Makridis, Necessary Beings, Contingent Beings, and Possible Worlds
One of the most baffling of Aquinas' proofs speaks of necessary and contingent beings. We need to be clear on the definitions first. I am also giving you here a neat analytical tool that allows to check and better understand these definitions - an analytical tool which Aquinas did not have available to him.
Aquinas is trying to prove that at least one necessary being exists; and that necessary being is God.
[Notice a big problem for most of Aquinas' proofs: EVEN if he succeeds, why does there to be ONE prime mover or necessary being or designer of the world? Wouldn't it do as well if there were more than one - this means more than one Gods? Of course, as a devout monotheist, Aquinas would not abide by this, but it is a problem his proofs cannot avoid EVEN if they work.]
Definitions: Necessary Being is one that cannot be thought of as not existing. Do what you may, let your imagination rampant, you can never subtract this being, you can never think of the world as a world without this thing.
A Contingent Being, on the other hand, is one that you can think of as not existing.
After you think about it, you should realize that it is odd to claim that ANY necessary being exists. Is there ANYONE you couldn't take out of the world? Even if I am the one who is doing the thinking, I can still take even myself out: I can think of a world that does not contain me. I can take my parents out - I can think of a world that does not have my parents in it, and of course in that case I must follow the consequence that this world does not have me in it either. Bid deal. It seems that there is no one who cannot not exist.
Aquinas is trying to prove that there is a [at least one] NECESSARY BEING and that being is God.
Notice also that in math we can easily think of necessary "beings" - except that these are not beings in the sense of persons, so this does not really help with trying to prove that someone exists. [For instance, the smallest even number, =2, exists necessarily. Try to think of the world and keep taking out anyone you like; you CANNOT take out numbers no matter what you do. Numbers are necessary beings. And if you want to start with an attribute, e.g. the smallest even number which is the number 2, then the number 2 so defined EXISTS NECESSARILY. But would Aquinas say that God is a number? Which number anyway? There is infinity of numbers. So, this does not really help. We need to figure out how a necessary being that is like the beings we know can be said to be necessarily existent.]
Try to follow Aquinas' proof. It is not very easy but, on the other hand, also keep in mind that almost no one is convinced. It is still a good effort.
2) Here is the trick I promised you.
Think of possible worlds. As if you were writing the software program for a video game. You can let your imagination go wild and concoct any kind of world you like. If there is a being that you CANNOT possible omit, no matter what you do, from any such possible world, then this is a NECESSARY BEING. But, here is the problem for Aquinas again: Can you think of any such being?
Try to run this experiment in your mind.
Here is additional guidance on how to think of possible worlds diagrammatically:
Assume we call our world the ACTUAL WORLD = AW
Let’s symbolize it with a straight line:
AW __________________________________________________
Similarly with possible worlds, and we can have any number of them we like: PW1, PW2, PW3, and so on.
PW1 _________________________________________________
PW2__________________________________________________
PW3__________________________________________________
And so on.
A necessary being looks like this:
AW____________________necessary being_________________
PW1___________necessary being_________________________
PW3___________________________necessary being_________
And if I try to imagine any random possible world, no matter how weird this world is, I must still include this necessary being:
PWn________necessary being____________________________
(Obviously it is the same being we are talking about in every case. If more than one necessary beings can be imagined, then each and every one of them will be on the worldline of every possible world you can imagine, as well as on the worldline of the actual world we live in {after all, our actual world must be possible or imaginable as well..})
So, Aquinas’ point is that, no matter how hard you try, there is [at least one] being that you cannot leave out; this being is GOD, indicated by N (necessary being). [Check Aquinas’ proof again for details.
Actual World: _N_---------__________________________________
Possible World 1: ____________N___________________________
Possible World 2: _____________________N___________________
Possible World 3:_______________________________N__________
And so on.
Possible World 1,000,000: __________N_____________________
Possible World 2,000,000: ___N____________________________
No matter how hard you try to imagine a world, you cannot leave this necessary being out.
Possible World N [for any number N]: __N__________________________________________________
A good question is this: Does this necessary have to have the attributes of Aquinas’ God? [Such attributes include being eternal, being omnipotent and being omniscient.]
Also, why does there have to be only one necessary being?
But the most important question: can you imagine a necessary being?
On the other hand, contingent beings look like this.
PW1______contingent being x____________________________
PW2___________________________________________________
PW3______________contingent being x____________________
Or,
PW1___________________________________________________
PW2___________________________________________________
PW3___________________________________________________
PW2220_______contingent being x______________________
PW2221________________________________________________
Or any other combination you like: A contingent being can exist only in one world; or in a million, but not in the millionth-and-first. If there is at least one world, in which the being is not included (it can be left out logically), then it cannot be a necessary being; it is a contingent being.
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