The Ontological Argument and the Loch Ness monster

[Spock]

Hey, everybody. I told myself and told myself I wasn’t going to jump into this discussion, but— Here we go, anyway.

Why wouldn’t you jump in? You are always welcome.

I agree that the concept of the “null-world” and God are mutually exclusive. But all that means is, given the definition of God as the Supreme Being, the concept of the “null-world” becomes meaningless. How could a Supreme Being not exist in all possible worlds?

You put the cart in front of the horse. The ontological argument did not presume anything about God. It was supposed to be the “proof” for God’s existence - without first postulating anything about God.

Maybe the problem is the word “in.” What would it mean for God to exist “in” a possible world? I mean, in one sense, God does not exist “in” any naturally constituted worlds, right? At least not in the sense of “spatially” “in.”

So if what you mean is “spatially in,” I agree; God does not exist “in” the null-world. But this takes away nothing from the classical conception of God. The null-world would have to contain at least one “thing” or relationship: namely, the cause of its existence. If it has no cause of its existence, then it does not exist and we don’t have to worry about it. (The same is true of the one-electron world, and the others.)

If the null-world does have a cause of its existence, at least it “contains” the cause.

You introduced some “cause”. That is not part of the ontological argument either. The ontological argument does not deal with with classical definition of God. I am not arguing here against God’s existence, I am arguing against the “ontological argument”.

The concept of “necessary” existence is simple (and false). We look at all the possible worlds (the ones which have no logical contradiction in them) and analyze if there is at least one entity, which appears in all of them. Not necessarily spatially exists. The number of entities is not specified. It can be any “N” number of entites, where N is some non-negative number. We can set up two possible worlds, where each contains zillions of entites, and there is not one entity which would appear in both of them.

Both the null-world and the one-worlds are without logical contradiction. Therefore by definition, they are possible worlds. By their definition, they are mutually disjunctive. Therefore there is no entity which is “shared” by all the possible worlds, there is no necessary existence. That is all there is to it.

 

[Spock]

So the laws of logic are necessary in every possible world? By the way you have been writing I’m led to believe they rather transcend (which includes in as well) all possible worlds. They’re real are they not…

Perhaps necessary existence of God is in this latter sense of transcendence?

Let’s be precise. The laws of logic are not ontological entites. They abstract constructs of our mind, the mental realization of certain facts about reality.

We “look” at these hypothetical worlds, but we are not in them. In this world we realize the laws of logic, and apply them to those worlds. But these laws are not in those worlds which contain no intelligent beings.

 

[Spock]

Spock:

I am trying to think of “possible worlds” in terms of my “Whole of Reality.” The Whole of Reality presently is what it is. We can conceive of the WOR actualized in different states (other possible WOR’s). However, I cannot conceive of a WOR which is absolutely nothing. I can conceive of the WOR being some being which is empty of everything except himself.

It is a difficult abstraction. When the concept of “zero” was first introduced, there was a tremendous resistence. People argued that there is “one” apple, “two” apples, maybe even a “half” of an apple. But “zero” apple? Or, even worse, “minus one apple”??? They could not make heads or tails of it. It was considered absolute lunacy.

Only much later, after a long time did people accept that it is meaningful to speak of “zero” apple, the lack of an apple. And they eventually realized that having “minus one” apple means that you “owe” one apple to someone else.

Not simple or easy at all. These concepts cannot be “visualized”. But they are very useful abstract concepts. Just like the null-world. The one-worlds are a bit simpler. A hypothetical world with one ontological entity in them. The “N”-world, with exactly “N” ontological entities in them.

 

[Shike]

Let’s be precise. The laws of logic are not ontological entites. They abstract constructs of our mind, the mental realization of certain facts about reality.

If they are the realization of certain facts about reality… then surely the laws of logic are at least implicitly present whether we realize them or not.

We “look” at these hypothetical worlds, but we are not in them. In this world we realize the laws of logic, and apply them to those worlds. But these laws are not in those worlds which contain no intelligent beings.

If “our” laws of logic aren’t in those worlds which contain no intelligent beings, what right do we have to project them onto those worlds?

And if “our” laws of logic end up matching those worlds which contain no intelligent beings, why do we label them specifically “our” laws of logic… they would seem to be the same… somthing transcendental, for they even apply to a null-world as you said.

So just how empty is a null-world? How can you have certain facts about absolutely nothing?

Oh and you probably know this… but Aquinas’ position is that God is uncaused and therefore “always was”/eternal. So he would probably argue that the statement “Something can come from absolutely nothing” is absurd. I think this matches the Catholic position, if I’m not mistaken.

 

[Spock]

If they are the realization of certain facts about reality… then surely the laws of logic are at least implicitly present whether we realize them or not.

What do you mean by “implictly”?

In a world without intelligent beings there is no “music”, even though there is vibration of the air (if there is air). There are attributes of the ontological entities. If there is light, with different wavelengths, the attributes which make “colors” possible are present, but colors are the perception of an organ (the eye) processed by the brain. Without eyes and brain there are no colors, even though the physical attributes which make the colors possible are present.

Let me stress it again: the “attributes” of ontological entities are not ontological entities themselves. In other words they do not exist “on their own”, they exist only as mental models or “images” of the ontological objects.

If “our” laws of logic aren’t in those worlds which contain no intelligent beings, what right do we have to project them onto those worlds?

And if “our” laws of logic end up matching those worlds which contain no intelligent beings, why do we label them specifically “our” laws of logic… they would seem to be the same… somthing transcendental, for they even apply to a null-world as you said.

I never said anything about “our” laws of logic. The laws of logic are simply the realizations of a few facts:

1. “everything is itself”, or “if something is true, then it is true”, or symbolically “A = A”.
2. “something cannot be both true and false at the same time in the same context” or symbolically “A and ~A = 0”
3. “someting and its negation is all there is”, symbolically “A or ~A = 1”.

The first one is called the law of identity, the second one is called the law of non-contradiction and the third one is called the law of excluded middle.

So just how empty is a null-world? How can you have certain facts about absolutely nothing?

The same way as we know that the “lack of an apple” is “zero apple”. The concept of “possible worlds” was introduced as an abstraction. It is not necessary that such worlds are physically actualized. You could argue the same thing about the “zero”, and many people did, for a long time. Zero is the mathematical equivalent of the philosophical concept of the “empty world”.

Oh and you probably know this… but Aquinas’ position is that God is uncaused and therefore “always was”/eternal. So he would probably argue that the statement “Something can come from absolutely nothing” is absurd. I think this matches the Catholic position, if I’m not mistaken.

That is not part of the ontological argument.

 

[Kilbourne]

Greetings:

Touchstone, you said this:

I think we can say #2 is necessarily true, on a transcendental basis; we would not be here to discuss this, if not (and even if one of us is imaginary, one mind must necessarily not be). So I think #2 is true, and necessarily true. To be explicit:

2’) It is necessarily true that some existence is necessary.

Yet you claim to be agnostic as to whether absolute nothingness make sense.

If we hold that some propositions are necessarily true, and we hold that #2 (some existence is necessary) is necessarily true, haven’t we conclusively established that absolute nothingness is impossible?

 

[Kilbourne]

Greetings Spock:

I am still taking your “world” to be my “Whole of Reality”. Given that, in addition to our world as it is presently exists, there other alternative worlds which exist conceptually. Some of them may even be possible (able to be actualized) and others are merely conceivable. I think these categories (actual, possible, merely conceivable) comprise all “worlds.” When we operate within a world, I agree that the concept of nullity makes sense, for then it can operate relatively. But the concept of nullity and the concept of a world are mutually contradictory. To speak of a null world is nonsensical. I think Parmenides was right. All attempts to think of nothingness in an absolute sense end up being self-contradictory.

Something must exist.

 

[Touchstone]

Greetings:

Touchstone, you said this:

Yet you claim to be agnostic as to whether absolute nothingness make sense.

I didn’t claim that. Conceptually, absolute nothingness – the ‘null-world’ as Spock describes it – makes perfect sense. I do not agree that it is necessary that there must be such a world. But it’s a logical possibility, and conceptually coherent.

If we hold that some propositions are necessarily true, and we hold that #2 (some existence is necessary) is necessarily true, haven’t we conclusively established that absolute nothingness is impossible?

No, not at all. Why would that make it impossible?

-TS

 

[Spock]

I am still taking your “world” to be my “Whole of Reality”.

That is fine.

Given that, in addition to our world as it is presently exists, there other alternative worlds which exist conceptually. Some of them may even be possible (able to be actualized) and others are merely conceivable.

How would you differentiate between these two categories?

I think these categories (actual, possible, merely conceivable) comprise all “worlds.” When we operate within a world, I agree that the concept of nullity makes sense, for then it can operate relatively. But the concept of nullity and the concept of a world are mutually contradictory. To speak of a null world is nonsensical. I think Parmenides was right. All attempts to think of nothingness in an absolute sense end up being self-contradictory.

The null-world is just an abstraction. The null-world contains nothing. Therefore it contains no logical contradiction. Therefore it is a possible world. I certainly agree that a null-world cannot be physically actualized, because that would be a contradiction. But to be able to be physically actualized was not a prerequisite for a possible world.

Something must exist.

That is our intuition speaking. Let’s suppose it is true. It does not help the ontological argument, because the “one-worlds” can be physically actualized, and two different “one-worlds” do not have a common element in them. And that is all we need to discard the ontological argument.

 

[Touchstone]

Greetings Spock:

I am still taking your “world” to be my “Whole of Reality”. Given that, in addition to our world as it is presently exists, there other alternative worlds which exist conceptually. Some of them may even be possible (able to be actualized) and others are merely conceivable. I think these categories (actual, possible, merely conceivable) comprise all “worlds.” When we operate within a world, I agree that the concept of nullity makes sense, for then it can operate relatively. But the concept of nullity and the concept of a world are mutually contradictory. To speak of a null world is nonsensical. I think Parmenides was right. All attempts to think of nothingness in an absolute sense end up being self-contradictory.

Something must exist.

I see Spock has already responded to this, and this part isn’t addressed to me, but this explains to me what was otherwise a confusing question you put to me. I understand, I think, why you are struggling with this, the idea of a “null-world” being a contradiction because it is a “kind-of-world” so it has to be something.

The difficulty is resolved by keeping clear the symbols and their referents. A “null world” is a concept in our brains, and is something we treat for practical purposes as a “member of the set of all worlds”. That makes it conceptually a “world”, but only in a practical sense. The void we are referring to by “null-world” is not existentially anything at all. It is the absence of existence. In explicit terms, it’s not a world in any existential sense. So you are correct in seeing a contradiction there, in that the referent of “null world” is actually not a world, but the absence of existence.

This is not a logical contradiction, but rather difficulty in language. Linguistically, anything we conceptually refer to is a de facto thing, even when what we are trying to discuss is the absence of a thing, or the absence of existence; this is the nature of language. This is why “zero” was such a late development in man’s intellectual history and why it was so controversial when it did get integrated into our conceptual toolkit (someone here on this forum, IIRC, was expressing his/her incredulity at the concept even now). Because language is intrinsically positive in its expression, concepts like zero, void, and non-existence must be dealt with as “negative concepts with positive nomenclature”. We must talk about a “null world” as a thing, when conceptually what we mean is the absence of a thing, the absence of all things.

-TS

 

[Kilbourne]

Greetings Touchstone and Spock:

The set of all worlds is comprised of our present world (everything that exists presently) as well as all possible worlds. In order to be possible, a world just has to be conceivable (not nonsensical). It can be very improbable, violate known physical laws, etc. but still bepossible. It just can’t involve a contradiction.

Given that, a null-world cannot be included in the set. A null-world is a contradiction in terms. It purports to be absolutely nothing and something at the same time. Akin to speaking of triangular circles. Nonsense.

 

[Kilbourne]

Spock said above:

The null-world is just an abstraction. The null-world contains nothing. Therefore it contains no logical contradiction. Therefore it is a possible world. I certainly agree that a null-world cannot be physically actualized, because that would be a contradiction. But to be able to be physically actualized was not a prerequisite for a possible world.

If an idea involves a contradiction, then it fails to express anything at all. What is the information content of “The set of all worlds includes a triangular circle”?

 

[Spock]

Greetings Touchstone and Spock:

The set of all worlds is comprised of our present world (everything that exists presently) as well as all possible worlds. In order to be possible, a world just has to be conceivable (not nonsensical). It can be very improbable, violate known physical laws, etc. but still bepossible. It just can’t involve a contradiction.

Given that, a null-world cannot be included in the set. A null-world is a contradiction in terms. It purports to be absolutely nothing and something at the same time. Akin to speaking of triangular circles. Nonsense.

Are you familiar with the concept of “sets”? A set is a collection of some objects, called the “elements”. For example S1 = {1, 3, 5} would be a set with the elements of the first three odd numbers. Another set S2 = {2, 4, 6} is another set with the elements of the first three even numbers. Another one could be S3 = {1, 2, 7}. Sets are usually shown as a list of the elements in curly braces. By the way, the elements do not have to numbers. They can be anything, like S(males) = {Joe, Tom, Steve}, and S(females) = {Lisa, Mary, Agnes, Julie}. S(family) = {father, mother, child, uncle, grandfather,…}.

We can define two operations, the conjunction (let’s use the symbol “+”) and the intersection (let’s use the symbol “*”). The conjunction of S1 and S2 (S1 + S2) is the new set of {1, 2, 3, 4, 5, 6}. The conjunction of S1 and S3 is {1, 2, 3, 5, 7}. The intersection of S1 and S3 (S1 * S3) is the set which contains the common element {1}. The intersection of S1 and S2 (S1 * S2) is an empty set, without any elements at all, usually depicted as 0 (sometimes with a slash across it). Formally 0 = {} a set without elements.

The empty set is exactly the same “thing” as the null world. It is just an abstraction, not a “physical” object. Think about sets as boxes with some things in them. The empty box with nothing in it is the equivalent of an empty set (or the null world).

Let’s concentrate on the one-worlds, which present no such problems.

 

[Kilbourne]

Greeting Spock and Touchstone:

I’ve been thinking about necessary existence and possible worlds.

According to Spock, a necessary being is one which must exist in all “possible worlds.” In order to be possible, a world cannot contain a logical contradiction. for example, a world cannot contain a round square.

Given that, we can conceive of a null-world, one that is completely empty. Since a null-world is a possible world, it is impossible for any one being to be in all possible worlds. It is possible that our candidate for necessary existence is in all other possible worlds, but it cannot, by definition, be in the null-world. Therefore, necessary existence is impossible, there being at least one possible world it cannot reside in.

One-worlds also disprove necessary existence. If it is conceivable for a world to contain only one entity, and it is conceivable for a certain one-world to contain only entity A and for another to contain a different solitary entity B, then again it is impossible for one being to be in all possible worlds. Even if every other possible world contains B, B’s existence is not necessary, there being at least one possible world which does not have B.

Spock claims that the idea of a null-world does not contain a logical contradiction. I have tried to argue that it is a logical contradiction. It purports to be something (a world) and absolutely nothing at the same time.

But even given that, Spock and Touchstone claim that the idea of a one-world still proves necessary existence to be impossible.

But I can think of one entity which exists in each and every possible world, even the null world as Spock has defined it. In each and every possible world there is a world. There must be a “container” to hold all the entities. So we have necessary existence after all. It is inescapable. There has to be one kind of world or another.

 

[Spock]

But I can think of one entity which exists in each and every possible world, even the null world as Spock has defined it.

Well, let’s go back to set theory. Some sets contain other sets as elements, while others do not. My examples S1 = {1, 3, 5} etc… do not contain themselves as elements. The set is a collection, while the elements are numbers. We can create new sets at our leisure, of course. For example S2 = {1, 2, 3, S1}, which would be S2 = {1, 2, 3, {1, 3, 5}}.

The point is that the elements are usually ontological entites, while the “set” is always a logical construct. The “set” does not actually “exist”, it is just a convenient method to group “stuff” together.

So to say that each set, even the empty set contains “something”, namely itself (and therefore not “really” empty) is just a misunderstanding of what sets are.

In each and every possible world there is a world. There must be a “container” to hold all the entities. So we have necessary existence after all. It is inescapable. There has to be one kind of world or another.

No, that is just a misunderstanding. The logical construct called “world”, does not contain itself as an element. The “one”-world, S1 = {1} is not the same as S2 = {1. S1}, which is obvious, since S2 contains 2 elements…

 

[Kilbourne]

Greetings Spock and Touchstone,

Let me take another run at it.

It seems to me that the idea of possible worlds must always begin with the present world as a beginning point. Possible worlds are simply conceivable alternatives to that which presently exists, and they inescapably refer to something existent. This is why it makes no sense to speak of a null-world or a no-world. All talk of Zero and empty sets notwithstanding, when it comes to worlds, we are talking about ontological entities, things that exist. Zero is a useful construct in the realm of numbers, but when applied to reality it is always a relative term. There are 0 apples or whatever. 0 or nothing in the context of the actual world always is relative. There are none of whatever we are interested in. 0, as an attempt to refer to the absence of every thing, makes no sense.

Each possible world constitutes the whole of reality, and in that sense, each possible world is a “one-world,” there being nothing outside of it, no container containing it, and no environment surrounding it. Possible worlds will differ in terms of their constitutent parts.

So with this understanding, it is inescapable that there will be be some world or another, and in that sense, there is necessary existence. How the whole of reality is actualized at any given time is not necessary, but it is necessary that it be actualized somehow or another.

Now the conversation up to this point assumed that Deity is just another ontological object in the world among others. In other words, it is assumed that Deity is just another contingent object. And quite inevitably the possible worlds analysis leads to the conclusion that Deity is contingent and not necessarily existing. But if we conceive of Deity as the whole of what exists, then necessary existence flows from that.

 

[Spock]

Greetings Spock and Touchstone,

Let me take another run at it.

It seems to me that the idea of possible worlds must always begin with the present world as a beginning point. Possible worlds are simply conceivable alternatives to that which presently exists, and they inescapably refer to something existent. This is why it makes no sense to speak of a null-world or a no-world. All talk of Zero and empty sets notwithstanding, when it comes to worlds, we are talking about ontological entities, things that exist. Zero is a useful construct in the realm of numbers, but when applied to reality it is always a relative term. There are 0 apples or whatever. 0 or nothing in the context of the actual world always is relative. There are none of whatever we are interested in. 0, as an attempt to refer to the absence of every thing, makes no sense.

Each possible world constitutes the whole of reality, and in that sense, each possible world is a “one-world,” there being nothing outside of it, no container containing it, and no environment surrounding it. Possible worlds will differ in terms of their constitutent parts.

So with this understanding, it is inescapable that there will be be some world or another, and in that sense, there is necessary existence. How the whole of reality is actualized at any given time is not necessary, but it is necessary that it be actualized somehow or another.

Now the conversation up to this point assumed that Deity is just another ontological object in the world among others. In other words, it is assumed that Deity is just another contingent object. And quite inevitably the possible worlds analysis leads to the conclusion that Deity is contingent and not necessarily existing. But if we conceive of Deity as the whole of what exists, then necessary existence flows from that.

What you say and said before that “something” must exist - which is too vague to be of any help.

But that is not a logical necessity. The null-world is just as free from logical contradictions as our present existence. Nevertheless to say that “something” must exist in all the possible non-null worlds is true, but meaningless. The concept of necessary existence says that the same thing must exist across all the possible worlds - and that is not true.

Even referring to the conceptual deity as an equivalent of the “whole existence” does not help. Any two possible worlds differ in at least one detail, therefore they are not identical. Besides the conventional Christian concept of deity is most certainly separate from the “whole of existence”.

 

[Kilbourne]

Greetings Spock:

How does one prove that something or other must exist? Hopefully someone smarter than me can respond to this better, but here goes.

We know the present actual world exists. But can we conceive of a future state of the world completely devoid of being? Does the idea of no-being refer to anything at all? No. In any other context a word that has absolutely no purchase on reality is meaningless. We can differentiate the mathematical constructs of Zero and Empty Sets which are useful in the abstract, but whenever they are applied to reality they are always used in a relative sense. Yes, we have no bananas, etc. We can never meaningfully say, “Yes, we have no bananas and absolutely anything else (including “we”).”

Take the example of a container. If we say that it has absolutely nothing in it, we have to ask, what then is between the sides of the container? A container with absolutely nothing means that the sides of the container are touching each other with no space in between, in which case we don’t have a container.

So it seems to me that any attempts to refer to absolutely nothing are self-contradictory. I can only conclude that some thing or other is necessary.

 

[Kilbourne]

The concept of necessary existence says that the same thing must exist across all the possible worlds - and that is not true.

Starting with the present world, we can posit our world in future, changed states. The future world is not exactly the same as the present world, but it still has the same identity.

 

[Kilbourne]

Even referring to the conceptual deity as an equivalent of the “whole existence” does not help. Any two possible worlds differ in at least one detail, therefore they are not identical.

As I explained above, they don’t have to be. All we have to work with is 1) the whole of reality (all the presently exists) and its conceivable future states (possible worlds). Any future world is still “our world”, just in a different and changed state.

It doesn’t make sense to think of different, distinct wholes of everything that exists with separate histories. We are, after all, beginning with All That Exists. No separate being is conceivable by definition. There is nothing else presently. Any future state of All That Exists is going to originate from the present whole of reality.

And here is another thought on necessary existence and nothingness. If it is logically impossible in the present world to conceive of no world at all, then it must have been just as impossible to do so in any past world. So there never was a time when absolute nothingness was conceivable.