On 03 Oct 2011, at 21:00, benjayk wrote:



Bruno Marchal wrote:

Just a little correction. I wrote (on 30 Sep 2011) :


On 30 Sep 2011, at 17:26, benjayk wrote:

<snip>
The only thing that COMP does is to propose a complicated thought
construct
which essentially reveals its own emptiness. What can COMP possibly
mean?
For it to have any use we have to make a bet grounded on pure
faith... So we
could just as well believe in God,

Why not if you make it enough precise so that people can see the
scientific problem. usually God is used as an empty (indeed) answer.
But with comp, both comp and God is a question, not an answer.



or  - better  -just take the stance of
observing whatever happens! Maybe that we have to bet on an
substitution
level for COMP to have any meaning, and our inability to know any
substitution level should lead us to conclude that there probably
is no
substitution level, or it is undefined, which would just make
sense, given
that apparently COMP is undefined in its very foundations.

So how would react if your daughter want to say yes to a digitalist
doctor? Or what if your doctor says that this is the only chance for
her to survive some disease?

You are using a machine to send this post, which would not even
exist if comp did not make sense.

I mean " ... if comp did not make sense for the reason you gave above".

Obviously computer makes sense even if comp is false. But computer
would not have appeared if we did not grasp the elementary
arithmetical ideas.
But we did grasp the elementary ideas. My point is just that it makes no sense to treat arithmetics as something that is meaningful without concrete
objects.

I don't see why.
Concrete objects can be helpful to grasp elementary ideas about numbers for *some* people, but they might be embarrassing for others.

The diophantine equation x^2 = 2y^2 has no solution. That fact does not seem to me to depend on any concreteness, and I would say that concreteness is something relative. You seem to admit that naive materialism might be false, so why would little "concrete" pieces on stuff, or time, helps in understanding that no matter what: there are no natural numbers, different from 0, capable to satisfy the simple equation x^2 = 2y^2.






If it isn't, the whole idea of an abstract machine as an
independent existing entity goes down the drain, and with it the
consequences of COMP.

Yes. But this too me seems senseless. It like saying that we cannot prove that 17 is really prime, we have just prove that the fiollowing line

.................

cannot be broken in equal non trivial parts (the trivial parts being the tiny . and the big ................. itself).
But we have no yet verify this for each of the following:


.................
.................
.................
.................
.................
.................
.................
.................
.................
.................
.................

etc.

On the contrary: to understand arithmetic, is quasi-equivalent with the understanding that a statement like 17 is prime, is independent of all concrete situation, in which 17 might be represented.









1, 2, 3,... make only sense in terms of one of something, two of
something,... OK, we could say it makes sense to have one of nothing, two of nothing, etc, but in this case numbers are superfluous, and all numbers, and
all computations are equivalent.

I think that 0, 1, 2, and many others are far more simple conceptually than any something you can multiply them by.

But comp needs only that you belief that the elementary arithmetical truth does not depend on you or us (little ego). Are you thinking that if an asteroid rips of humanity from the cosmos, the number 17 would get a non trivial divisor?

That does not make sense, I think.

Bruno


http://iridia.ulb.ac.be/~marchal/



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