I have come across a paper written by James N. Anderson and Greg Welty and entitled "The Lord of Non-Contradiction:An Argument for God from Logic". The full paper can be found at http://www.proginosko.com/docs/The_Lord_of_Non-Contradiction.pdf. It was also twitted on by a user named @ChoosingHats.
The paper provides a philosophical argument that seeks to conclude that a god exists. This is based on the very existence of logic. "God", in the paper, is defined as "necessarily existent, personal, spiritual being" (see p20 for example).
The flow of the argument is as follows (I will not be entering into details at this point):
1. The Laws of Logic are Truths
2. The Laws of Logic are Truths About Truths
3. The Laws of Logic are Necessary Truths
4. The Laws of Logic Really Exist
5. The Laws of Logic Necessarily Exist
6. The Laws of Logic are Non-Physical
7. The Laws of Logic are Thoughts
8. The Laws of Logic are Divine Thoughts (in other words, they are the product of a "necessary mind" - ie God).
I will not attack each premise in turn, althought I have to stress that they are very much open to attack on a number of grounds. To illustrate, the paper includes arguments such as "if we believe in the laws of logic existing then tney must exist". This of course is a non-argument. There are numerous other examples in the paper of similar (and occasionally worse) errors.
That said, I don't wish to focus on those. Suffice it to say that my attack below is by no means the only attack that can be made. Instead, I want to focus on a lethal flaw of the argument itself. The flaw is that the argument either contradicts its own premise or it DISPROVES (rather than proving) God, by making Him impossible. Let's move to the crunch.
A. The Laws of Logic as Necessary
The paper argues (under the heading "The Laws of Logic are Necessary") that a world where the laws of logic don't apply is an impossible world. In other words, the authors claim, it's impossible to have a world in which P (any entity) can exist and not exist at the same time, to give one example (see p7 of the paper). If we disagree with this premise (and claim that a world without logic is in fact possible), the paper fails in its entirety because it can no longer claim that logic is either necessary or universal. And, of course, if logic is neither necessary nor universal, it may simply be a human construct that only applies to the way we ourselves observe our world as we see it.
However, for the purposes of the argument, let's assume that the Laws of Logic are in fact necessary, as is claimed by the authors. Let's assume also that they are universal in the sense that no conceivable world can exist in which they do not apply. Such a world, the authors claim, is impossible. Let's keep in mind that the use of the term "world" in this context doesn't apply to any known physical world, such as a planet, galaxy or universe. It's a philosophical term that simply refers to an imaginable "state of affairs".
Now, having agreed with the paper's premise that a world without logic is impossible, let us consider the paper's conclusion.
B. The paper's conclusion. I will quote it verbatum (page 20 of the paper):
"Propositions are real entities, but cannot be physical entities; they are essentially thoughts. So the laws of logic are necessarily true thoughts. Since they are true in every possible world, they must exist in every possible world. But if there are necessarily existent thoughts, there must be a necessarily existent mind; and if there is a necessarily existent mind, there must be a necessarily existent person."
Now, here's the problem with this:
1. There is a claimed existence of a "necessary mind". It's called "God".
2. The Laws of Logic are (according to the paper's argument) a product of this mind. In other words, they only exist (as thoughts, so the authors say) because the mind (God) has thought them up.
3. Since The Laws of Logic were thought up by God, they do not exist independently. This is to be contrasted with their (claimed by the authors of the paper) existence that is independent of the human mind (this is part of their being "necessary"; they would exist even if no human ever walked the Earth).
4. When we say that God has thought up the Laws of Logic we can only mean one of two things; either God has invented them or God has discovered them. If God has discovered them then they exist independently of God and therefore are not His product at all. It's no different to humans discovering logic but not in fact creating it (as per the paper's claims). And if Laws of Logic exist independently of God (albeit He discovers them and thinks about them) then God is not a valid logical conclusion from the premise that the Laws of Logic are necessary. They are in fact necessary DESPITE God and would be necessary even had God not discovered them or had not Himself existed. What follows is that, for the paper's argument to make sense at all, it must be said that the authors claim that God INVENTED Laws of Logic.
5. If God invented laws of logic then God is not bound by them. They do not apply to God. From God's point of view, they are not necessary at all. To God, they are just one of His inventions. He could have, had He wanted to, created other (different) laws of logic. And this means that it's not necessary for God to CONFORM with the Laws of Logic.
6. From 5 above, we can conclude that God exists in a "world" (again, in the philosophical sense) in which the Laws of Logic do not apply. The law of Non-Contradition (as one of the Laws of Logic) also does not apply in God's world. If it did, it couldn't have been created by God and God wouldn't have the freedom to invent such Laws of Logic as He pleased (and we'd be back to point 4 above).
7. But a world in which the Laws of Logic do not apply is an impossible world (see point A above). This is a permise of the authors' own argument; a premise without which the argument would have no feet to start with; it could never get off the ground.
8. Since God is said to exist in an impossible world, God cannot exist in reality.
What follows is that either the Laws of Logic are not truly necessary (and the paper fails at its premises) or that they are truly necessary and a god who thought them up cannot exist.
One might attempt to counter this by special pleading. For example, one might say that the the laws of logic are only necessary in our world and not in God's (although that is not how the authors put it). But that doesn't help the authors' argument. Once we agree that a world in which the Laws of Logic are not necessary is possible, we refute any universality of the Laws of Logic. Put simply, our world is such that things in it can't exist and not exist at the same time (what does Quantum Theory say about that by the way?) and the creatures in it are conditioned to see it in that same way. But other worlds (whether it be "God's world" or just "another type of universe"), in which different Laws of Logic apply (or none at all) are equally possible (and may in fact be more numerous!). You just can't have your cake and eat it too.
Thanks,
@Allocutus
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