```Date: Jan 29, 2013 6:32 PM
Author: Zaljohar@gmail.com
Subject: A philosophical interlude into sets and mathematics

A set is a singular entity that corresponds to a totality of singularentities orotherwise signifies their absence.So set-hood is about framing plurality of singular entities within asingular frame.A set may be understood as a 'name' for some plurality of singularentities. Butthis would lead to immense naming under standard setting of ZFC, sincethiswould obviously lead to "infinite" naming procedures, and even'uncountably' sowhich is something not easy to grasp.Another way of understanding sets is in a more 'active' manner, sounlike theabove rather 'passive' context, we rather think of sets as'collectors' and thepluralities they collect as 'collections' of course of singularentities. Clearlya collector is a 'singular' entity, so this confers with the aboverather abstractdefinition of sets.Of course the 'collector' setting doesn't naturally explainExtensionality. Anaggressive fix would be to understand sets as "Essential" collectors,whichpostulates the existence of a 'collector' for each collectibleplurality such thatEVERY collector of the same plurality must 'involve' it to be able tocollect thatplurality. Under such reasoning it would be natural to assumeuniqueness ofthose kinds of collectors. So ZFC for example would be understood tobe aboutcollectors of infinite collections, and not about immense kind ofdescriptiveprocedural discipline.So for example under the essential collector explanation of sets, onewould saythat ZFC claims the existence of 'uncountably' many essentialcollectors ofpluralities (i.e. collections) of natural numbers, most of whichalready exceedsour 'finite' human vocabulary, and even exceeds a 'countably' infinitevocabulary.The collector interpretation despite being somehow far fetched stillcan explaina lot of what is going in set/class theories in a flawless spontaneousmanner. Itis very easy to interpret for example non well foundedness, also it iseasy tounderstand non extensional versions, even the set theoretic paradoxesarealmost naively interpreted.Of course as far as interpret-ability of what sets stands for this isnot a fixedissue, one is left free to choose any suitable interpretation thatenable him tobest understand what's going on in various set/class theories anddifferentmanipulations and scenarios involved.That was a philosophical interlude into what sets are. On canpostulate the'possibility' of Ontologically extending our physical world with theworld of setsand even consider all possibilities of so extending it. A minimalrequirement forsuch 'possibility' setting is of course to have a 'consistent' recordabout suchassumptionally existing entities, since inconsistent record virtuallyrule outhaving such possibilities.Would mathematics be the arena of such Ontological extension? Howwould thatrelate to increasing our interaction with the known physical world?Zuhair
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