Monday, August 27, 2007

What Logic Requires Us To Believe About The Existence of God--Part 1

Since one of my tactics when defending the existence of God has been to look at what accepting logic requires us to believe (most recently found in my critique of Russell’s teapot analogy), I have decided that it may be beneficial to go through this argument slower, step by step, so that it is easier to see exactly how the logical argument follows. One thing that should be noted right off the bat is, despite the fact that I like presuppositional approaches to argumentation a great deal and think ultimately they are the best approach to dealing with atheists in particular, this argument is not a presuppositional argument. As such, there are some places where this argument will be ineffective; then again, no one argument should be considered a “magic bullet” in the first place. The argument I present does not “prove beyond all doubt” that the Christian God exists (although I believe it does prove beyond all reasonable doubt that there must be some kind of deity, and I also allow that atheists can be as unreasonable as they desire to avoid this argument).

Since this will be a step-by-step look at the argument, I will not present the entire argument at one time as I have done in the past. Instead, I shall start with some basic bare-bones rules of logic that we can keep in mind as we examine the rest of the argument.

The Law of Identity

The logical law of identity is perhaps best represented by the Greek philosopher Parmenides’ statement: “Whatever is, is.” This statement can be symbolically represented in the logical format:

A is A.

In such a case, whatever A is, is (by definition) A. Because we are dealing with abstract levels of thought here, it does not concern us to actually flesh out what A is. We are concerned with seeing the relationships that go on between all objects, and therefore A can stand for any object—it could be an apple or it could be the entire universe (viewed as one lump sum), or it could be an immaterial thought (e.g. “love”); but whatever A is, that is what A is.

This is what is known as an analytically true statement (that is, it’s true by definition). Other examples of analytically true statements include: “A bachelor is an unmarried man” and “A square has four sides.” Analytically false statements, on the other hand, are statements that are false by definition: “A bachelor is a married man” would be analytically false, as would “A square has seven sides.” (Note that “A square has three sides” is still a true statement, since if an object has four sides it is also true that it has three sides; but a square cannot have more than four sides by definition.)

Since we will be discussing the difference between “being” and “becoming” in more detail later, it may be helpful to make a quick philosophical detour now. Parmenides’ statement, “Whatever is, is” was challenged by Heraclitus who stated, “Whatever is, is changing.” Heraclitus has given us some clichés that survive to this day based on this concept, such as: “You cannot step into the same river twice.” Because the river is moving, it is altered through time. The difference between Parmenides and Heraclitus boils down to the difference between “being” and “becoming”, which is often restated as the difference between “actuality” and “potentiality.” We will consider this in more detail in a later post (when we deal with existence), but I wanted to introduce it now so it won’t surprise you. For the moment, we can note that even Heraclitus’ statement can be reduced to “A is A.” If “whatever is, is changing” is valid, then we cannot define A without including the property of change. Thus, A is A remains valid because A includes within the definition of “A” the property of “becoming” if, in fact, A is becoming.

If we do not wish to include the changing aspect of A in the definition, there is another way to get around it. Since “becoming” carries with it a temporal aspect (that is, change can only happen through time) then we can also intentionally view A non-temporally to avoid that aspect. Thus, we can say “A is A” is a truth about A frozen in a specific time. Either way, the Law of Identity as expressed by “A is A” is analytically true.

The Law of Non-Contradiction

Immediately following the law of identity is the Law of Non-Contradiction. This is most simply put in the form:

A cannot be both A and ~A at the same time and in the same relationship.

To clarify, the tilde (~) represents the word “non”, and the “non” refers to the contrary of A. If A is “a horse” then ~A would be that which is not “a horse.” The Law of Non-Contradiction follows easily enough because if we know that A is A, then we know that A is not whatever A is not. A is not ~A immediately follows from A is A, because in defining A we are distinguishing A from everything else (~A). Whatever is not A, is not A.

I’ve always found the above definition of the Law of Non-Contradiction to be a bit misleading though. To demonstrate, let us define A as “A man” and restate the sentence: “A man cannot be both a man and not a man at the same time and in the same relationship.” This statement is still valid, to a point, but it can be simplified to: “A man cannot be not a man.” The rest of the sentence is ultimately superfluous because there will never be a case when a man might be not a man without violating the definition of the terms involved with ambiguity. Instead, I believe it is more precise to define the Law of Non-Contradiction as:

A cannot be (or “A cannot have the property of”) both B and ~B at the same time and in the same relationship.

Now if we substitute “A man” for A, we do not immediately run into definitional gibberish. We need to establish what B is, so let us define it as “a father.” Thus we can say: “A man (A) cannot be both a father (B) and not a father (~B) at the same time and in the same relationship.” This sentence now makes sense, because while there will never be a time when a man will be a non-man, there are times when a man may be a non-father, just as there are times a man may be a father.

In both definitions of the Law of Non-Contradiction (the classic definition and my tweaking of it), we see the temporal aspect come into play (“at the same time”), and there is also a relational aspect that we deal with (“in the same relationship”). To be sure, a man can be both a father and not a father at the same time, as long as it is not in the same relationship (indeed, this is the definition of every father: every father is the father to his own sons and daughters, but is not the father to anyone else’s children). Thus, the Law of Non-Contradiction automatically deals with the existence of multiple objects and temporal relationships—we do not need to create another law of logic when we expand out from single objects frozen in time.

These two laws of logic are the most important Laws of Logic, and from them we derive several other rules for rationality (for example, we say that circular reasoning is invalid because both sides of a contradiction can be “proven” with circular reasoning, thus resulting in a violation of the law of non-contradiction). However, we shall look at those rules of reason only as we need to in the following argument, in order to save on time.

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