This is (Possibly, Necessarily) Madness!

Hey guys, remember me?

This school year has been a blast, but it has also kept me busy. I’m by no means down for the count, and with this blog I want to bring everybody up to date on something I’ve been studying on the side and with assistance from faculty. It’s a bit obtuse, and I am by no means an expert, but I hope to be able to simplify it somewhat and make it of interest to you.

We often talk of being logical and rational in respect to how we think and speak. The problem with this is language itself often gets in the way. Because of this, philosophers and mathematicians often use symbolic logic. In its simplest form, it looks something like this.



∴ Q

Translated this would read P implies Q, P, therefore Q. We could say that P stands for “Today is monday” and Q stands for “I will go to class”, which would then read “If today is monday, then I will go to class, today is Monday, therefore I will go to class.” Pretty basic stuff.

Now let’s jump ahead from logic 101 to logic 10-fuckyou. Modal logic. The logic of possibility, necessity and possible worlds (or possible states of affairs). To get into this opens a Pandora’s box of discussion and problems that I am in no mood to write about at the current time. Instead, I’m going to talk about an argument that’s been around for quite some time that a contemporary philosopher gave a shiny new coat using modal logic.

The Ontological Argument (yes, the, because it’s rather famous and I don’t feel the need to discriminate it from other arguments that would fit in that category) is an argument for the existence of God that seeks to get from premise to conclusion through reason and intuition alone. There are two classical formulations which I shall quote at length, mostly to try to fool you into thinking I took a long time writing this when really I just have an uncanny ability to do basic internet “research”. The first is Anselm’s:

“Therefore, Lord, who grant understanding to faith, grant me that,
in so far as you know it beneficial, I understand that you are as we believe and you are that which we believe. Now we believe that you are something than which nothing greater can be imagined.

Then is there no such nature, since the fool has said in his heart: God is not? But certainly this same fool, when he hears this very thing that I am saying – something than which nothing greater can be imagined –
understands what he hears; and what he understands is in his understanding, even if he does not understand that it is. For it is one thing for a thing to be in the understanding and another to understand that a thing is.

For when a painter imagines beforehand what he is going to make, he has in his understanding what he has not yet made but he does not yet
understand that it is. But when he has already painted it, he both has in his understanding what he has already painted and understands that it is.

Therefore even the fool is bound to agree that there is at least in the understanding something than which nothing greater can be imagined, because when he hears this he understands it, and whatever is understood is in the understanding.

And certainly that than which a greater cannot be imagined cannot be in the understanding alone. For if it is at least in the understanding alone, it can be imagined to be in reality too, which is greater. Therefore if that than which a greater cannot be imagined is in the understanding alone, that very thing than which a greater cannot be imagined is something than which a greater can be imagined. But certainly this cannot be. There exists, therefore, beyond doubt something than which a greater cannot be imagined, both in the understanding and in reality.”

To paraphrase:

(1) Suppose (with the fool) that God exists in the understanding

(2) Given our definition, this means that a being than which none
greater can be conceived exists in the understanding alone.

(3) But this being can be conceived to exist in reality. That is, we can conceive of a circumstance in which theism is true, even if we do not believe that it actually obtains.

(4) But it is greater for a thing to exist in reality than for it
to exist in the understanding alone.

(5) Hence we seem forced to conclude that a being than which none
greater can be conceived can be conceived to be greater than it is.

(6) But that is absurd.

(7) So (1) must be false. God must exist in reality as well as in
the understanding.

The second famous formulation is Descartes:

“But if the mere fact that I can produce from my thought the idea of
something that entails everything which I clearly and distinctly perceive to belong to that thing really does belong to it, is not this a possible basis for another argument to prove the existence of God? Certainly, the idea of God, or a supremely perfect being, is one that I find within me just as surely as the idea of any shape or number. And my understanding that it belongs to his nature that he always exists is no less clear and distinct than is the case when I prove of any shape or number that some property belongs to its nature.”

You mad, bro?

Give these arguments careful consideration. It’s easier to see that they are wrong than to see WHY they are wrong. There are several refutations out there and I won’t waste time getting into them. Instead, I’ll show where modern modal logic comes in.

Alvin Plantinga is a theistic philosopher who teaches at Notre Dame in South Bend, Indiana, my old stomping grounds. He took the ontological argument to a whole new level using modal operators. Before looking at the argument, we have to understand something called S5 in modal logic. This axiom basically entails that strings containing both ◊ (possibility) and □ (necessity)are equivalent to the last operator in the string. So:



and ◊□P–>□P.

It’s that last one that is of special interest to us. It reads possibly necessarily P implies necessarily P. See that jump from possibility to necessity? That’s a jump from what is possible in a possible world to what is necessary in all possile worlds (hang with me, bros). Now we’re ready for the modal form of the ontological argument as put forth by Alvin Plantinga in The Nature of Necessity:

1.A being has maximal excellence in a given possible world W if
and only if it is omnipotent, omniscient and wholly good in W; and

2.A being has maximal greatness if it has maximal excellence in every possible world.

3.It is possible that there is a being that has maximal greatness.

4.Therefore, possibly it is necessarily true that an omniscient, omnipotent and perfectly good being exists.

5.Therefore it is necessarily true that an omniscient, omnipotent and perfectly good being exists.

6.Therefore, an omniscient, omnipotent and perfectly good being exists.

How fun is that? Want to know where it goes wrong? You tell me and I’ll talk about it
more in a later post, which I’ll be sure to have out sooner than later.

-Mike S.-


One Response to “This is (Possibly, Necessarily) Madness!”

  1. I’m no philosopher but it looks to me like we’re jumping straight from the possibility of existence to existence. We’re supposing and assuming but proving nothing. It’s possible that Puff the magic dragon is invisible, omniscient, omnipotent and perfectly good and living in my back yard. However, possibility does not dictate reality. Nor does my conception of crazy shit. I can conceive of a lot of crazy shit. …Virgin births, talking snakes, walking dead, compassionate Republicans… But my ability to imagine these things and propose that they are at least possible, proves nothing.

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