*<<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.
*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.*
On Wed, May 30, 2012 at 12:38 AM, 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. 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*"
> 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*
> then all their common properties at a single really existing object.
> Therefore two different mathematicians will necessarily obtain the same
> On Wed, May 30, 2012 at 12:13 AM, Jesse Mazer <laserma...@gmail.com>wrote:
>> On Tue, May 29, 2012 at 3:01 PM, 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
>> 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
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