Essence and Existence

[Byblos]

PART 2

and second, the reason you make this first faulty assumption is that you are not considering the essence of what it is to be a human being (and more fundamentally the distinction between essence and existence of anything that exists).

I don’t know or understand how you define “essence” and which is the distinction between it and “existence”, please tell me.

I really think this is the crux of this type of debate, i.e. from which worldview vantage point one is arguing. I subscribe to the natural law and by extension to natural theology and classical theism. In my estimation it is the only worldview that can make sense of EVERYTHING. That's the preamble to saying I'm not sure this thread is the place to discuss such topics but I'll leave it to the Mods to decide if they want to split it.

Before discussing essence and existence, let me ask you this question: do you believe that universals exist? By universals I don't mean propositions (although they could be) but abstract ideas that are shared with common things. Take for example the concept of triangularity. Would you agree with me that triangularity exists whether or not any triangles ever existed?

Byblos, I think that you are right. I have split your post in two parts, see above, and I think that it is good to continue part 2 in a separate thread. If I knew what to name it I would have done it already. The issue you raise will need some rounds and it will be difficult to follow that discussion intermingled with the ongoing free will discussion. Do you want to do it or shall I?

To answer your questions I need some time.

Nils

If I could ask one of the mods to split this into a new thread titled "Essence and Existence".

Thanks much.

[Nils]

PART 2

and second, the reason you make this first faulty assumption is that you are not considering the essence of what it is to be a human being (and more fundamentally the distinction between essence and existence of anything that exists).

I don’t know or understand how you define “essence” and which is the distinction between it and “existence”, please tell me.

I really think this is the crux of this type of debate, i.e. from which worldview vantage point one is arguing. I subscribe to the natural law and by extension to natural theology and classical theism. In my estimation it is the only worldview that can make sense of EVERYTHING. That's the preamble to saying I'm not sure this thread is the place to discuss such topics but I'll leave it to the Mods to decide if they want to split it.

Before discussing essence and existence, let me ask you this question: do you believe that universals exist? By universals I don't mean propositions (although they could be) but abstract ideas that are shared with common things. Take for example the concept of triangularity. Would you agree with me that triangularity exists whether or not any triangles ever existed?

If I could ask one of the mods to split this into a new thread titled "Essence and Existence".

Thanks much.

Byblos, I would express me a bit different. Things that have triangular form have existed independent of us for a very long time. We have named such forms “triangular”. If this means that I believe in Universals, I don’t know.

But on the other hand, mathematical theorems as that there are an infinite number of prime numbers have always been valid. Perhaps that’s Universals.

As you see, I am not familiar with the discussion of Universals.

Good to have a new thread!

Nils

[Byblos]

Before discussing essence and existence, let me ask you this question: do you believe that universals exist? By universals I don't mean propositions (although they could be) but abstract ideas that are shared with common things. Take for example the concept of triangularity. Would you agree with me that triangularity exists whether or not any triangles ever existed?

Byblos, I would express me a bit different. Things that have triangular form have existed independent of us for a very long time. We have named such forms “triangular”. If this means that I believe in Universals, I don’t know.

But on the other hand, mathematical theorems as that there are an infinite number of prime numbers have always been valid. Perhaps that’s Universals.

As you see, I am not familiar with the discussion of Universals.

Good to have a new thread!

Actually we're off to a great start. You've already identified 2 types of abstract objects, i.e. 'universals' (let's leave aside for the moment whether or not they actually exist as that will be the subject under discussion), such as triangular, and numbers and mathematical truths such as 2+2=4. There are other types of abstract objects, one I already mentioned, i.e. propositions such as Steve is a bachelor (propositions are either true or false). Yet another type of abstract objects is possible worlds.

So the question is, what are these abstract objects? Do they really exist? If so, where? If not, are they simply constructs of our mind? There are 3 philosophical schools of thought with respect to abstract objects and they are as follows:

• Nominalism, which denies the existence of abstract objects altogether

• Conceptualism, which says abstract objects do exist but only as constructs in the human mind

• Realism, abstract objects are real and are neither constructs of the human mind (they are in fact abstracted by it), nor are they reducible to anything material. Note that there are several types of realism but we'll get to that later.

I will stop here and give you time to do some research and see toward which category you might lean and why.

[Nils]

Before discussing essence and existence, let me ask you this question: do you believe that universals exist? By universals I don't mean propositions (although they could be) but abstract ideas that are shared with common things. Take for example the concept of triangularity. Would you agree with me that triangularity exists whether or not any triangles ever existed?

Byblos, I would express me a bit different. Things that have triangular form have existed independent of us for a very long time. We have named such forms “triangular”. If this means that I believe in Universals, I don’t know.

But on the other hand, mathematical theorems as that there are an infinite number of prime numbers have always been valid. Perhaps that’s Universals.

As you see, I am not familiar with the discussion of Universals.

Good to have a new thread!

Actually we're off to a great start. You've already identified 2 types of abstract objects, i.e. 'universals' (let's leave aside for the moment whether or not they actually exist as that will be the subject under discussion), such as triangular, and numbers and mathematical truths such as 2+2=4. There are other types of abstract objects, one I already mentioned, i.e. propositions such as Steve is a bachelor (propositions are either true or false). Yet another type of abstract objects is possible worlds.

So the question is, what are these abstract objects? Do they really exist? If so, where? If not, are they simply constructs of our mind? There are 3 philosophical schools of thought with respect to abstract objects and they are as follows:

• Nominalism, which denies the existence of abstract objects altogether

• Conceptualism, which says abstract objects do exist but only as constructs in the human mind

• Realism, abstract objects are real and are neither constructs of the human mind (they are in fact abstracted by it), nor are they reducible to anything material. Note that there are several types of realism but we'll get to that later.

I will stop here and give you time to do some research and see toward which category you might lean and why.

I doubt that the way forwards you suggest is possible. I have started reading the Stanford entry on Realism https://plato.stanford.edu/entries/realism/. There are so many alternatives and so many question involved it seems impossible to me to find a position to which I can adhere to. What does “abstract”, “object”, “exist” mean? What areas are we talking about, physics, moral, ethics etc? I can express my preliminary position as I done above but to relate it to the extensive set of ideas, arguments and terminology seems to be a huge project and my experience from similar endeavors is that in the end, I don’t agree fully with anyone. (That depends, I think, on that philosophers mostly have to take positions arguing for those, while I as a layman can pick from the smorgasbord what I like)
What I can say is that I believe that there are entities that “exist” independent of if there are humans or life on other planets. I am thinking of the physical laws, mathematics and probably probably logic. Besides that I doubt that there are Universals that exist outside our minds.

Nils

[Byblos]

Before discussing essence and existence, let me ask you this question: do you believe that universals exist? By universals I don't mean propositions (although they could be) but abstract ideas that are shared with common things. Take for example the concept of triangularity. Would you agree with me that triangularity exists whether or not any triangles ever existed?

Byblos, I would express me a bit different. Things that have triangular form have existed independent of us for a very long time. We have named such forms “triangular”. If this means that I believe in Universals, I don’t know.

But on the other hand, mathematical theorems as that there are an infinite number of prime numbers have always been valid. Perhaps that’s Universals.

As you see, I am not familiar with the discussion of Universals.

Good to have a new thread!

Actually we're off to a great start. You've already identified 2 types of abstract objects, i.e. 'universals' (let's leave aside for the moment whether or not they actually exist as that will be the subject under discussion), such as triangular, and numbers and mathematical truths such as 2+2=4. There are other types of abstract objects, one I already mentioned, i.e. propositions such as Steve is a bachelor (propositions are either true or false). Yet another type of abstract objects is possible worlds.

So the question is, what are these abstract objects? Do they really exist? If so, where? If not, are they simply constructs of our mind? There are 3 philosophical schools of thought with respect to abstract objects and they are as follows:

• Nominalism, which denies the existence of abstract objects altogether

• Conceptualism, which says abstract objects do exist but only as constructs in the human mind

• Realism, abstract objects are real and are neither constructs of the human mind (they are in fact abstracted by it), nor are they reducible to anything material. Note that there are several types of realism but we'll get to that later.

I will stop here and give you time to do some research and see toward which category you might lean and why.

I doubt that the way forwards you suggest is possible. I have started reading the Stanford entry on Realism https://plato.stanford.edu/entries/realism/. There are so many alternatives and so many question involved it seems impossible to me to find a position to which I can adhere to. What does “abstract”, “object”, “exist” mean? What areas are we talking about, physics, moral, ethics etc? I can express my preliminary position as I done above but to relate it to the extensive set of ideas, arguments and terminology seems to be a huge project and my experience from similar endeavors is that in the end, I don’t agree fully with anyone. (That depends, I think, on that philosophers mostly have to take positions arguing for those, while I as a layman can pick from the smorgasbord what I like)

I hear what you're saying as I was in the same predicament when I started looking into such matters. It gets to be overwhelming at times, particularly as laymen (trust me, I'm no philosopher either), to sift through the material and to make sense of it at some basic level beyond physics, ethics and such. But that did not sway me from looking into the most fundamental levels of reality and that entails some presuppositions that we can both hopefully agree on. 1) that the world around us (in fact, reality itself) is intelligible, and 2) that we are rational beings capabale of discovering realty's intellgibility. Let's start with that at least.

What I can say is that I believe that there are entities that “exist” independent of if there are humans or life on other planets. I am thinking of the physical laws, mathematics and probably probably logic. Besides that I doubt that there are Universals that exist outside our minds.

Physical laws depend on the universe in which they operate, which are subsets of the 'possible worlds'. I do agree that mathematics and logic are truly universal and transcend possible worlds. So we can, at least for now, confine the discussion on those three topics. Let me know what you think.

[Nils]

I doubt that the way forwards you suggest is possible. I have started reading the Stanford entry on Realism https://plato.stanford.edu/entries/realism/. There are so many alternatives and so many question involved it seems impossible to me to find a position to which I can adhere to. What does “abstract”, “object”, “exist” mean? What areas are we talking about, physics, moral, ethics etc? I can express my preliminary position as I done above but to relate it to the extensive set of ideas, arguments and terminology seems to be a huge project and my experience from similar endeavors is that in the end, I don’t agree fully with anyone. (That depends, I think, on that philosophers mostly have to take positions arguing for those, while I as a layman can pick from the smorgasbord what I like)

I hear what you're saying as I was in the same predicament when I started looking into such matters. It gets to be overwhelming at times, particularly as laymen (trust me, I'm no philosopher either), to sift through the material and to make sense of it at some basic level beyond physics, ethics and such. But that did not sway me from looking into the most fundamental levels of reality and that entails some presuppositions that we can both hopefully agree on. 1) that the world around us (in fact, reality itself) is intelligible, and 2) that we are rational beings capabale of discovering realty's intellgibility. Let's start with that at least.

1) No problems
2) Yes, In principle. A reservation, even if we have the capability it requires that we can acquire correct evidence. (I am slowly writing on a thread about this.)

What I can say is that I believe that there are entities that “exist” independent of if there are humans or life on other planets. I am thinking of the physical laws, mathematics and probably probably logic. Besides that I doubt that there are Universals that exist outside our minds.

Physical laws depend on the universe in which they operate, which are subsets of the 'possible worlds'. I do agree that mathematics and logic are truly universal and transcend possible worlds. So we can, at least for now, confine the discussion on those three topics. Let me know what you think.

It seems that we agree regarding physics, mathematics and logic so I don’t know what you want do discuss and how that relates to the issue ”essence and existence”, but go ahead.

Nils

[Byblos]

I doubt that the way forwards you suggest is possible. I have started reading the Stanford entry on Realism https://plato.stanford.edu/entries/realism/. There are so many alternatives and so many question involved it seems impossible to me to find a position to which I can adhere to. What does “abstract”, “object”, “exist” mean? What areas are we talking about, physics, moral, ethics etc? I can express my preliminary position as I done above but to relate it to the extensive set of ideas, arguments and terminology seems to be a huge project and my experience from similar endeavors is that in the end, I don’t agree fully with anyone. (That depends, I think, on that philosophers mostly have to take positions arguing for those, while I as a layman can pick from the smorgasbord what I like)

I hear what you're saying as I was in the same predicament when I started looking into such matters. It gets to be overwhelming at times, particularly as laymen (trust me, I'm no philosopher either), to sift through the material and to make sense of it at some basic level beyond physics, ethics and such. But that did not sway me from looking into the most fundamental levels of reality and that entails some presuppositions that we can both hopefully agree on. 1) that the world around us (in fact, reality itself) is intelligible, and 2) that we are rational beings capabale of discovering realty's intellgibility. Let's start with that at least.

1) No problems
2) Yes, In principle. A reservation, even if we have the capability it requires that we can acquire correct evidence. (I am slowly writing on a thread about this.)

Your reservation is well noted. That reality is intelligible does not entail it is wholly discoverable. We are, after all, limited by our contingencies. The point being, if we agree that reality is intellgible (and I think we do), then there must exist an explanation for everything. For if anything whatsoever is inexplicable (noting your reservation above), the entire kit and caboodle as it were collapses.

What I can say is that I believe that there are entities that “exist” independent of if there are humans or life on other planets. I am thinking of the physical laws, mathematics and probably probably logic. Besides that I doubt that there are Universals that exist outside our minds.

Physical laws depend on the universe in which they operate, which are subsets of the 'possible worlds'. I do agree that mathematics and logic are truly universal and transcend possible worlds. So we can, at least for now, confine the discussion on those three topics. Let me know what you think.

It seems that we agree regarding physics, mathematics and logic so I don’t know what you want do discuss and how that relates to the issue ”essence and existence”, but go ahead.

Nils

First to address your point vis-a-vis the relation between essence and existence and universal truths, on the surface they are distinct topics each of which requires in-depth analysis. But they do converge nonetheless, in due time and depending on how far we are both willing to take it.

As to the current topic, there is plenty to be said. Since we seem to agree at minimum that possible worlds (including possible laws of physics), mathematics, and logic are universal truths, this entails two things:

1) that they do in fact exist (at least potentially for all possible worlds with the exception of ours), and
2) that they are independent of the human mind.

I am curious then to know your thoughts on how you explain their existence.

[Nils]

I doubt that the way forwards you suggest is possible. I have started reading the Stanford entry on Realism https://plato.stanford.edu/entries/realism/. There are so many alternatives and so many question involved it seems impossible to me to find a position to which I can adhere to. What does “abstract”, “object”, “exist” mean? What areas are we talking about, physics, moral, ethics etc? I can express my preliminary position as I done above but to relate it to the extensive set of ideas, arguments and terminology seems to be a huge project and my experience from similar endeavors is that in the end, I don’t agree fully with anyone. (That depends, I think, on that philosophers mostly have to take positions arguing for those, while I as a layman can pick from the smorgasbord what I like)

I hear what you're saying as I was in the same predicament when I started looking into such matters. It gets to be overwhelming at times, particularly as laymen (trust me, I'm no philosopher either), to sift through the material and to make sense of it at some basic level beyond physics, ethics and such. But that did not sway me from looking into the most fundamental levels of reality and that entails some presuppositions that we can both hopefully agree on. 1) that the world around us (in fact, reality itself) is intelligible, and 2) that we are rational beings capabale of discovering realty's intellgibility. Let's start with that at least.

1) No problems
2) Yes, In principle. A reservation, even if we have the capability it requires that we can acquire correct evidence. (I am slowly writing on a thread about this.)

Your reservation is well noted. That reality is intelligible does not entail it is wholly discoverable. We are, after all, limited by our contingencies. The point being, if we agree that reality is intellgible (and I think we do), then there must exist an explanation for everything. For if anything whatsoever is inexplicable (noting your reservation above), the entire kit and caboodle as it were collapses.

What I can say is that I believe that there are entities that “exist” independent of if there are humans or life on other planets. I am thinking of the physical laws, mathematics and probably probably logic. Besides that I doubt that there are Universals that exist outside our minds.

Physical laws depend on the universe in which they operate, which are subsets of the 'possible worlds'. I do agree that mathematics and logic are truly universal and transcend possible worlds. So we can, at least for now, confine the discussion on those three topics. Let me know what you think.

It seems that we agree regarding physics, mathematics and logic so I don’t know what you want do discuss and how that relates to the issue ”essence and existence”, but go ahead.

Nils

First to address your point vis-a-vis the relation between essence and existence and universal truths, on the surface they are distinct topics each of which requires in-depth analysis. But they do converge nonetheless, in due time and depending on how far we are both willing to take it.

As to the current topic, there is plenty to be said. Since we seem to agree at minimum that possible worlds (including possible laws of physics), mathematics, and logic are universal truths, this entails two things:

1) that they do in fact exist (at least potentially for all possible worlds with the exception of ours), and
2) that they are independent of the human mind.

I am curious then to know your thoughts on how you explain their existence.

I think that we have to be more precise. I think that there are universal mathematical properties or rules ( I am unsure which is the best wording). But if that means that “mathematics” can be said to “exist”, I don’t know. Perhaps it is preferable to call it “potentially existing” as you do.

With 2) I agree.

You say that “there must exist an explanation for everything”. I don’t agree at all. With a materialistic world view there is no ultimate explanation of everything. With a theistic world view there is a God and I have never heard that a God can be explained. Some say that God doesn’t need an explanation but that is ad hoc.
To me it seems that there is no possible world where for instance the properties of the natural numbers (1, 2, 3, … ) are not valid. I have no idea how to explain that or explain that there is something instead of nothing. I am pretty sure that nobody can do that. When you wrote earlier “1) that the world around us (in fact, reality itself) is intelligible”, I agreed but I should have made a reservation. I don’t think that the origin of everything is knowable or intelligible. But I don’t know if this is important for the further discussion.
Nils

[PaulSacramento]

The difference between "essence" and existence" was explained this way to me:
The essence of something is NOT dependent on it's existence.
2+2=4 would be that even if there were no items to count that equaled 4.
Triangularity would still be something with 3 angled sides even if there were no material triangle sin existence.

While the essence of something may be perfect ( a perfect triangle), what that thing is in existence may not be perfect or may be different from one another ( a triangle that is now drawn perfect, a red triangle as opposed to a blue one, etc).

Hence the essence of what something is MUST be separate from THAT it is.

[Byblos]

I think that we have to be more precise. I think that there are universal mathematical properties or rules ( I am unsure which is the best wording). But if that means that “mathematics” can be said to “exist”, I don’t know. Perhaps it is preferable to call it “potentially existing” as you do.

With 2) I agree.

Stating that some things exist potentially doesn't absolve us of how or where this potentiality exists. In the case of possible worlds and their laws of physics, the number of potentials are obviously infinite but each and every one of which may be instantiated, otherwise they would not be potential. And we know of at least one potential world that was actually instantiated.

Regarding mathematics, I don't agree at all that math is potential (nor is logic for that matter). A square circle is not a potential because it is not a thing to begin with, it is a logical contradiction. Similarly, 2 + 2 = 5 is not a potential that can ever be instantiated in any potential world because it is false. So no, math is not a potential, it is a universal truth and its existence must have an explanation independent of the human mind.

You say that “there must exist an explanation for everything”. I don’t agree at all. With a materialistic world view there is no ultimate explanation of everything.

And that's the self-defeating position materialism necessarily entails. Materialism claims to have a materialistic explanation for everything except explaining the reality in which it makes such claims. If I were to tell you I have a book sitting on a shelf, the shelf has sturdy brackets with solid steel screws and anchors. But the shelf is not attached to anything. Have I explained how the book sits on the shelf? Of course not. That's the materialist's worldview in a nutshell, when it comes to the ultimate explanation they balk and claim brute facts with no explanatory power, therefore nothing is explained.

With a theistic world view there is a God and I have never heard that a God can be explained. Some say that God doesn’t need an explanation but that is ad hoc.

I don't know who you've been talking to but God is neither ad hoc (like the brute facts claimed by materialism) nor lacks an explanation. I meant when I said that everything must have an explanation and that includes God. This ties in with the other thread I was having with our friend the professor, in which I was discussing the Principle of Sufficient Reason.

To summarize:
- Everything must have an explanation
- Either the explanation is extrinsic, in which case the thing explained is contingent on the thing that explains it
- Or the explanation is intrinsic, in which case the thing explained is not contingent on anything but absolutely necessary.

To me it seems that there is no possible world where for instance the properties of the natural numbers (1, 2, 3, … ) are not valid. I have no idea how to explain that or explain that there is something instead of nothing. I am pretty sure that nobody can do that.

But of course we can explain it. My aim in this thread is to show how.

When you wrote earlier “1) that the world around us (in fact, reality itself) is intelligible”, I agreed but I should have made a reservation. I don’t think that the origin of everything is knowable or intelligible. But I don’t know if this is important for the further discussion.
Nils

Of course it's important, it goes to the heart of our discussion. On the one hand, on materialism, there is no ultimate explanation for reality, therefore no ultimate explanation for anything. On the other hand, on theism, there is an explanation for everything, God included.

[neo-x]

Byb, I am enjoying this discussion however, there was a point I'd like to comment on:

mathematics,...is a universal truth and its existence must have an explanation independent of the human mind.

It is not necessary that:
1. Math is a universal truth
It fails on the QM. At the quantum level 1=2, literally.
2. That it is independent of the human mind.

At best these things are up for debate however, you make it seem like accepted facts.

I personally think that mathematics is part of artificial intelligence that humans have created to solve patterns they observe around them. Nothing more. However, again the debate is not settled on this, so just to be the DA, I'd challenge your basic premise.

[PaulSacramento]

Byb, I am enjoying this discussion however, there was a point I'd like to comment on:

mathematics,...is a universal truth and its existence must have an explanation independent of the human mind.

It is not necessary that:
1. Math is a universal truth
It fails on the QM. At the quantum level 1=2, literally.
2. That it is independent of the human mind.

At best these things are up for debate however, you make it seem like accepted facts.

I personally think that mathematics is part of artificial intelligence that humans have created to solve patterns they observe around them. Nothing more. However, again the debate is not settled on this, so just to be the DA, I'd challenge your basic premise.

Math does NOT fail at the quantum level, it simply is, IN THEORY, not the same.
1 never equal 2 at the quantum level, unless of course you can PROVE that.

Remember, a lot of QM is purely speculative theory, which means it may or MAY NOT be correct.

[Byblos]

Byb, I am enjoying this discussion however, there was a point I'd like to comment on:

mathematics,...is a universal truth and its existence must have an explanation independent of the human mind.

It is not necessary that:
1. Math is a universal truth
It fails on the QM. At the quantum level 1=2, literally.

Source please.

2. That it is independent of the human mind.

At best these things are up for debate however, you make it seem like accepted facts.

First, where exactly did I claim it was a settled issue. I certainly do claim it is the only position (that of scholastic realism) that makes the most sense since the other two positions, nominalism and conceptualism (what you seem to have adopted) fail on many levels.

I personally think that mathematics is part of artificial intelligence that humans have created to solve patterns they observe around them. Nothing more. However, again the debate is not settled on this, so just to be the DA, I'd challenge your basic premise.

And again, I did not claim that debate is settled and you are certainly entitled to adopt whatever worldview you wish but at minimum you need to be consistent about it. In my view I see many issues with adopting a worldview where math is not a universal truth but rather a human construct and at the same time claiming to be a theist.

But here's a small challenge to your challenge, if math is a human construct to aid us in explaining certain patterns we observe around us, then how is it possible that we can use this same supposed man-made construct to predict patterns in reality we have yet to observe?

[neo-x]

Any quantum particle exists in [atleast]two states at any given time, Virtualy two realities. Imagine you being in the West and me in Pakistan and we both have a ball in our hand. It is the same ball. So you start bouncing it on the wall and I just put it on the table. So is the ball at rest or is it boucning?

What I meant by 1=2 is precisely that the common assumption that somehow 2+2=4 is a universal truth is simply not true. It is perhaps true in many cases but it will always have that odd exception somewhere. And that IT is not the same. At the QM 2+2 is not four always. 1 may be the same as two. It is the uncertainty in there that makes your earlier statement superflous.

In my view I see many issues with adopting a worldview where math is not a universal truth but rather a human construct and at the same time claiming to be a theist.

I have never seen that. In fact I find this absurd but we can talk about it.

But here's a small challenge to your challenge, if math is a human construct to aid us in explaining certain patterns we observe around us, then how is it possible that we can use this same supposed man-made construct to predict patterns in reality we have yet to observe?

If you could cite an example of such "yet to observe" reality, it will be easier to discuss as it is such a big topic. However, I do think there can be made a good case for it being completely manmade e.g. triangles don't exist in reality, do they?
It is an abstract construct which is very helpful to solve things.

[PaulSacramento]

What I meant by 1=2 is precisely that the common assumption that somehow 2+2=4 is a universal truth is simply not true. It is perhaps true in many cases but it will always have that odd exception somewhere. And that IT is not the same. At the QM 2+2 is not four always. 1 may be the same as two. It is the uncertainty in there that makes your earlier statement superflous

2+2=4 is an observable scientific fact.
Can you show me one observable case in which 2+2 does NOT equal 4 ?