St. Anselm of Canterbury once tried to show, through an ontological argument, the existence of god from reason alone. He said, "Thus even the fool is compelled to grant that something greater than which cannot be thought exists in thought, because he understands what he hears, and whatever is understood exists in thought. And certainly that greater than which cannot be understood cannot exist only in thought, for if it exists only in thought it could also be thought of as existing in reality as well, which is greater. If, therefore, that than which greater cannot be thought exists in thought alone, then that than which greater cannot be thought turns out to be that than which something greater actually can be thought, but that is obviously impossible. Therefore something than which greater cannot be thought undoubtedly exists both in thought and in reality.... And you, Lord God, are this being." His argument can be reformulated, in English, as:

X is "something than which nothing greater can be thought"

1. If someone understands X then X exists in thought 
2. Someone understands X 
3. X exists in thought [modus ponens, 1-2] 
4. Suppose X exists solely in thought
5. You could conceive of Y so it has all of X's properties but also exists outside the mind
6. To exist outside the mind is greater than to exist in thought alone [axiom] 
7. Y would therefore be greater than X [from 4-6]
8. X would therefore not be the greatest conceivable [from 7]
9. Contradiction with the definition of X [from 8]
10. X (God) exists not only in thought but also in reality [proof by contradiction, 4-9]

The problem with this argument is the definition of X. If greatness entails existence, then why would one accept a definition that includes greatness? Wouldn't the dispute between theists and atheists center upon the inclusion of greatness in the definition then? An atheist could simply respond, "I do not accept that definition," then the argument collapses because there's no reason to accept any reasoning that relies upon a disputed definition. The argument is subtley circular, and the circle was drawn through presupposition. By presupposing definitions that necessarily entail certain conclusions, other arguments can be made that result in empirically false conclusions. Here is a rebuttal to Anselm's Ontological Argument using the same line of reasoning to establish an empirically false claim, thus proving Anselm's reasoning is unsound:

X is "the greatest conceivable credit card with an infinite amount of cash on it in all conceivable currencies"

1. If I understand X, then X exists in thought 
2. I understand X 
3. X exists in thought [modus ponens, 1-2]
4. Suppose X exists solely in thought
5. I can conceive of Y such that Y has all the properties of X, but Y exists in reality 
6. To exist in reality is greater than to exist in thought alone [axiom]
7. Y is therefore greater than X [from 4-6]
8. X is therefore not the greatest conceivable [from 7]
9. Contradiction with the definition of X [from 8]
10. X not only exists in thought, but in reality [proof by contradiction, 4-9]
11. Suppose X exists solely outside my pocket
12. We can conceive of Y such that Y has all the properties of X, but Y is inside my pocket 
13. To exist inside my pocket is greater than to exist outside [axiom]
14. Y is therefore greater than X [from 11-13]
15. X is therefore not the greatest conceivable [from 14]
16. Contradiction with the definition of X [from 15]
17. X not only exists in reality, but also inside my pocket [proof by contradiction, 10-16]
18. If Anselm's argument is sound then my argument is sound 
19. If my argument is sound then X is inside my pocket 
20. X is not inside my pocket 
21. If X is not inside my pocket then my argument is not sound [contraposition of 19]
22. My argument is not sound [modus ponens, 20-21] 
23. If my argument is not sound then Anselm's argument is not sound [contraposition of 18]
24. Anselm's argument is not sound [modus ponens, 22-23]