[quote author=“Bruce Burleson”]
[quote author=“waltercat”] But suppose God did have the power to create a universe where the law of non-contradiction did not hold. So, in this universe, it could be the case that both A and NOT-A are true. So, in this universe, logical contradictions (which is what “A and NOT-A” is) can be true. However, we have a problem because, from a logical contradiction, it is possible to prove anything whatsoever. Thus, we could prove that God does not exist. We could also prove that God does exist. We could prove that God is subject to the laws of logic. We could also prove that God is not subject to the laws of logic. If logical contradictions can be true, then we can prove any damn thing we please. ANYTHING GOES.
I think this is where I will make my stand - my Alamo.
Okay, Davy. (I’m sure you want to think of yourself as Sam, but if you are thinking of yourself as at the Alamo . . .)
Why do you assume that God could not create a universe in which one “logical contradiction” (as we would understand that term in our universe) could hold true, but another “logical contradiction” could not?
Well, I have made no such assumption. Rather, I have put forward argument after argument that demonstrate that God cannot do it. He can’t do it because logical contradictions cannot be true (and they undermine the possibility of rational discourse).
But why not let’s throw logic (or at least some of it) out the window, since you asked us to. This will be interesting. We’re going to pretend to throw logic out the window (since we cannot actually do it). One interesting question is, “are there any constraints on this game? Can we imagine anything we want?” And, since we are explicitly going to imagine that a logical contradiction is true (which it can’t possible be), I don’t see that there are any constraints on our imagining. Once we’ve dispensed with logic, anything goes:
Why could an omnipotent God (if he exists) not create a universe in which both “Jason is brilliant” and “Jason is an idiot” hold true, but “God exists” and “God does not exist” not both hold true? You seem to be saying that if there is one logical contradiction (as we understand contradictions in this universe) in a system, then ANYTHING GOES. But why does this have to be the case? Why can’t God create a system, and brains to understand the system, in which there is one “contradiction” but not another?
I’ve explained why He can’t do it. But since we are throwing logic out the window (well, actually, we can’t throw logic out the window, it’s not logically possible to, but we’re pretending), I’ll give this to you: God can (he can’t really—we’re just pretending) create a universe where only one contradiction is true. And that contradiction is “Jason is brilliant and Jason is not brilliant.”
Now we have to do some housekeeping before we move on. First, we need to make sure that both occurrences of the name ‘Jason’ refer to the same individual (if there are two Jasons, we don’t have a contradiction). It would be nice to be able to point out a particular person whom the name refers to, but this is only an imaginary (not even possible) world we’re talking about, so, unfortunately such a person does not exist. However, we can stipulate that in this imaginary world, both occurrences of the name ‘Jason’ will refer to one and the same individual.
Second, we must ensure that we aren’t playing on a pun of the term ‘brilliant.’ If the statement were to read, “Jason is very smart and Jason is not shiny” we would not have a contradiction. So, let’s stipulate that the term ‘brilliant’ means the same in both of its occurrences. (We can do the same for ‘is’, in case you’re worried about that.)
We should also insist that each of the two component statements of our contradiction (“Jason is brilliant” and “Jason is not brilliant”) are to be true at the same time.
Now we have a genuine contradiction: “Jason is brilliant and Jason is not brilliant.” And I have done a brilliant job of explaining why such a statement cannot possible be true. But we’ve thrown that out the window here and are pretending that such a statement can be true.
So, the world we are imagining is one in which a single contradiction, “Jason is brilliant and Jason is not brilliant,” is true, but no other contradiction is true. In particular, the statement, “God exists and God does not exist” is NOT true in this word.
Fine, none of this makes much sense, but so be it. As I’ve indicated, I’ll give this one to you, since we’re just pretending.
However, we’re not finished. Since I’ve been so generous, it’s now time for you to give something back. And what I want will not be hard for you to give. Indeed, given your previous statements concerning the extent of God’s power, it will be very difficult for you not to give it.
Here is what I want:
I want you to grant that it is possible for God to create a world that is very much like our actual world (and very much like the pretend world we pretended to envision above). In this new imaginary world (which I am going to call “Bruce’s World”), all of the laws of logic hold that hold in the actual world. In fact, Bruce’s World is exactly like the actual world (with respect to logical rules, natural laws, facts, etc.) except for one point: in Bruce’s World, there is a single logical contradiction that is true.
Again, it is important to remember that we are just pretending to imagine. Bruce’s World is worse than a fiction; it is a logical fiction, which means that it cannot possibly exist. However, Bruce Burleson (the actual one, the one that likes Texas beer) must believe that Bruce’s World is possible. In particular, Bruce believes that it is possible for God to create Bruce’s World since, according to Bruce, God can do anything (including the logically impossible).
So, the single logical contradiction that is true in Bruce’s world is “Jason is brilliant and Jason is not brilliant.” This statement has the logical form of a conjunction. It is a compound statement which is a conjunction of two atomic statements. The two atomic statements are “Jason is brilliant” and “Jason is not brilliant.”
We can use the capital letter A to represent the statement, “Jason is brilliant” And we can use the symbol ‘&’ to represent the logical relation of conjunction (which is what an “and” statement is). The symbol ‘~’ will represent the logical operator of negation. Thus “~P-” will be read as “it is not the case that P.” So, since"Jason is not brilliant” is equivalent in meaning to “It is not the case that Jason is brilliant,” we can represent the statement “Jason is not brilliant” as follows: ‘~A.’
The entire conjunction “Jason is brilliant and Jason is not brilliant” thus becomes:
A & ~A.
Now, since I have stipulated that the logical rules that apply in Bruce’s World are the same as those that apply in the actual world (with the exception that we are pretending that Bruce’s World allows that single logical contradiction), we know that, in Bruce’s World, we can prove any statement whatsoever.
How do I know this? Well, I know it because I know that in the actual world a logical contradiction can be used to prove any statement whatsoever. That is what I was getting at when I said that if we abandon logic, then anything goes. And since we’re pretending that the same logical rules apply in Bruce’s World that apply in the actual world (with that one exception), we know that in Bruce’s World a logical contradiction can be used to prove any statement whatsoever.
But How does it work, you might be asking yourself. How can a logical contradiction be used to prove any other statement whatsoever? Well I’ll explain, but my explanation will assume some basic understanding of logic (If you lack such understanding, I’m sure you can figure out how to educate yourself).
Suppose a person living in Bruce’s world wants to prove the following: “California beer is better than Texas beer.” Let us use the letter ‘C’ to represent this statement. This statement is incredibly easy to prove if we have access to a logical contradiction. Here is how it works:
Premise 1: A & ~A
(note: all that we have done here is assume the truth of our logical contradiction from above, namely that Jason is both brilliant and not brilliant. Since we have stipulated that this will be true in Bruce’s World, we know that, in Bruce’s World, Premise 1 is true.)
Derived Line 2: A _______ Justification: Simplification of premise 1
(note: the logical rule of simplification allows us to go from a conjunction (e.g., P & Q) to one of the conjuncts (e.g., P). The motivation for this rule is that if we know that “it is snowing and it is cold” then we know that it is cold. Thus, if I know that Jason is brilliant and Jason is not brilliant, then I know that Jason is brilliant.)
Derived Line 3: ~A _______ Justification: Simplification of premise 1
Derived Line 4: A v C _______ Justification: Disjunction Introduction from line 2
(note: the rule of disjunctive introduction (DI) allows us to go from some statement we know is true to a disjunction of that statement and any other statement whatsoever. A disjunction is an ‘or’ statement. Thus ‘A v C’ should be read ‘A or C’, or, in other words, ‘Either Jason is brilliant or California beer is better than Texas beer.’ The motivation for DI is that if we know that ‘P’ is true, then we certainly know that statement ‘P or Q’ is true. We are using the inclusive ‘or’ here. On this interpretation of ‘or’, an ‘or’ statement (otherwise known as a disjunction) is true when either or both of the disjuncts (the statements that make up the disjunction) is true. Thus, ‘P v Q’ is true when either P is true or Q is true or both P is true and Q is true. Given this definition of the disjunction operator (‘v’), we know that if statement P is true, then ‘P v Q’ will be true as well)
Derived Line 5: C ________ Justification: DS from lines 4 and 3
(note: The rule DS is disjunctive syllogism. This rule allows is to go from a disjunction and the falsity of one of the disjuncts to the truth of the other disjunct. So, if we know that ‘P v Q’ is true, and then we find out that P is false, we can conclude that Q must be true. Remember that we are using the inclusive sense of ‘or.’ If we know that either Obama will win or McCain will win, and then we find out that McCain did not win, we know that Obama won.)
And that does it. We have our conclusion: C. California beer is better than Texas beer.
This method is completely general. It doesn’t matter what statement we use for C, here. It can be any statement whatsoever, and we can use the same method to prove it. Thus a logical contradiction can be used to prove any statement whatsoever.
Now I want to demonstrate that, in Bruce’s World, it is possible to prove that God does not exist.
Let the letter G stand for the statement: “God exists.”
So, the statement ~G will mean: “God does not exist”
Premise 1: A & ~A _______ note: our contradiction again
Line 2: A _______ justification: simplification of 1
Line 3: ~A _______ justification: simplification of 1
Line 4: A v ~G _______ justification: DI from 2
Line 5 ~G _______ justification: DS from 3 and 4
So, in Bruce’s World, we know that God does not exist.
Now, we have shown that, if Bruce is correct that God can do anything, then we know that God can create Bruce’s World. Hence we know that God can create a world in which He does not exist.
But of course this doesn’t make any sense whatsoever. And the reason is that it makes no sense to believe that God is the author of logical laws.
God is not the author of logical laws. He is subject to them.
You lack imagination.
NO. I lack ignorance of logic.