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 > > 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 > 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."

## Advertising

There is nothing to the kicking-back argument except that you cannot always grasp all the implications of your assumptions immediately. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.