Re: free will and mathematics

meekerdb Tue, 29 May 2012 22:40:05 -0700

On 5/29/2012 10:12 PM, Aleksandr Lokshin wrote:

/<<It is certainly physically possible for me to consider the class of persons with nofeet. Whether I have an operational test for "no feet" or whether I can apply it abillion times or infinitely many times is irrelevant. The function is defined, i.e.made definite. It is not "physically constructed" whatever that may mean because thefunction is not a physical object.>>//**/* You are not right. I insist that it is physically impossible to consider(simultaneously!) all common properties of all triangles.
*

First, is easy to consider the common properties of triangles because there are only a fewof them, e.g. having three sides as line segments which meet pairwise at vertices.Second, there is no necessity to consider all of them simultaneously in order to makeinferences about triangles, e.g. all triangles have exactly three vertices.

/<< No, we say "for every x an element of X" or "for any x, an element of X". 
/>>
*When we say "for every element" we hide what we are really doing. *


No, it is you who are muddling what we are really doing.

*It is physically impossible to consider all (every) triangles simultaneously.
*

But it's easy to consider the properties of all triangles, e.g. having sides which meetpairwise => there are three vertices.

**But we use a physically prohibited operation of considering ( = choosing) an arbitraryelement. I will try again to explain why in my opinion it is normal to say that we dealwith free will choice here.
 A) We really consider a single element about which we say that it is "an arbitrary 
one".

No we don't. We don't actually pick out an element from an infinite set. If I were in arestaurant looking at the menu and the waiter asked, "Which item will you have?" and Ireplied "I'll eat any item on the menu." I would NOT have picked one. I can refer to allthe items on the menu without picking one.

Therefore we psycologically deal with a choice. This choice is neither a random one nora determinate one. Therefore *formally* I can give it the name of "a free will choice inmathematics".


Except considering an indefinite element in a defined class is not a choosing.

B) Now I begin considering the "arbitrary element"*informally*. What i am really doingwhen I consider "an arbitrary element"? First of all, by *using my free will* I comparethe infinite number of (for exapple) triangles between them

"Triangles between them"?? what's "them" and why are you considering only trianglesbetween them?

, I do this with an infinite speed and as a result I know which properties turn out tobe common to all triangles.

Nonsense, you define the class of triangles by specifying their common properties. Youhave not and cannot inspect all possible triangles.


Brent

Then I can choose a random triangle under the following restriction. I can take intoconsideration only those common properties of all triangles which I have obtained byusing the "journey" of my free will.

 Alex

On Wed, May 30, 2012 at 8:16 AM, meekerdb <meeke...@verizon.net<mailto:meeke...@verizon.net>> wrote:


    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
    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 constructed" whatever that may mean 
because
    the function is not a physical object.

    I say "choice", because when proving some theorem we already say : "let us
consider/choose an arbitrary x belonging to X".


    No, we say "for every x an element of X" or "for any x, an element of X".  
Maybe you
    should just stop saying "choose/consider".

    Brent

    If you say "function" it is all the same. You give another name to your
    infinitely/finitely repeated choice.
    Alexander

    On Wed, May 30, 2012 at 7:52 AM, meekerdb <meeke...@verizon.net
    <mailto:meeke...@verizon.net>> wrote:

        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 process.
        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.


        We haven't even agreed that it is a choice.  It's just using a 
function, as in
        (. is an element of X) so (x is an element of X)->true and (y is an 
element of
        X)->false.  (all x |x an element of X) doesn't involve choosing an 
element x,
        just specifying a function that defines X.  Then it is a "choice 
determinate by
        some law."  And whether X is infinite or finite is a red herring.  
Suppose I

said,"Consider an arbitrary person with no feet. Then he has no toenails."This is a perfectly valid inference whether there are finitely many or

        infinitely many persons in the multiverse.

        Brent

        4)Therefore I do call it "a free will choice in mathematics". One can 
consider
        it as a definition of a specific "free will choice in mathematics".
        5) If one uses mathematics, then one operates with a process which is
        prohibited in physics. Therefore an investigator who uses mathematics 
cannot
        deny existence of mental processes which cannot be described by physics 
(and,
        in particular, cannot deny existence of free will, even if "free will" 
is not
        introduced explicitly).
        Good luck.



        On Wed, May 30, 2012 at 6:39 AM, Stephen P. King <stephe...@charter.net
        <mailto:stephe...@charter.net>> wrote:

            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 ( 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.


            Precisely. The original poster should introduce some sensible 
definition
            of free will. Good luck!


                The "belief" in a particular perceived outcome given some state 
of
            affairs?

--Onward!


            Stephen

            "Nature, to be commanded, must be obeyed."
            ~ Francis Bacon