On 19 Jan 2015, at 20:36, meekerdb wrote:
On 1/19/2015 7:23 AM, Bruno Marchal wrote:
On 19 Jan 2015, at 04:51, meekerdb wrote:
On 1/18/2015 7:24 PM, LizR wrote:
On 19 January 2015 at 07:14, meekerdb <meeke...@verizon.net> wrote:
On 1/18/2015 12:16 AM, Jason Resch wrote:
Because 2+2=4, and there's nothing you (or anyone/anything) can
do to change that.
Sure there is. 2+2=0 in mod 4 arithmetic - which is good for
describing some things.
I hope you are being flippant and don't really think that
disproves what Jason has said!
If in doubt consider whether the phrase "in mod 4 arithmetic" was
necessary to what you wrote. If it is, then arithmetic remains
necessarily so until you can come up with something that is self-
contradictory without any such qualifiers being required.
As you must know from my other posts, I don't consider self-
consistency to entail existence. So the fact that 2+2=4 is true
doesn't imply anything about existence.
We suppose that you agree with elementary arithmetic, and notably
with the use of existential quantification.
From 2+2= 4 it is valid to deduce Ex(x + x = 4).
And as we have chosen arithmetic to define the basic ontology, it
means that we have the existence of 2 in the basic ontology. The
rest is playing with words.
You know very well that the "E" of symbolic logic is not the same as
"exists" in English. There are different meanings of existence
determined by context.
That is my point, so each time we use "exist" we must give the
context. Now, in the TOE, one notion of existence can be more
fundamental than another. With computationalism, we can take the "E"
of the logicians doing arithmetic, and all other notion of existence
are recovered by the modal variant of it, like the physical existence
is sum up in
[]<>Ex[]<>P(x), which is itself well defined in arithmetic (without
modal operator) but by a much longer sentences, or collections of
sentences.
Ex(x+x=4) just means there is number
OK.
as defined by Peano's axioms that provably satisfies the expression.
Not at all. That means that PA believes Ex(x+x=4).
Ex(x+x=4) means that N satisfies the idea that there is some number n
having the property that n + n = 4.
The meaning is in the semantics, not in the theory.
It no more proves that 2 exists in the general sense than
Ex(x=Holmes sidekick) proves that Dr. Watson exists.
OK, but with computationalism we use the result that we don't need to
assume anything more than 0, 1, 2, (together with the addition and
multiplication laws).
So, once and for all, we accept that our most primitive object, which
"really" exist are 0, 1, 2, ... and nothing else.
We would use string theory as fundamental theory, we would assume the
strings. But with comp any theory will do, and the less physical it
looks, the more we can explain the physical without assuming it, which
is the goal. (and the necessity for solving the mind-body problem).
Now, we could us S and K, and (K,K), ((K,K),S), etc. instead of 0,
and s(0) ..., as physics and consciousness have been shown to not
depend on the particular ontology used.
That you consider "mod 4" to be a qualifier is just a convention
of language. If we were talking about time what's six hours after
1900: answer 0100, because there the convention is mod 24. But my
serious point is that arithmetic is a model of countable things we
invented and it's not some magic that controls what exists.
OK, but then computationalism is false. What is the magic thing you
believe in making a brain non Turing emulable?
I think a brain is Turing emulable by a physical device.
First a brain is provably emulable by many non physical device, using
the original definition of emulable, by the mathematicians who
discovered the concept. Second, even "physucally emulable" relies on
this mathematical definition, and if that definition leads to many
problems (already discussed a lot here, like Putnama-Mallah
implementation problems, the mind-body problem itself, etc.).
You purport to show that numbers alone are sufficient, but I find
this doubtful. I think your numbers must also instantiate physics
to emulate thought.
Then UDA is wrong somewhere, or you reify magical matter, and a
magical mind, and a magical identity thesis.
In which case it a physical as well as mental theory. That's a
good thing, but I think it's a theory of reality - not necessarily a
proof that reality must be that.
It has to be like that, or you ascribe to universal machine an ability
to distinguish, in direct introspective way, physical from
arithmetical. How? The MGA shows that you *can* do that, only by
adding non Turing emulable magic to both mind and matter.
Bruno
Brent
Bruno
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