On Mon, Feb 14, 2011 at 11:23 AM, Brent Meeker <meeke...@dslextreme.com>wrote:

>  On 2/13/2011 11:24 PM, Jason Resch wrote:
> On Mon, Feb 14, 2011 at 12:52 AM, Brent Meeker <meeke...@dslextreme.com>wrote:
>>  On 2/13/2011 10:13 PM, Jason Resch wrote:
>> On Sun, Feb 13, 2011 at 10:46 AM, Brent Meeker 
>> <meeke...@dslextreme.com>wrote:
>>> On 2/13/2011 5:21 AM, 1Z wrote:
>>>> On Feb 12, 3:18 am, Brent Meeker<meeke...@dslextreme.com>  wrote:
>>>>>  What do you think the chances are that any random object in
>>>>>>>> Plato's heaven, or any random Turing machine will support
>>>>>>>> intelligent life?
>>>>>>>> 1 in 10, 1 in 1000, 1 in a billion?
>>>>>>>  Zero.
>>>> Does that allow us to argue:
>>>> 1) A universe selected from an uncountably infinite number of
>>>> possibilities has measure
>>>> 0
>>>> 2) Our universe exists so it has measure>0
>>>> 3) Our universe is not selected from uncountably infinite
>>>> possibilities
>>>> 4) MUH indicates any universe must be selected from uncountable
>>>> infinite possibilities (since all
>>>> of maths includes the real line, etc)
>>>> 5) MUH is false.
>>>  Hmmm.  I think we argue that objects in Plato's heaven and Turing
>>> machines are not the right kind of things to support life.
>> I am very puzzled by this statement.  You could help me understand by
>> answering the following questions:
>> Why couldn't there be an accurate simulation of life on a Turing machine?
>>  Because a Turing machine is an abstraction.  If you mean a realization
>> of a Turing machine, then I suppose there could be a simulation of life on
>> it.
>> How can entities within a universe that exists in Plato's heaven
>> distinguish it from a universe that does not?
>>  I doubt that Plato's heaven exists.  So no universes would exist in it.
>> Brent
> Exists is a funny word.  It seems to embody knowledge and opinion from one
> observer's viewpoint based on their own limited experiences and interactions
> within their local portion of reality.
> Indeed.  I'm not sure it's unqualified use is meaningful.
>  If Plato's heaven is such a thing that contains all possible structures,
> does the fact that it contains all possible structures hold true whether or
> not it exists?
> All possible brick structures?  Please explain as precisely as possible
> what Platonia is.
>  If there are universes existing abstractly inside Plato's heaven, and
> some of those universes contain conscious observers, does ascribing the
> property of non-existence to Plato's heaven or to those universes make those
> observers not conscious, or is the abstraction enough?
> What does "abstractly existing" mean.?  How is it different from just
> exsiting?
>   What properties can something which is non-existent have?
> It seems there are two choices: 1. Things which are non-existent can have
> other properties besides non-existence.
> Sure.  Sherlock Holmes is non-existent and has the property of being a
> detective.
>  E.g., a non-existent universe has atoms, stars, worlds, and people on
> some of those worlds.  Or 2. Non-existent things cannot have any other
> properties besides non-existence.  It sounds like you belong to this second
> camp.
> However, this seems to lead immediately to mathematical realism.  As there
> are objects with definite objectively explorable properties in math.  7's
> primality and parity are properties of 7.  But how can 7 have properties if
> it does not exist?  If non-existent things can have properties, why can't
> consciousness be one of those properties?  What is the difference between a
> non-existent brain experiencing a sunset and an existent brain experiencing
> a sunset?
> Only one of them exists.
>  Please explain as precisely as possible what it means for something to
> not exist.
> If I can kick it and it kicks back it exists.
> Brent

What do you think about this passage from Fabric of Reality, where David
Deutsch argues numbers do "kick back":

"*Do* abstract, non-physical entities exist? Are they part of the fabric of
reality? I am not interested here in issues of mere word usage. It is
obvious that numbers, the laws of physics, and so on do ‘exist’ in some
senses and not in others. The substantive question is this: how are we to
understand such entities? Which of them are merely convenient forms of
words, referring ultimately only to ordinary, physical reality? Which are
merely ephemeral features of our culture? Which are arbitrary, like the
rules of a trivial game that we need only look up? And which, if any, can be
explained only in a way that attributes an independent existence to them?
Things of this last type *must* be part of the fabric of reality as
{222} defined in this book, because one would have to understand them
in order to
understand everything that is understood.

This suggests that we ought to apply Dr Johnson's criterion again. If we
want to know whether a given abstraction really exists, we should ask
whether it ‘kicks back’ in a complex, autonomous way. For example,
mathematicians characterize the ‘natural numbers’ i, 2, 3,... in the first
instance through a precise definition such as:

1 is a natural number.

Each natural number has precisely one successor, which is also a natural

1 is not the successor of any natural number.

Two natural numbers with the same successor are the same.

Such definitions are attempts to express abstractly the intuitive
*physical*notion of successive amounts of a discrete quantity. (More
precisely, as I
explained in the previous chapter, that notion is really
quantum-mechanical.) The operations of arithmetic, such as multiplication
and addition, and further concepts such as that of 1 prime number, are then
defined with reference to the ‘natural numbers’. But having created abstract
‘natural numbers’ through that definition, and having understood them
through that intuition, we find that there is a lot more that we still do
not understand about them. The definition of a prime number fixes once and
for ill which numbers are primes and which are not. But the
*understanding*of which numbers are prime — for instance, how prime
numbers are distributed
on very large scales, how clumped they are, how ‘random’ they are, and why —
involves a wealth of new insights and new explanations. Indeed, it turns out
that number theory is a whole world (the term is often used) in itself. To
understand numbers more fully we have to define many new classes of abstract
entities, and postulate many new structures and connections among those
structures. We find that some of these abstract structures are related to
other intuitions that we already had but  {223}  which, on the face of it,
had nothing to do with numbers — such as *symmetry, rotation*, the *continuum,
sets, infinity*, and many more. Thus, abstract mathematical entities we
think we are familiar with can nevertheless surprise or disappoint us. They
can pop up unexpectedly in new guises, or disguises. They can be
inexplicable, and then later conform to a new explanation. So they are
complex and autonomous, and therefore by Dr Johnson's criterion we must
conclude that they are real. Since we cannot understand them either as being
part of ourselves or as being part of something else that we already
understand, but we *can* understand them as independent entities, we must
conclude that they *are* real, independent entities.

Nevertheless, abstract entities are intangible. They do not kick back
physically in the sense that a stone does, so experiment and observation
cannot play quite the same role in mathematics as they do in science. In
mathematics, *proof* plays that role. Dr Johnson's stone kicked back by
making his foot rebound. Prime numbers kick back when we prove something
unexpected about them especially if we can go on to explain it too. In the
traditional view, the crucial difference between proof and experiment is
that a proof makes no reference to the physical world. We can perform a
proof in the privacy of our own minds, or we can perform a proof trapped
inside a virtual-reality generator rendering the wrong physics. Provided
only that we follow the rules of mathematical inference, we should come up
with the same answer as anyone else. And again, the prevailing view is that,
apart from the possibility of making blunders, when we have proved something
we know with *absolute certainty* that it is true.

Mathematicians are rather proud of this absolute certainty, and scientists
tend to be a little envious of it. For in science there is no way of being
certain of any proposition. However well one's theories explain existing
observations, at any moment someone may make a new, inexplicable observation
that casts doubt on the whole of the current explanatory structure. Worse,
someone may reach a better understanding that explains not only all existing
observations but also why the previous explanations seemed to work but are
nevertheless quite wrong. Galileo, for instance, found  {224}  new
explanation of the age-old observation that the ground beneath our feet is
at rest, an explanation that involved the ground actually moving. Virtual
reality — which can make one environment seem to be another — underlines the
fact that when observation is the ultimate arbiter between theories, there
can never be any certainty that an existing explanation, however obvious, is
even remotely true. But when proof is the arbiter, it is supposed, there can
be certainty."

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