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 <aaloks...@gmail.com<mailto: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 inworking memory, so that you can name the distinctive features of each one after theyare removed from your sense experience (seehttp://www.intropsych.com/ch06_memory/magical_number_seven.html ). But I'm not talkingabout actually visualizing each and every member of an infinite set, such that I amaware 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 toevery member, perhaps simply by definition (for example, triangles are defined to bethree-sided, so three-sidedness is obviously one of the common properties of the set ofall triangles). Do you think it's impossible to have an abstract understanding that alarge (perhaps infinite) set of objects all share a particular property?A single finite and faithful (to within the finite margin of error) representationof "triangle" works given that definition. This is there nominalism and universalismcome 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 besuggesting that mathematicians could only prove things by making specific choices ofexamples 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 IFthat was indeed what you meant, THEN you should find it impossible to explain howmathematicians could be confident that a theorem could not be falsified by a new choiceof example. But of course I might be misunderstanding your argument, that's why I askedif 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 elementto consider? Then how is free will supposed to be relevant if there is no actual choicewhatsoever being made?--Why do you keep insisting on a "specific" property to the "choice" while being shownthat 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.`

The point is is that what ever the choice is, there are ab initio alternatives that arenot exactly known to be optimal solutions to some criterion and somenot-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 --You received this message because you are subscribed to the Google Groups "EverythingList" 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.

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