On Tue, May 29, 2012 at 4:38 PM, Aleksandr Lokshin <aaloks...@gmail.com>wrote:
> It is impossible to consider common properties of elements of an infinite
> set since, as is known from psycology, a man can consider no more than 7
> 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
> 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?
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