Can xians define their ordering?

[Goliath]

Having participated in many verbal battles against xians, I often see them spewing out something about an ordering (eg. "god has a higher moral standard", "xians are greater than atheists", etc).

Yet I have never gotten a rigorous definition of this ordering from a single xian. Not once.

Since there are only two theists on this board that I know of, this probably isn't the place to post this, but since I'm banned from the IIDB (and would never want to go back, even if I were unbanned...), I'll go ahead and ask:

Will a xian ever be able to define this mysterious ordering? Or will this be yet another reason why xians never seem to be able to ever defeat atheists in the arena of religious debate?

[trendkill]

Maybe it would help if you were clearer about what you mean by "ordering", and why Christian ordering of things is different than other types. Are you talking about the concept of "greatness", as in the Ontological Argument, e.g. "that than which nothing greater can be conceived?" If that is what you are talking about, I agree that it seems nonsensical to talk about something being "great" or "perfect" in a general sense, since these things are relative measurements and have no meaning on their own. It's like saying "something than which nothing farther can be conceived". Er, okay, but farther from what? "Farness" is not an attribute that relates to all things in the same way.

[wade-w]

Maybe it would help if you were clearer about what you mean by "ordering", and why Christian ordering of things is different than other types. Are you talking about the concept of "greatness", as in the Ontological Argument, e.g. "that than which nothing greater can be conceived?" If that is what you are talking about, I agree that it seems nonsensical to talk about something being "great" or "perfect" in a general sense, since these things are relative measurements and have no meaning on their own. It's like saying "something than which nothing farther can be conceived". Er, okay, but farther from what? "Farness" is not an attribute that relates to all things in the same way.

In mathematics a partial ordering < on a set S is a binary relation on S such that for all x, y, z in S,

1. x < x (reflexivity)
2. if x < y and y < x then x = y (antisymmetry)
3. if x < y and y < z then x < z (transitivity)

Note that all non-empty subsets of a partially ordered set inherit this ordering.

Now, if X is a subset of a partially ordered set S, then we say:

• The element u of S is an upper bound for X if x < u for all x in X.
• The element s in X is the largest (or greatest) element in X if s is an upper bound for X and is an element of X.

If a set is ordered then we can compare any two elements of the set to see which is "greater." The language Goliath refers to in the OP implies that there is such an ordering on the set of beings. Thus the statement "that than which nothing greater can be conceived" is meaningless until the specific relation that gives the set of beings it's order is defined.

[wade-w]

One more thing on ordered sets: if a partially ordered set S also has the property that for all x, y in S

• One and only one of x = y, x < y or y < x (trichotomous)

then S is said to be totally ordered, and < is a total ordering on S.

Anyway, if I'm not mistaken, Goliath is asking for a definition of the binary relation involved.

[trendkill]

Oh. Possibly the reason that Goliath can't find a rigorous definition of the ordering of the set of beings is because he hasn't found a Christian that knows any more about mathematics than I do.

Maybe a professional philosopher of religion or theologian would have an answer to this.

[wade-w]

Disclaimer: The above posts are what "a rigorous definition of this ordering" means to me. Since the terms "order" and "ordering" have different meanings in different contexts, Goliath could mean something else.

[Goliath]

Yup, wade almost completely nailed what I was after. One correction, though: a totally ordered (or linearly ordered) set X is a partially ordered set where for every x,y in X either x<=y or y<=x.

A couple other definitions:

A set X with a relation <= is said to be quasi-ordered if <= is reflexive and transitive. A quasi-ordering is weaker than a partial ordering. Quasi-orderings come up in various parts of homological algebra.

A partially ordered set X is well ordered if every non-empty subset has a least element (exercise for the reader: prove that a well ordered set is necessarily linearly ordered).

When xians say that one being is "greater" than another, or that one moral system is "higher" than another, I just want what anyone should want: for them to explain precisely what the hell they're talking about.

[viscousmemories]

Originally Posted by Goliath

When xians say that one being is "greater" than another, or that one moral system is "higher" than another, I just want what anyone should want: for them to explain precisely what the hell they're talking about.

I'm not sure I understand this issue, but I'll try anyway. I won't pretend to understand any of the mathematical looking stuff in the posts above ('cause I don't) but does the fact that I can't prove it mathematically mean that I'm mistaken or lying if I say my love for my cat is greater than my love for my neighbor's cat?

[Goliath]

Originally Posted by viscousmemories

but does the fact that I can't prove it mathematically mean that I'm mistaken or lying if I say my love for my cat is greater than my love for my neighbor's cat?

I'm not talking about mathematical proof, I'm talking about definitions. What do you mean by "greater"?

[viscousmemories]

Originally Posted by Goliath

I'm not talking about mathematical proof, I'm talking about definitions. What do you mean by "greater"?

Hmm...

Well first of all there's no reason to believe that every Chrisitian means the same thing in every context when they make that statement. So I don't think "What do Christian's mean when they say..." is ever going to result in a reasonable question.

If I were to make the above hypothetical statement about cat love, though, I suppose I would be trying to express that my love for my own cat is... I guess stronger than my love for my neighbor's cat. But I guess that's the problem I'm seeing with this question. Since 'love' is intangible, it can't really be quantified using material terms like "stronger", can it? Yet most human's seem to believe that it is possible to have a stronger love for one cat than another, don't we?

[Dingfod]

I'd like a cheeseburger, large fries and a chocolate malt.

Oh? You're not taking orders? Damn.


Warren

[seebs]

I would have to reject just about any concept of ordering as at best ill-defined. Certainly, I reject emphatically the notion that Christians are "better" or "greater" than other people; such a notion is actually fairly hard to reconcile with the Gospels. (Yes, I'm aware that many people assert it anyway.)

[seebs]

Oh, as to moral systems: Since I believe that there exists an objective morality, I call that hypothesized system the "highest" moral standard, and other moral standards are "higher" as they approach it. Of course, we can't necessarily tell when a system is closer to this standard, which I think is probably unknowable, and almost certainly unknown.

[Goliath]

Originally Posted by seebs

I would have to reject just about any concept of ordering as at best ill-defined. Certainly, I reject emphatically the notion that Christians are "better" or "greater" than other people; such a notion is actually fairly hard to reconcile with the Gospels.

Thank you.

Oh, as to moral systems: Since I believe that there exists an objective morality, I call that hypothesized system the "highest" moral standard, and other moral standards are "higher" as they approach it. Of course, we can't necessarily tell when a system is closer to this standard, which I think is probably unknowable, and almost certainly unknown.

I'm undecided on whether or not morality is objective...some of it at least seems to be so. However, even if morality is objective, it seems difficult to put a metric on moral standards.

[Goliath]

Originally Posted by viscousmemories

Well first of all there's no reason to believe that every Chrisitian means the same thing in every context when they make that statement.

Very true. I just wish that one of them would specify what they mean by their ordering in that instance.

If I were to make the above hypothetical statement about cat love, though, I suppose I would be trying to express that my love for my own cat is... I guess stronger than my love for my neighbor's cat.

But we're at the same problem: what do you mean by stronger?

Now I will, of course, grant you that your feelings for your cat are different than those for your neighbor's cat. In fact, I don't doubt that such a difference can be detected by some kind of neural scan (or whatever those thingies are that scan your brain for chemical reactions).

It seems difficult to put an ordering on those kinds of feelings, however. Also, keep in mind that we're talking about something different than what was in the OP. IMO, it's easier to get an unrigorous intuitive feel for "my love for my cat is greater than my love for my neighbor's cat" than "god is a higher being than any of us". I still have no idea what is even meant by the latter.

[Goliath]

Originally Posted by warrenly

I'd like a cheeseburger, large fries and a chocolate malt.

Oh? You're not taking orders? Damn.

I'm reminded of a funnier version of a part of The Rock:

"What's wrong with you?! That customer ordered his cheeseburger 5 minutes ago! Take that order, cook!"

"I CANNOT TAKE THAT ORDER!!"

"TAKE THAT ORDER!!"

"I CANNOT TAKE THAT ORDER!!"

[seebs]

Originally Posted by Goliath

I'm undecided on whether or not morality is objective...some of it at least seems to be so. However, even if morality is objective, it seems difficult to put a metric on moral standards.

Indeed.

I am not sure exactly what people mean by a "higher" moral standard, except with appeal to objectivity.

It isn't "closer to my own", because we can recognize another moral standard as higher than our own.

It isn't "more difficult to follow", because "give to charity while juggling" is not generally believed to be a higher moral standard than "give to charity".

It isn't "riskier", because "run in front of traffic" is not a high moral standard at all.

It's... Well, that thing. That I recognize intuitively, but can't explain.

[viscousmemories]

Originally Posted by Goliath

IMO, it's easier to get an unrigorous intuitive feel for "my love for my cat is greater than my love for my neighbor's cat" than "god is a higher being than any of us". I still have no idea what is even meant by the latter.

Ah, I see. I think I have a better idea what you're talking about now. In fact I think this is kinda what I was getting at with my What Are Humans Worth thread. I meant to ask how it is that we order life forms and conclude that human life is at the top of the set. What makes humans higher than ants? Perhaps the answer to that (if we can find one) will give us a hint about this? Or perhaps I don't have the slightest idea what I'm talking about...

[wade-w]

I've seen the trichotomy property defined in both ways. The two definitions seem synonymous to me. Also a quasi-order is often called a preorder. I guess it depends on the text you're using.

If you accept the Axiom of Choice, then you also have to accept that any set can be well ordered (to me, this is a major argument against accepting the AC). Thus this mysterious ordering must exist. However, that still doesn't give us a clue as to what the ordering is, so there's no guarantee that it's being applied correctly, nor is it necessary that the ordering has the usual connotation of "worthiness."

[wade-w]

Originally Posted by viscousmemories

Ah, I see. I think I have a better idea what you're talking about now. In fact I think this is kinda what I was getting at with my What Are Humans Worth thread. I meant to ask how it is that we order life forms and conclude that human life is at the top of the set. What makes humans higher than ants? Perhaps the answer to that (if we can find one) will give us a hint about this? Or perhaps I don't have the slightest idea what I'm talking about...

I think you're right on target, vm.

[Goliath]

Originally Posted by wade-w

I've seen the trichotomy property defined in both ways. The two definitions seem synonymous to me.

Well, technically you can't have a poset with exactly one of x<=y, x=y, or x>=y.

However, I do understand what you mean. You can make an equivalent definition of linear ordering by starting out with < instead of <= and insisting that < be transitive and obey trichotomy (I thought about it for a bit, just to make sure that I didn't make an idiotic mistake...and then looked it up to make certain).

Also a quasi-order is often called a preorder. I guess it depends on the text you're using.

Yes, very true.

If you accept the Axiom of Choice, then you also have to accept that any set can be well ordered (to me, this is a major argument against accepting the AC).

Well, that's the kooky thing about it: you can either accept the AoC or not. Personally, I find that it seems to be more or less consistent with the rest of mathematics. Also, my field (Commutative Algebra) wouldn't be able to go very far without it, since without the AoC, we wouldn't know if every commutative ring with identity had a maximal ideal!

Thus this mysterious ordering must exist.

If we take the AoC, yes. However, good luck finding it!

However, that still doesn't give us a clue as to what the ordering is, so there's no guarantee that it's being applied correctly, nor is it necessary that the ordering has the usual connotation of "worthiness."

Worthiness to whom and in what sense?

[wade-w]

Originally Posted by Goliath

Well, technically you can't have a poset with exactly one of x<=y, x=y, or x>=y.

However, I do understand what you mean. You can make an equivalent definition of linear ordering by starting out with < instead of <= and insisting that < be transitive and obey trichotomy (I thought about it for a bit, just to make sure that I didn't make an idiotic mistake...and then looked it up to make certain).

Yes, and you then define < to be x < y or x = y.

Well, that's the kooky thing about it: you can either accept the AoC or not. Personally, I find that it seems to be more or less consistent with the rest of mathematics. Also, my field (Commutative Algebra) wouldn't be able to go very far without it, since without the AoC, we wouldn't know if every commutative ring with identity had a maximal ideal!

Yeah, there are a lot of fields that rely on the AC for fundamentally important results. Another one is Linear Algebra. Can you imagine not being able to say that every vector space has a basis?

And the AC is so obviously true on the face of it. But when you consider that it's logically equivalent to the Well Ordering Theorem, and leads to other even more counter intuitive results as the Banach Tarski Paradox, I think it can be reasonably called suspect. On the whole I think you're right though, and it's probably better to accept it than not in the long run.

Worthiness to whom and in what sense?

To whomever is defining this ordering, and I've never been quite clear on what exactly sense they mean it.