On 15 May 2014, at 04:26, Dennis Ochei wrote:
G*, G, arithmetical hypostases, PA, ZF?
I must not know the lingo round here
In your answer to Liz, you show that you know what ZF (and ZFC) are,
and what PA is.
G and G* are the sound and complete modal logic describing the
behavior of the provability predicate of PA (described in PA), or in
ZF, or actually in any arithmetical sound machine.
G described the logic of provability that the machine can prove, and
G* described the true logic of provability.
For example, take consistency (~[]f = non provable false). G* proves
both ~[]f, and ~[]f -> ~[](~[]f) (Gödel second incompleteness
theorem), but G proves only ~[]f -> ~[](~[]f), as PA or ZF cannot
prove their consistency.
To see the link with "open individualism" you might read my paper (or
any more recent one):
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
I show that if we take seriously the idea that we are digitalizable
machine, then eventually physics is a phenomenological reality
emerging from the machine's dream in arithmetic (or any Turing
universal theory). Then G and G* are used to find the coherence
condition explaining the quantization of arithmetic, and where the
quantum laws come from. You need to understand that your consciousness
is not a product of your body, but more of the infinite relative
bodies (self-representations) that you have in the arithmetical reality.
This eventually forces us to backtrack on Plato's and the mystics'
conception of reality, instead of the current naturalism/materialism
of Aristotle.
Bruno
On Wednesday, May 14, 2014, Bruno Marchal <[email protected]> wrote:
On 14 May 2014, at 06:05, Dennis Ochei wrote:
Under Daniel Kolak's open individualism there exists one
numerically distinct person who is everyone at all times. What I
want to explore is the implications of this theory for a self
interested individual. For those unfamiliar with Open
Individualism, you might instead imagine a demon appears to you,
and informs you that after you die you will experience what it is
like to be every person that ever lived.
I think that is consitent, and perhaps true with comp, but perhaps
not communicable, so, like many good religious idea, to present them
can be too much, and prevent people to discover that by themselves.
It would be a proposition belonging to G* minus G. What can be
justified, is that if comp is true then it follows.
The only rational course of action seems to be to maximize utility
across lives. Meaning if $1 will buy you in your current life 1
unit of utility, but would afford another person 10 units, it would
be rationally self interested to donate the money, if you expect to
experience what they shall experience. This is essentially Singer's
Effective Altruism at work. Are there any other rational courses of
action if Open Individualism is true (or if the hypothetical demon
appeared) and one is self interested?
When amoebas does that, it gives mold, mixomycete.
I am not sure, because it depends what people do with the money, and
with the short term, middle term, long term conflicts.
Social amoebas lives a selfish life until they starve, and then they
make sacrifice and assure the next generations:
https://www.youtube.com/watch?v=5h8WOWEqP6o
"We are all the same person" is close to spoiling the end of the
movie, somehow.
And which "we"? I assume you take all living creatures in arithmetic
from the jumping spider to "divinities" (non computable sets,
oracles).
But OK, the arithmetical hypostases describes an abstract ideally
correct machines instanciated into its infinitely many variants or
extensions. It is a universal person. But with different beliefs and
experiences, and that has its role too.
It is a process of recognition. I recognize myself in PA and ZF, in
some sense.
Bruno
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