Volume 11 Number 45
Produced: Wed Jan 26 23:18:44 1994
Subjects Discussed In This Issue:
G-d and Infinity
[Mitch Berger]
God's Power and Logic
[Bernard Katz]
Heavy Stones
[Frank Silbermann]
more metaphysics
[Jonathan Goldstein]
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From: <mitch@...> (Mitch Berger)
Date: Wed, 5 Jan 94 09:15:01 -0500
Subject: G-d and Infinity
In 11.2 Jonathan Goldstein wrote an eloquent analysis of the nature of
G-d and infinity. To be precise, he touches on three points:
1- What it means for G-d to be infinite,
2- Is G-d above the laws of logic, and
3- Why the holocaust.
I want to discuss each one separately.
----------------------------------------------------
Infinity and G-d
When we describe an attribute of G-d, we can't mean "attribute" in the
normal sense. For G-d to have properties that are not His essence, He
would be divisible. Therefor, the Jewish philosophers take these
"attributes" to be one of two things: 1- descriptions of how G-d relates
to man, 2- descriptions of how G-d is unfathomable by man.
When we describe an attribute of G-d, we can't mean "attribute" in the
normal sense. For G-d to have properties that are not His essence, He
would be divisible. Therefor, the Jewish philosophers [1] take these
"attributes" to be one of two things: 1- descriptions of how G-d relates
to man, 2- descriptions of how G-d is unfathomable by man.
In the first category, we find such terms as Rachum (merciful), Chanun
(kind, generous), Go'el (redeemer), etc... In the latter, there is
Unity, Omnipresence, Omnipotence, Omniscience, and the like. The
Rambam explains (Dalalat al-Hairin I 58):
It has thus been shown that every attribute
predicated of G-d either denotes the quality of an
action, or... the negation of the opposite. Even
these negative attributes must not be formed and
applied to G-d, except in the way which, as you
know, sometimes an attribute is negatived is
reference to some thing, although that attribute can
naturally never be applied to it in the same sense,
as, eg, we say, "This wall does not see."... Thus we
say the heavens are not light, not heavy, not
passive and therefor not subject to impressions, and
that they do not possess the sensations of of taste
and smell; or we use similar negative attributes.
All this we do because we do not know the substance.
There are two ways to understand "infinite." Either we mean (as Jonathan
seems to) transfinite, large without end. Like the number of integers or
the number of real numbers. The other is that the concept related to that
limit is meaningless for the subject we are discussing. In the case of the
unknowable, the Rambam insists that the second usage is intended.
If we were to ask "where is '1+1=2'?" there are two valid answers,
"everywhere" since "1+1=2" is true throughout the universe, and "nowhere"
since the concept of location does not apply to mathematical truths.
The Rambam clearly indicates that G-d's infinity is to be taken in this
second sense. Thus it is true that G-d is everywhere, yet that he is
also remote, in heaven - location is meaningless.
When we say that He is Omnipotent we don't mean that He has infinite
power, rather that "potency" is not a meaningful concept with respect
to G-d. Unfortunately, I can not even explain the previous sentence,
which is why things are stated in their traditional forms.
----------------------------------------------------
G-d and Logic
Can G-d make a square-circle, or a thing which is both red and not-red,
or a rock so heavy even He can't lift it? In other words, must G-d obey
the laws of logic?
This question is more serious than it seems. In Principia Mathematica,
Bertrand Russell derives all of mathematics from the roots of symbolic
logic. This means that if He can not defy logic, he also can not make
pi=3.5. Even worse, if physicists ever get a theory of everything, or
if such a theory exists and is never found, than the laws of nature are
forced by the laws of math which in turn are all derivable from the
laws of logic.
Both extreme positions are supported. The Ramchal (Pischei Chachmah 30)
insists that G-d's omnipotence is absolute, even with regard to things
we would regard as impossible. The Rambam, on the other hand, (ibid
3:15) states:
That which is impossible has a permanent and constant
property, which is not the result of some agent, and
can not in any way change, and consequently we do not
ascribe to G-d the power of doing what is impossible.
No thinking man denies the truth of this maxim; none
ignore it, but such as have no idea of Logic....
Likewise it is impossible that G-d should produce a
being like Himself... to produce a square whose
diagonal is equal to one of its sides....
We have shown that according to each of these theories
there are things that are impossible, whose existence
cannot be admitted, and whose creation is excluded
from the power of G-d, and the assumption that G-d
does not change their nature does not imply weakness
in G-d, or a limit to his power.
R. Aryeh Kaplan, in "Jewish Life - Summer '74" discusses the question
of paradox. He raises a number of classical paradoxes: Omniscience vs
Free-will, Immutability of G-d and Creation, the immobile stone. In
short he concludes that the problem is with man, that we have "double
vision", paralleling the two types of attributes we outlined above.
A very good analogy would be trick glasses in which
the right lens is red and the left is green. Therefor,
if a person wearing such glasses looks at a white paper,
he sees it as red with his right eye, and as green with
his left. If he looks at it through both eyes he
sees some psychedelic mixture of red and green, but under
no conditions can he perceive the color white.
With respect to the stone:
The attributes of action would say that He can create such a stone, "G-d
is omnipotent and can do all things." The negative attributes would indicate
that such a stone could not exist.
So, the authorities are split, yes, no, and all of the above. This leaves
me free reign to speculate.
We defined G-d's omnipotence to mean that G-d gets results without
invoking the notion of "power". Thus, it is meaningless to invoke
the notion of "a rock too heavy for Him to lift" as it is to talk
about "a song too red." G-d cannot just lift a stone of infinite weight,
omnipotence means that weight is a non-issue to what He can lift, just
as color is.
The other question is can G-d defy paradox in general. I'd have to agree
with the Rambam personally, although there is obvious support either way.
My personal preference is because G-d intended us to use logic to come
to understand what we can of Him. If He is above logic, what use is it.
To put it a different way, how can we have this whole discussion if we
didn't already assume that logic works?
The nice thing about logic, however, is that anything can be proven as
long as you pick the right set of postulates. While all of math
including geometry are derivable from boolean logic, there is no
indication that reality has to map to Euclid's postulates. (In fact, it
doesn't.) Math gives us many models, reality only conforms to one/some
of them.
----------------------------------------------------
G-d and the Holocaust
For this one I have two answers. The Rav, in Qol Dodi Dofeq, tells
us that Judaism is about halachah, how to react to the situation.
For Halachic Man, the correct question about the holocaust is not
"why" but "what does this empower me to do?" It is not our job,
or even within our abilities to understand G-d's reasons.
Personally, I realize the truth of this statement, but still need more.
So, much as Huqim are commandments that cannot be understood, yet
have many proposed explanation, I propose exploring history in a
similar spirit.
What is our job to to perfect the self (again, I warn that this is
the misnagdish view only). We are here to become the perfect receptacles
of G-d's goodness in the afterlife.
We tend to think of benevolence as something which increases happiness.
But if we are here for a purpose, then goodness is that which advances
that purposes. Even if we take the more naive view, happiness in the
afterlife, which is infinite in duration, out-weighs happiness in this
finite lifetime.
Either way, G-d's guideline would be "what will help man become the
best receptacle of My Glory?" Not "what will make him happy?" or
"what is fair?"
Unfortunately, this is totally un-verifiable. Since we never know the
"could have beens", we will never know how we would have turned out
had the holocaust never happened. So, we can only accept on faith that
things would have been worse.
| Mitchel Berger, TFI Systems, 26th fl. | Voice: (212) 504-3144 |
| Donaldson, Lufkin & Jenrette | Fax: (212) 504-4581 |
| 140 Broadway New York, NY 10005-1285 | Email: <mitch@...> |
----------------------------------------------------------------------
From: <bkatz@...> (Bernard Katz)
Date: Tue, 4 Jan 1994 21:14:27 -0500 (EST)
Subject: God's Power and Logic
In Vol. 10, No. 87, Jonathan Mark asks:
Did God create logic? If so, how can God be bound by it? If
not, and the universe flows from logic, then how could God be
the creator of the universe?
Discussing this issue, Jonathan Goldstein, in Vol. 11, No. 2, says:
By definition G-d is not bound by any rules. This in itself
applies a (meta)rule to G-d, until it is pointed out that G-d
infinitely transcends all limitation, even an infinite
meta-rule limitation. Accepting this paradox and my inability
to follow it to a logical conclusion is part of recognising
the infinite gap between my mind and G-d.
I think that there is a sense in which God is bound by the
rules of logic; but it doesn't follow that this constitutes a
genuine limitation in God's power.
One of God's essential attributes is omnipotence; i.e., God is
unlimited in power. But what does it mean to say that God is
omnipotent? One answer that someone might venture is that God has
the ability to do anything whatsoever. On this view, it would be
within God's power to violate the laws of logic, to bring about
states of affairs that are logically impossible: for example, bring
it about that someone is at one and the same time exactly 5 feet
tall and exactly 6 feet tall or that some object is both a perfect
sphere and a perfect cube.
This view is, in my opinion, incoherent. And it is one that
the Rambam, amongst others, clearly rejects. The Rambam's
discussion of it is quite instructive; he says:
The impossible has a stable nature, one whose stability is
constant and is not made by a maker; it is impossible to
change it in any way. Hence, the power over the maker of the
impossible is not attributed to the deity. [The Guide, III,
15]
He goes on to give several examples of items that fall outside of
God's power:
Thus, for example, the coming together of contraries at the
same instant and at the same place . . . or the existence of
corporeal substance without there being an accident in it--all
these things belong to the class of the impossible . . . .
Likewise that God should bring into existence someone like
Himself, or should annihilate Himself, or should become a
body, or should change--all these things belong to the class
of the impossible; and the power to do any of these things
cannot be attributed to God.
Does this mean that there are things that God cannot do? In
one sense, it clearly does. For example, God cannot make a triangle
that has four sides. But it would be a mistake to conclude from
this that God's power is somehow limited, that there are things
that He could do if only he were more powerful. Thus, the Rambam
notes:
. . . there are impossible things that whose existence cannot
be admitted. Power to bring them about cannot be ascribed to
the deity. The fact that He does not change them signifies
neither inability nor deficiency of power on His part.
Power extends only to whatever is possible. And there is nothing
that it is possible to do that God's power is inadequate to
accomplish.
A mistaken understanding of the constraints of logic may give
rise to the idea that inability to do the impossible is some sort
of limitation in power. Someone may think that logic constrains
one's behaviour in the same way that, say, physics does, but only
more so. But this is a mistake. In the case of something that is
physically impossible, we can specify an intelligible task, even
though we cannot do it. But in the case of the logically impossible
there is nothing to specify. It is not as though we could bring it
about that a triangle has four sides if only we were stronger, or
smarter, or faster, etc. In the case of what is logically impossible
there is simply nothing to do; whatever we do, we are going to fall
short, not because of a lack in our power or ability but because
there is no intelligible task to do.
Bernard Katz
University of Toronto
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From: Frank Silbermann <fs@...>
Date: Tue, 4 Jan 94 15:34:36 -0500
Subject: Heavy Stones
In an earlier post I wrote:
>>>
>>> It is said that G-d cannot do a logical impossibility
>>> (e.g. to create a stone so heavy that G-d could not lift it).
In Vol.10 #87 Jonathan Mark asks:
>>
>> Did God create logic? If so, how can God be bound by it?
In Vol. 11 #2 Jonathan Goldstein answers:
>
> the fact that this universe is bound by logic does not limit G-d
> in any way. This universe can be thought of as a limitation that G-d
> imposes upon Himself.
Exactly. Let me make an analogy to cricket, an English ball game.
A king is not bound by the rules of cricket. However, should a king
lower himself to compete with his subjects, this implies his submission
to the rules. It is a logical impossibility for him both to play cricket
and to break the rules. Being King, no one could stop him from breaking
the rules at any time, but the moment he does the game ceases to be cricket
(and becomes instead some other unnamed game).
Then Joanathn G. adds:
> As far as we know, *this* universe is bound by logic.
> So G-d will (probably) *not* create a stone too heavy
> (for G-d) to lift in our universe, but that does not mean
> that He cannot do it.
Suppose G-d did create such a stone. Now he cannot lift it.
What kind of a G-d is he?
> If tomorrow G-d creates a stone (so heavy He cannot lift it)
> and places it my backyard, I would only say that my understanding
> of *this* universe is less than I had previously thought.
The assumption is that G-d cannot lift it. If anyone is to place
it in your back yard, it would have to be someone else -- G-d can't do it.
Or are you arguing that G-d could create a logic whereby He both
can and cannot lift the stone. It doesn't take G-d to create
such a logic. I can do it myself. All I have to do is change
the meaning of the word "not." But if we are going to change
the meanings of words mid-argument, then we cannot talk about anything.
------------------------------------------
Frank Silbermann <fs@...>
Tulane University New Orleans, Louisiana USA
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From: <Jonathan.Goldstein@...> (Jonathan Goldstein)
Date: Tue, 4 Jan 94 20:03:50 -0500
Subject: more metaphysics
With reference to my recent (long) post about G-d, Man's ability to understand
Him, and His ability to create a stone that cannot be lifted:
Via private email someone who wishes to remain unnamed very succintly
expressed the following objection:
You had asserted that G-d could create a stone He could not lift - albeit
in a different universe.
I don't accept that answer, and address the issue in a totally different
fashion:
To borrow an example from Isaac Assimov: If I were to ask you "How much
does justice weigh?" - you could not answer this question. The reason
being is that the term "weigh" can only be used in conjunction with
certain nouns - i.e. those exhibiting physical properties. Justice is not
one of them, and the word 'weigh' is meaningless in such a context.
Thus, a meaningless question can have no answer.
By the same token, what happens if an irrestible force hits an immovable
object? Again, this question has no answer because it assumes 2
self-contradictory terms --- irresistable and immovable. Only 1 of those
words can be valid in any context.
Thus, again, since the question is meaningless, there can be no answer.
So, in our case, can G-d create something that He cannot xxx --- this is
again internally inconsistent. The word G-d implies infinity, the mere
existance of something more than G-d contradicts this notion of infinity.
The question obviously subsumes the meaningless possibility of such an
object.
Thus, there can be no answer to a meaningless question.
To which I reply:
Thanks for clearing up my misunderstanding. I agree that the idea of a
non-liftable stone is meaningless to us.
Perhaps I was not explicit enough in my original posting, where I should have
said that any linguistic games are possible and can make "sense" (albeit, not
our idea of "sense") to the Infinite.
However, within the realms of commonly accepted use of natural language,
"unliftable weight", "dry water", and "black visible light" are all
meaningless.
It appears to me that it doesn't make sense to talk about human language
outside the human experience. Once this boundary is crossed, only the
paradoxes win.
--
Jonathan Goldstein <Jonathan.Goldstein@...> +61 2 339 3683
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End of Volume 11 Issue 45
