This is a very short course in logic for those who like to use the Socratic method in leading believers to see the falsity of theism. Even such a small course as this will prove helpful, for it is the very basis, the foundation of, logical discourse.
In your questioning of theists in order to lead them to the realization that theism has no basis in reality always remember, and when possible, utilize the three laws of logic, in establishing the truth or falsity of a thing.
What are the three laws of logic ? They are as follows.
(1) The Law of Identity, which states that something is itself, and not something else. The term being used corresponds and coincides with the thing being described.
(2) The Law of Non-contradiction. This law develops more fully the first law, in that it teaches that the thing being described in the first law cannot be both itself and not itself at the same time and in the same sense.
(3) The Law of the Excluded Middle. This final law says that a thing must be either true or false, it cannot be both. In other words, there is no middle ground. In other words, as an example, a woman cannot be a little pregnant.
Christians have tried to sneak in a fourth law, called the Law of Sufficient Cause. This is not one of the true laws of logic, there are only three, the three enumerated above. The purpose of this spurious fourth law is meant only to justify the existence of God as the sufficient cause of the universe.
So, there you have it. In using your Socratic questioning it would be only helpful to remember these three laws in establishing the truth or falsity of a thing.
Giving an honest answer to your question involves technical language not easily explained, but the general ideas are clear. It will be better to divide the answer into two parts.
There have been devised quite a number of different logics either revising or extending classical logic: modal, tense, deontic, epistemic, preference, imperative, and erotetic logics all extend classical logic in some way while many-valued, intuitionist, quantum and free logics revise it.
In addition to all these a systematic analysis of logic using category theory has been developed over the last half century. It reveals new properties of the underlying structure of logic and provides a clear definition and axiomatization of classical logic.
The two values of classical logic—true and false—are related to the roles of unique terminal and initial objects in a category and therefore have an essential character difficult to remove.
In Aristotelian logic much was missing that classical logic has supplied, but classical logic has its own problems of an entirely different sort.
One serious problem is paradoxes of material implication. In classical logic a statement A implies a statement B if either B is true or A is false. This is very far from the semantic interpretation of A implies B in ordinary language. It leads to absurdities such as 2+2=5 implies 2+2 = 4.
This problem appears to be unresolvable in the abstract realm of truth-functional logic. It is only within a context that we say A imples B. In the abstraction of logic the context is stripped away.
That's the logic of religion: God exists therefore anything you want is true.
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