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
On Tue, May 29, 2012 at 12:01 PM, Aleksandr Lokshin
<aaloks...@gmail.com <mailto: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
On 5/29/2012 10:52 AMOne cannot, John Clark wrote:
On Sun, May 27, 2012 Aleksandr Lokshin <aaloks...@gmail.com
> 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.
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.
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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