On 5/30/2012 4:45 AM, Bruno Marchal wrote:

On 30 May 2012, at 08:12, Stephen P. King wrote:On 5/30/2012 12:06 AM, meekerdb wrote: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 informationyou can hold in working memory, so that you can name thedistinctive features of each one after they are removed from yoursense experience (seehttp://www.intropsych.com/ch06_memory/magical_number_seven.html ).But I'm not talking about actually visualizing each and everymember of an infinite set, such that I am aware of the distinctivefeatures of each one which differentiate them from the others. I'mtalking about a more abstract understanding that a certainproperty applies to every member, perhaps simply by definition(for example, triangles are defined to be three-sided, sothree-sidedness is obviously one of the common properties of theset of all triangles). Do you think it's impossible to have anabstract understanding that a large (perhaps infinite) set ofobjects all share a particular property?A single finite and faithful (to within the finite margin oferror) representation of "triangle" works given that definition.This is there nominalism and universalism come 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 thatthis was how *I* thought mathematicians actually operated--I wasjust saying that *you* seemed to be suggesting that mathematicianscould only prove things by making specific choices of examples toconsider, using their free will. If that's not what you weresuggesting, please clarify (and note that I did ask if this iswhat you meant in my previous post, rather than just assumingit...I then went on to make the conditional statement that IF thatwas indeed what you meant, THEN you should find it impossible toexplain how mathematicians could be confident that a theorem couldnot be falsified by a new choice of example. But of course I mightbe misunderstanding your argument, that's why I asked if myreading 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 ofa specific element to consider? Then how is free will supposed tobe relevant if there is no actual choice whatsoever being made?--Why do you keep insisting on a "specific" property to the"choice" while being shown that the a priori "specificity" itselfthat is prohibited by the definition.He didn't refer to a specific property but to a specific choice ofelement, which is what Loskin says entails the magic ability toselect one among an infinite number. He apparently thinks of itlike the complement of the axiom of choice: to pick an element youneed to say,"Not this one. Not this one. Not..." an infinite numberof times.Hi Brent,Yes, that is a very good point! The axiom of choice is a suspecthere. Banach and Tarsky proved a paradox of the axiom of choice, itis the "scalar field" of mathematics, IMHO; you can get from itanything you want.Banach and Tarski proved an amazing theorem with the axiom of choice,but it is not a paradox, in the sense that it contradicts nothing, andyou can't get anything from it.Bruno

`The axiom of choice allows for violation of conservation laws, if`

`it where to be a physical law.`

-- Onward! Stephen "Nature, to be commanded, must be obeyed." ~ Francis Bacon -- 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.