On 26 Oct 2015, at 07:32, Stathis Papaioannou wrote:
On 26 October 2015 at 17:08, Bruce Kellett
<[email protected]> wrote:
On 26/10/2015 5:01 pm, Russell Standish wrote:
On Mon, Oct 26, 2015 at 03:40:45PM +1100, Bruce Kellett wrote:
I think Carroll's Paradox (or 'What the Tortoise Said to Achilles')
effectively undermines computationalism, or any argument that
arithmetic is prior to physics.
See: https://en.wikipedia.org/wiki/What_the_Tortoise_Said_to_Achilles
In order to escape the paradox, you have to resort to a formalist
approach, and that renders the formalism devoid of semantic content.
I don't see why that undermines computationalism. Could you please
expand?
Modus ponens is only a formal manipulation of symbols, with no
semantic content.
This is an argument John Searle has made. The problem is, the brain
can also be described as manipulating symbols with no semantic
content - so where does semantic content come from?
It can be see as a not to bad formulation of the mind body problem.
And a large part of theoretical computer science and mathematical
logic studies just that. The semantics is the theory of models. The
proof theory, or the computation theory is related with rule
preserving truth. So a rule, like the modus ponens, preserve the
tautologicalness (truth in all worlds/models/interpretation)?
There is a semantical notion of entailment. A entails semantically B
when All models which satisfies A satisfies B. A theory is "complete"
when this makes the (theory + A) capable of deducing B.
The main of logic consists in the relation between theories/machines
with their proofs/computations and their semantic and semantic
preserving transformations.
With computationalism, we have the math of the ideal case of a simple
(Löbian, self-referentially correct in a Gödel+Tarski sense) machine.
This per se does not solve the mind-body problem, but it helps to make
clearer the formulation, with the beginning of the reason why the
universal machine can't solve it in a communicable way, for its
"ultimate" first person view (eventually describing []p & p, but with
some weakening on "[]".
Price: super Everett vertigo, I guess. But in this list, I mean we are
supposed to be every-thingers not fearing Everett, or the more
"obvious" multiplications of the computations in the elementary
arithmetical reality.
It is up to someone believing in any thing not definable in arithmetic
used for consciousness support to show what it is, and how does it
select the computation: how can a universal number distinguish a
physical universal number emulated by an arithmetical universal number
from a physical universal number emulated by a physical universal
number?
Bruce Kellet is right. If you believe that a physical numbers can do
that, but not a digital number, then say no to the computationalist
surgeon.
I don't know the truth, I just look at the consequences.
Bruno
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Stathis Papaioannou
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