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.
* * * * * * On Tue, May 29, 2012 at 11:05 PM, Brian Tenneson <tenn...@gmail.com> wrote: > It doesn't take free will to prove that every even number is divisible by > 2. How to prove a statement with a universal quantifier is pretty basic. > > > On Tue, May 29, 2012 at 12:01 PM, Aleksandr Lokshin > <aaloks...@gmail.com>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 <meeke...@verizon.net> wrote: >> >> On 5/29/2012 10:52 AMOne cannot, John Clark wrote: >>> >>> >>> On Sun, May 27, 2012 Aleksandr Lokshin <aaloks...@gmail.com> wrote: >>> >>> > All main mathematical notions ( such as infinity, variable, integer >>>> number) implicitly >>>> depend on the notion of free will. >>> >>> >>> Because nobody can 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 >>> >>> >>> >>> >>> >>> >>> -- >>> You received this message because you are subscribed to the Google >>> Groups "Everything List" group. >>> To post to this group, send email to everything-list@googlegroups.com. >>> To unsubscribe from this group, send email to >>> everything-list+unsubscr...@googlegroups.com. >>> For more options, visit this group at >>> http://groups.google.com/group/everything-list?hl=en. >>> >>> >>> -- >>> You received this message because you are subscribed to the Google >>> Groups "Everything List" group. >>> To post to this group, send email to everything-list@googlegroups.com. >>> To unsubscribe from this group, send email to >>> everything-list+unsubscr...@googlegroups.com. >>> For more options, visit this group at >>> http://groups.google.com/group/everything-list?hl=en. >>> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To post to this group, send email to everything-list@googlegroups.com. >> To unsubscribe from this group, send email to >> everything-list+unsubscr...@googlegroups.com. >> For more options, visit this group at >> http://groups.google.com/group/everything-list?hl=en. >> > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to everything-list@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
