Possible Worlds: An Answer to a student

Here is an answer I gave to a student of mine asking about what a possible world is meant to mean in regards to philosophy, enjoy!

Colin,

Whenever you hear someone talking about possible worlds its important to know exactly what they mean, so I am glad you asked about this. I am by no means an expert so I will take some aid from Dr.Craig on this as he evaluates the way Alvin Plantinga sets up his version of the Ontological Argument.

First off when we speak of possible worlds we don't mean planets or universes rather we mean to speak of a maximal description of reality, or basically the way reality might be. Plantinga and others use a huge conjunction of p&q&r&s..., whose individual conjuncts are the propositions p,q,r,s...Thus a possible world is a conjunction which comprises every proposition or its contradictory, so that it yields a maximal description of reality - nothing is left out of such a description. By negating different conjuncts in a maximal description we can arrive at different possible worlds, see below for examples of such possible worlds:

W1: p&q&r&s...

W2: p&-q&r&-s... (this is actually supposed to be a negation symbol but gmail won't let me put in the correct symbol)

W3: -p&-q&r&s...
W4: p&q&-r&s...

...

...

...

Now only one of these descriptions will be composed of conjuncts all of which are true and so this will be seen as the way reality actually is, or the actual world.

It is also important to keep in mind that these possible worlds have to have conjuncts that must be capable of being both true individually and together. For example the proposition that the "Prime Minister is a prime number" is not even possibly true, for numbers which are abstract objects cannot be conceivably identical to a concrete object like the Prime Minister. Therefore there is no possible world in which the Prime Minister would be a prime number. However, if you were to say that "John McCain is the President of the United States" though this is false in the actual world (where all the conjuncts are true) this could be true in some maximal description of reality having this relevant proposition as one of its conjuncts (p&-q&-r&s&John McCain is president&...) Now it is similarly to say that "God exists" is true in some maximal description of reality. Now below you will find Plantinga's ontological argument using God as the greatest conceivable being (maximally great being), it is genius how he comes to his conclusion, the conclusion he uses as his reformed epistemology that states that belief in God is a properly basic belief, it is from this argument that we can come to see why he says this:

Plantinga's Ontological Argument:

1. It is possible that a maximally great being exists.

2. If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.

3. If a maximally great being exists in some possible world, then it exists in every possible world.

4. If a maximally great being exists in every possible world, this it exists in the actual world.

5. If a maximally great being exists in the actual world, then a maximally great being exists.

6 Therefore, a maximally great being exits.

According to Craig most philosophers don't even argue about premises 2-5, they agree if God's existence is even possible, then he must exist. The arguments are over whether there is warrant for believing that a maximally great being exists which is premise 1. People complain that its a logically incoherent statement like a married bachelor. I don't see how a maximally great being is even remotely incoherent. Most detractors of the first premise will say things like the concept of "a most perfect island" or "a necessarily existent lion" also seem prima facie coherent concepts but I hope you see how this is grossly misunderstood. A most perfect island isn't truly that, what if I wanted softer sand, more alcohol in my drinks, a brighter sun, more palm trees. The same goes for the lion, for if it was possible that a lion could exist in every possible world that description of the lion wouldn't be true of a lion at all. By contrast when Plantinga speaks about maximal excellence he is referring to intrinsic maximal values, for example omniscience is the property of knowing any and all truth, its impossible to know anymore truth, but when thinking about an island as I said above you could always add different things to make it better, those things are subjective. Also a material thing cannot transcend all of space-time, density and or temperature, however, a maximally great being, if it is immaterial (metaphysical), could transcend such physical limitations and so be conceived as necessarily existent. 

One then might say how do we know this being transcends physical limitations making it a metaphysically necessary being? Well we covered the necessity for a being outside of the physical world when we touched on the Cosmological arguments and hopefully your on board there (I hope you are comfortable defending the premises of those arguments, that article from Dr. Craig should have helped a little). Here is an argument Dr. Craig offers from a conceptualist point of view for God's existence:

1. Abstract objects, such as numbers and propositions, are either independently existing realities or else concepts in some mind.

2. Abstract objects are not independently existing realities.

3. If abstract objects are concepts in some mind, then an omniscient, metaphysically necessary being exists.

4. Therefore, an omniscient, metaphysically necessary being exists.

As premise 2 states we can defend this by asking ourselves if the number 7 exists independently of a mind, I would have to say it most certainly doesn't. It also goes to note that abstract objects don't exist in causal relations, for example, the number 7 doesn't cause anything at all, this should help when defending the cosmological argument and showing the necessity of a metaphysically necessary being as the agent which acted in causal relation with the creation of the universe. So if number 2 is true then according to 1, 3 has to follow as the explanation therefore the conclusion follows logically from the premises.

Also, keep in mind as we understand the concept of God He is in an immaterial existent mind, or a metaphysical being, which shows where we get the description of the mind in premise 3.

I hope this stuff helps. I love how Dr. Craig speaks about the use of these theistic arguments when he writes, "theistic arguments need not be taken like links in a chain, in which one link follows another so that the chain is only as strong as its weakest link. Rather they are like links in a coat of chain mail, in which all of the links reinforce one another so that the strength of the whole exceeds that of any single link."

Bottom line, when used as a whole argument for the existence of God, the Cosmological argument, Ontological argument, Moral argument, Teleological argument and so on can be employed to make an effective case for theism. Once we break the bonds of disbelief in God then we can present the gospel in its entirety to a lost soul or souls that need to hear the saving grace of our Lord Jesus Christ.

I hope this helped you and didn't confuse you, it was confusing to me in the beginning (what am I saying, it was confusing me while I was typing it!!!) but stick with it and hopefully you can see how it makes sense.

Let me know if I can help in any other way, your questions help me to continue to grow in my understanding of the nature and existence of our Heavenly father.

God Bless little brother!

p.s To answer your question... the possible world does have to be logically coherent...hopefully I answered that in the above response...I guess I could have just said yes to your question and that would have saved you a lot of time reading this, oh well, it was fun typing!