- Contemporary messages sorted: [ by date ] [ by thread ] [ by subject ] [ by author ] [ by messages with attachments ]

From: Marchal <marchal.domain.name.hidden>

Date: Tue Jun 26 08:24:16 2001

Joel wrote:

*>If we cannot program it... it's not a Theory of EVERYTHING. It's just a
*

*>description.
*

You really should be an intuitionist mathematicien. It is consistent

with most intuitionist mathematical system that

1) all function from N to N is computable.

2) all function from R to R is continuous.

In my approach the intuitionist philosophy

correspond to the first person viewpoint.

But I'm a Platonist, at least about numbers and functions from N to N.

This includes a lot of uncomputable functions. For exemple the function

which gives for each n the greatest number you can compute in fortran

with program of length n. (This function grows quickly than any

computable function; you can "approximate" it, in a very weak sense by

using transfinite induction: this illustrates that higher infinities can

help to manage finite combinatorial problems).

*>Let us take the realist approach and focus on the things we can actually
*

*>compute fully.
*

Would you formalise that by the total (defined everywhere) functions from

N to N, or do you accept the partial computable functions as well?

And why would you not accept also the functions computable relatively to

the

halting problem? They correspond naturally to the function computable in

the

limit and are quite usefull if you accept infinite histories ...

Bruno

PS I will comment you other post (from the same thread), where you say

you are a materialist, ASAP.

Received on Tue Jun 26 2001 - 08:24:16 PDT

Date: Tue Jun 26 08:24:16 2001

Joel wrote:

You really should be an intuitionist mathematicien. It is consistent

with most intuitionist mathematical system that

1) all function from N to N is computable.

2) all function from R to R is continuous.

In my approach the intuitionist philosophy

correspond to the first person viewpoint.

But I'm a Platonist, at least about numbers and functions from N to N.

This includes a lot of uncomputable functions. For exemple the function

which gives for each n the greatest number you can compute in fortran

with program of length n. (This function grows quickly than any

computable function; you can "approximate" it, in a very weak sense by

using transfinite induction: this illustrates that higher infinities can

help to manage finite combinatorial problems).

Would you formalise that by the total (defined everywhere) functions from

N to N, or do you accept the partial computable functions as well?

And why would you not accept also the functions computable relatively to

the

halting problem? They correspond naturally to the function computable in

the

limit and are quite usefull if you accept infinite histories ...

Bruno

PS I will comment you other post (from the same thread), where you say

you are a materialist, ASAP.

Received on Tue Jun 26 2001 - 08:24:16 PDT

*
This archive was generated by hypermail 2.3.0
: Fri Feb 16 2018 - 13:20:07 PST
*