free will and mathematics

[Aleksandr Lokshin]

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
mathematics when modeling nature cannot deny the existence of the free
will. (Unfortunately , Stephen Hawking made this incorrect conclusion
in “The Grand Design”).
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 apply the
operator of the free will choice which cannot be replaced by the
random choice. In fact, let us imagine that our proof begins in such a
way : “Let us consider A RANDOMLY SELECTED triangle…” Surely, such a
beginning will not lead us to the desired proof. The formula obtained
for a randomly selected triangle is not necessarily valid for all
triangles!
On the other hand when proving the formula S=ab/2, obviously, it is
impossible to consider all the triangles simultaneously. Thus the
operator of the free will choice must be used inevitably.
More widely, let us consider a variable x which is running about a
sphere of radius 1. Let us pose a question: what does x denote?
Clearly,
a) x does not denote an object,
b) x does not denote a multitude,
c) x does not denote a physical process.
In my opinion, x denotes the free will choice which the reader of the
mathematical text must do. So, the notion of a variable inevitably is
based on the notion of the free will.
Moreover, considerations adduced in the book show that the notion of
an integer number is based on the notion of the free will as well.
In fact, when constructing integers by means of one-to-one
correspondence we implicitly assume that the mentioned correspondence
is realized by means of continuous lines connecting pairs of objects.
But to ensure continuity of lines above-mentioned one must consider an
arbitrary point on such a line!
A new approach to the Alan Turing problem (how to distinguish a person
from an android) is also proposed ; this approach is based on the idea
that an android cannot generate the notion of an arbitrary object.

[John Clark]

On Sun, May 27, 2012  Aleksandr Lokshin <aalo...@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. 

> A new approach to the Alan Turing problem (how to distinguish a person from an android) is also proposed ; this approach is based on the idea that an android cannot generate the notion of an arbitrary object.

But "arbitrary" just means picking something for no reason or picking something just because you like it but you like it for no reason; in other words it means random. It's true that a pure Turing machine can not produce randomness, however this limitation can be easily overcome by attaching a very simple and cheap hardware random number generator to it. Then the android could be as arbitrary as any arbitrary person, if you think being arbitrary is a virtue that is.

  John K Clark 

[Joseph Knight]

On Tue, May 29, 2012 at 12:52 PM, John Clark <johnk...@gmail.com> wrote:

On Sun, May 27, 2012  Aleksandr Lokshin <aalo...@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!

 

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[Jesse Mazer]

On Sun, May 27, 2012 at 2:51 PM, Aleksandr Lokshin <aalo...@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 begin as follows:
“Let us consider AN ARBITRARY triangle…” Here we obviously apply the
operator of the free will choice which cannot be replaced by the
random choice. In fact, let us imagine that our proof begins in such a
way : “Let us consider A RANDOMLY SELECTED triangle…”  Surely, such a
beginning will not lead us to the desired proof. The formula obtained
for a randomly selected triangle is not necessarily valid for all
triangles!

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". In formal logic this would be expressed in terms of the upside-down A symbol that represents "universal quantification" in a given "universe of discourse" such as the set of all triangles ( http://en.wikipedia.org/wiki/Universal_quantification ). In fact, in proofs like this one typically *doesn't* imagine choosing any specific triangle, one just thinks about properties that would apply to every member of the set and thus every "arbitrary member", like the property of having three sides or or the property of having its angles add up to 180 degrees in the case of a triangle obeying Euclidean axioms. And note that any mathematical proof can be expressed in a formal symbolic way using logical symbols/rules as well as some symbols/rules specific to the domain of mathematics under consideration (see http://en.wikipedia.org/wiki/Formal_proof ), and in this form the proof will often contain the universal quantification symbol, but there is no separate symbol corresponding to the notion of "pick an arbitrary member of the set".

 

On the other hand when proving the formula S=ab/2, obviously, it is
impossible to consider all the triangles simultaneously.

Why not? One can consider the properties that all these triangles are defined to share, and then show that these properties, along with the axioms of geometry, can be used to derive some other properties they will all share.

 

Thus the
operator of the free will choice must be used inevitably.
More widely, let us consider a variable x which is running about a
sphere of radius 1. Let us pose a question: what does x  denote?
Clearly,
a) x does not denote an object,
b) x does not denote a multitude,
c) x does not denote a physical process.
In my opinion, x denotes the free will choice which the reader of the
mathematical text must do. So, the notion of a variable inevitably is
based on the notion of the free will.

If it really depended on free choice, then you would have no way of being sure that just because *your* choice obeyed a certain rule, every other possible choice of examples from the same set would do so as well.

Jesse

[Aleksandr Lokshin]

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 a physicist when he is choosing an object for his experiment the difference between an arbitrary element and a randomly choosen elemen is of no importance.

On the contrary, for a mathematician the mentioned difference is of principal importance. 

Now I explain why the situations in physics (biology, psycology etc) on the one hand, and in mathematics on the other hand are not equivalent.

In physics (byology , psycology, etc) one does not establish theorems . All physical laws are obtained inductively (not deductively). Therefore in case when a new experiment contradicts the previous ones nothing horrible happens.The physical law is modified and that's all.

In mathematics we do not find approximate laws, but we deduce exact theorems which must be valid not only for a randomly chosen object, but for each  object belonging to an infinite set cosisting of analogous objects. It is impossible to prove mathematical theorems by using randomly chosen objects.

All what I have written above is absolutely clear for each mathematician, but, unfortunately, is hard to understand for certain philosophers.     
 

[meekerdb]

On 5/29/2012 10:52 AM, John Clark wrote:

On Sun, May 27, 2012  Aleksandr Lokshin <aalo...@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. 

> A new approach to the Alan Turing problem (how to distinguish a person from an android) is also proposed ; this approach is based on the idea that an android cannot generate the notion of an arbitrary object.

But "arbitrary" just means picking something for no reason or picking something just because you like it but you like it for no reason; in other words it means random. It's true that a pure Turing machine can not produce randomness, however this limitation can be easily overcome by attaching a very simple and cheap hardware random number generator to it.

Or by computing psuedo-random numbers with a sufficiently long period that no one will be able to determine the algorithm.

Brent

Then the android could be as arbitrary as any arbitrary person, if you think being arbitrary is a virtue that is.

  John K Clark 

[Aleksandr Lokshin]

<<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 inside of it. I do insist that  one cannot consider an infinite set of onjects simultaneously!  Instead of so doing one considers an arbitraryly chosen object. It is a very specific mathematical operation . By using operator "every" we construct a formalism which hides the essens of matter - the using of a free will choice. 

On Tue, May 29, 2012 at 10:30 PM, meekerdb <meek...@verizon.net> wrote:

[Brian Tenneson]

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.

[Aleksandr Lokshin]

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 same, but my explanation will not base on this fact.

According to phisics, free will choice (if it does exist) is a choice which 

1) is not random,

2) is not determined by some law.

Now , consider a Theorem: statement A is valid for all x belonging to X.

Proof. Let x be an arbitrary element of X. We demonstrate that A(x) is valid.

Since x was chosen arbitrarily, A is valid for all x.

Comment. As I have pointed out earlier , if x was chosen randomly, the theorem is not proved.

Analogously, if x was chosen according to some rule, the theorem is not proved.

Therefore, since we are sure that we have proved the theorem by using the arbitrarily chosen element, we must inevitably agree that 

the element was chosen by using free will choice.

[Jesse Mazer]

On Tue, May 29, 2012 at 3:01 PM, Aleksandr Lokshin <aalo...@gmail.com> 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">>

No, the logical operator  "every" contains the free will choice inside of it. I do insist that  one cannot consider an infinite set of onjects simultaneously!

Why do you think we can't do so in the way I suggested earlier, by considering common properties they are all defined to have, like the fact that each triangle consists of three straight edges joined at three vertices? If I construct a proof showing that, if I take some general properties as starting points, I can then derive some other general properties (like the fact that the angles add up to 180), where in such a proof have I considered any specific triangle? 

Do you think mathematicians actually have to pick specific examples (like a triangle with sides of specific lengths) in order to verify that a proof is correct? If they did choose specific examples, and only verified that it worked for those specific examples, how would they be able to achieve perfect confidence that it would be impossible to choose a *different* example that violated the rule? If you prove something is true for an "arbitrarily chosen member" of the set, this implies that in a scenario where someone other than you is doing the choosing, you should be totally confident in advance that the proof will apply to whatever choice they make. If the set they are choosing from is infinitely large, how could you have such perfect confidence prior to actually learning of their choice, without considering shared properties of "an infinite set of objects simultaneously"?

[David Nyman]

On 29 May 2012 20:42, Aleksandr Lokshin <aalo...@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 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 performance against these criteria can only ever be evaluated to
some limit. If this is a problem for mathematicians or mathematics,
AFAICS it is an unavoidable one.

David

[meekerdb]

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" and    "free will". In Russian thre roots are the same, but my explanation will not base on this fact.

According to phisics, free will choice (if it does exist) is a choice which 

1) is not random,

2) is not determined by some law.

Now , consider a Theorem: statement A is valid for all x belonging to X.

Proof. Let x be an arbitrary element of X. We demonstrate that A(x) is valid.

Since x was chosen arbitrarily, A is valid for all x.

But in this application "arbitrary" just means "without any distinguishing characteristic"; we specify *only* that x belongs to X and do not specify or use any other property.  That's why "any x" is equivalent to "every x" and the theorem stated in terms of "every x" doesn't imply any choosing at all.

Brent

[Aleksandr Lokshin]

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 multitudes and obtain results which seem to be true. The method we employ is comsideration of a very specific "single but arbitrary" object. 

Your remarkable objection that "if two mathematicians consider two different arbitrary objects they will obtain different results" demonstrates that you are not a mathematician. Arbitrary element is not an object, it is a  mental but non-physical process  which enables one to do a physically impossible thing : to observe an infinite set of objects simultaneously considering then all their common properties at a single really existing object. Therefore two different mathematicians will necessarily obtain the same result.   

--

[Brian Tenneson]

So you believe that the set of all numbers divisible by two is not the set of all even numbers?

[Aleksandr Lokshin]

<<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 performance against these criteria can only ever be evaluated to
some limit.  If this is a problem for mathematicians or mathematics,
AFAICS it is an unavoidable one.
David>>

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

[Jesse Mazer]

On Tue, May 29, 2012 at 4:38 PM, Aleksandr Lokshin <aalo...@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 objects simultaneously.

That's just about the number of distinct "chunks" of information you can hold in working memory, so that you can name the distinctive features of each one after they are removed from your sense experience (see http://www.intropsych.com/ch06_memory/magical_number_seven.html ). But I'm not talking about actually visualizing each and every member of an infinite set, such that I am aware of the distinctive features of each one which differentiate them from the others. I'm talking about a more abstract understanding that a certain property applies to every member, perhaps simply by definition (for example, triangles are defined to be three-sided, so three-sidedness is obviously one of the common properties of the set of all triangles). Do you think it's impossible to have an abstract understanding that a large (perhaps infinite) set of objects all share a particular property?

 

Your remarkable objection that "if two mathematicians consider two different arbitrary objects they will obtain different results" demonstrates that you are not a mathematician.

Huh? I didn't write the phrase you put in quotes, nor imply that this was how *I* thought mathematicians actually operated--I was just saying that *you* seemed to be suggesting that mathematicians could only prove things by making specific choices of examples to consider, using their free will. If that's not what you were suggesting, please clarify (and note that I did ask if this is what you meant in my previous post, rather than just assuming it...I then went on to make the conditional statement that IF that was indeed what you meant, THEN you should find it impossible to explain how mathematicians could be confident that a theorem could not be falsified by a new choice of example. But of course I might be misunderstanding your argument, that's why I asked if my reading was correct.)

 

Arbitrary element is not an object, it is a  mental but non-physical process  which enables one to do a physically impossible thing : to observe an infinite set of objects simultaneously considering then all their common properties at a single really existing object. Therefore two different mathematicians will necessarily obtain the same result.   

So you agree mathematicians don't have to make an actual choice of a specific element to consider? Then how is free will supposed to be relevant if there is no actual choice whatsoever being made?

[Aleksandr Lokshin]

<<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 performance against these criteria can only ever be evaluated to
some limit.  If this is a problem for mathematicians or mathematics,
AFAICS it is an unavoidable one.
David>>

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

[Stephen P. King]

On 5/29/2012 2:09 PM, Joseph Knight wrote:

On Tue, May 29, 2012 at 12:52 PM, John Clark <johnk...@gmail.com> wrote:

On Sun, May 27, 2012  Aleksandr Lokshin <aalo...@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

[Stephen P. King]

On 5/29/2012 2:22 PM, Jesse Mazer wrote:

On Sun, May 27, 2012 at 2:51 PM, Aleksandr Lokshin <aalo...@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 begin as follows:
�Let us consider AN ARBITRARY triangle�� Here we obviously apply the

operator of the free will choice which cannot be replaced by the
random choice. In fact, let us imagine that our proof begins in such a

way : �Let us consider A RANDOMLY SELECTED triangle�� �Surely, such a

beginning will not lead us to the desired proof. The formula obtained
for a randomly selected triangle is not necessarily valid for all
triangles!

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". In formal logic this would be expressed in terms of the upside-down A symbol that represents "universal quantification" in a given "universe of discourse" such as the set of all triangles ( http://en.wikipedia.org/wiki/Universal_quantification ). In fact, in proofs like this one typically *doesn't* imagine choosing any specific triangle, one just thinks about properties that would apply to every member of the set and thus every "arbitrary member", like the property of having three sides or or the property of having its angles add up to 180 degrees in the case of a triangle obeying Euclidean axioms.�And note that any mathematical proof can be expressed in a formal symbolic way using logical symbols/rules as well as some symbols/rules specific to the domain of mathematics under consideration (see http://en.wikipedia.org/wiki/Formal_proof ), and in this form the proof will often contain the universal quantification symbol, but there is no separate symbol corresponding to the notion of "pick an arbitrary member of the set".

�

On the other hand when proving the formula S=ab/2, obviously, it is
impossible to consider all the triangles simultaneously.

Why not? One can consider the properties that all these triangles are defined to share, and then show that these properties, along with the axioms of geometry, can be used to derive some other properties they will all share.

�

Thus the
operator of the free will choice must be used inevitably.
More widely, let us consider a variable x which is running about a

sphere of radius 1. Let us pose a question: what does x �denote?

Clearly,
a) x does not denote an object,
b) x does not denote a multitude,
c) x does not denote a physical process.
In my opinion, x denotes the free will choice which the reader of the
mathematical text must do. So, the notion of a variable inevitably is
based on the notion of the free will.

If it really depended on free choice, then you would have no way of being sure that just because *your* choice obeyed a certain rule, every other possible choice of examples from the same set would do so as well.

Jesse

--

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 "choice" of a basis of a linear space comes to mind. The idea is that one it is not necessary to specify the method of identification ab initio.

[Stephen P. King]

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 <aalo...@gmail.com> 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">>

No, the logical operator  "every" contains the free will choice inside of it. I do insist that  one cannot consider an infinite set of onjects simultaneously!  Instead of so doing one considers an arbitraryly chosen object. It is a very specific mathematical operation . By using operator "every" we construct a formalism which hides the essens of matter - the using of a free will choice. 

On Tue, May 29, 2012 at 10:30 PM, meekerdb <meek...@verizon.net> wrote:

On 5/29/2012 10:52 AMOne cannot, John Clark wrote:

On Sun, May 27, 2012  Aleksandr Lokshin <aalo...@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. 

> A new approach to the Alan Turing problem (how to distinguish a person from an android) is also proposed ; this approach is based on the idea that an android cannot generate the notion of an arbitrary object.

But "arbitrary" just means picking something for no reason or picking something just because you like it but you like it for no reason; in other words it means random. It's true that a pure Turing machine can not produce randomness, however this limitation can be easily overcome by attaching a very simple and cheap hardware random number generator to it.

Or by computing psuedo-random numbers with a sufficiently long period that no one will be able to determine the algorithm.

Brent

Then the android could be as arbitrary as any arbitrary person, if you think being arbitrary is a virtue that is.

  John K Clark 

    The Universal quantifier is not a bijection between a known function and some unknown function. It is more like a one-to-many mapping. This removes its ability to be considered as definite as required by our notions of proofs. If a person or Marchalian machine cannot definitely some result, that result is by no means proven.

[Aleksandr Lokshin]

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. 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.

  

 

--

[Stephen P. King]

Hi David,

    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.

[Stephen P. King]

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 be impossible. Nevertheless we consider such multitudes and obtain results which seem to be true. The method we employ is comsideration of a very specific "single but arbitrary" object. 

Your remarkable objection that "if two mathematicians consider two different arbitrary objects they will obtain different results" demonstrates that you are not a mathematician. Arbitrary element is not an object, it is a  mental but non-physical process  which enables one to do a physically impossible thing : to observe an infinite set of objects simultaneously considering then all their common properties at a single really existing object. Therefore two different mathematicians will necessarily obtain the same result.  

Hi Aleksandr,

    This makes mathematicians very special as they are able to escape the bounds of resources that all non-mathematicians are subject to. How would a mathematican prove to a layman that he truly has such powers? Would they tend to be incorrigible? :-P

On Wed, May 30, 2012 at 12:13 AM, Jesse Mazer <laser...@gmail.com> wrote:

On Tue, May 29, 2012 at 3:01 PM, Aleksandr Lokshin <aalo...@gmail.com> 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">>

No, the logical operator  "every" contains the free will choice inside of it. I do insist that  one cannot consider an infinite set of onjects simultaneously!

Why do you think we can't do so in the way I suggested earlier, by considering common properties they are all defined to have, like the fact that each triangle consists of three straight edges joined at three vertices? If I construct a proof showing that, if I take some general properties as starting points, I can then derive some other general properties (like the fact that the angles add up to 180), where in such a proof have I considered any specific triangle? 

Do you think mathematicians actually have to pick specific examples (like a triangle with sides of specific lengths) in order to verify that a proof is correct? If they did choose specific examples, and only verified that it worked for those specific examples, how would they be able to achieve perfect confidence that it would be impossible to choose a *different* example that violated the rule? If you prove something is true for an "arbitrarily chosen member" of the set, this implies that in a scenario where someone other than you is doing the choosing, you should be totally confident in advance that the proof will apply to whatever choice they make. If the set they are choosing from is infinitely large, how could you have such perfect confidence prior to actually learning of their choice, without considering shared properties of "an infinite set of objects simultaneously"?

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[Jesse Mazer]

On Tue, May 29, 2012 at 11:11 PM, Aleksandr Lokshin <aalo...@gmail.com> 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 specific "free will choice in mathematics". 

What do you mean, "we have agreed"? Only David Nyman agreed as far as I can see, and he seems to misunderstand the phrase just as you do. I and others have told you that "an arbitrary element" means the exactly the same thing as "every element" (and you didn't reply to my last post asking where exactly you think a "choice" is made in the course of a mathematical proof).

[Jesse Mazer]

On Tue, May 29, 2012 at 10:49 PM, Stephen P. King <step...@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 that is not a subset (or faithfully represented) in X, yet x => y : x /subset X"? The "choice" of a basis of a linear space comes to mind. The idea is that one it is not necessary to specify the method of identification ab initio.

I can't really tell what you're asking here. As I said, "an arbitrary member of set Y will have property X" just means "every member of set Y has property X", nothing more complicated. For example, Y might be the set of all triangles in Euclidean geometry, and X might be the property of having all the inner angles add up to 180 degrees. It would be easier to understand your question if you similarly supplied some simple of what Y, y, j, X, and x could stand for, such that your description above would make sense.

Jesse

[Stephen P. King]

On 5/29/2012 5:18 PM, Jesse Mazer wrote:

On Tue, May 29, 2012 at 4:38 PM, Aleksandr Lokshin <aalo...@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 objects simultaneously.

That's just about the number of distinct "chunks" of information you can hold in working memory, so that you can name the distinctive features of each one after they are removed from your sense experience (see http://www.intropsych.com/ch06_memory/magical_number_seven.html ). But I'm not talking about actually visualizing each and every member of an infinite set, such that I am aware of the distinctive features of each one which differentiate them from the others. I'm talking about a more abstract understanding that a certain property applies to every member, perhaps simply by definition (for example, triangles are defined to be three-sided, so three-sidedness is obviously one of the common properties of the set of all triangles). Do you think it's impossible to have an abstract understanding that a large (perhaps infinite) set of objects all share a particular property?

    A single finite and faithful (to within the finite margin of error) representation of "triangle" works given that definition. This is there nominalism and universalism come to blows....

 

Your remarkable objection that "if two mathematicians consider two different arbitrary objects they will obtain different results" demonstrates that you are not a mathematician.

Huh? I didn't write the phrase you put in quotes, nor imply that this was how *I* thought mathematicians actually operated--I was just saying that *you* seemed to be suggesting that mathematicians could only prove things by making specific choices of examples to consider, using their free will. If that's not what you were suggesting, please clarify (and note that I did ask if this is what you meant in my previous post, rather than just assuming it...I then went on to make the conditional statement that IF that was indeed what you meant, THEN you should find it impossible to explain how mathematicians could be confident that a theorem could not be falsified by a new choice of example. But of course I might be misunderstanding your argument, that's why I asked if my reading was correct.)

 

Arbitrary element is not an object, it is a  mental but non-physical process  which enables one to do a physically impossible thing : to observe an infinite set of objects simultaneously considering then all their common properties at a single really existing object. Therefore two different mathematicians will necessarily obtain the same result.   

So you agree mathematicians don't have to make an actual choice of a specific element to consider? Then how is free will supposed to be relevant if there is no actual choice whatsoever being made?

--

    Why do you keep insisting on a "specific" property to the "choice" while being shown that the a priori "specificity" itself that is prohibited by the definition. 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.

[meekerdb]

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

[meekerdb]

He didn't refer to a specific property but to a specific choice of element, which is what Loskin says entails the magic ability to select one among an infinite number.  He apparently thinks of it like the complement of the axiom of choice: to pick an element you need to say,"Not this one. Not this one. Not..." an infinite number of times.

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 advance, e.g. "triangles" is a function that picks out things with three sides meeting pairwise as three vertices.  But I have no idea what you mean by "optimality".

Brent

-- 
Onward!

Stephen

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

--

[Aleksandr Lokshin]

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. I say "choice", because when proving some theorem we already say : "let us consider/choose an arbitrary x belonging to X". If you say "function" it is all the same. You give another name to your infinitely/finitely repeated choice.

Alexander  

[meekerdb]

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

[Stephen P. King]

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 agreed that it is not determined by some law and is not a random process. 

    But we need to take care to define "determined" carefully.

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 specific "free will choice in mathematics".

    How about "not ab initio specifiable" or "not reproducible in an exact way"?

5) If one uses mathematics, then one operates with a process which is prohibited in physics.

    Rubbish!

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).

    We can do better by pointing out that to only prove or communicate that which involves physical processes, this makes the "knowledge" in teh 1p sense only possibly non-physical. We can never prove that it is non-physical.

Good luck.

 

    Fortune favors the prepared mind.

[Aleksandr Lokshin]

<<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.>>

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

  But we use a physically prohibited operation of considering ( = choosing) an arbitrary element. I will try again to explain why in my opinion it is normal to say that we deal with free will choice here.

 A) We really consider a single element about which we say that it is "an arbitrary one". Therefore we psycologically deal with a choice. This choice is neither a random one nor a determinate one. Therefore formally I can give it the name of "a free will choice in mathematics".

B) Now I begin considering the "arbitrary element" informally. What i am really doing when I consider "an arbitrary element"? First of all, by using my free will I compare the infinite number of (for exapple) triangles between them , I do this with an infinite speed and as a result I know which properties turn out to be common to all triangles. Then I can choose a random triangle under the following restriction. I can take into consideration only those common properties of all triangles which I have obtained by using the "journey" of my free will.  

 Alex

[Aleksandr Lokshin]

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

[meekerdb]

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, i.e. made definite.  It is not "physically constructed" whatever that may mean because the function 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 few of 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 make inferences 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 meet pairwise => there are three vertices.

  But we use a physically prohibited operation of considering ( = choosing) an arbitrary element. I will try again to explain why in my opinion it is normal to say that we deal with 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 a restaurant looking at the menu and the waiter asked, "Which item will you have?" and I replied "I'll eat any item on the menu." I would NOT have picked one.  I can refer to all the items on the menu without picking one.

Therefore we psycologically deal with a choice. This choice is neither a random one nor a determinate one. Therefore formally I can give it the name of "a free will choice in mathematics".

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 doing when I consider "an arbitrary element"? First of all, by using my free will I compare the infinite number of (for exapple) triangles between them

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

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

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

Brent

[Stephen P. King]

--

Hi Jesse,

    You previously 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"." and not " "an arbitrary member of set Y will have property X" just means "every member of set Y has property X" ", a small but possibly important difference.

    Are you assuming a commutative relation for Y and X? Details...

[Stephen P. King]

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 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

Brent,

    You are assuming that there is no difference between an known and an unknown quantity. A big mistake!

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 <step...@charter.net> wrote:

On 5/29/2012 2:09 PM, Joseph Knight wrote:

On Tue, May 29, 2012 at 12:52 PM, John Clark <johnk...@gmail.com> wrote:

On Sun, May 27, 2012  Aleksandr Lokshin <aalo...@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!

 

[Stephen P. King]

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 <aalo...@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 objects simultaneously.

That's just about the number of distinct "chunks" of information you can hold in working memory, so that you can name the distinctive features of each one after they are removed from your sense experience (see http://www.intropsych.com/ch06_memory/magical_number_seven.html ). But I'm not talking about actually visualizing each and every member of an infinite set, such that I am aware of the distinctive features of each one which differentiate them from the others. I'm talking about a more abstract understanding that a certain property applies to every member, perhaps simply by definition (for example, triangles are defined to be three-sided, so three-sidedness is obviously one of the common properties of the set of all triangles). Do you think it's impossible to have an abstract understanding that a large (perhaps infinite) set of objects all share a particular property?

    A single finite and faithful (to within the finite margin of error) representation of "triangle" works given that definition. This is there nominalism and universalism come to blows....

 

Your remarkable objection that "if two mathematicians consider two different arbitrary objects they will obtain different results" demonstrates that you are not a mathematician.

Huh? I didn't write the phrase you put in quotes, nor imply that this was how *I* thought mathematicians actually operated--I was just saying that *you* seemed to be suggesting that mathematicians could only prove things by making specific choices of examples to consider, using their free will. If that's not what you were suggesting, please clarify (and note that I did ask if this is what you meant in my previous post, rather than just assuming it...I then went on to make the conditional statement that IF that was indeed what you meant, THEN you should find it impossible to explain how mathematicians could be confident that a theorem could not be falsified by a new choice of example. But of course I might be misunderstanding your argument, that's why I asked if my reading was correct.)

 

Arbitrary element is not an object, it is a  mental but non-physical process  which enables one to do a physically impossible thing : to observe an infinite set of objects simultaneously considering then all their common properties at a single really existing object. Therefore two different mathematicians will necessarily obtain the same result.   

So you agree mathematicians don't have to make an actual choice of a specific element to consider? Then how is free will supposed to be relevant if there is no actual choice whatsoever being made?

--

    Why do you keep insisting on a "specific" property to the "choice" while being shown that the a priori "specificity" itself that is prohibited by the definition.

He didn't refer to a specific property but to a specific choice of element, which is what Loskin says entails the magic ability to select one among an infinite number.  He apparently thinks of it like the complement of the axiom of choice: to pick an element you need to say,"Not this one. Not this one. Not..." an infinite number of times.

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, it is the "scalar field" of mathematics, IMHO; you can get from it anything you want.

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 advance, e.g. "triangles" is a function that picks out things with three sides meeting pairwise as three vertices.  But I have no idea what you mean by "optimality".

    What does that word mean? Try this  from http://encyclopedia2.thefreedictionary.com/Optimality

1.	(mathematics)	optimal - Describes a solution to a problem which minimises some cost function. Linear programming is one technique used to discover the optimal solution to certain problems.
2.	(programming)	optimal - Of code: best or most efficient in time, space or code size.

    Is that helpful?

[Stephen P. King]

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.

-- 
Onward!

Stephen

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

[Bruno Marchal]

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 <aalo...@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 objects simultaneously.

That's just about the number of distinct "chunks" of information you can hold in working memory, so that you can name the distinctive features of each one after they are removed from your sense experience (see http://www.intropsych.com/ch06_memory/magical_number_seven.html ). But I'm not talking about actually visualizing each and every member of an infinite set, such that I am aware of the distinctive features of each one which differentiate them from the others. I'm talking about a more abstract understanding that a certain property applies to every member, perhaps simply by definition (for example, triangles are defined to be three-sided, so three-sidedness is obviously one of the common properties of the set of all triangles). Do you think it's impossible to have an abstract understanding that a large (perhaps infinite) set of objects all share a particular property?

    A single finite and faithful (to within the finite margin of error) representation of "triangle" works given that definition. This is there nominalism and universalism come to blows....

 

Your remarkable objection that "if two mathematicians consider two different arbitrary objects they will obtain different results" demonstrates that you are not a mathematician.

Huh? I didn't write the phrase you put in quotes, nor imply that this was how *I* thought mathematicians actually operated--I was just saying that *you* seemed to be suggesting that mathematicians could only prove things by making specific choices of examples to consider, using their free will. If that's not what you were suggesting, please clarify (and note that I did ask if this is what you meant in my previous post, rather than just assuming it...I then went on to make the conditional statement that IF that was indeed what you meant, THEN you should find it impossible to explain how mathematicians could be confident that a theorem could not be falsified by a new choice of example. But of course I might be misunderstanding your argument, that's why I asked if my reading was correct.)

 

Arbitrary element is not an object, it is a  mental but non-physical process  which enables one to do a physically impossible thing : to observe an infinite set of objects simultaneously considering then all their common properties at a single really existing object. Therefore two different mathematicians will necessarily obtain the same result.   

So you agree mathematicians don't have to make an actual choice of a specific element to consider? Then how is free will supposed to be relevant if there is no actual choice whatsoever being made?

--

    Why do you keep insisting on a "specific" property to the "choice" while being shown that the a priori "specificity" itself that is prohibited by the definition.

He didn't refer to a specific property but to a specific choice of element, which is what Loskin says entails the magic ability to select one among an infinite number.  He apparently thinks of it like the complement of the axiom of choice: to pick an element you need to say,"Not this one. Not this one. Not..." an infinite number of times.

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, it is the "scalar field" of mathematics, IMHO; you can get from it anything you want.

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

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 advance, e.g. "triangles" is a function that picks out things with three sides meeting pairwise as three vertices.  But I have no idea what you mean by "optimality".

    What does that word mean? Try this  from http://encyclopedia2.thefreedictionary.com/Optimality

1.	(mathematics)	optimal - Describes a solution to a problem which minimises some cost function. Linear programming is one technique used to discover the optimal solution to certain problems.
2.	(programming)	optimal - Of code: best or most efficient in time, space or code size.

    Is that helpful?

-- 
Onward!

Stephen

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

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[Jesse Mazer]

Sorry, I was speaking informally, so I wasn't being too careful about keeping my use of the symbols X and Y consistent from one post to another. In the sentence "an arbitrary member of set Y will have property X" I was using "Y" to refer to a set and "X" to refer to a property, while in the sentence "pick an arbitrary member of the set X, and you will find it obeys Y" it was X that referred to a set, and Y that referred to a property. I'll try to stick to the second usage from now on to be consistent. Also, if I was worrying more about notation it would be more standard to use Y(x) to refer to the notion that some mathematical object x has a property Y, and then if X refers to a set, I could write ∀x (x ∈ X -> Y(x) ), which means "for all objects x in our domain of discourse, if x is a member of the set X, this implies that x has property Y."

[David Nyman]

On 30 May 2012 04:16, Stephen P. King <step...@charter.net> 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 wish, to mean neither random nor constrained
by law. Then, simply by convention, an arbitrary choice is freely
willed. But this cannot by itself exhaust the analysis of any
particular agency because, as you say, we cannot be certain that it is
not constrained by some unknown or unknowable computational process.
Some particular agent can only be known to be free, in this sense, to
some limit. Consequently, I don't see how we can argue from the
limitations of mathematicians as agents to the metaphysics of
mathematics.

David

[David Nyman]

On 30 May 2012 04:41, Jesse Mazer <laser...@gmail.com> wrote:

> Only David Nyman agreed as far as I can see

See my reply to Stephen.

David

[Stephen P. King]

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 <aalo...@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 objects simultaneously.

That's just about the number of distinct "chunks" of information you can hold in working memory, so that you can name the distinctive features of each one after they are removed from your sense experience (see http://www.intropsych.com/ch06_memory/magical_number_seven.html ). But I'm not talking about actually visualizing each and every member of an infinite set, such that I am aware of the distinctive features of each one which differentiate them from the others. I'm talking about a more abstract understanding that a certain property applies to every member, perhaps simply by definition (for example, triangles are defined to be three-sided, so three-sidedness is obviously one of the common properties of the set of all triangles). Do you think it's impossible to have an abstract understanding that a large (perhaps infinite) set of objects all share a particular property?

    A single finite and faithful (to within the finite margin of error) representation of "triangle" works given that definition. This is there nominalism and universalism come to blows....

 

Your remarkable objection that "if two mathematicians consider two different arbitrary objects they will obtain different results" demonstrates that you are not a mathematician.

Huh? I didn't write the phrase you put in quotes, nor imply that this was how *I* thought mathematicians actually operated--I was just saying that *you* seemed to be suggesting that mathematicians could only prove things by making specific choices of examples to consider, using their free will. If that's not what you were suggesting, please clarify (and note that I did ask if this is what you meant in my previous post, rather than just assuming it...I then went on to make the conditional statement that IF that was indeed what you meant, THEN you should find it impossible to explain how mathematicians could be confident that a theorem could not be falsified by a new choice of example. But of course I might be misunderstanding your argument, that's why I asked if my reading was correct.)

 

Arbitrary element is not an object, it is a  mental but non-physical process  which enables one to do a physically impossible thing : to observe an infinite set of objects simultaneously considering then all their common properties at a single really existing object. Therefore two different mathematicians will necessarily obtain the same result.   

So you agree mathematicians don't have to make an actual choice of a specific element to consider? Then how is free will supposed to be relevant if there is no actual choice whatsoever being made?

--

    Why do you keep insisting on a "specific" property to the "choice" while being shown that the a priori "specificity" itself that is prohibited by the definition.

He didn't refer to a specific property but to a specific choice of element, which is what Loskin says entails the magic ability to select one among an infinite number.  He apparently thinks of it like the complement of the axiom of choice: to pick an element you need to say,"Not this one. Not this one. Not..." an infinite number of times.

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, it is the "scalar field" of mathematics, IMHO; you can get from it anything you want.

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

    The axiom of choice allows for violation of conservation laws, if it where to be a physical law.

[John Clark]

On Tue, May 29, 2012  Aleksandr Lokshin <aalo...@gmail.com> 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, it is agreed that it is not determined by some law

In other words "free will" has no cause and thus is random.
 

> and is not a random process.

In other words "free will" is random and not random. In still other words when a human
makes the "free will" noise it conveys just as much information as a cow does when it
makes the "moo" noise.
 

 >We have agfeed that the choice of "an arbitrary element" is not a random chaice

and is not a choice determinate by some law.

In other words we have agreed that "free will" is gibberish. 

 

> If one uses mathematics, then one operates with a process which is prohibited in physics.

"Free will" is not just prohibited in physics, it is prohibited in logic too.
 

> 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

That is true, you can't deny "free will" because there is nothing to deny, there is no there there.
It would be like denying a duck's "quack".

  John K Clark

[Bruno Marchal]

The axiom of choice is not a physical law.

Bruno

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

[meekerdb]

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 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

Brent,

    You are assuming that there is no difference between an known and an unknown quantity. A big mistake!

Can you quote where I have made this assumption?

Brent

[meekerdb]

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 advance, e.g. "triangles" is a function that picks out things with three sides meeting pairwise as three vertices.  But I have no idea what you mean by "optimality".

    What does that word mean? Try this  from http://encyclopedia2.thefreedictionary.com/Optimality

1.	(mathematics)	optimal - Describes a solution to a problem which minimises some cost function. Linear programming is one technique used to discover the optimal solution to certain problems.
2.	(programming)	optimal - Of code: best or most efficient in time, space or code size.

    Is that helpful?

No. It doesn't explain what a "solution to a critereon" would be, much less by what measure such a solution might be "optimal".

Brent

[meekerdb]

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

[John Clark]

On Wed, May 30, 2012  Bruno Marchal <mar...@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 associated cause, and like all good axioms it is not intuitively obvious that its opposite must be true. And as a bonus it appears that our Universe follows the Axiom of Choice, some things really do happen for no reason, some things are random.

 John K Clark 

 

[Brian Tenneson]

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.

--

[meekerdb]

I don't see what it has to do with physical events and causes?

Brent

[meekerdb]

Yes, there is more than one thing that contradicts intuition.

Brent

[Bruno Marchal]

The axiom of choice just asserts that an arbitrary product of a family of non empty set is non empty. It is equivalent with the statement that all set can be well ordered. It is trivial on finites sets, and looks rather intuitive on infinite sets. 

There is no clue of direct relationship with physics, other than assuring (another consequence) that infinite linear spaces have alway a base, and things of that type.

It has a priori nothing to do with free will, neither with physics, and the term "choice" has no serious relation with the notion of human choice.

Interestingly ZF and ZFC which proves much more arithmetical sentences than PA, are actually equivalent, i.e. proves the same arithmetical sentences. The choice (C) add nothing to arithmetic from ZF pov. This is not obvious and the proof relies on Gödel constructible universes. I refer you to a good book on axiomatic set theory.

This does not mean I am not using it, as you need it to prove the completeness of the predicate logic, which uses the fact that each consistent set of first order sentences can be extended into one maximal consistent set. This needs the axiom of choice. This allows the fundamental relation (consistent <=> having a model), and (proof <=> true in all models).

Bruno

 John K Clark 

 

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[Bruno Marchal]

Intuition is the logic of the self-extending self. The other, for that self, is already counter-intuitive. 

That is why the platonist suspect reality of not being WYSIWYG  (what you see is what you get).

QM is counter-intuitive, and when I was young I found the idea that the Earth was a sort of ball quite counter-intuitive too.

Comp mirrors the conflict between intuition and  counter-intuition by the difference between the logic of Bp and Bp & p (G extending classical logic) and an epistemic account of a intuitionist knower.

(the real counter-intuitive shock is with matter Bp & Dt, it makes things symmetrical)

Bruno

Brent

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[John Clark]

On Wed, May 30, 2012  Bruno Marchal <mar...@ulb.ac.be> wrote:

> The axiom of choice just asserts that an arbitrary product of a family of non empty set is non empty.

True, but my dictionary says "arbitrary" means "based on a random choice or personal whim".

> There is no clue of direct relationship with physics

If modern physics said randomness does not exist then there would be a conflict with the Axiom of Choice, they could not both be true; but physics says randomness DOES exist so they are compatible. 

> It has a priori nothing to do with free will

Of course it doesn't, nothing real can have anything to do with "free will" because "free will" is gibberish. But the Axiom of Choice does have something to do with cause and effect and randomness because those things are not gibberish, it even has something to do with intelligence. When Alan Turing designed the first stored program electronic digital computer, the Manchester Mark 1, he insisted it have a hardware random number generator incorporated in it because he felt that pseudo-random numbers being produced by a numerical process could not be truly random. He thought that if a machine could sometimes make purely random guesses and then use logic to examine the validity of those guesses it might be able to overcome some of the limitations he himself had found in pure Turing Machines (although he never used that name for them), and then you could make what he called a "Learning Machine. He thought that in this way the limitations all deterministic processes have that he and Godel had found might be overcome, at least in part.

  John K Clark

 

 

[Brian Tenneson]

Of course it doesn't, nothing real can have anything to do with "free will" because "free will" is gibberish.

http://plato.stanford.edu/entries/freewill/

 

[John Mikes]

Brian,

 thanks for the excerpt from the Stanford Enc. It is the usual 'scientifically' diluted 'everything', yet includes some supprt for John's quoted phrase.

May I add my contribution (not included in the Enc.-txt:

In -MY- belief system we are part of that infinite complexity we may call "world" - or: "Everything" with very limited knowledge of its structure and 'content' (if it has such).

WITHIN those possibilities the complexity provides we can choose from those chances we know of - and we do. Other 'chances' are hidden, "no-chances" are excluded. So whatever we 'will' is a limited choice - but freely so. It is yet our responsibility from the limited sortiment - faith-based philosophies have it almost right - except for the influence of the 'hidden' part from us, playing a part in our cognition. It is not "partially free": rather it is "partially deterministic". We THINK it is free will.

 

R A N D O M  is another thorn in my views: if such thing was real and available (in any aspect) we were wrong in ANY prediction we made and make upon the belief that data will fall into position. Unless, of course, one restricts random to those instances where it would interfere with a non-random computation. (Nice random, indeed!)

Then there is another flaw: random is thought of in our known logical systems, a restricted domain and not controling Nature (Everything) at all. We don't even know if the 'infinite complexity' is a dynamic set of relations only, or an infinite(?) system(?) of everything in an interchange?

Or: whatever we cannot even think of?

 

But we are proud of our Free Will. Good for us.

John Mikes

On Thu, May 31, 2012 at 11:07 AM, Brian Tenneson <ten...@gmail.com> wrote:

Of course it doesn't, nothing real can have anything to do with "free will" because "free will" is gibberish.

http://plato.stanford.edu/entries/freewill/

 

--

[John Clark]

On Thu, May 31, 2012 at 11:07 AM, Brian Tenneson <ten...@gmail.com> wrote:

>> Of course it doesn't, nothing real can have anything to do with "free will" because "free will" is gibberish.

http://plato.stanford.edu/entries/freewill/

I stopped reading after the first line:

“Free Will” is a philosophical"

Already I have a bad feeling about this.

 "term of art or a particular sort of capacity of rational agents to choose a course of action from among various alternatives. "

If they are "rational agents" then it's rational and if it's rational then there is a reason behind it and if there is a reason behind it then it's deterministic. Like I said, gibberish, but that shouldn't be surprising, it was after all written by philosophers.

  John K Clark

[Bruno Marchal]

On 31 May 2012, at 17:03, John Clark wrote:

On Wed, May 30, 2012  Bruno Marchal <mar...@ulb.ac.be> wrote:

> The axiom of choice just asserts that an arbitrary product of a family of non empty set is non empty.

True, but my dictionary says "arbitrary" means "based on a random choice or personal whim".

It math, if P(x) is true for arbitrary x, it just means that P(x) is true for all x. 

> There is no clue of direct relationship with physics

If modern physics said randomness does not exist then there would be a conflict with the Axiom of Choice,

The axiom of choice has nothing to with randomness, a priori. I can imagine the existence of theories bringing relation, for divine (non turing emulable) entities. But then you have to present those theories.

they could not both be true; but physics says randomness DOES exist so they are compatible. 

Comp says randomness does exist, and physics confirms that, OK. But again, this has nothing to do directly with the axiom of choice which concerns set theory. 

There are evidence that 'mathematical" physics can live in little constructive toposes, and if I remember well the reading of papers some time ago, I think that the axiom of choice makes those toposes, or topoi, boolean, that is still obeying classical logic, which is not so much liked by the constructive people. Physics lives in very short initial segment of ZF, it is not clear if the axiom of choice says anything about the physical reality, nor even of the math, except by making true some nice completing property, like having *all* Hilbet space having orthonormal base, in physics, or like all consistent set of sentences having unique consistent extensions. But, with comp, this concerns the epistemology, and things are very difficult.

Consciousness surfs on coherent dreams, and it is just an open question if that converges to a unique physical universe, or a unique multiverse, or a unique multi-multiverse, or and this on all ordinals (in which theory? With AC?.

> It has a priori nothing to do with free will

Of course it doesn't, nothing real can have anything to do with "free will" because "free will" is gibberish.

That is *your* theory, and to be honest, I don't find it so much interesting. I do agree that some definition of free will are "gibberish", that is either inconsistent, or empty, but some are not.

I suggest that free-will is the machine awareness of the possibility of hesitating in front of a spectrum of possibilities. 

Butterflies are close to free will, imo, because of the spectrum of flowers and nectars, but I have no evidence that butterfly have free will because I have no evidence that butterfly can infer and reflect. They might be mainly attracted. But I gave evidence that jumping spiders and octopi have free will in the sense that they do infer the possibilities, and reflect on it. 

Relatively to their cognitive abilities, they have as much free will than you, me and PA (with the definition above).

But the Axiom of Choice does have something to do with cause and effect and randomness because those things are not gibberish,

We could make that true if we would formalize physics in set theory. But there are conceptual reason why such an enterprise is doomed at the start. 

ZF is the "fortran" of the mathematical theories. Just an altar for category theory and "natural transformations" (Eilenberg and MacLane). 

I love ZF, but as a very imaginative Löbian machine.

To say that the axiom of choice has something to do with the notion of cause and effect, without saying in which theory you work is confusing.

it even has something to do with intelligence. When Alan Turing designed the first stored program electronic digital computer, the Manchester Mark 1, he insisted it have a hardware random number generator incorporated in it because he felt that pseudo-random numbers being produced by a numerical process could not be truly random. He thought that if a machine could sometimes make purely random guesses and then use logic to examine the validity of those guesses it might be able to overcome some of the limitations he himself had found in pure Turing Machines (although he never used that name for them), and then you could make what he called a "Learning Machine. He thought that in this way the limitations all deterministic processes have that he and Godel had found might be overcome, at least in part.

For problem solving this in vindicated by the result that Random Oracle can enlarged classes of problem solving. Those are given by necessary non constructive proofs. This does not overcome Incompleteness or insolubility, but can reduce complexities in relative way. That might play a role in the first person indeterminacy comp measure problem, as it gives freely a first person "random Oracle" a priori, relativized by their many computational extensions.

Bruno

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

[meekerdb]

On 5/31/2012 10:24 AM, John Clark wrote:

On Thu, May 31, 2012 at 11:07 AM, Brian Tenneson <ten...@gmail.com> wrote:

>> Of course it doesn't, nothing real can have anything to do with "free will" because "free will" is gibberish.

http://plato.stanford.edu/entries/freewill/

I stopped reading after the first line:

�Free Will� is a philosophical"

Already I have a bad feeling about this.

�"term of art or a particular sort of capacity of rational agents to choose a course of action from among various alternatives. "

If they are "rational agents" then it's rational and if it's rational then there is a reason behind it and if there is a reason behind it then it's deterministic.

That's not logically the case.� People who believe in 'free will' think the reason is in front of it, i.e. the reason for posting this is to communicate.� If they believe in 'libertarian free will' they think that this teleological reason can be an efficient physical cause with no determinate antecedents. A random event could satisfy the 'efficient physical cause' but they rule out random events as inconsistent with obviously purposeful decisions and actions.� This contradicts our theories of physics and the brain - but it is not a logical contradiction as you imply.�

Brent

Like I said, gibberish, but that shouldn't be surprising, it was after all written by philosophers.

� John K Clark

[meekerdb]

On 5/31/2012 10:57 AM, Bruno Marchal wrote:

it even has something to do with intelligence. When Alan Turing designed the first stored program electronic digital computer, the Manchester Mark 1, he insisted it have a hardware random number generator incorporated in it because he felt that pseudo-random numbers being produced by a numerical process could not be truly random. He thought that if a machine could sometimes make purely random guesses and then use logic to examine the validity of those guesses it might be able to overcome some of the limitations he himself had found in pure Turing Machines (although he never used that name for them), and then you could make what he called a "Learning Machine. He thought that in this way the limitations all deterministic processes have that he and Godel had found might be overcome, at least in part.

For problem solving this in vindicated by the result that Random Oracle can enlarged classes of problem solving. Those are given by necessary non constructive proofs. This does not overcome Incompleteness or insolubility, but can reduce complexities in relative way. That might play a role in the first person indeterminacy comp measure problem, as it gives freely a first person "random Oracle" a priori, relativized by their many computational extensions.

Bruno

And it is a very likely trick for evolution to have developed since making random choices is part of optimum strategies in games with incomplete information.

Brent

[John Clark]

On Thu, May 31, 2012 at 2:20 PM, meekerdb <meek...@verizon.net> wrote:

> If they are "rational agents" then it's rational and if it's rational then there is a reason behind it and if there is a reason behind it then it's deterministic.

> That's not logically the case.  People who believe in 'free will' think the reason is in front of it,

In front of it? I don't know what that means and I would bet money you don't either. It sounds good though as long as you don't examine it.

> the reason for posting this is to communicate.

You wish to communicate your ideas, and there is a reason for this desire (maybe genes maybe environment probably both), or maybe there is no reason for this desire and is thus random.

> A random event could satisfy the 'efficient physical cause' but they rule out random events as inconsistent with obviously purposeful decisions and actions. 

So fans of the "free will" noise think purposeful events, things that happen for a reason, are not random, that is to say they did not happen for no reason. Or to say the same thing with different words fans of the "free will" noise think random events are random and purposeful events are purposeful. Well, it may not be deep but at least it's true.

  John K Clark

[meekerdb]

On 5/31/2012 12:39 PM, John Clark wrote:

On Thu, May 31, 2012 at 2:20 PM, meekerdb <meek...@verizon.net> wrote:

> If they are "rational agents" then it's rational and if it's rational then there is a reason behind it and if there is a reason behind it then it's deterministic.

> That's not logically the case.  People who believe in 'free will' think the reason is in front of it,

In front of it? I don't know what that means and I would bet money you don't either. It sounds good though as long as you don't examine it.

Look up 'teleology'. Almost any reason a person will give for their actions will be a reference to some future state.  In a deterministic world all physics is time reversible so there's no fundamental distinction between being determined by a future state and being determined by a past state.  But if successive states are not physically determined by prior states the two are not the same.

> the reason for posting this is to communicate.

You wish to communicate your ideas, and there is a reason for this desire (maybe genes maybe environment probably both),

There is a reason; I gave one.  But the question is whether this reason in terms of future purpose had a *physical* cause.  Believers in 'contra causal free will' suppose that it did not, that my 'soul' or 'spirit' initiated the physical process without any determinative physical antecedent.

or maybe there is no reason for this desire and is thus random.

> A random event could satisfy the 'efficient physical cause' but they rule out random events as inconsistent with obviously purposeful decisions and actions. 

So fans of the "free will" noise think purposeful events, things that happen for a reason, are not random, that is to say they did not happen for no reason. Or to say the same thing with different words fans of the "free will" noise think random events are random and purposeful events are purposeful.

No, they think some events are physically uncaused but not-random (because they are purposeful). This is difficult to disprove empirically because the brain is very complex and has lots of random events in it (radioactive decay of potassium K40, gamma ray strikes,...).  So it is hard to eliminate the possibility that a 'spirit' might influence the distribution of these random events, in a way that our relatively crude monitoring could not detect, so that chaotic amplification would produce an action in accordance with the 'spirit' purpose.

I don't believe this theory because I think the apparent markers of 'free will', unpredictability and purposefulness, are easily explained without invoking 'spirits'.  But it's still an empirical question.

Brent

Well, it may not be deep but at least it's true.

  John K Clark

[John Clark]

On Thu, May 31, 2012  meekerdb <meek...@verizon.net> wrote:

> Look up 'teleology'.

Why? I already know it means things happen for a purpose, although it is never made clear who's purpose were talking about or what his purpose is supposed to be. One thing is clear, they had a purpose for a reason or they had a purpose for no reason, there is no third alternative.

> Almost any reason a person will give

If he has a reason then he is deterministic.

> for their actions will be a reference to some future state. 

I did it because I desire to be in state X and I believe my present action will bring that about; and my desire and my belief have a cause or they do not have a cause, there is no third alternative. 

> In a deterministic world all physics is time reversible

Not necessarily, in a deterministic world X and Y will always produce Z, but Q and T could also always produce Z, so if you detect the existence of Z you can't reverse things and figure out what the world was like in the past, you don't know if it was a world of X and Y or a world of Q and T.  In a universe like that you could predict the future but you wouldn't know what happened in the past. Of course this is really moot, we probably don't live in a deterministic world, some things happen for no reason, some things are random.   

> the question is whether this reason in terms of future purpose had a *physical* cause.

I don't understand your emphasis, even information is physical, it determines entropy and takes energy to manipulate.  I don't know what on earth would a non physical cause be like but I do know that the non physical cause would itself have a cause or it would not have a cause, there is no third alternative.

> Believers in 'contra causal free will' suppose that it did not, that my 'soul' or 'spirit' initiated the physical process without any determinative physical antecedent.

A belief that was enormously popular during the dark ages and led to a thousand years of philosophical dead ends; not surprising really, confusion is inevitable if you insist on trying to make sense out of gibberish. 

> they think some events are physically uncaused

So they think it had no cause

> but not-random

So they "think" it happened for no cause and didn't happen for no cause and once again we enter into the merry world of gibberish.

> because they are purposeful.

Then the purpose is the cause, and the purpose exists for a reason or the purpose exists for no reason, there is no third alternative.

> it is hard to eliminate the possibility that a 'spirit' might influence the distribution of these random events

Then of course they would not be random but determined by the spirit, and the spirit influenced those things for a reason or for no reason, there is no third alternative.

> I think the apparent markers of 'free will', unpredictability and purposefulness, are easily explained without invoking 'spirits'. 

Cannot comment, don't know what ASCII string "free will" means and neither do you.

  John K Clark

[Brian Tenneson]

Cannot comment, don't know what ASCII string "free will" means and neither do you.

  John K Clark

 Of course there are various degrees to which it can be free but that doesn't mean "free will" is a meaningless string.  Freedom is defined by the observer.  I note the freedom I have in choosing my beliefs.  I am not bound to agree with you nor am I bound to disagree with you. 
The Stanford Encyclopedia of Philosophy defines free will as follows

"“Free Will” is a particular sort of capacity of rational agents to choose a course of action from among various alternatives. "

So what is the fuss about?

[meekerdb]

On 6/1/2012 8:59 AM, John Clark wrote:

> Believers in 'contra causal free will' suppose that it did not, that my 'soul' or 'spirit' initiated the physical process without any determinative physical antecedent.

A belief that was enormously popular during the dark ages and led to a thousand years of philosophical dead ends; not surprising really, confusion is inevitable if you insist on trying to make sense out of gibberish. 

So you think the existence of soul or spirit is not just false but incomprehensible.  I disagree since there are experiments (e.g. healing prayer, NDE tests) that could have provided evidence for these extra-physical phenomena.  By their null result they provide evidence against them.  But on your view there cannot be evidence for or against because the concept cannot be given any meaning, much less an operational meaning that can be tested.

Brent

[meekerdb]

On 6/1/2012 11:43 AM, Brian Tenneson wrote:

Cannot comment, don't know what ASCII string "free will" means and neither do you.

� John K Clark

�Of course there are various degrees to which it can be free but that doesn't mean "free will" is a meaningless string.� Freedom is defined by the observer.� I note the freedom I have in choosing my beliefs.� I am not bound to agree with you nor am I bound to disagree with you.�

The Stanford Encyclopedia of Philosophy defines free will as follows

"�Free Will� is a particular sort of capacity of rational agents to choose a course of action from among various alternatives. "

So what is the fuss about?

The fuss is because the concept is thought to be fundamental to jurisprudence and social policy (it's even cited in some Supreme Court decisions).� The concept of free will has been carried over from past theological and philosophical ideas.� But now the concept is attacked by scientists and some philosophers as incoherent or empirically false.� If they are right it would seem to imply revision of the social/legal concepts and laws derived from it.� Can existing practice be justified on a purely utilitarian basis?

Brent

[Brian Tenneson]

The fact that free will is debated lends credence to the notion that "Free will" is not meaningless.  "Free will" has to mean something before it can be attacked.

On Fri, Jun 1, 2012 at 12:30 PM, meekerdb <meek...@verizon.net> wrote:

On 6/1/2012 11:43 AM, Brian Tenneson wrote:

Cannot comment, don't know what ASCII string "free will" means and neither do you.

  John K Clark

 Of course there are various degrees to which it can be free but that doesn't mean "free will" is a meaningless string.  Freedom is defined by the observer.  I note the freedom I have in choosing my beliefs.  I am not bound to agree with you nor am I bound to disagree with you. 

The Stanford Encyclopedia of Philosophy defines free will as follows

"“Free Will” is a particular sort of capacity of rational agents to choose a course of action from among various alternatives. "

So what is the fuss about?

The fuss is because the concept is thought to be fundamental to jurisprudence and social policy (it's even cited in some Supreme Court decisions).  The concept of free will has been carried over from past theological and philosophical ideas.  But now the concept is attacked by scientists and some philosophers as incoherent or empirically false.  If they are right it would seem to imply revision of the social/legal concepts and laws derived from it.  Can existing practice be justified on a purely utilitarian basis?

Brent

--

[John Clark]

On Fri, Jun 1, 2012 Brian Tenneson <ten...@gmail.com> wrote:

> Freedom is defined by the observer. 

Exactly! A man is walking down a road and spots a fork in the road far ahead. He knows of advantages and disadvantages to both paths so he isn't sure if he will go right or left, he hadn't decided. Now imagine a powerful demon able to look into the man's head and quickly deduce that he would eventually choose to go to the left.

Meanwhile the man, whose mind works much more slowly than the demon's, hasn't completed the thought process yet. He might be saying to himself I haven't decided, I'll have to think about it, I'm free to go either way. From his point of view he is in a sense correct, even a robot does not feel like a robot, but from the demon's viewpoint it's a different matter, he simply deduced a purely mechanical operation that can have only one outcome.

Or it may not be deterministic at all, perhaps I took the left path for no reason at all, either way the "free will" noise that some human beings like to make is of no more help clarifying the situation than the "quack" noise ducks like to make.  

 

>The Stanford Encyclopedia of Philosophy defines free will as follows

 “ Free Will” is a particular sort of capacity of rational agents

If they're rational there is a reason they do what they do, hence they are deterministic.

> to choose a course of action from among various alternatives. "

And there is a reason for making that particular choice or there is not a reason for making that particular choice, there is no third alternative.

> So what is the fuss about?

No fuss at all as long as you don't examine too closely what it is actually trying to say; but to be fair that definition of free will is not significantly more idiotic and self contradictory than the verbiage most professional philosophers churn out.

  John K Clark  

[Evgenii Rudnyi]

On 01.06.2012 20:48 meekerdb said the following:

From Understanding Consciousness by Max Velmans:

p. 300 "To make matters worse, there are four distinct ways in which
body/brain and mind/consciousness might in principle, enter into casual
relationship. There might be physical causes of physical states,
physical causes of mental states, mental causes of mental states, and
mental causes of physical states. Establishing which forms of causation
are effective in practice has clear implication for understanding the
aetiology and proper treatment of illness and disease.

Within conventional medicine, physical -> physical is taken for granted.
Consequently, the proper treatment for physical disorders is assumed to
be some from of physical intervention. Psychiatry takes the efficacy of
physical -> mental causation for granted, along with the assumption that
the proper treatment for psychological disorders may involve
psychoactive drugs, neurosurgery and so on. Many forms of psychotherapy
take mental -> mental causation for granted, and assume that
psychological disorders can be alleviated by means of 'talking cures',
guided imagery, hypnosis and other form of mental intervention.
Psychosomatic medicine assumes that mental -> physical causation can be
effective ('psychogenesis'). Consequently, under some circumstances, a
physical disorder (for example, hysterical paralysis) may require a
mental (psychotherapeutic) intervention. Given the extensive evidence
for all these causal interactions (cf. Velmans, 1996a), how we to make
sense of them?"

Velmans, M. 1996a: The Science of Consciousness: Psychological,
Neuropsychological and Clinical Reviews, London: Routledge.

Evgenii

[Evgenii Rudnyi]

On 01.06.2012 21:30 meekerdb said the following:

> On 6/1/2012 11:43 AM, Brian Tenneson wrote:
>>
>>
>> Cannot comment, don't know what ASCII string "free will" means and
>> neither do you.
>>

>> John K Clark

>>
>>
>>
>> Of course there are various degrees to which it can be free but

>> that doesn't mean "free will" is a meaningless string. Freedom is
>> defined by the observer. I note the freedom I have in choosing my
>> beliefs. I am not bound to agree with you nor am I bound to
>> disagree with you. The Stanford Encyclopedia of Philosophy defines

>> free will as follows
>>
>> "�Free Will� is a particular sort of capacity of rational agents to
>> choose a course of action from among various alternatives. "
>>
>> So what is the fuss about?
>
> The fuss is because the concept is thought to be fundamental to
> jurisprudence and social policy (it's even cited in some Supreme

> Court decisions). The concept of free will has been carried over from
> past theological and philosophical ideas. But now the concept is

> attacked by scientists and some philosophers as incoherent or

> empirically false. If they are right it would seem to imply revision
> of the social/legal concepts and laws derived from it. Can existing

> practice be justified on a purely utilitarian basis?

What about that if you see something working (like a human society) and
you do not understand how it is working, then it might be a good idea
not to try to change it. The drive for change usually comes from people
who are not satisfied with their position in the current society. Why
the drive for change should come from some metaphysical discussions?

Evgenii

[John Clark]

On Fri, Jun 1, 2012 at 2:48 PM, meekerdb <meek...@verizon.net> wrote:

>> A belief that was enormously popular during the dark ages and led to a thousand years of philosophical dead ends; not surprising really, confusion is inevitable if you insist on trying to make sense out of gibberish. 

> So you think the existence of soul or spirit is not just false but incomprehensible. 

There are aspects of the soul theory that are comprehensible, in fact there are aspects about it that I think are true, but a much better name for it would be "information". What I think is gibberish is "free will", it is incomprehensible because their is nothing to comprehend, it isn't saying anything, there is no there there.

> there are experiments (e.g. healing prayer, NDE tests) that could have provided evidence for these extra-physical phenomena.  By their null result they provide evidence against them.

The God theory is not gibberish, it's just wrong. Free will is not even wrong. And they got null results only when the sick people didn't know they were being prayed over, when they did know they actually got worse.

  John K Clark

 

[John Clark]

On Fri, Jun 1, 2012  Brian Tenneson <ten...@gmail.com> wrote:

> The fact that free will is debated lends credence to the notion that "Free will" is not meaningless.  "Free will" has to mean something before it can be attacked.

But I'm not saying "free will" does not exist, and I'm not attacking it because there is nothing to attack, it would be like attacking a duck's "quack". I'm saying I don't know what the hell you're talking about when you type the ASCII characters "free will" and neither do you. I'm not saying the idea is wrong, I'm saying there is no idea there. How do I know this? Because whenever anybody talks about "free will" the resulting verbiage  is ALWAYS a blizzard of contradictory statements, circular definitions, vague illusions, pious speeches, and just plain old idiocy; there is never any substance there. Never.

  John K Clark 
    

 

[John Clark]

On Fri, Jun 1, 2012  meekerdb <meek...@verizon.net> wrote:

 > Can existing practice be justified on a purely utilitarian basis?

Yes.

  John K Clark

[Brian Tenneson]

The capacity (which can be defined) of an agent (which can be defined) to be able (which can be defined) to choose (which can be defined) when (which can be defined)  presented (which can be defined) with a choice (which can be defined).

Certainly not meaningless.

--

[John Mikes]

Did ANYBODY so far - among those ~100(+?) posts (so far  erased in this discussion)  I D E N T I F Y  free will?

I red about a 'relatively' free will, (= among (given) choices)  as well as 'totally freely chosen' decisions etc. etc. - none of them too impressive.

I tried to substantiate several time that we live in a steadily  evolving state of cognition and consider (observe?) as of yesterday more than earlier, consequently (by induction) there is more to the "world" than our today-s position. Whatever we know - either consciously, or not knowingly: subconsciously adds to our decision making and by tomorrow we may be able to draw different conclusions.

(When I wrote my reply up to this point, my mailbox induced Brian's post:)

-------------------------------

"The capacity (which can be defined) of an agent (which can be defined) to be able (which can be defined) to choose (which can be defined) when (which can be defined)  presented (which can be defined) with a choice (which can be defined).Certainly not meaningless. - Brian Tenneson"

---------------------------------------------------

(emphasis of the ID words by me) - and I reflect:

It certainly IS not meaningless and IS an identification, however not of a FREE will. It is a decision between "given" choices. "Tomorrow" more info may be given to us and our today's choice may be overridden.

What I consider a "free will"  is independent of the 'choices' we  G E T and is solely formatted by our (pesonal? inside?) mindset (call it will?). We, however, are part of a more extended (expanded?) world, I like to call it 'Everything' (an infinite complexity of so far(?) unknowable content) and all of its influences (may) contribute to our 'decisionmaking' although we may not know about either the nature of most of those influences, nor that we ARE responding to them.

 

Brent Meeker (if it really came from YOUR post <ha ha>):

" Can existing practice be justified on a purely utilitarian basis?"

Of course it can, in the 'purely utilitarian sense'. Just do not mix such into a theoretical aspect and don't call it (rational?) truth.

(Let me stay out of discussing Max Velman's position. I appreciate his scientific base - however different from my agnostic views).

 

John M

 

 

 

 

Evgenii

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[Brian Tenneson]

FREE means being able to choose any among a number of choices.  You want freedom of will to mean an agent can choose something beyond what the given choices are?  That would imply free will does not exist yet, in that event, free will is still NOT meaningless.

Right now I am unconcerned with whether free will exists or not.  I am concerned with the statement ""free will" is meaningless."  I have given a definition, borrowed from the SEP, that is as good a definition as for any concept (outside mathematical ones). 

[meekerdb]

The hard one to define with falling into circularity is "agent" which is often defined as an entity with free will.  To test something you need an operational definition.  "Agent" might be defined as an entity with acts unpredictably but purposefully.  But both of those are a little fuzzy.

Brent

[meekerdb]

On 6/2/2012 11:45 AM, John Mikes wrote:

Did ANYBODY so far - among those ~100(+?) posts (so far  erased in this discussion)  I D E N T I F Y  free will?

I've tried to identify two meanings: One, which I consider unproblematic, is the social and legal attribute of decisions which are not coerced.  The other is the folk meaning attributing decisions to a spirit or soul which can initiate physical events but which is independent of all prior physical events.

Brent

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[meekerdb]

On 6/1/2012 11:25 PM, Evgenii Rudnyi wrote:
>> The fuss is because the concept is thought to be fundamental to
>> jurisprudence and social policy (it's even cited in some Supreme
>> Court decisions). The concept of free will has been carried over from
>> past theological and philosophical ideas. But now the concept is
>> attacked by scientists and some philosophers as incoherent or
>> empirically false. If they are right it would seem to imply revision
>> of the social/legal concepts and laws derived from it. Can existing
>> practice be justified on a purely utilitarian basis?
>
> What about that if you see something working (like a human society) and you do not
> understand how it is working, then it might be a good idea not to try to change it.

I agree with that. An oddly after spending 60 pages attacking free will as an illusion of
an illusion, Sam Harris seems to that we may need retributive punishment anyway.

> The drive for change usually comes from people who are not satisfied with their position
> in the current society. Why the drive for change should come from some metaphysical
> discussions?

Every successful revolution has its ideology and philosophy though.

Brent
"Without the pen of Paine, the sword of Washington would have been wielded in vain."
--- John Adams

[Brian Tenneson]

How about define agent to be a type 4 agent as explained here:
http://cs.wallawalla.edu/~aabyan/Colloquia/Aware/aware2.html

[meekerdb]

I don't think any of us qualify since you have to believe and be aware of your belief of every tautology which means all possible mathematical proofs.

Actually it seems to me that so much self awareness is contrary to the common notion of 'free will'.  The feeling of 'free will' comes about because not only or our decisions unpredictable, they are unpredictable even by us.  If you had really complete self-awareness you could trace your every decision back to various external inputs or random events and you would be disabused of the feeling that "I could have done otherwise".

Brent

[John Clark]

On Sat, Jun 2, 2012  Brian Tenneson <ten...@gmail.com> wrote:

> The capacity (which can be defined) of an agent (which can be defined) to be able (which can be defined) to choose (which can be defined)

If it can be done then do so!  Explain "choose" in a way that shows it is not deterministic and also not random, find a way to say that a choice did not happen for a reason and did not happen for no reason, and do so in a way that is not embarrassingly self contradictory. Do that and you have won the argument.

> when (which can be defined)  presented (which can be defined)

By the way, "defined" can't be defined unless you already know what "defined" means, that's why examples are more important than definitions;  so if a definition is too hard for you just give me examples of things that can make choices  and things that can't, but be prepared to defend your reasoning (a deterministic process) why they are in one category and not the other.   
 

> with a choice (which can be defined). Certainly not meaningless.

The word "choice" is perfectly respectable, I use it myself, but you are a fan of the "free will" noise so I would bet money that any definition you give of it will be self-contradictory or circular or both. 

  John K Clark

[John Clark]

On Sat, Jun 2, 2012  meekerdb <meek...@verizon.net> wrote:

> "Agent" might be defined as an entity with acts unpredictably

Without a reason.

> but purposefully. 

With a reason.

> But both of those are a little fuzzy.

That's not fuzzy, it's idiotic. You can arrange the words free, decide, choose, purpose, reason, pick, voluntary and unpredictable in any order you like but it won't change the fact that at the end of the day things happen for a reason or things don't happen for a reason. 

   John K Clark

[John Clark]

On Sat, Jun 2, 2012 at 8:55 PM, meekerdb <meek...@verizon.net> wrote:

> oddly after spending 60 pages attacking free will as an illusion of an illusion, Sam Harris seems to that we may need retributive punishment anyway.

I don't understand what's odd about that, certainly we need retributive punishment if we don't want to be murdered in our beds. And I disagree about "free will" being a illusion, a illusion is a real subjective phenomenon, "free will" is just a noise.

 John K Clark

[Craig Weinberg]

On Jun 3, 12:38 pm, John Clark <johnkcl...@gmail.com> wrote:

> On Sat, Jun 2, 2012  Brian Tenneson <tenn...@gmail.com> wrote:
>
> > The capacity (which can be defined) of an agent (which can be defined) to
> > be able (which can be defined) to choose (which can be defined)
>
> If it can be done then do so!  Explain "choose" in a way that shows it is
> not deterministic and also not random, find a way to say that a choice did
> not happen for a reason and did not happen for no reason,

How about this. You try moving your arm with an explanation or a
reason or with no reason. Did it move? Now just move your arm. Was it
a lack of explanation or reason or randomness that was preventing you
from FREEly excercising your WILL over your own arm?

Please explain how your arm moved in a way that shows it is purely
deterministic or purely random, find a way to say that a reason or non-
reason alone caused it without the assistance of your choice, and do
so in away that is not embarrassingly self contradictory. Do that and
you have not lost the argument.

Craig

[Craig Weinberg]

On Jun 3, 1:00 pm, John Clark <johnkcl...@gmail.com> wrote:

> On Sat, Jun 2, 2012 at 8:55 PM, meekerdb <meeke...@verizon.net> wrote:
> > oddly after spending 60 pages attacking free will as an illusion of an
> > illusion, Sam Harris seems to that we may need retributive punishment
> > anyway.
>
> I don't understand what's odd about that, certainly we need retributive
> punishment if we don't want to be murdered in our beds.

I don't understand why anyone could not see that as a glaring
violation of common sense, except that I think it must be like
handedness or gender orientation. Why would punishment work in any way
if people are determined to commit crimes regardless? How could
punishment act on anything except the will? What law of physics
supports the effectiveness of punishment? Can you punish phosphorus
until phosphorus changes? Why not?

> And I disagree
> about "free will" being a illusion, a illusion is a real subjective
> phenomenon, "free will" is just a noise.

I have never seen anyone with such a personal axe to grind about this
subject. You hate free will. It is unworthy of even a hallucinatory
status. It is intolerable to you. It's as if you were trying to...deny
something that is undeniable.

Craig

[meekerdb]

On 6/1/2012 8:59 AM, John Clark wrote:

On Thu, May 31, 2012  meekerdb <meek...@verizon.net> wrote:

> Look up 'teleology'.

Why? I already know it means things happen for a purpose, although it is never made clear who's purpose were talking about or what his purpose is supposed to be. One thing is clear, they had a purpose for a reason or they had a purpose for no reason, there is no third alternative.

But is you have a purpose, even for no reason, it doesn't follow that your actions are random.

> Almost any reason a person will give

If he has a reason then he is deterministic.

You keep equating 'having a purpose', 'having a reason' and 'being determined', but I don't think they are the same thing.  If your purpose is to win money at poker your optimum strategy includes some random actions.

> for their actions will be a reference to some future state. 

I did it because I desire to be in state X and I believe my present action will bring that about; and my desire and my belief have a cause or they do not have a cause, there is no third alternative. 

People who believe in 'free will' also agree that their decisions and beliefs and actions have causes or not.  The difference is they believe that the causes are immaterial.

> In a deterministic world all physics is time reversible

Not necessarily, in a deterministic world X and Y will always produce Z, but Q and T could also always produce Z, so if you detect the existence of Z you can't reverse things and figure out what the world was like in the past, you don't know if it was a world of X and Y or a world of Q and T.  In a universe like that you could predict the future but you wouldn't know what happened in the past. Of course this is really moot, we probably don't live in a deterministic world, some things happen for no reason, some things are random.   

> the question is whether this reason in terms of future purpose had a *physical* cause.

I don't understand your emphasis, even information is physical, it determines entropy and takes energy to manipulate.  I don't know what on earth would a non physical cause be like but I do know that the non physical cause would itself have a cause or it would not have a cause, there is no third alternative.

> Believers in 'contra causal free will' suppose that it did not, that my 'soul' or 'spirit' initiated the physical process without any determinative physical antecedent.

A belief that was enormously popular during the dark ages and led to a thousand years of philosophical dead ends; not surprising really, confusion is inevitable if you insist on trying to make sense out of gibberish. 

It was, and is, enormously popular.  It's not gibberish since it can be empirically tested.  The idea that all events are either physically determined or random is relatively recent.  Before it was recognized how complex the activity of physical systems can be and how physically complex biota are it was reasonable to suppose there was something extra-physical about people and animals that made them unpredictable but purposeful.

> they think some events are physically uncaused

So they think it had no cause

No they think the cause is an immaterial spirit.

> but not-random

So they "think" it happened for no cause and didn't happen for no cause and once again we enter into the merry world of gibberish.

> because they are purposeful.

Then the purpose is the cause, and the purpose exists for a reason or the purpose exists for no reason, there is no third alternative.

> it is hard to eliminate the possibility that a 'spirit' might influence the distribution of these random events

Then of course they would not be random but determined by the spirit, and the spirit influenced those things for a reason or for no reason, there is no third alternative.

> I think the apparent markers of 'free will', unpredictability and purposefulness, are easily explained without invoking 'spirits'. 

Cannot comment, don't know what ASCII string "free will" means and neither do you.

  John K Clark

There's no point explaining something to someone determined not to understand.

Brent

[meekerdb]

On 6/3/2012 9:53 AM, John Clark wrote:

On Sat, Jun 2, 2012  meekerdb <meek...@verizon.net> wrote:

> "Agent" might be defined as an entity with acts unpredictably

Without a reason.

> but purposefully. 

With a reason.

> But both of those are a little fuzzy.

That's not fuzzy, it's idiotic.

You're hung up on the idea that purposeful action must be predictable.  Apparently you never studied game theory.

You can arrange the words free, decide, choose, purpose, reason, pick, voluntary and unpredictable in any order you like but it won't change the fact that at the end of the day things happen for a reason or things don't happen for a reason. 

   John K Clark

Brent
"I've given you an argument. I'm not obliged to give you an understanding."
    --- Oliver Heaviside

[meekerdb]

[meekerdb]

OOPS. I hit "send" instead of "delete".

Brent

[John Clark]

On Sun, Jun 3, 2012 Craig Weinberg <whats...@gmail.com> wrote:

> You try moving your arm with an explanation or a reason or with no reason. Did it move?

That's like asking how long is a piece of string. It depends on if I wanted to move my arm or not. 

> Now just move your arm.

This time I wanted to move my arm and so, unless it was tied down it moved. If it was tied down then a desire of my will remained unfulfilled and I will be unhappy and that will cause me to look for a way to untie my arm. And my will was in the state it was in, the state of wanting to move my arm, for a reason or for no reason, there is no third alternative.  

> Was it a lack of explanation or reason or randomness that was preventing you from FREEly excercising your WILL over your own arm?

I didn't move my arm because I didn't want to move my arm, and I don't know if I didn't want to because of determinism or randomness, but I do know it was one or the other, I do know there was a reason I didn't want to move it (although I might not know what it is) or there was no reason I didn't want to move it .

> Please explain how your arm moved in a way that shows it is purely deterministic or purely random

You seem to believe that if you combine determinism and randomness you can make the "free will" noise more meaningful than a duck's "quack", but you refuse to answer a question I have asked several times before; if I combine a calculator with a roulette wheel so that on average one time in 39 it gives the wrong answer to a calculation does that hybrid device have free will?  If not why not. 

> find a way to say that a reason or non- reason alone caused it

Well that's not very difficult and I don't even need to know what the word "reason" means!  I can also say without fear of contradiction that klogknee caused it or non klognee  caused it.

  John K Clark

[John Clark]

On Sun, Jun 3, 2012  meekerdb <meek...@verizon.net> wrote:

> You're hung up on the idea that purposeful action must be predictable.  Apparently you never studied game theory.

I'm no world class expert but I've taken several college courses on game theory and I know enough to understand that there has been no difficulty in incorporating the ideas of that discipline into computer programs, indeed many recent advances in game theory have come from the results of computer experiments. So are computers purposeful? Do computers have this thing you call "free will"? If not why not.

  John K Clark

     

 

[John Clark]

On Sun, Jun 3, 2012  Craig Weinberg <whats...@gmail.com> wrote:

> > I don't understand what's odd about that, certainly we need retributive punishment if we don't want to be murdered in our beds.

I don't understand why anyone could not see that as a glaring violation of common sense, except that I think it must be like handedness or gender orientation. Why would punishment work in any way if people are determined to commit crimes regardless?

If people are determined then if we change them ( fine them, confine them, kill them, perform surgery on them) or change the environment (make the possibility of severe punishment more likely) then they're behavior will change. That's the nature of determinism, change the input and the output changes, otherwise it wouldn't be deterministic. 

> How could punishment act on anything except the will?

As I've said I have no problem with the word "will" and it does act on the will, if I change things their will will change and either they will no longer want to commit crimes (fear of punishment) or no longer able to fulfill the desire of their will because they are in jail or dead.

> Can you punish phosphorus until phosphorus changes?

Yes, I can put it into a fireproof box or combine the phosphorous with other chemicals and turn it into fertilizer, something that is actually useful.  

> I have never seen anyone with such a personal axe to grind about this subject.

Thank you.

>You hate free will.

Well, a lot of quacking ducks can become annoying. 

 

> It is unworthy of even a hallucinatory status.

Correct.

  John K Clark

[meekerdb]

On 6/4/2012 10:07 AM, John Clark wrote:

On Sun, Jun 3, 2012  meekerdb <meek...@verizon.net> wrote:

> You're hung up on the idea that purposeful action must be predictable.  Apparently you never studied game theory.

I'm no world class expert but I've taken several college courses on game theory and I know enough to understand that there has been no difficulty in incorporating the ideas of that discipline into computer programs, indeed many recent advances in game theory have come from the results of computer experiments.

And so you know that pursuant to the purpose of winning a game it may be useful to make a random choice.

So are computers purposeful?

It depends on their program. Deep Blue purposefully acted to win chess games. Spirit and Opportunity purposely explored parts of Mars.

Do computers have this thing you call "free will"? If not why not.

Depends on what you mean by "free will".  I think that with certain AI programming a computer could have the so called "feeling of free will", i.e. it could infer that it made a choice that was purposeful but not determined (even in cases where it was determined). If it were equipped to act it could act free of coercion. 

Brent

[John Clark]

On Mon, Jun 4, 2012  meekerdb <meek...@verizon.net> wrote:

> And so you know that pursuant to the purpose of winning a game it may be useful to make a random choice.

Certainly!  Random choice is a key part of the Monte Carlo method of statistical mechanics and it is one of the most important computer algorithms ever made, the H-bomb could never have been invented without it.

> Deep Blue purposefully acted to win chess games. Spirit and Opportunity purposely explored parts of Mars.

Agreed.

> Depends on what you mean by "free will". 

There are only two things I mean by "free will" because they are the only two that are not gibberish, but nobody around here except me likes either definition:
1) Free Will is the inability to always know what you are going to do before you do it.
2) Free Will is a noise made by the mouth by a certain subset of bipedal creatures.  

> I think that with certain AI programming a computer could have the so called "feeling of free will"

Yes, as Turing proved, even computers don't know what they will do until they do it.

  John K Clark

 

[meekerdb]

On 6/5/2012 9:02 AM, John Clark wrote:

On Mon, Jun 4, 2012  meekerdb <meek...@verizon.net> wrote:

> And so you know that pursuant to the purpose of winning a game it may be useful to make a random choice.

Certainly!  Random choice is a key part of the Monte Carlo method of statistical mechanics and it is one of the most important computer algorithms ever made, the H-bomb could never have been invented without it.

> Deep Blue purposefully acted to win chess games. Spirit and Opportunity purposely explored parts of Mars.

Agreed.

> Depends on what you mean by "free will". 

There are only two things I mean by "free will" because they are the only two that are not gibberish, but nobody around here except me likes either definition:
1) Free Will is the inability to always know what you are going to do before you do it.

I like it.  I called it upredictability (even by yourself).  But I also added that it included acting purposefully; otherwise simple randomness is 'free will'.

Brent

[Bruno Marchal]

On 05 Jun 2012, at 18:02, John Clark wrote:

On Mon, Jun 4, 2012  meekerdb <meek...@verizon.net> wrote:

> And so you know that pursuant to the purpose of winning a game it may be useful to make a random choice.

Certainly!  Random choice is a key part of the Monte Carlo method of statistical mechanics and it is one of the most important computer algorithms ever made, the H-bomb could never have been invented without it.

> Deep Blue purposefully acted to win chess games. Spirit and Opportunity purposely explored parts of Mars.

Agreed.

> Depends on what you mean by "free will". 

There are only two things I mean by "free will" because they are the only two that are not gibberish, but nobody around here except me likes either definition:
1) Free Will is the inability to always know what you are going to do before you do it.

That would be too large. Pebbles does not know what they will do, for example. Free will is more in the knowledge of that inability, including its exploitation to accelerate the decision in absence of complete information. OK.

2) Free Will is a noise made by the mouth by a certain subset of bipedal creatures.  

I don't think so. Here you confuse the concept of free will with the noise made by mouth when talking on that concept in english.

> I think that with certain AI programming a computer could have the so called "feeling of free will"

Yes, as Turing proved, even computers don't know what they will do until they do it.

I can see what you mean, but you should say, *some* computers, in special states (actually also knowing that they don't know, as above). I mean there are many situation when a computer can predict its doing, and even with free will conditions, there will be a mixing of self-determinacy and self-indeterminacy, leading to possible hesitations. Free will is what makes us hesitating, very often.

Bruno

  John K Clark

 

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[John Clark]

On Tue, Jun 5, 2012  on Bruno Marchal <mar...@ulb.ac.be> wrote:

>> There are only two things I mean by "free will" because they are the only two that are not gibberish, but nobody around here except me likes either definition:
1) Free Will is the inability to always know what you are going to do before you do it.

> That would be too large. Pebbles does not know what they will do, for example.

Yes, so pebbles have free will. I didn't say my definition of free will was useful, I only said it was not gibberish. 

> Free will is more in the knowledge of that inability,

But many people lack that knowledge including everyone on this list except me, it is a fact that they can be absolutely positively 100%  certain they will do X at future time Y but when the time comes they find themselves doing something not even close to X.  In fact such a thing is not even rare.

> including its exploitation to accelerate the decision in absence of complete information.

Computers can make guesses based on the most probable outcome too, and if fitted with a simple hardware random number generator can make guesses based on nothing at all; as I've said computers used that fact to tell people how to build a H-bomb with the Monty Carlo algorithm.

> 2) Free Will is a noise made by the mouth by a certain subset of bipedal creatures.  

I don't think so. Here you confuse the concept of free will with the noise made by mouth when talking on that concept in english.

But that's exactly the problem, there is no concept of free will, there is only the noise "free will", a noise like a duck's "quack" that stands for nothing.

> there are many situation when a computer can predict its doing

Yes, but in general they can not.

 John K Clark

 

[meekerdb]

On 6/5/2012 10:35 AM, John Clark wrote:

On Tue, Jun 5, 2012  on Bruno Marchal <mar...@ulb.ac.be> wrote:

>> There are only two things I mean by "free will" because they are the only two that are not gibberish, but nobody around here except me likes either definition:
1) Free Will is the inability to always know what you are going to do before you do it.

> That would be too large. Pebbles does not know what they will do, for example.

Yes, so pebbles have free will. I didn't say my definition of free will was useful, I only said it was not gibberish. 

> Free will is more in the knowledge of that inability,

But many people lack that knowledge including everyone on this list except me,

It's a matter of degree though.  People may very reliably predict that they will not choose to drive to Phoenix tonight and that they will have coffee with breakfast tomorrow.  So while you do not *always* know what you're going to do, you know your preferences most of the time.

it is a fact that they can be absolutely positively 100%  certain they will do X at future time Y but when the time comes they find themselves doing something not even close to X.  In fact such a thing is not even rare.

But this doesn't affect their belief in 'free will' because they just think, "I changed my mind." They may even regard it as evidence of contra-causal free will since there was no cause known to them that changed their mind and yet the choice was still purposeful.  The feeling of 'free will' comes from the inability retrospectively to see all the causes; so that, out of ignorance, it seems that one could have done otherwise.

Brent

> including its exploitation to accelerate the decision in absence of complete information.

Computers can make guesses based on the most probable outcome too, and if fitted with a simple hardware random number generator can make guesses based on nothing at all; as I've said computers used that fact to tell people how to build a H-bomb with the Monty Carlo algorithm.

> 2) Free Will is a noise made by the mouth by a certain subset of bipedal creatures.  

I don't think so. Here you confuse the concept of free will with the noise made by mouth when talking on that concept in english.

But that's exactly the problem, there is no concept of free will, there is only the noise "free will", a noise like a duck's "quack" that stands for nothing.

> there are many situation when a computer can predict its doing

Yes, but in general they can not.

 John K Clark