Leibniz's Modal Proof for God's Existence

[The_Exodus]

Personally, I’m not a fan of modal ontology to prove anything, since it seems to me to alienate “being” from reality and make it a concept or “mere” predicate. But I know some are adherents to the Anselmian logic. In fact, many great thinkers have found the ontological proof convincing: St. Bonadventure, Descartes, and Leibniz for example.

I wanted to present Leibniz’s proof here because it is much more condensed and simpler than any other ontological proof I’ve read, and it doesn’t rely on a “perfect” being (which calls into question all sorts of ideas as to what “perfection” means) but only a “necessary” one (although this may raise the same sort of questions in the end.)

Anyway, here it is:

If a necessary being is possible, it actually exists.
For let us suppose it does not exist - from that I shall argue like this:
A necessary being does not exist, by the hypothesis.
Whatever does not exist can possibly not exist.
It is falsely said of whatever can possibly not exist that it cannot not-exist.
Of whatever it is falsely said that it cannot not-exist, it is falsely said that it is necessary.
For necessary is that which cannot not exist.
Therefore it is falsely said that a necessary being is necessary.
This conclusion is either true or false.
If it is true, it follows that a necessary being implies contradiction, or is impossible, because contradictory things are demonstrated of it, namely that it is not necessary. For a contradictory conclusion can be shown only when a thing implies contradiction.
If the conclusion is false, it is necessary that something is wrong with the premises. yet the hypothesis can only be false because of the premises, namely that a necessary being does not exist.
Therefore we have concluded that a necessary being is either impossible or exists.
Therefore if we define God as ens a se [being from itself], or as a being from whose essence existence follows, or as a necessary being, it follows that if God is possible he actually exists.

 

[tonyrey]

1. A sceptic could say that a necessary being is a figment of the imagination.
2. It is necessary to explain why there must be a necessary being.
3. It is logically possible that there is an infinite series of contingent beings.
4. It is also logically possible that the first being(s) appeared spontaneously!

 

[Anselm33]

Interesting. Thanks.
Anselm

 

[The_Exodus]

1. A sceptic could say that a necessary being is a figment of the imagination.

Well, the proof moves forward from the idea that “a necessary being is possible.” So long as this is conceded, one can move on. The sceptic would have to claim “a necessary being is not possible.” Or, as I would probably do (since I reject Ontologism) the sceptic could say that “necessary being” adds nothing provable, and perhaps nothing even intelligible to “being” proper.

2. It is necessary to explain why there must be a necessary being.

Actually, a necessary being needs no explanation outside itself, else it would not be necessary.

3. It is logically possible that there is an infinite series of contingent beings.

Actually, this is logically impossible, given that no set of contingents, regardless of the number, is necessary, since necessity is in mode or quality, rather than in number or quantity.

As some would say, the metaphysically necessary cannot be individuated into parts or pieces. It must be whole.

4. It is also logically possible that the first being(s) appeared spontaneously!

Eh… I tend to disagree.

 

[MindOverMatter2]

What if I ask you, why is this particular being necessary as opposed to other beings which are not? Why is it different from other beings. Wouldn’t you then need to invoke inductive qualifiers other than necessity? I think so.

Thus I conclude that the meaning of necessary would come under attack. For example if we are not merely talking about the meaning of a “word”, but rather a distinct being with a distinct nature, one must ask what a necessary being is exactly that we must think of it as necessary. How does one get beyond semantics? I can state in words that If I bounce a ball this implies that the ball would have to be bouncing on something “real”, it would require a necessary ground of some sort. But by stating this I have not demonstrated by this fact alone that this so called ground necessarily exists in reality, let alone the ball. I have merely stated a conceptual truth. I cannot say that it is real just because it is necessary in-order for the ball to bounce. It is true that if I did have a ball in reality and I bounced it, it would bounce on a real ground of some sort; but I have to first have a real ball and then bounce it in order to “know” that the ground exists in reality. In other words, apart from myself, I only have initial knowledge of a things existence through an inductive inference of some sort. Necessity is just a word if we cannot demonstrate its reality. If one cannot determine a things objective nature deductively, then one can only infer it inductively as that which must exist in order to account for the “existence” of other natures which we “know” to exist. It is only by induction that we come to understand that a thing is necessary, simply because it must be in-order to account for something already existing.

 

[tonyrey]

            *1. A sceptic could say that a necessary being is a figment of the imagination.*

It does not seem possible to prove that a necessary being is impossible if “necessary being” is understood to mean “the Source of all that exists”.

2. It is necessary to explain why there must be a necessary being.

Actually, a necessary being needs no explanation outside itself, else it would not be necessary.

That is true but we still need to explain the basis for our belief in the Necessary Being.

3. It is logically possible that there is an infinite series of contingent beings*.*

Actually, this is logically impossible, given that no set of contingents, regardless of the number, is necessary, since necessity is in mode or quality, rather than in number or quantity.

I was using the term “contingent” simply to distinguish them from “necessary” without meaning to imply that physical necessity is a reality! I should have just written: It is logically possible that there is an infinite series of beings.

As some would say, the metaphysically necessary cannot be individuated into parts or pieces. It must be whole.

But the sceptic can dispute the very notion of metaphysical necessity. It is not self-evident that an unknown being **must **exist - unless we accept the principle of causality as absolute and an extraordinary meaning of the term “being”.

4. It is also logically possible that the first being(s) appeared spontaneously!

Eh… I tend to disagree.

I disagree that the first being(s) appeared spontaneously but I don’t see why it is logically impossible