# Re: Maudlin & How many times does COMP have to be false before its false?

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On Feb 15, 12:12 am, Jason Resch <jasonre...@gmail.com> wrote:
> 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
>
> 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
> number.
>
> 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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There is  nothing to the kicking-back argument except that you cannot
always grasp all the