists are able to agree upon the definition of “God,” whether it be monotheism, monolatrism, polytheism, or pantheism, we are justified in rejecting that belief.
Not only does the definition of God need to be coherent, but it must also be able to be falsified, and it cannot be ambiguous. Thus, we come to this formulation in formal logic:
- If God were to exist, then an agreement upon the definition of God would be able to be reached;
- However, there is no unified agreement on the definition of God. Even religions have disagreements within itself about what or whom God is;
- Therefore, God probably does not exist.
4: The Incoherence of God
The standard definition of “God” is largely incoherent. According to the National Catholic Almanac, there are 22 attributes of “God”:
“[A]lmighty, eternal, holy, immortal, immense, immutable, incomprehensible, ineffable, infinite, invisible, just, loving, merciful, most high, most wise, omnipotent, omniscient, omnipresent, patient, perfect, provident, supreme, true.
At least two of the above attributes (“incomprehensible” and “ineffable”) contradict the others. How can the other attributes of God be known if he can be neither understood nor described? If God has free-will, as some Christians believe that he does, then how can he know everything? These are some of the attributes of God that are logically incompatible, thus making the Theist God impossible. So “[t]hus the characteristics of God as supplied by Christian theologians (and other theologians) are nothing more than meaningless and contradictory concepts wrapped in theological garb.” 
1. The mainstream concept of God is logically impossible;
2. The problem of evil is proof positive for the nonexistence of an omnipotent, omniscient, omnibenevolent God;
3. The demographics of Theism are better explained by Atheism;
4. Theism does not have a good explanation for the problems of suffering and the arguments for Atheism.
 An example is from an e-mail I received from Nadir Ahmed from http://examinethetruth.com and Slick, M. from the CARM: The Christian Apologetics and Research Ministry: https://carm.org/atheism/is-atheism-viable/
 Bradlaugh, Humanity’s Gain From Unbelief: p28-29. Quoted in Tobin, P. (2000) The Rejection of Pascal’s Wager: The Skeptic’s Guide to Christianity.
 As presented in a debate between debate.org users WriterDave and SuburbiaSurvivor:
 This is taken from an instance in Flint, Michigan in 1986.
 This is the famous Epicurus Dilemma from Aphorisms of Epicurus (c300BC).
 99% of Saudi Arabians are Muslim: http://www.state.gov/j/drl/rls/irf/2008/108492.htm
 80% of East Indians are Hindu.
 See http://www.mythweb.com/ for some of the world’s myths.
 Quoted in Smith, G. Atheism: The Case Against God.
 Quoted in Smith, G. Atheism: The Case Against God.