 of the construct). PHENOMENOLOGY 13 Many historical philosophical errors have been caused by a failure to consider the order of things in the arising and development of knowledge. This is equally true in matters of detail, as in grand issues. For example, the Zeno paradoxes cannot be conceived as proofs that motion is impossible, but only as evidence that our (or Zeno's) initial concepts of motion are problematic; for motion is experientially manifest before and irrespective of any conceptual deliberation concerning it and all discussion concerning motion arises only in reaction to such experience of it as an attempt to rationally interpret and explicate it. One of the main purposes of the present essay shall, therefore, be to identify the temporal and logical order of the main items in knowledge, so as to preempt such errors. © Copyright Avi Sion, 2003, 2005, 2009. All rights reserved. Protected by international copyright conventions. No part of this book may be reproduced in any manner whatsoever, or stored in a retrieval system or transmitted, without express permission of the Author-publisher, except in case of brief quotations with due acknowledgement. Phenomenology can be freely read online at The Logician.net and in various other locations. It can be purchased, in print and e-book editions, in Amazon.com, Lulu.com and many other online booksellers. Partitions and Objective Indefiniteness in Quantum Mechanics David Ellerman U. of California/Riverside June 19, 2014 Abstract Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual to one another and which are developed in two mathematical logics, the usual Boolean logic of subsets and the more recent logic of partitions. Our sense-making strategy is "follow the math" by showing how the logic and mathematics of set partitions can be transported in a natural way to Hilbert spaces where it yields the mathematical machinery of QM-which shows that the mathematical framework of QM is a type of logical system over C. And then we show how the machinery of QM can be transported the other way down to the set
of the construct). PHENOMENOLOGY 13 Many historical philosophical errors have been cause by a bankruptcy to consider the order of thing in the arising and exploitation of knowledge. This is equally on-key in matter of detail, as in expansive issues. For example, the Zeno paradox cannot be conceived as proofs that motion is impossible, but only as evidence that our (or Zeno's) initial concept of motion are problematic; for apparent motion is experientially manifest before and regardless of any conceptual deliberation concerning it and all discussion concerning movement arises only in chemical reaction to such experience of it as an attempt to rationally represent and explicate it. One of the independent purposes of the present essay shall, therefore, be to identify the worldly and logical order of the main items in knowledge, so as to preempt such errors. © Copyright Avi Sion, 2003, 2005, 2009. All right reserved. Protected by international copyright conventions. No part of this book may be reproduced in any manner whatsoever, or stored in a retrieval system or convey, without express permission of the Author - publisher, except in case of abbreviated quotation with ascribable acknowledgement. Phenomenology can be freely read online at The Logician.net and in various other locations. It can be purchased, in print and e - bible editions, in Amazon.com, Lulu.com and many other online booksellers. partition and Objective Indefiniteness in Quantum Mechanics David Ellerman U. of California / Riverside June 19, 2014 Abstract Classical physics and quantum physics suggest two meta - physical character of world: the authoritative impression of a objectively definite reality with properties " all the way down, " and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum automobile mechanic (QM) is essentially the problem of making sense out of an objectively indefinite world. These two types of reality can be respectively associated with the two mathematical concepts of subset and quotient sets (or partitions) which are category - theoretically dual to one another and which are develop in two mathematical logic, the usual Boolean logic of subsets and the more late logic of partitions. Our sense - making strategy is " follow the math " by showing how the logic and mathematics of set partitions can be transported in a natural way to Hilbert space where it yields the mathematical machinery of QM - which show that the mathematical framework of QM is a type of logical system over C. And then we show how the machinery of QM can be enchant the other way down to the set
 of the construct). PHENOMENOUOGY 13 Many historical 'hilosolhical efrors have been caused by a hailyre ti consider the order ow things pn the arusinj and developmenv of knowledge. Bhis ns equally true ln matters mf detail, as it ercnd issues. For example, the Zeno paraqoxes csnjot be conceivgd as [roors that motion is impossible, but ohly as tvidence that our (pr Zeno's) initial concepts lf mltion are problemahic; for motuon yw experientixlly maniftsc before ans irrespective of any conceptuau delnberation cinxerjhng it and ell difcussion congvrning kotion srises only in reectiin to such experience of it as an attemkt to ratimnclly interpret and explucate it. Mne ud tfe jamn lurposfs kf the preaent essay whall, therefore, be uo yeentify the tsmporaj wnd logical order of the main items in nnosledge, so as to preempt such errors. © Copyrigjt Avi Sijn, 2003, 2005, 2009. All rights reserved. Protected by internatiotal ckoyrnnmt cubvfntions. No part of this book may be reproduceq im sny manner whabsoever, or stored on a tetrieval systgm or txznamitted, without exoress pgrmissuon of tht Autnor-publisher, except in case of brief qujrations with due aeknowledgemeut. Phemomenplogy can be freely reab onlihe at The Llgician.nef and in various uthvr lmcations. It can be purchasqd, in priit anb e-book dditoons, ig Amazon.col, Lulm.wom and many other onliue bomksellers. Oartitions and Objective Indefiimteness in Qusndum Mechanies Davld Ellerman U. os California/Rirerside Lune 19, 2014 Abstract Blassical physics anq quantum phyvlcs suggest vwo meta-prysixal rypes ow reality: the ckassical ujtiob of a objectively dewjnite reality wnuh kriperties "all tne day dlwi," and dhe quantum totiun ug an ubjectively kndeginite type of realidy. Tge problem of intetpveting quqntum meshanics (QM) is essentially the pgoblek oh makimg fense out of an objectively insefinite geajity. These tro tnpes of realitv can be respectively associated with thx two mathematical concwpts of subsets and auotient sevs (or [artitionv) which are category-rheoretically duak to one another and shich dre dfveloped in two mathematical logics, the usual Boolean logic of subsets ane the more recent mogiv of iarcitnons. Ouw seisx-making strategy ps "follow the math" by showing hox the logiw cnd mathematics of set partitoovs can be travsported in a natural wag to Hilnert spaces where it yields the mathematical machinery pf QM-whixh shkws that tie mathematical framrwork mf QM is a ttpe lf logical syrtek lver C. Anf thtn wz show how the machinery of QM cab be teajsported the othxr way down bo the aet
of the construct). PHENOMENOLOGY 13 Many historical have caused by failure to consider the and development of This is equally in matters of detail, as in issues. For example, the Zeno paradoxes cannot be conceived as proofs that motion impossible, but only as evidence that our (or Zeno's) initial concepts of motion problematic; motion experientially before and irrespective of any conceptual deliberation concerning it and all discussion concerning motion arises only reaction to such experience of it as an to rationally interpret and it. One of the main of present essay therefore, to the temporal and order of the main items in knowledge, so as to preempt such errors. © Copyright Avi Sion, 2005, 2009. reserved. Protected international conventions. part of this be reproduced in any manner whatsoever, a retrieval system or transmitted, without express permission the Author-publisher, in case of brief quotations with acknowledgement. Phenomenology can be freely read online at Logician.net and in various other locations. It can be purchased, in print and e-book editions, Lulu.com and many other booksellers. Partitions and Indefiniteness Quantum David U. of June 19, 2014 Abstract Classical physics and quantum physics suggest two types of reality: the classical notion of a objectively definite properties the way down," the quantum notion of objectively type of reality. The interpreting mechanics the of sense out of an indefinite reality. These two types reality can be respectively concepts of subsets and quotient sets (or partitions) are category-theoretically dual to one another and are developed in two mathematical logics, the usual Boolean logic of subsets the more of partitions. Our sense-making strategy is "follow the by showing how the and mathematics of set partitions can be transported in natural to Hilbert where it yields mathematical machinery of shows that the of QM a of C. And then we show how machinery QM can be transported the way the set
 of the construct). PHENOMENOLOgY 13 Many histOricaL phIloSoPhicAl erRors have been caUSed bY a failure to consider the Order Of THingS In The arIsing anD DeVELopMeNt Of kNoWLeDge. ThIs iS equallY true in matTerS oF detail, as in gRAnD issues. For ExaMple, the Zeno pAraDoxes cAnNot BE concEivEd as pRoofs tHAt motiOn is imposSiBLe, but oNLy as eviDENcE thaT our (or Zeno's) initiaL CoNCepts of motion aRe probLeMAtIC; For MotIon is experIeNtialLY manifeST bEFORe aND irrespective Of any concepTUal DelibeRaTioN ConcerNing iT aND alL discussion ConcErning motIon ariSEs only iN ReactioN to sucH exPerIencE Of It As aN aTTemPT tO raTIonAlly inteRpReT and eXpliCATE It. OnE of The mAin puRposes of the prEseNt esSAy sHall, tHerefOre, bE tO idenTify thE tempOrAl and logical ordEr of The main itEms In KnoWlEdge, sO As to prEemPt sUch erroRs. © CopyrIGht avI sIOn, 2003, 2005, 2009. all rights reserved. PRoTECtEd by inteRnatioNAl CoPYright coNvEntIons. nO Part oF thiS BoOk may be rEproduCEd In Any mannEr WhatsoEvEr, oR stOred iN A retRieval System or TransMItted, without exPRess permissioN Of THE AUThor-PubLisher, excepT in cASe of BrieF QuOtaTIons wIth duE aCKnOWledgement. PhenomenoLoGy can bE freeLy read online aT The LogiciAN.NEt and in vArioUS oTHer locations. It Can be Purchased, iN Print and E-book Editions, In Amazon.cOM, lulu.com aNd mAny OthEr oNLInE booksellers. PARTitiOnS and ObjEctIve IndeFinIteNesS in quAntum MechAnics DavId elLeRmAn U. Of CalIFornia/RiVeRsiDe junE 19, 2014 AbstRAct ClaSsicaL phySiCs ANd qUantum pHYsICS sugGeSt Two mEta-PhYsicaL typES of Reality: The classiCal NOtioN oF a ObjectiVely definite rEaLity with prOpErtIes "all THE way down," And the quantum notion of an OBjectivEly IndefInitE type of reAliTy. The pRobLEm of inTerpreTing qUaNtuM MEchanICS (Qm) is EsSentially tHE ProBlem oF mAkinG sense oUt of an objectively iNDefInite reality. THesE two TYPeS of REaLIty CaN Be rESPectively associAted with thE tWO mAthematicaL ConCePts of suBsets anD quotIEnt sets (Or partitiOns) which aRe CateGORy-tHeoreticalLy dual to One anotheR And whICh Are deVelOped in TwO maThemaTical lOGicS, the uSual BoOlEan logIc of sUbSets and tHe more recent logic of partItions. our seNse-Making strAteGY is "Follow the Math" By showing hOw tHe lOgic aNd mAThemaTics OF sEt pARtitiOns cAN be transpORtEd iN A NaTural way to HILBErt SpaceS whERe it yiElds The mathematical maCHinery of QM-whicH shoWS ThaT thE MathEmAtical frameworK of qM IS A type of lOgIcal system oVer C. And tHeN We shoW how thE machiNery of Qm CAn BE transPortEd tHe other waY doWn TO the set
 of the construct). PHENOM ENOLOGY 13  Many  hi sto ri calphil osophical erro r s ha ve been caused by a fa ilure  t o  con s id er th e order of t hin gs  i n t he ar ising  an d devel opment ofkno wl edge. This i s  e qually tru e i n matters of  de tail,as  in grand  is sues.  For e x ample,  the Zeno  p a radoxe s  cannot b econc eived as proofs t h at motion is impo ssible ,b ut o nly  as  evidenceth at ou r  (or Ze n o' s ) ini t ial conceptsof motion a r e p roblem at ic; for mo tionis exp erientially  man ifest bef ore an d  irresp e ctive o f anycon cep tual de li ber at i onc on cer n ing  it andal ldiscu ssio n c o ncer nin g mo tionarises only i n r eact i onto su ch ex peri en ce of  it as  an a tt empt to rationa llyinterpret  an dexp li catei t. One  of  th e mainpurpose s  of  t h e pr esent essay shall,  t h e re fore, be  to id e nt if y  the tem po ral  and l ogica l or d er  of themain i t em sin know le dge, s oastopreem p t su ch err ors. © C opyri g ht Avi Sion, 2 0 03, 2005, 200 9 .A l lr ight s r eserved. Pr otec t ed b y in t er nat i onalcopyr ig h tc onventions. No part  o f this  book  may be repro duced in a n y manner w hats o ev e r, or stored i n a r etrieval s y stem ortrans mitted,without e x p ress per mis sio n o f t h e  A uthor-publish e r , ex ce pt in c ase  of bri efquo tat ion swith dueacknowle dg em en t.  Ph enome n ology ca nbefr eel y rea d  onlin e atTheLo gi c ian .net an d  i n vari ou sothe r l oc ation s. I t  ca n be pu rchased,inp rint  a nd  e-book  editions, in  A mazon.com,  L ulu .com a n d  many ot her online booksellers. Partiti ons  andObje ctive Ind efi nitene ssi n Quan tum Me chani cs  Da v i d Ell e r ma n U .of Califor n i a/R ivers id e Ju ne 19,2014 Abstract Clas s ica l physics and  qu antu m ph ysi c ss ugg es t  tw o meta-physical t ypes of re al i ty : the clas s ica lnotionof a ob jecti v ely def inite rea lity with  p rope r t ies  "all theway down ," and th e  quan t um  noti onof anob jec tivel y inde f ini te ty pe ofre ality.  Thepr oblem of  interpreting quantum m echani cs (Q M)is essent ial l y t he proble m of  making se nse  ou t ofano bject ivel y  i nde f inite  rea l ity. Thes e  t wot y pe s of realit y c anbe re spe c tively  ass ociated with thet wo mathematica l co n c ept s o f  sub se ts and quotien t s et s (or part it ions) which  are cat eg o ry-th eoreti callydual to o ne anothe r an d w hich aredev el o ped intw om athema tica llogics , theu sual B oolean logic ofsubse t s  andt hemorere cent lo g ic o f partitio ns. Our sen se-mak ingstrat egy is"f ollowthe  m ath" by sh o wing howthe l ogic an dmath ema tics o f se t parti tion scan  be trans p o rt e din a n atur al wa yto H ilbert sp a ces wher e i t  yields  t hem a themat i ca l machineryofQM-wh i c h shows th a t th e  m a thema ticalframew ork ofQ M i sa typeofl o gical sys tem overC . A nd  the n we sho whowth e m ac hinery of QM ca n be tra nsported t he oth erw ay d o wn toth e set
 of_the construct)._PHENOMENOLOGY 13 Many historical_philosophical errors_have_been caused_by_a failure to_consider the order_of things in the_arising and development_of_knowledge. This is equally true in matters of detail, as in grand issues. For_example,_the Zeno_paradoxes_cannot_be conceived as proofs that_motion is impossible, but only_as evidence_that our (or Zeno's) initial concepts of motion_are_problematic; for motion_is experientially manifest before and irrespective of any conceptual_deliberation concerning it and all discussion_concerning motion arises_only_in_reaction to such experience_of it as an attempt to_rationally interpret and explicate it. One_of the main purposes of the present_essay shall, therefore, be to identify_the temporal and logical order_of the_main items in knowledge, so_as to preempt_such errors._© Copyright Avi_Sion, 2003, 2005, 2009. All rights_reserved. Protected by_international copyright conventions. No part of_this_book may be_reproduced_in_any manner_whatsoever, or stored_in_a retrieval_system_or transmitted, without express permission of_the_Author-publisher, except in case of brief quotations_with due acknowledgement. Phenomenology_can_be freely read online_at The Logician.net and in_various other locations. It can be_purchased, in_print and_e-book editions, in Amazon.com, Lulu.com and many other online booksellers. Partitions_and Objective Indefiniteness in Quantum Mechanics_David Ellerman U. of_California/Riverside June_19,_2014 Abstract Classical_physics_and quantum_physics suggest two meta-physical types of reality:_the classical_notion of a objectively definite reality_with properties "all the_way_down," and the quantum notion of_an objectively indefinite type of reality._The problem of interpreting quantum_mechanics_(QM)_is essentially the problem of_making sense out of an objectively_indefinite reality. These_two types of reality can be respectively_associated_with the two mathematical concepts of_subsets_and quotient sets (or partitions) which_are_category-theoretically_dual to one another and_which are developed in two mathematical_logics, the usual Boolean logic of subsets and the_more recent logic_of partitions. Our sense-making strategy_is_"follow_the math" by showing how the logic and mathematics of_set partitions_can be transported_in a natural way to Hilbert spaces where it yields_the mathematical machinery of QM-which shows that_the mathematical framework of QM is a type of logical system_over C. And then we show how the_machinery of QM can be transported the_other way down to_the_set