On 5/29/2012 11:12 PM, Stephen P. King wrote:
The point is is that what ever the choice is, there are ab initio alternatives that
are not exactly known to be optimal solutions to some criterion and some
not-specified-in-advance function that picks one.
??? The function is specified in
On 5/30/2012 1:45 AM, Bruno Marchal wrote:
Banach and Tarski proved an amazing theorem with the axiom of choice, but it is not a
paradox, in the sense that it contradicts nothing, and you can't get anything from it.
Bruno
It contradicts intuition.
Brent
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On Wed, May 30, 2012 Bruno Marchal marc...@ulb.ac.be wrote:
The axiom of choice is not a physical law.
That is true, but it is consistent with empirical physical evidence about
how the universe works. In non-mathematical language the Axiom of Choice
says that every event need not have an
What about Gabriel's Horn or the Koch Snowflake curve?
They may also contradict intuition but the results are not dependent upon
the axiom of choice.
On Wed, May 30, 2012 at 9:17 AM, meekerdb meeke...@verizon.net wrote:
On 5/30/2012 1:45 AM, Bruno Marchal wrote:
Banach and Tarski proved an
On 5/30/2012 9:31 AM, John Clark wrote:
On Wed, May 30, 2012 Bruno Marchal marc...@ulb.ac.be
mailto:marc...@ulb.ac.be wrote:
The axiom of choice is not a physical law.
That is true, but it is consistent with empirical physical evidence about how the
universe works. In non-mathematical
On Sun, May 27, 2012 Aleksandr Lokshin aaloks...@gmail.com wrote:
All main mathematical notions ( such as infinity, variable, integer
number) implicitly
depend on the notion of free will.
Because nobody can explain what the ASCII string free will means the
above statement is of no value.
On Tue, May 29, 2012 at 12:52 PM, John Clark johnkcl...@gmail.com wrote:
On Sun, May 27, 2012 Aleksandr Lokshin aaloks...@gmail.com wrote:
All main mathematical notions ( such as infinity, variable, integer
number) implicitly
depend on the notion of free will.
Because nobody can
On Sun, May 27, 2012 at 2:51 PM, Aleksandr Lokshin aaloks...@gmail.comwrote:
To make the general idea more clear , suppose we are proving the well-
known formula S = ah/2 for the area of a triangle. Our proof will
necessarily begin as follows:
“Let us consider AN ARBITRARY triangle…” Here
On 5/29/2012 10:52 AM, John Clark wrote:
On Sun, May 27, 2012 Aleksandr Lokshin aaloks...@gmail.com
mailto:aaloks...@gmail.com wrote:
All main mathematical notions ( such as infinity, variable, integer
number) implicitly
depend on the notion of free will.
Because nobody can
It doesn't take free will to prove that every even number is divisible by
2. How to prove a statement with a universal quantifier is pretty basic.
On Tue, May 29, 2012 at 12:01 PM, Aleksandr Lokshin aaloks...@gmail.comwrote:
*The notion of choosing isn't actually important--if a proof says
I'll try to explain why choosing an arbitrary element should be interpreted
as *a free will choice in mathematics*.
The difficulty of understanding depends, IMHO, on the fact that in English
different roots of the words are employed in arbitrary andfree
will. In Russian thre roots are the
On Tue, May 29, 2012 at 3:01 PM, Aleksandr Lokshin aaloks...@gmail.comwrote:
*The notion of choosing isn't actually important--if a proof says
something like pick an arbitrary member of the set X, and you will find it
obeys Y, this is equivalent to the statement every member of the set X
On 29 May 2012 20:42, Aleksandr Lokshin aaloks...@gmail.com wrote:
I'll try to explain why choosing an arbitrary element should be interpreted
as a free will choice in mathematics.
I agree with you that an arbitrary decision cannot be either random or
the consequence of an explicit rule or
It is impossible to consider common properties of elements of an infinite
set since, as is known from psycology, a man can consider no more than 7
objects simultaneously. Therefore consideration of such objects as a
multitude of triangles seems to be impossible. Nevertheless we consider
such
*I agree with you that an arbitrary decision cannot be either random or
the consequence of an explicit rule or law. Hence an arbitrary choice
is indeed freely willed, by convention. What I do not see, however, is
how this can have any metaphysical implications for particular agents,
whose
On Tue, May 29, 2012 at 4:38 PM, Aleksandr Lokshin aaloks...@gmail.comwrote:
It is impossible to consider common properties of elements of an infinite
set since, as is known from psycology, a man can consider no more than 7
objects simultaneously.
That's just about the number of distinct
*I agree with you that an arbitrary decision cannot be either random or
the consequence of an explicit rule or law. Hence an arbitrary choice
is indeed freely willed, by convention. What I do not see, however, is
how this can have any metaphysical implications for particular agents,
whose
On 5/29/2012 2:09 PM, Joseph Knight wrote:
On Tue, May 29, 2012 at 12:52 PM, John Clark johnkcl...@gmail.com
mailto:johnkcl...@gmail.com wrote:
On Sun, May 27, 2012 Aleksandr Lokshin aaloks...@gmail.com
mailto:aaloks...@gmail.com wrote:
All main mathematical notions (
On 5/29/2012 2:22 PM, Jesse Mazer wrote:
On Sun, May 27, 2012 at 2:51 PM, Aleksandr Lokshin
aaloks...@gmail.com mailto:aaloks...@gmail.com wrote:
To make the general idea more clear , suppose we are proving the well-
known formula S = ah/2 for the area of a triangle. Our proof
On 5/29/2012 3:05 PM, Brian Tenneson wrote:
It doesn't take free will to prove that every even number is divisible
by 2. How to prove a statement with a universal quantifier is pretty
basic.
On Tue, May 29, 2012 at 12:01 PM, Aleksandr Lokshin
aaloks...@gmail.com mailto:aaloks...@gmail.com
On 5/29/2012 4:14 PM, David Nyman wrote:
On 29 May 2012 20:42, Aleksandr Lokshinaaloks...@gmail.com wrote:
I'll try to explain why choosing an arbitrary element should be interpreted
as a free will choice in mathematics.
I agree with you that an arbitrary decision cannot be either random or
On 5/29/2012 4:38 PM, Aleksandr Lokshin wrote:
It is impossible to consider common properties of elements of an
infinite set since, as is known from psycology, a man can consider no
more than 7 objects simultaneously. Therefore consideration of such
objects as a multitude of triangles seems to
On Tue, May 29, 2012 at 11:11 PM, Aleksandr Lokshin
aaloks...@gmail.comwrote:
3)We have agfeed that the choice of an arbitrary element is not a random
chaice and is not a choice determinate by some law. 4)Therefore I do call
it a free will choice in mathematics. One can consider it as a
On 5/29/2012 5:18 PM, Jesse Mazer wrote:
On Tue, May 29, 2012 at 4:38 PM, Aleksandr Lokshin
aaloks...@gmail.com mailto:aaloks...@gmail.com wrote:
It is impossible to consider common properties of elements of an
infinite set since, as is known from psycology, a man can consider
On 5/29/2012 8:11 PM, Aleksandr Lokshin wrote:
The original poster introduces what free will means.
1) Every choice which is allowed in physics is a random choice or a determinate
one.
2) If human free will choice exists, it is agreed that it is not determined by some law
and is not a random
On 5/29/2012 8:47 PM, Stephen P. King wrote:
On 5/29/2012 5:18 PM, Jesse Mazer wrote:
On Tue, May 29, 2012 at 4:38 PM, Aleksandr Lokshin aaloks...@gmail.com
mailto:aaloks...@gmail.com wrote:
It is impossible to consider common properties of elements of an infinite
set
since, as is
On 5/29/2012 9:06 PM, Aleksandr Lokshin wrote:
It is a question of terminology. If you say a function it is necessary to construct it
(from physical point of view). But, physically it is impossible to do so.
It is certainly physically possible for me to consider the class of persons with no
On 5/29/2012 11:11 PM, Aleksandr Lokshin wrote:
The original poster introduces what free will means.
1) Every choice which is allowed in physics is a random choice or a
determinate one.
Hi,
IMHO, if it is either random or determined, it is not free.
2) If human free will choice exists,
*It is certainly physically possible for me to consider the class of
persons with no feet. Whether I have an operational test for no feet or
whether I can apply it a billion times or infinitely many times is
irrelevant. The function is defined, i.e. made definite. It is not
physically
5) If one uses mathematics, then one operates with a process which is
prohibited in physics.
Rubbish!
I insist on my statement which, unfortunately, is not understood. I stop
taking part in the discussion.
Best wishes
Alex
On Wed, May 30, 2012 at 9:12 AM, Aleksandr Lokshin
On 5/29/2012 10:12 PM, Aleksandr Lokshin wrote:
/It is certainly physically possible for me to consider the class of persons with no
feet. Whether I have an operational test for no feet or whether I can apply it a
billion times or infinitely many times is irrelevant. The function is defined,
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