Hegel's "Absolute" vs. the "wholly other" (LONG!)
Offline I read a post here from a mathematics student, in which he reasoned that claiming God is infinite does not fit the other things theists claim about God. Honestly I, though being a theist, agree with him. I don't start, as people often do, with the problem of evil and from there either defend or reject the concept of God; I rewrite the model for God, -according- to what I'm pretty sure mathematics tells us about infinity.
At my current stage of thinking, the idea of an omniscient, omnipotent, omnibenevolent god that is also transcendent of all known finite entities is itself contradictory, regardless of whether such entities are considered evil. The error is in the thought that infinity only moves in one direction -- that an object can only be infinitely great or large. However, I like to use particle theory to demonstrate the falsehood of such a thought.
One can take any object visible to us, and examine its apparent infinitely-thorough texture. However, we know that with close enough examination, what becomes apparent is that the object is really a sort of cloud of smaller objects -- atoms. These atoms, we realize now, are themselves groups of particles smaller than the whole of the atom itself. Physicists speculate by a priori logic that one will find a smaller class of matter beyond those particles ("quark" is such a fun word, I love that). I think it's safe to say that there -is- a pattern of increasingly smaller classes of matter, until one realizes that smallness also moves toward infinity.
When applied to models for God, then, one can no longer claim that God is infinite and that this only means certain things, such as that God is above all moral evil (moral entities too small to equal any part of God), or that God is greater than the universe (physical entities too small to equal any part of God). If God can be said to be infinite in size, then God must be infinitely small as well as infinitely great; if God can be said to be infinite in 'holiness', or transcendence from finite moralities, then God must be infinitely close to them as well as infinitely distant from them -- and that's the kicker, there. In order to be infinitely close to something, one must -be- that something, or at least that something must partially compose oneself. Anything less and one is distant from the object. (Side-note: a finite object, then, is never infinitely close to itself, because it is constantly becoming something slightly different.)
Infinity itself, then, if defined positively as "the sum of all things" or "thing-ness (being) itself" would have to be synonymous with the whole of existence. A few theologians have accepted this definition as the proper one for God, and further nuance it into pantheism (such as Spinoza's model) or panentheism (such as Hegel's model).
Many theologians, of which I have only read the Jewish and Christian ones, would rather consider God to be limited in some ways, defining God as did Anselm the medieval theologian -- "of which one can conceive nothing greater" -- and not infinite in the sense I describe. Reasons for doing so often include the concern for God's 'holiness' (or transcendence from evil or finite entities) or their conviction that such definition of God is necessary for human free will to exist.
However, now I don't see how this is logically plausible; as far as I can tell from what I think mathematics teaches us -- unless the mathematicians have been false in their thoughts so far (and I doubt that) -- only infinity itself is 'above' the possibility or reality of a greater (or lesser) entity. (I disagree with the concept of 'possibility' as separate from reality, but I use those terms because people know what I'm talking about when I use them.) I wish I could remember enough from my calculus class, but there are two definitions of infinity, and one is infinity in a practical sense (which I think is what mathematics describes as "transfinite" ) and the other is to simply state, for lack of a better phrase, the infinity that is 'already there' and is not expressed as a stairway moving toward infinity to which there is no conceivable last step, though never itself reaching infinity (because there can always be a higher step). For this reason, in order to say that God is "of that which no greater thing can be conceived," God must be -- again -- either 1) a name for everything or thing-ness/being itself (pantheism) or 2) composed of all things (panentheism).
Of course, dang near all Christians who have heard or read my thoughts about the matter have protested this definition, because logically it not only points to God as the creator of evil things, but eliminates the distinction between creator and creation; God's 'creation' is the developing self of God, though as the infinite whole God is 'unchanging'. Therefore, God is partially composed of all that which humans consider evil. As far as I can see this view of God/existence makes a human conception of morality as relative (some actions are simply better than others; some things are greater than others).
The objection from Christians that conversed with me is the same as some atheists' objection to the existence of God; these objections seem to come from the concern to keep their ideals of morality as distant or transcendent from entities they consider unacceptable, or those things from which they desire to keep distant. If God is 'good' or the greatest thing conceivable, then God as represented by their ideal must keep as far distant from things conceived of as unacceptable as can be conceived. Concerning this, the atheist rejects the usual creator-god model of the monotheists and argues that probably only an extension of the heavens exist beyond what is observable; the theist argues that God created the possibility but not the reality of evil (which finite self-conscious beings created through their actions) or that God created evil to somehow point to the superior goodness of God.
My model (Hegel's model, really) acknowledges both, however -- that God cannot be good and fit the traditional theist model for God, which the atheist also affirms (and concludes that God cannot exist) -- and that God creates evil to point to the goodness of God, because God's goodness is a holistic goodness (morality as a whole by necessity includes those things we would consider insufficient morality for human living).
Now any naturalist-pantheist ("sexed-up atheists" as Richard Dawkins calls them) could look at this and say, "You can stop calling infinity by the name of God, then, if you want, because you no longer believe that the universe was created by a great person." I don't think it's that easy, however. According to Spinoza, God-or-Nature -- rather, God-or-existence, as he might have called God if he knew people would interpret his use of "nature" as only the planets and stars -- is the "being of infinitely many attributes" (slightly revising Wikipedia's term for Spinoza's model for God). Why would it be assumed that in the unity of those infinitely many attributes, there would not be infinite self-consciousness, morality (however it should now be properly understood), and energy/power -- all the things attributed to God in most of the traditional monotheist models? Perhaps the famous paradox of Epicurus should not lead to rejection of God, but to a reworking of how one would understand God.
I'm trying to base all this on a correct understanding of infinity, along with the basic structure of Hegel's panentheistic "Absolute." I am curious as to whether I have understood infinity accurately, at least as far as modern mathematics knows.
Otherwise, please discuss with me what I've said, what it means to you -- whether you agree with it, what you may wonder about any of its implications or logical conclusions that should derive from it.
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Bump -
wow friend , I will say for now , thanks for this interesting after midnight post.
"Perhaps the famous paradox of Epicurus should not lead to rejection of God, but to a reworking of how one would understand God."
..... Me god will rest and be back tomorrow, with gods luck .....
, thanks, GOD
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This view is not accepted anymore, which is good, since the a priori conclusion doesn't make sense. It is generally acknowledged that there is an iron limit to reductionism at the Planck limits. All the Base Planck units designate the various physical constants or the limits that are associated with them because of the properties of matter. The Planck Temperature, of approximately 10^32K, is the hottest possible temperature. Temperature is a direct measure of the average speed of particles within a measured system. Temperature can be increased by an input of energy in an endothermic reaction (this should not be confused with a state change, which does not change the temperature because of the chem. potential). It is meaningless to speak of matter being "hotter" than the Planck temperature since matter breaks down at the Planck temperature into energy (the mass-energy equivalence).
In the same way, the Planck Length and the Planck Time set fundamental limits to reductionism. At the Planck levels on which this occur, motion is said to occur in "jumps". The Planck length is 10^-35m. It is not possible to say anything is "shorter" than 10^-35m. At this length, space-time, which is normally sheet-like and curved in the Einstein Field Equations, becomes foamy and kinked. If matter could be observed at this level, there would be "jumps" between Planck lengths because one cannot "transverse" anything less than 10^-35m. This is usually considered a better answer to Zeno's Paradox than is the notion of the limit in calculus, simply because in integration and differentiation, quantities are split up into infinitesamally small parts that are still existent quality, just not nearly enough to make a difference in the equation. But as an answer to Zeno it operates under the presumption that physical qualities operate in a similar manner. Now it has been suggested that it is likely that they do. Just like the Planck length, there is also the Planck time, which is 10^-35s. There cannot be anything "shorter" than the Planck time, and in the same way that things "jump" rather than transverse in quantum foam through space, so too, through time. The Base Planck units will set the limits for Temperature, Mass, Length, Time and Charge.
"Physical reality” isn’t some arbitrary demarcation. It is defined in terms of what we can systematically investigate, directly or not, by means of our senses. It is preposterous to assert that the process of systematic scientific reasoning arbitrarily excludes “non-physical explanations” because the very notion of “non-physical explanation” is contradictory.
-Me
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I don't think infinity will ever "make sense." It seems like one will come up with paradox no matter how one approaches it. The only reason we try to solve the paradox is to be able to come to a practical level of understanding of how things work, something 'you can work with,' and test with observable concrete objects. Physicists may be content for the time being with Planck units, but it doesn't satisfy philosophers.
A question about physics though: what is fundamentally different with matter and energy? Is there a clear distinction between the two? I thought that matter was simply all substance considered to have mass (which would include energy).
No, not all matter has mass. Most elementary particles have no mass. Photons do not have mass. These things are still called "matter", however (this is disputable, see below). "Mass" is simply that which is the constant of proportionality between force and acceleration, that is to say, when equal force is applied to a more massive body, it will accelerate more than the same amount of force applied to a less massive body , roughly corresponding to "how much" of an object there is, which is not to be confused with molarity, which is a measure of "what number" of objects there is.
Many people are confused and think that matter and energy are the same thing. THey aren't. Mass and energy are the same thing. In relativity, even inertially massless particles have mass because they are never at rest. This means, for example, that an input of energy can increase mass, but in everyday life this is irrelevant since even a single gram of mass is equivalent to over 10e^11J. "Energy" simply constitutes a scalar physical quantity used to do work on bodies, and all things have an associated energy quantity, as a scalar conserved property, constrasted to something like momentum, which is a vector conserved property. As for "matter" the notion is virtually impossible to define. Some people only consider massive bodies to be "matter", therefore excluding things like photons. Other scientists define it as "anything that takes up space". It's not clear and the debate does not show signs of resolution.
"Physical reality” isn’t some arbitrary demarcation. It is defined in terms of what we can systematically investigate, directly or not, by means of our senses. It is preposterous to assert that the process of systematic scientific reasoning arbitrarily excludes “non-physical explanations” because the very notion of “non-physical explanation” is contradictory.
-Me
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I don't believe in zero or negativity as a rational concept. Nothing does not exist; to negate something is rather a convenient way of affirming its existence elsewhere or as arranged in another order. So: the idea of something being completely devoid of, or separate from, -any- existent property seems to be impossible. I could not say if I went for technical accuracy, then, that anything is immaterial, or massless, or inertialess. For instance, I think this concept of "antimatter" is implausible. I'd rather conject that existence as a whole is completely filled without gaps by one substance, and the analysis of this is the spectrum of relative diversity. (How do you move on from such a point? There's no first step 'down' from infinity, is there?) But from that perspective I would argue over classification.
It's really messing with my head, this trying to be a monist.
Concepts of null and negative are only irrational in a sort of material accounting manner. That is, you can't owe people hydrogen in any physical way that I can think of (and hope not to find!). But we have created anti-hydrogen since 1995, being composed of the anti-particles of matter that makes up ordinary hydrogen.
Zero can be viewed simply as an absence. While it is true that nothing, as a state-position in space, does not exist, the concept of zero is still a rational quantity without which many fallacies are averted. For instance: how many lithium particles have I in this vacuum? If, in fact, there are none then I have zero lithium particles. This may seem pedantic, but it's important for other issues I will address shortly.
If I say that I have obtained zero grams of unobtainium, this is not to say that there is unobtainium physically available anywhere. In fact, by etymology we can see that unobtainium is unobtainable no matter what since if you found some it wouldn't be unobtainium. Unfortunately there are no examples of paradoxical elements such as this in the universe save the notes of certain engineers. This is my reductio ad absurdum for the formal fallacy Affirming the Consequent.
I think you are right to conjecture that the universe as a whole is made of something. This something seems to be, in a metaphorical sense, similar to a bitmap. As you noticed yourself there is no step down from what I assume you mean a transfinite state. You wrote infinity, though infinity is an operator used to mean "ever increasing in value" rather than an actual value. Infinity is something you use in relative terms, it's a destination rather than a position. Since we would have to cross vast amounts of infinity to get anywhere in life if the universe was mathematically concrete, movement would be impossible. Thus we come to deludedgod's Planck length, the very pixel dimension of matter.
Planck measurement is a difficult thing to absorb. It is a constant, but it varies depending on where it is used. If an atom is seated on the edge of a bit of warped space, part of the atom will have to work according to one Planck scale, while the other to a different one. Even so, space itself is conserved as the particles that make up the atom will only occupy spaces exactly so many plank lengths apart. We know this as the simplest possible solution for all known physical problems related to this matter.
Perhaps while I have your attention I can address something related. Though there is no integer decrement (step down) from a transfinite number, there are aleph steps up and down from different transfinite number. Similarly there is no such thing as a non-specific real decrement, since you cannot arbitrarily subtract a value from a real number and call it the same thing as the operation performed on another number. For example, the specificity of any real number (numbers with or without decimals) is greater OR lesser than the number of real numbers greater than the given value, but equal to the number of real numbers greater AND lesser than the number. The specificity of any given number makes the comparison between all of the integers and all of the reals look like child's play. This is just the tip of the iceberg as well; the set of imaginary numbers outmatches the reals by several magnitudes.
Thus, since we must agree that all sorts of complexity with influence to reality can be ultimately reduced to a collection of possibly strange numbers, the existence of any god with even basic complexity must have an origin. Since numbers are merely a concept and not a source in themselves it is impossible to have a self-sufficient god that predates everything.
Wikipedia reports these 2 values as approximately 1.616252x10-35m and approximately 5.39121x10-44s, respectively. These values are MUCH LESS CREEPY than having them both be the same number considering that the meter and the second were defined from the size of the earth (also according to Wikipedia) and the speed of the earth's rotation... two seemingly unrelated and cosmically arbitrary measurements.
Rejecting zero for me came from the idea of an unlikely "perfect vacuume" where absolute nothing or zero is true.
Mass, Matter, Energy. These words ( and wild definitions) also totally confound me. I thought mass was a measurement of matter and or energy. The building blocks of m/e being the undiscovered same, and heart of Quantum science, or "theory of everything" ???
I AM not the only dummy reading these science RRS threads !
I can do a bit of parroting e=mc2, but I gave up trying to "really really" digest it. DG helped me a bit with it. Also, the idea of nothing moving faster than 186,000 miles per second is another I can't digest ???
Sadly, this all leads somewhat to the public thinking science is half quackery, and that ain't good ...... Can't this stuff be explained to a 12 yr old, please ???! (me)
Planck Time , Zeno's Paradox ??? How long will this take ?
Goddamn it , What AM I ?????
Frustrating it can be , Buddha said don't worry about it ! 
Okay but I still want to know ..... 
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I did some googling
"Planck time" is the smallest time bit in the universe. Why can't I accept that ?
"Zeno's paradoxes" are a set of problems devised by Zeno of Elea to support
Parmenides' doctrine that "all is one" and that, contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.
Recently, physicists studying quantum mechanics have noticed that the dynamical evolution (motion) of a quantum system can be hindered (or even inhibited) through observation of the system. This effect is usually called the quantum Zeno effect as it is strongly reminiscent of (but not fundamentally related to) Zeno's arrow paradox.
"Quantum Zeno effect"
WTF ? Say again ??? One thing is for sure, I AM definitley retarded ! Is there no cure ?! .....
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Yeah. I was going to point that out, too. I think deludedgod just mixed it up while writing.
It also appears he mixed it up here.
Not that I don't appreciate the physics lessons, especially the bit concerning particle physics (one of my faves from high school many, many moons ago). Please don't think I'm picking, deluded. Really.
Please don't hurt me.
"Yes, I seriously believe that consciousness is a product of a natural process. I find that the neuroscientists, psychologists, and philosophers who proceed from that premise are the ones who are actually making useful contributions to our understanding of the mind." - PZ Myers
Ummm yeah, thanks .... I thought this was backwards ..... but got to thinking, is that possible regarding certain kinds of "energized" particles reacting to one another ? Beats me .....
. . . "when equal force is applied to a more massive body, it will accelerate more than the same amount of force applied to a less massive body" . . .
Hey DG, careful brother .... don't blow yourself up in the lab !
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[small rant]
There is a reason why Schopenhauer hated Hegel. Hegelian "philosophy of history" has been "kaput" since historians realized that history was wissenshaft, not metaphysics....despite what Hegel proposed.
[/end small rant]
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My mistake, it should have been the other way around. When a more massive body has the same acceleration as a less mass body, more force must be applied to cause that acceleration.
"Physical reality” isn’t some arbitrary demarcation. It is defined in terms of what we can systematically investigate, directly or not, by means of our senses. It is preposterous to assert that the process of systematic scientific reasoning arbitrarily excludes “non-physical explanations” because the very notion of “non-physical explanation” is contradictory.
-Me
Books about atheism
Nice point. It was a romantic notion of the 19th century that every atom contained a universe, and that, each atom in that micro-universe contained a universe, ad infinitum.... But the idea is about as sensible as Democritus' belief that atoms were infinitely dense....
Very interesting, I have looked at Planck length as a solution to Zeno's paradox too, as well as falling to discussing potential vs. actual infinities...
Very nice, very interesting. Thank you.
"Hitler burned people like Anne Frank, for that we call him evil.
"God" burns Anne Frank eternally. For that, theists call him 'good.'
How can I feel truly "saved", when I don't know jack shit nothing much ? Well, empathy to that odd one in the mirror, me .....
Ever look at yourself for even a whole hour ?! WTF is going on there ? ..... Some run to the church. I giggle , sip beer, and say hi to the perfect Christ, ME. 
Is mathematics a religion ? What ever it is, I sure do like it. Ummm what's next ?!?! 
The "theory of everything" ! Yeah, cool, as J/B suggested long ago, "All is ONE" ! 
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Mustard:
"You can't owe people hydrogen in any physical way that I can think of ... we have created anti-hydrogen since 1995, being composed of the anti-particles of matter that makes up ordinary hydrogen."
Ah -- I was using only that example. I suppose with hydrogen, my response would that if anti-matter is considered the negative counterpart to matter, I would posit that probably what they are viewing is the interplay between two (positively-defined) forms of substance. I guess all I'm saying is that I don't like defining this newly discovered form of substance merely by its relation to the more visible form of substance we've exclusively called "matter." Physicists should look at more of its relations between other physical elements besides 'matter' to define it more fully.
"Since we would have to cross vast amounts of infinity to get anywhere in life if the universe was mathematically concrete, movement would be impossible."
Hence: Zeno's paradox, yes -- or at least no way of measuring our relation to the One (or whatever one wants to call "the unity of all things" ). We cannot fathom the infinite smallness nor largeness to all that exists, and exactly where we stand within it. The most constant unit of measurement physics currently has (from Planck) still varies in use according to the circumstance to which it is applied or related. The Planck unit itself is a finite object whose relation to various objects will vary. I'd like to read about how it was constructed, and what objects of which it was constructed as a consideration (since, as you said, the meter was constructed considering the size of the Earth).
"The specificity of any given number makes the comparison between all of the integers and all of the reals look like child's play."
Yeah -- I had a conversation with a mathematics professor at my university about my thoughts on this subject, and their descriptions of the same things really made me realize the limits to mathematical thought. (Also: I notice that undergraduate mathematics, and the more serious research afterward, starts to turn into a degree in what amounts to a certain track within 'meta'physics and logic. Makes me wish I could have kept track of numbers long enough to survive to the college stage. But anyway.)
I am confused as how "all sorts of complexity with influence to reality can be ultimately reduced to a collection of possibly strange numbers" leads to that "the existence of any god with even basic complexity must have an origin."
Moving a little ahead of that, before you respond to that point of the discussion, though, I will say: I reject the claims of classical theism, for the same reasons deludedgod explained near the top of your thread.
Ironically, though, the claim of most pantheists that God (or whichever name they choose for the unity of all things) is impersonal seems unfounded to me. Benedictus de Spinoza defines God in his magnum opus, Ethics, in this way: God is "substance consisting of infinitely many attributes." It seems that many pantheists and naturalists make the error of thinking that everything stops more or less at the furthest object from us which we have observed. Sure: our standing definitions of things can only come from that which we have observed, but a priori logic reminds us to predict that there is always more. I predict that indeed, there is the synthesis of "infinitely many attributes," and so wonder why personality, or that which composes personality, does not seem to be included in most conceptions of the pantheist model of God.
I also wonder why deistic notions of the absolute (as completely separate from the subjective) quietly persist in pantheistic models of existence -- that God or the One cannot relate to and is unaffected by subjective entities. It's still an effort to separate the unity from the unified; sure, for practical reasons, when we speak of the unity, we cannot in the same breath describe all of its parts, but technically the unity is inseparable from its unlimited many parts, because 'unlimited unity' and 'unlimited many' (or 'unlimited diversity') are the same or inseparable in being-itself. Therefore: the whole (the 'all-parts') does not only communicate to the parts (the 'some-of-the-wholes'), but there is no whole or parts without relation between the 'two'. God is that which is personal and that which is impersonal; God is that which is 'separate' (distant) and that which is 'unified' (close).
Beyond establishing this thing: what the reasoning person must determine is the best way to relate to the whole, or the other parts of the whole, or the "not-Self" as Bertrand Russell called it. I call that one's ethics, and it's where I see every system of philosophy and every cultural tradition diverge to varying degrees from one another.
P.S. I gotcha on the difference between transfinity and infinity. I quoted Spinoza using "infinitely" as what, if I've paid sufficient attention to your correction, mathematicians would now translate as "transfinitely."
Rook:
I was more making reference to him for his pre-process philosophy and the pantheistic/panentheistic doctrine of God. Whether his optimism about the general direction of the world would survive Schopenhauer's pessimism in a fight, I don't know.
I would say something in the 'middle'. Hegel's claim, that the eventual predominance of the good justifies the existence of evil, is unnecessary, I think. Schopenhauer needed some happy pills or something, but I might agree more with him in saying that that one's attitude toward history should be realistic. One should try to learn history without an attempt to make an ascending moral scale out of it as Hegel did.
Ah, it's been a while. I'd almost forgotten about this! Where to begin. . .
For the sake of simplicity we'll leave out time for the moment, since things come out about the same if you include it. If we enumerate every specific attribute of an entity in such a manner as to completely describe it, for example
1. Entity X is capable of generating a set larger than the number of prime numbers but smaller than the number of semi-prime numbers given a finite period of time.
2. Entity X is more blue than red.
3. ... etc.
then either we must either run out of attributes to describe and enumerate or the list of qualities never ends. In the first case, the set of attributes would be, at most, countable. In the second case, the set would be countably infinite. If an entity has a countable number of attributes then it is finite. I'll call any entity with attributes which change over time dynamic. In order for an entity to do anything it must also be dynamic, since its description must also include some of its history such as
50678. Entity X created a particle at t=7*10^1022.
If the finite entity has always existed then its attributes which relate to its history is not at most countable, which would mean that it can't be a finite entity!
So any entity that has always existed has a transfinite number of attributes. Is it possible to assign a positive integer to every attribute of an entity that has always existed? No, because that would mean that some parts of a dynamic entity's historical attributes would appear before and after the attributes describing its identity. Thus, the only way to sufficiently describe the entity would be to assign reals to each attribute, making it uncountably infinite in complexity.
As you said
there's no such thing as a finite existant that has always existed. There is no identity for that thing which is said to be existing.
Philosophical ethics are always questions of ethics. That is, they are probably best phrased "Do you value X? If so, then you should (or should not) do Y because Z will happen to X if you do/don't." This is why there are no experts on morality - what is moral for person A may be immoral for person B depending on the differences in their situations. Game theory provides an excellent foundation for ethics, but if you examine it you'll see that the outcome depends greatly on the goals of the individual.
Yeah. It's hard to know what Spinoza actually meant in the strictest terms, but I would go with transfinite.