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# Greatest Possible Beings and Posets

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I contend that the concept of an objectively Greatest Possible Being ("GPB" for short) isn't a coherent concept. As the concept is about being greater than other things, we're talking about Partially Ordered Sets ("posets" for short).

To argue a fortiori, I will be making the following GPB friendly assumptions:
0) The greatness interval is bound for all Great Making Property ("GMP" for short) orderings.
1) The orderings for all GMP are chains (totally ordered).
2) The greatness orderings for each GMP are objective. There is an objective fact of the matter that more moral is greater than less moral.
3) There are objective GMP. There is an objective fact of the matter as to whether a given property is a GMP.

For the beginning, we'll stick with independent GMP to make things easy and to clearly illustrate the problem.

Let's look at two great-making properties, P and Q.

The value ordering of P is <P, <> = P1 < P2 < ... < Pn.
The greatness ordering of P is <P, ≺> = P1 ≺ P2 ≺ ... ≺ Pn.

Similarly, for Q, we have both value ordering and greatness ordering.

The value ordering for Q is <Q, <> = Q1 < Q2 < ... < Qm.
The greatness ordering for Q is <Q, ≺> = Q1 ≺ Q2 ≺ ... ≺ Qm.

Where "X < Y" is "the value of X is less than the value of Y" and "X ≺ Y" is "X is less great than Y".

Now, consider two beings, A and B, who exemplify both P and Q to varying degrees. Being A exemplifies P7 and Q12, while entity B exemplifies P12 and Q7.

Of the entities A and B, which is greater?

To answer that question, we need to look at the product space: PxQ. That's the set of all possible combinations of values of P and Q.

So, the entity A, on PxQ, corresponds with point (P7, Q12), and, likewise, B corresponds with point (P12, Q7).

Even with the objective ranking, it's not possible to give an objective answer. The product ordering on PxQ only gives a partial ordering, and it's one such that there is no answer as to which of A and B is the greater being [(A ≺ B ) iff ((P(A) ≺ P(B)) and (Q(A) ≺ Q(B)))].

So, the only way to compare them is if one entity is greater in both properties than the other entity. That makes tons of entities not directly comparable.

Each added GMP makes more entities incomparable. If we have three GMP, than one entity is greater than another only if it is greater in terms of all three GMP.

At this point, you might be wondering, "So? GMP has the property value corresponding to the greatest greatness for all properties. It's (Pn, Qm).". And, if we only had independent properties to deal with, you'd have a point. I introduced independent properties first, so you could see that this is a problem with *ALL* GMP. Not all, GMP, however, are independent. The values of some GMP are linked to the value of other GMP. Sometimes, the more one GMP is exemplified, the less another is.

If we then move on to great-making properties such that they aren't independent, but are rather somewhat inversely related (such as moral goodness and potence), then you can't max out the product ordering, since raising one property lowers the other.

They come in pairs:
(P1, Qm), (P2, Qm-1), ... , (Pn-1, Q2), (Pn, Q1)

There is no place in this space of property pairs where one entity is greater than another in all properties. Thus, when we introduce inversely related GMP, we go from losing some ordering to losing all ordering.

There is no objective ordering such that a GPB exists.

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Interesting.... (I think )

I only have a couple of comments:

• Shouldn't GMP be Greatness Making Property? (sorry, am pedantically editing a long document)
• Do we know that there are GMPs that are inversely related? (I am not too convinced by moral goodness vs potence.) I assume it only takes one such pair to confirm your conclusion?

And another thought: can we really have an objective ordering of GMPs? What one person/culture thinks is better might be considered worse by another. But, again, I guess you only need some objective GMPS, rather than all of them being objective.

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50 minutes ago, Strange said:

Interesting.... (I think )

I only have a couple of comments:

• Shouldn't GMP be Greatness Making Property? (sorry, am pedantically editing a long document)
• Do we know that there are GMPs that are inversely related? (I am not too convinced by moral goodness vs potence.) I assume it only takes one such pair to confirm your conclusion?

And another thought: can we really have an objective ordering of GMPs? What one person/culture thinks is better might be considered worse by another. But, again, I guess you only need some objective GMPS, rather than all of them being objective.

Does a chaotic neutral god not have more options for action than a lawful good god?

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1 hour ago, ydoaPs said:

I contend that the concept of an objectively Greatest Possible Being ("GPB" for short) isn't a coherent concept. As the concept is about being greater than other things, we're talking about Partially Ordered Sets ("posets" for short).

To argue a fortiori, I will be making the following GPB friendly assumptions:
0) The greatness interval is bound for all Great Making Property ("GMP" for short) orderings.
1) The orderings for all GMP are chains (totally ordered).
2) The greatness orderings for each GMP are objective. There is an objective fact of the matter that more moral is greater than less moral.
3) There are objective GMP. There is an objective fact of the matter as to whether a given property is a GMP.

For the beginning, we'll stick with independent GMP to make things easy and to clearly illustrate the problem.

Let's look at two great-making properties, P and Q.

The value ordering of P is <P, <> = P1 < P2 < ... < Pn.
The greatness ordering of P is <P, ≺> = P1 ≺ P2 ≺ ... ≺ Pn.

Similarly, for Q, we have both value ordering and greatness ordering.

The value ordering for Q is <Q, <> = Q1 < Q2 < ... < Qm.
The greatness ordering for Q is <Q, ≺> = Q1 ≺ Q2 ≺ ... ≺ Qm.

Where "X < Y" is "the value of X is less than the value of Y" and "X ≺ Y" is "X is less great than Y".

Now, consider two beings, A and B, who exemplify both P and Q to varying degrees. Being A exemplifies P7 and Q12, while entity B exemplifies P12 and Q7.

Of the entities A and B, which is greater?

To answer that question, we need to look at the product space: PxQ. That's the set of all possible combinations of values of P and Q.

So, the entity A, on PxQ, corresponds with point (P7, Q12), and, likewise, B corresponds with point (P12, Q7).

Even with the objective ranking, it's not possible to give an objective answer. The product ordering on PxQ only gives a partial ordering, and it's one such that there is no answer as to which of A and B is the greater being [(A ≺ B ) iff ((P(A) ≺ P(B)) and (Q(A) ≺ Q(B)))].

So, the only way to compare them is if one entity is greater in both properties than the other entity. That makes tons of entities not directly comparable.

Each added GMP makes more entities incomparable. If we have three GMP, than one entity is greater than another only if it is greater in terms of all three GMP.

At this point, you might be wondering, "So? GMP has the property value corresponding to the greatest greatness for all properties. It's (Pn, Qm).". And, if we only had independent properties to deal with, you'd have a point. I introduced independent properties first, so you could see that this is a problem with *ALL* GMP. Not all, GMP, however, are independent. The values of some GMP are linked to the value of other GMP. Sometimes, the more one GMP is exemplified, the less another is.

If we then move on to great-making properties such that they aren't independent, but are rather somewhat inversely related (such as moral goodness and potence), then you can't max out the product ordering, since raising one property lowers the other.

They come in pairs:
(P1, Qm), (P2, Qm-1), ... , (Pn-1, Q2), (Pn, Q1)

There is no place in this space of property pairs where one entity is greater than another in all properties. Thus, when we introduce inversely related GMP, we go from losing some ordering to losing all ordering.

There is no objective ordering such that a GPB exists.

On top of this being the most productive thread in religion since I came here, the proof is flawless...well almost flawless because its missing the GPB coolness ordering but that is always zero so it may be left out. Nevertheless, I think this is ready for the Newton Medal award.

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18 hours ago, koti said:

On top of this being the most productive thread in religion since I came here, the proof is flawless...well almost flawless because its missing the GPB coolness ordering but that is always zero so it may be left out. Nevertheless, I think this is ready for the Newton Medal award.

Newton Medal award? I don't know what that is, but it sounds shiny, and I just can't turn down shiny things.

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4 minutes ago, ydoaPs said:

Newton Medal award? I don't know what that is, but it sounds shiny, and I just can't turn down shiny things.

Oh it is shiny...and its got Isaac with the cool long hair on it:

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On 21.02.2018 at 7:42 PM, ydoaPs said:

There is an objective fact of the matter that more moral is greater than less moral.

Hm.. I don't agree with this statement..

You're trying to use mathematics, to classify human-made concepts like "morality".. What is this "morality"? What is this "greater moral" or "less moral".. ?

If you will kill bug, are you more moral than if you will kill fish?

If you will kill fish, are you more moral than if you will kill cow? How to judge it.. ?

What if that fish, or bug, was new specie which (if you wouldn't kill it) evolve to completely new branch of organisms, which would after millions of years become intelligent, create civilization, and start flying to cosmos.. basically replacing humans after e.g. nuclear war.. ?

How to convert it (human-made concepts like "morality") to math number (integer? real? irrational?), so you will be able to use comparison operator on them.. ?

One of my beloved examples: mass extinction of dinosaurs. From point of view of dinosaurs, it was the end of their life.. the worst est day in their entire history.. From point of view of mammals (at least the one which survived), the greatest thing that could happen.

Now, some humanist-religious person would say "thanks God, that dinosaurs died! He/she did it for us to be able to appear on the Earth!".. and it'll be example of anthropocentrism, misconception which is the core of the all major religions of this world, that Earth was made for humans, and source of many modern problems, with e.g. global warming, destruction and devastation of natural environment, etc. etc.

The same might say successor of fish, or bug, after millions years from now.. "thanks God, that humans died! He/she did it for us to be able to appear on the Earth!"..

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19 minutes ago, Sensei said:

You're trying to use mathematics, to classify human-made concepts like "morality".. What is this "morality"? What is this "greater moral" or "less moral".. ?

I like how Harris lays it out. A good overview on pages 6-10 here: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3501430/#s2title

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1 hour ago, Sensei said:

Hm.. I don't agree with this statement..

You're trying to use mathematics, to classify human-made concepts like "morality".. What is this "morality"? What is this "greater moral" or "less moral".. ?

If you will kill bug, are you more moral than if you will kill fish?

If you will kill fish, are you more moral than if you will kill cow? How to judge it.. ?

What if that fish, or bug, was new specie which (if you wouldn't kill it) evolve to completely new branch of organisms, which would after millions of years become intelligent, create civilization, and start flying to cosmos.. basically replacing humans after e.g. nuclear war.. ?

How to convert it (human-made concepts like "morality") to math number (integer? real? irrational?), so you will be able to use comparison operator on them.. ?

One of my beloved examples: mass extinction of dinosaurs. From point of view of dinosaurs, it was the end of their life.. the worst est day in their entire history.. From point of view of mammals (at least the one which survived), the greatest thing that could happen.

Now, some humanist-religious person would say "thanks God, that dinosaurs died! He/she did it for us to be able to appear on the Earth!".. and it'll be example of anthropocentrism, misconception which is the core of the all major religions of this world, that Earth was made for humans, and source of many modern problems, with e.g. global warming, destruction and devastation of natural environment, etc. etc.

The same might say successor of fish, or bug, after millions years from now.. "thanks God, that humans died! He/she did it for us to be able to appear on the Earth!"..

I don't actually agree with that assumption. It's part of arguing a fortiori. An argument has more force if you make assumptions that make it harder to make your point, but support the point against which you're arguing.

In this case, specifically, denying this assumption in the argument would be tantamount to circular reasoning. It would be arguing that there is no fact of the matter that there is a Greatest Possible Being because there is no fact of the matter that there is no Greatest Possible Being. While logically valid, it's not persuasive, and is in fact an informal fallacy.

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7 hours ago, Sensei said:

nd it'll be example of anthropocentrism, misconception which is the core of the all major religions of this world, that Earth was made for humans

I was under the impression that was almost unique to the Abrahamic religions.

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5 hours ago, Strange said:

I was under the impression that was almost unique to the Abrahamic religions.

Which may, in turn, be a misconception, given the whole meek angle.

On 21/02/2018 at 8:21 PM, koti said:

On top of this being the most productive thread in religion since I came here, the proof is flawless...well almost flawless because its missing the GPB coolness ordering but that is always zero so it may be left out. Nevertheless, I think this is ready for the Newton Medal award.

The logic is flawless, no argument here, so, I have even less reason to believe in a deity (however described). But it also seems to skirt a distinct possibility; god was only ever intended as a teaching aid. It makes sense if you want to teach people too, forgive, tolerate, accept, attempt, help... if your promise of peace ever after is actually true, not because God gave you heaven, but because the promise of peace gave you peace now.

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!

Moderator Note

I've hidden the last few posts as off-topic bickering. Staff request that members involved please refrain from this in the future.

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