Do you believe that Goldbach conjecture is either true or false? If you agree with this, then you accept arithmetical realism, which is enough for the comp consequences. Do you believe that Church thesis makes sense? That is enough to say that you believe in the 'arithmetical platonia'. People needs to be ultrafinitist to reject the arithmetical platonia. Personnaly I am a bit skeptical on set realism, because it is hard to define it, but for the numbers I have never met people who are not realist about them. Even to say "I am not arithmetical realist" is enough to be an arithmetical realist. A real anti-ariothmetical realist cannot even spaeak about arithmetical realism. You need to be an arithmetical realist to make sense of denying it.

Bruno



On 14 Feb 2011, at 09:23, Stephen Paul King wrote:


From: Jason Resch
Sent: Monday, February 14, 2011 1:13 AM
To: everything-list@googlegroups.com
Subject: Re: Maudlin & How many times does COMP have to be false before its false?


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? >How can entities within a universe that exists in Plato's heaven distinguish it from a universe that does not?


[SPK]

Don’t we need to be able to define exactly what Life is first, in order to know whether or not it is Turing Emulable? AFAIK there is no agreed upon definition of life and the folks that believe that Life is Turing emulable seem to do so as a act of faith, given that there is no evidence at all that such is possible or impossible. Additionally, the existence of the Platonic realm cannot be established by empirical means nor logical necessity even if some famous people wrote papers about it, its existence is mere conjecture. Thus it too is believed as an act of faith. There has not be a resolution to the debate between nominalism and universals that I know of, so the jury is still out on even the objective existence of numbers. I grew up among people with faith like that, except they believed in a God that would condemn mankind to an existence in a lake of fire for not accepting blah blah ... until I realized that it was all a power game to control my mind. Thus am very leery of beliefs that cannot be justified by either empirical evidence or logical necessity or some combination of the two. One can tentatively accept the existence of some entity for the sake of an argument and see what the implications are, but to base one’s ontology on such without very careful deliberation is to engage in the same kind of irrationality that we disdain religions fanatics for. I have been holding back on expressing this thought here, but seriously, we need to step back and reconsider what we are taking for granted in our “reasonings”. I must admit this because I have been advocating for a form of dualism that would claim that numbers and even information has an objective existence of sorts but this dualism is not so bold as the dualism that is inherent in the belief in Platonia. The Platonic realm is obviously not a physical place and thus has to be considered as separate from our world of experience. Roger Penrose seems to be the only person to be up front about this aspect of Platonism and he got his books panned for his honest attempt to defend his claims.

Onward!

Stephen

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