Logic can be best described as the study of truths based completely on the meanings of the tems they contain. Logic is a process for making a conclusion and a tool one can use. Logic can include the act of reasoning by humans in order to form thoughts, opinions, classifications and judgement. Even many modern computers, current software, animals use some form of logical reasoning based on evidence.
The foundation of a logical argument is its proposition, or statement. The Proposition therefore is either true or false. Premises are the propositions used to build an argument. The argument is then built on premises, then an inference is made from the premises and finally a conclusion is drawn.
Logical arguments try to show that God cannot possibly exist at least the ones as described by most theist. Barring any escape hatch arguments like God did it, some properties of God are not compatible with each other or known facts about the world, and thus a creator-god cannot be a logically consistent and existent entity. These arguments are heavily dependent on the use of common descriptions of the Abrahamic God as a target; things such as omnipotence, omnipresence, and omnibenevolence. As a result, they are not as useful in trying to refute the claims of, say, Neopaganism, and are also vulnerable to the tactic of moving the goalposts by changing the descriptions of God.
For example,The omnipotence paradox postulates that true omnipotence is not logically possible or not compatible with omniscience. This is primarily a logical argument based on the general question of whether an omnipotent being could limit its own power - if yes, it would cease to be omnipotent, if no, it wouldn't be omnipotent. Hence the paradox that shows, through contradiction, that God cannot exist as usually described. The Problem of evil states that a good god wouldn't permit gratuitous evil, yet such evil occurs, so a good god does not exist.The argument from design is often given as proof of a creator, but it raise the following logical question: if the world is so complex that it must have had a creator, then the creator must be at least as complex and must therefore have a creator, and this would have to have had a more complex creator. While believers hasten to point out that their gods don't need to follow logic, let alone the known laws of physics, this is really a case of special pleading and doesn't so much prove anything itself. Atheists therefore tend to reject these counters to the logical arguments as they mostly beg the question of a creator's existence and, very arbitrarily, plead that a creator can be exempt from the same logic that was used to "prove" its existence.
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