Re: The logic of atheism

Ben Goren wrote:


> As for the laws of math or logic, I don't think those are what
> anyone has in mind when they are talking about supernatural
> abilities, so I think your use of them to be able to sustain
> the argument that a supernatural being can't exist sort of
> reinforces my point that your argument is fallacious -- you're
> redefining what "supernatural" means and then claiming that
> inability to perform a supernatural act under your definition
> equates to a fundamental impossibility of the supernatural.

Hey, it ain't /my/ problem that theists are too stupid to
understand that math and logic are part of the natural world, too.

Well, as a theist myself, I certainly can't agree with this
pessimisstic estimation of the intelligence of theists, nor can I agree
with your statement below about theists lacking a good understanding of
math and physics. (I don't think I've personally said anything
egregiously foolish in this thread but I welcome polite correction if I
have). More importantly, I don't see how such statements really apply
to the case you're trying to make.

I disagree that math and logic are part of the natural world; I would
say, rather, that they are abstract mental constructs that assist us in
our description of the natural world, but they are not themselves part
and parcel of nature, except insofar as rules like the law of
non-contradiction, like the laws of physics or chemistry, accurately
describe phenomena we observe.

Besides, I've yet to come across a physical impossibility that
couldn't trivially be reduced to a logical one. Take the fact that
it's impossible for me to run a one-minute marathon. A big part of
that impossibility is the fact that my body doesn't have available
to it sufficient energy in a suitable form to accelerate my mass
to the requisite velocity and sustain that velocity against the
various forces for a sufficient period of time. It is, in a very
real sense, an exercise in attempting to make 1 + 1 equal
something quite larger than 2.

It's something altogether different entirely! The reason you cannot
run a marathon in 1 minute isentirely physical. There are no
mathematical or logical reasons why it is impossible for you to
complete this task. (Otherwise, you should be able to supply a formal
proof demonstrating the impossibility!) To run a marathon, you will
need to perform a total amount of work; let's call that amount of work
W, which is given by the instantaneous force you exert, F(d) (against
friction, gravity, viscous drag) integrated over the entire distance
that you travel. Now, to perform W worth of work in 1 minute, you need
to be able to supply power P = (W / 1 minute). But, your body, as a
biochemical machine that can convert energy into work, is, as you say,
unable to supply the power required to accomplish this task. But this
isn't a mathematical or logical limitation; a machine that could supply
sufficient power (a rocket, eg) *could* perform the task. Math simply
comes into play as a tool for expressing the relative amounts of power
required and available and comparing them to see whether the task can
be performed.

To see why math is a mental device rather than a physical reality,
let's do a thought experiment. How would you go about designing an
experiment to demonstrate that 2 + 2 = 4? "Duh", you might say. "Just
put two objects on the table. Then put two more on the table. Now
there are four objects on the table. 2+2=4. QED". But not so fast!
First, you need to define what the concepts "2" and "object" mean in
the first place. After all, what you're calling an object is actually
a system consisting of many atoms, which themselves consist of protons,
neutrons and electrons, which themselves consist of quarks, etc. So
you first have to make the mental distinction to consider an "object"
to be the individual set of such-and-such constituent particles. Very
well; whence do you begin with "two" objects on the table? Again, you
must specify that, for the present purposes, an object is specified by
a set of such-and-such constituent particles AND having a certain
minimum separation from any other similar set of particles. Ok, well
and good. So now you "add" two more objects to the table. What does
"add" mean? Again, here you must define your frame of reference to be
"that set of objects that are present on the table", and to "add" to
the system means to place additional objects onto the table. But this
is rather arbitrary; there were always 4 objects in existence. Your
ability to add them together is enabled on your part to focus your
attention on that subset of objects that are on the table, and to
separate from your consideration that subset of objects that are not.
When the two subsets are placed together in the frame of reference on
the table, the two subsets are said to have been "added", and the total
number of objects now present on the table is 4.

But the crucial thing to notice is that any "math" that has happened
here occured *entirely in your head* -- it is purely a notational
convenience to describe a particular set of relationships observed by
the physical objects, and the physical frame of reference. Math isn't
an inherent property of the universe; it's simply an extremely useful
contrivance for interpreting phenomena and objects that we encounter in
the universe. And the laws of math do not govern the way the universe
behaves -- they are not prescriptive -- but instead give us a set of
precepts that make the language internally consistent.


> Saying that God can't make 1+1=3 is pretty much akin to claims
> like "God can't make a square circle" or "God can't make a rock
> heavier than He can lift".

Well, now you're bringing in a very specific deity who has
a very specific essential supernatural power: omnipotence. And
``omnipotence'' can /only/ mean ``able to do absolutely anything
and everything.''

I would say it means "able to do anything that it is possible to do",
but I don't mean to take us down that path if that's not where you were
going. It's just that you used similar language, and I don't have a
terribly high opinion of the "stone so heavy he can't lift it" line of
reasoning. Your opinion of the cogency of such arguments may differ
from mine.

>
> It's not even clear how the ability to violate these "laws"
> would even be tested, since they are abstract concepts. How
> would God go about making 1+1 = 3? What would that even mean?

He could, as I hinted at above, use more energy than is present in
a system to accomplish some task, without adding energy to the
system.

Again, this would mean doing something in violation of a physical law
-- the law of the conservation of energy. Math only comes into play as
a device to describe how much energy is present in a system *relative
to some standard*. To say "he did 2 J of work with an exertion of only
1 J" is nothing more or less than saying "his act violated the law of
energy conservation -- more work was performed than was supplied". But
this has no mathematical implications that I can see. Again, math is a
language, not an objectively real observable. What would it mean for
God to make 1+1=3, without reference to any explicitly physical object
or system? You said that the laws of mathematics are universal in that
they transcend our particular reality, and would be equally applicable
in any type of universe. Well and good -- then they should be capable
of manifesting themselves without respect to a particular natural
system. Otherwise, violating a rule is simply a violation of one of
the physical rules of that reality, and not a violation of the
underlying mathematics itself.

> The act cannot even be specified, because it is nonsensical,
> just as "making your mother your daughter" or "making a square
> circle" are nonsensical.

But ``making a square circle'' /isn't/ nonsensical. All I have to
do is specify my required parameters for a geometric object and
demand of the supernatural being to construct it for me. Here's my
list:

o Must be done entirely in Euclidian space.

o Must be composed of four straight line segments of equal
length.

o The line segments must intersect at their endpoints and
must form equal angles.

o All points on all four line segments must be equidistant
from a single point.

You have under-specified the problem. Specifying a square with the 2nd
and 3rd criteria above brings along several other restrictions. For
example, a square is an object whose highest symmetry operation is a
four-fold rotation axis -- you can rotate the object 90 degrees and it
remains invariant; it looks exactly the same as it did, and has the
same position and orientation that it had, prior to the rotation.
Let's say that having a 4-fold axis means that the object possesses
property "R4". But the presence of a 4-fold axis precludes the
existance of a parallel three-fold rotation axis unless the axis has an
even higher symmetry (eg, an object with 12-fold rotational symmetry
also has 3- and 4-fold rotational symmetry). But as we said, a
square's highest symmetry axis is 4-fold, and so a square must also
have the property "~R3". Now, a circle, in contrast, has an axis that
has infinity-fold rotational symmetry -- you can rotate it by ANY angle
and the object looks exactly the same. That means that a circle has a
3-fold and 4-fold axis; it has properties R3 and R4. So a square
circle has properties R3 and ~R3, which violates the law of
non-contradiction, and thus is a logical absurdity. The object
*cannot* be specified.

>
> I don't think that shows very much intellectual honesty.
> Wouldnt' you agree that actions like creating the universe,
> foreknowing the future, and rising from the dead sort of go
> beyond parlor trickery? It's legitimate to question whether
> those events occured; I don't think it's reasonable to say that
> they are not of sufficient quality to merit designation as
> "supernatural".

Actually, I think you prove my point rather well with those
examples.


``Creating the universe'' is nonsensical.

Well, since you have previously argued that supernatural abilities must
entail the ability to violate the laws of logic, and since something
that violates the laws of logic is nonsense, then perhaps here we have
an example of what you might consider a supernatural occurence -- the
creation of the universe!

In this context, the only meaningful definition for ``universe'' is ``the set
of everything that exists.''

Say, rather, "the only definition that is convenient for me, Ben Goren,
for the purposes of this discussion" and I'd agree with you. I think
that the "universe" more conventionally refers to the material universe
-- to those entities and phenomena that are governed by the laws of
nature. You can't define nature to be "everything that exists,
including God" and then say "aha! therefore, God is not supernatural.
Therefore the supernatural does not exist. Therefore, God, who is
defined as a being with supernatural capabilities does not exist".
That logic is gravely flawed.

You're making this entire conversation much more philosophical and
mathy than it needs to be to get down to the core issues. We don't
need to appeal to physics or math to come up with an example of a
supernatural occurence-- we can be much more mundane. One thing human
experience teaches us is that if someone dies, and no one intervenes
with any kind of medical assistance, the dead person will stay dead.
Right? No one has ever buried a friend only to find him walking around
the next day. We can't guarantee that such a thing could never ever
ever happen (because our ability to observe nature and exhaustively
understand all physical processes is finite), but we've seen enough of
the world and experienced enough deaths to feel pretty comfortable in
asserting that, yes, once you die, your body will remain dead. But
hold the phone -- there's an account that a long time ago, someone
died, was confirmed to have been dead, was buried in a sealed tomb, and
several days later, the tomb was found to be open and the person was
alive and walking around again. Now, let's say for the sake of
argument that we had sufficient reason to believe that account was true
(a totally separate conversation, I grant). What is the more
reasonable explanation for such an event -- "hmm, I guess there is some
natural process by which people can come to life again!" or "something
outside-of-nature could have been responsible."

I think it's lame in the extreme for you to complain that, because
doctors can resuscitate someone from a state where they are medically
dead, (provided they do so very soon after the person has "died"), that
a person who was dead, cold, in the ground for three days, subsequently
rising wouldn't really be sufficiently impressive to count as a
"supernatural" occurence. We can agree to disagree on this one, but I
think your position is highly unreasonable.

-Jeff

.

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