Re: free will and mathematics

On 30 May 2012, at 18:31, John Clark wrote: On Wed, May 30, 2012 Bruno Marchal 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

Re: free will and mathematics

Yes, there is more than one thing that contradicts intuition. Brent On 5/30/2012 9:35 AM, Brian Tenneson wrote: 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

Re: free will and mathematics

On 5/30/2012 9:31 AM, John Clark wrote: On Wed, May 30, 2012 Bruno Marchal 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 language the Axi

Re: free will and mathematics

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 wrote: > On 5/30/2012 1:45 AM, Bruno Marchal wrote: > > Banach and Tarski proved an amazing theorem wi

Re: free will and mathematics

On Wed, May 30, 2012 Bruno Marchal 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 associated cause, an

Re: free will and mathematics

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 -- You received this message because

Re: free will and mathematics

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 advan

Re: free will and mathematics

On 5/29/2012 11:04 PM, Stephen P. King wrote: On 5/29/2012 11:52 PM, meekerdb 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 ch

Re: free will and mathematics

On 30 May 2012, at 16:08, Stephen P. King wrote: On 5/30/2012 4:45 AM, Bruno Marchal wrote: On 30 May 2012, at 08:12, Stephen P. King wrote: Hi Brent, Yes, that is a very good point! The axiom of choice is a suspect here. Banach and Tarsky proved a paradox of the axiom of choice

Re: free will and mathematics

On Tue, May 29, 2012 Aleksandr Lokshin wrote: > The original poster introduces what free will means. Every choice which is allowed in physics is a random choice OK, In other words it had no cause. > or a determinate one. > In other words it had a cause. > If human free will choice exists,

Re: free will and mathematics

On 5/30/2012 4:45 AM, Bruno Marchal wrote: On 30 May 2012, at 08:12, Stephen P. King wrote: On 5/30/2012 12:06 AM, meekerdb wrote: 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 mailto:aaloks...@gma

Re: free will and mathematics

On 30 May 2012 04:41, Jesse Mazer wrote: > Only David Nyman agreed as far as I can see See my reply to Stephen. David -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. T

Re: free will and mathematics

On 30 May 2012 04:16, Stephen P. King wrote: >   I think that the word "free" means that it is unconstrained by a pre-given > or knowable function; it is not the result of a known computational process. I'm sorry if my point was not clear. I simply meant that we can define "arbitrary", if we wi

Re: free will and mathematics

On Wed, May 30, 2012 at 2:02 AM, Stephen P. King wrote: > On 5/29/2012 11:46 PM, Jesse Mazer wrote: > > > > On Tue, May 29, 2012 at 10:49 PM, Stephen P. King > wrote: > >> >> Hi Jesse, >> >>Would it be correct to think of "arbitrary" as used here as meaning " >> some y subset Y identified b

Re: free will and mathematics

On 30 May 2012, at 08:12, Stephen P. King wrote: On 5/30/2012 12:06 AM, meekerdb wrote: 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 > wrote: It is impossible to consider common properties of ele

Re: free will and mathematics

On 5/30/2012 1:25 AM, Aleksandr Lokshin wrote: 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 Ale OK. --

Re: free will and mathematics

On 5/30/2012 12:06 AM, meekerdb wrote: 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 mailto:aaloks...@gmail.com>> wrote: It is impossible to consider common properties of elements of an infin

Re: free will and mathematics

On 5/29/2012 11:52 PM, meekerdb 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 deter

Re: free will and mathematics

On 5/29/2012 11:46 PM, Jesse Mazer wrote: On Tue, May 29, 2012 at 10:49 PM, Stephen P. King mailto:stephe...@charter.net>> wrote: Hi Jesse, Would it be correct to think of "arbitrary" as used here as meaning " some y subset Y identified by some function i or mapping j th

Re: free will and mathematics

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

Re: free will and mathematics

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 wrote: >

Re: free will and mathematics

*<>* * ** You are not right. I insist that it is physically impossible to consider (simultaneously!) all common properties of all triangles. * *<< 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. It

Re: free will and mathematics

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,

Re: free will and mathematics

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

Re: free will and mathematics

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 > wrote: It is impossible to consider common properties of elements of an infinite set since, as is known from psycolo

Re: free will and mathematics

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 pr

Re: free will and mathematics

On 5/29/2012 5:18 PM, Jesse Mazer wrote: On Tue, May 29, 2012 at 4:38 PM, Aleksandr Lokshin 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 no more than 7 objec

Re: free will and mathematics

On Tue, May 29, 2012 at 10:49 PM, Stephen P. King wrote: > > Hi Jesse, > >Would it be correct to think of "arbitrary" as used here as meaning " > some y subset Y identified by some function i or mapping j that is not a > subset (or faithfully represented) in X, yet x => y : x /subset X"? The >

Re: free will and mathematics

On Tue, May 29, 2012 at 11:11 PM, Aleksandr Lokshin wrote: > > 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 definition > of a

Re: free will and mathematics

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

Re: free will and mathematics

On 5/29/2012 4:14 PM, David Nyman wrote: On 29 May 2012 20:42, Aleksandr Lokshin 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 a

Re: free will and mathematics

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 mailto:aaloks...@gmail.com>> wrote: <>

Re: free will and mathematics

On 5/29/2012 2:22 PM, Jesse Mazer wrote: On Sun, May 27, 2012 at 2:51 PM, Aleksandr Lokshin 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 will necessarily b

Re: free will and mathematics

On 5/29/2012 2:09 PM, Joseph Knight wrote: On Tue, May 29, 2012 at 12:52 PM, John Clark > wrote: On Sun, May 27, 2012 Aleksandr Lokshin mailto:aaloks...@gmail.com>> wrote: > All main mathematical notions ( such as infinity, variable, integer

Re: free will and mathematics

*<>* *The consequence is as follows. If one uses mathematics he cannot deny existence of mental processes which are physically impossible (I do mean free will choice outside mathematics). Thank yoyu for understanding.* *Alexander* On Wed, May 30, 2012 at 1:18 AM, Jesse Mazer wrote: > > > On Tue,

Re: free will and mathematics

On Tue, May 29, 2012 at 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. That's just about the number of distinct "chunks" of informat

Re: free will and mathematics

*<>* *The consequence is as follows. If one uses mathematics he cannot deny existence of mental processes which are physically impossible (I do mean free will choice outside mathematics). Thank yoyu for understanding.* *Alexander* On Wed, May 30, 2012 at 12:38 AM, Aleksandr Lokshin wrote: >

Re: free will and mathematics

So you believe that the set of all numbers divisible by two is not the set of all even numbers? On Tue, May 29, 2012 at 1:38 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

Re: free will and mathematics

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 multit

Re: free will and mathematics

On 5/29/2012 12:42 PM, Aleksandr Lokshin wrote: 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"

Re: free will and mathematics

On 29 May 2012 20:42, Aleksandr Lokshin 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 law. Hence an arbitr

Re: free will and mathematics

On Tue, May 29, 2012 at 3:01 PM, Aleksandr Lokshin wrote: > <<*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 > obeys Y"*>> >

Re: free will and mathematics

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" and"free will". In Russian thre roots are the

Re: free will and mathematics

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 wrote: > <<*The notion of "choosing" isn't actually important--if a proof says > something like "

Re: free will and mathematics

<<*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 obeys Y"*>> No, the logical operator "every" contains the free will choice insi

Re: free will and mathematics

On 5/29/2012 10:52 AM, John Clark wrote: On Sun, May 27, 2012 Aleksandr Lokshin > 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 ASC

Re: free will and mathematics

No, in the text it is explained that the choice of an* arbitrary* element is just what one should take for a free will choice. It is the *definition*of the free will choice (in the domain of mathermatics). * Arbitrary* does not mean *random !!! Otherwise all mathematcal proofs couldn't exist.* *For

Re: free will and mathematics

On Sun, May 27, 2012 at 2:51 PM, Aleksandr Lokshin 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 will > necessarily begin as follows: > “Let us consider AN ARBITRARY triangle…” Here we obviously app

Re: free will and mathematics

On Tue, May 29, 2012 at 12:52 PM, John Clark wrote: > > On Sun, May 27, 2012 Aleksandr Lokshin 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 "fre

Re: free will and mathematics

On Sun, May 27, 2012 Aleksandr Lokshin 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. > A new approach

free will and mathematics

Alexander A. Lokshin FREE WILL AND MATHEMATICS Moscow, MAKS-Press, 2012 , 40 pages (abstract) The general idea of the booklet is as follows. All main mathematical notions ( such as infinity, variable, integer number) implicitly depend on the notion of free will. Therefore a scientist employing

<    1   2