 the case of the sets. The singletons {u} ⊆ S are "potential" in the objectively indefinite superpositionS, and, with further distinctions, the indefinite element S might "actualize" to {u} for one of the "potential" {u} ⊆ S. Starting with S, the other {u} " S (i.e., u /∈ S) are not "potentialities" that could be "actualized" with further distinctions. This terminology is, however, somewhat misleading since the indefinite element S is perfectly actual(in the objectively indefinite interpretation); it is only the multiple eigen-elements {u} ⊆ S that are "potential" until "actualized" by some further distinctions. A non-degenerate measurement is not a process of a potential entity becoming an actual entity, it is a process of an actual indefinite element becomes an actual definite element. Since a distinction-creating measurement goes from actual indefinite to actual definite, the potential-to-actual language of Heisenberg should only be used with proper care-if at all. Note that there are two conceptually distinct connotations for the mathematical subset S ⊆ U. In the classical interpretation, it is a set of fully definite elements of u ∈ S. In the quantum interpretation of a subset S, it is a single indefinite element that with further distinctions could become one of the singleton definite-elements or eigen-elements {u} ⊆ S. Consider a three-element universe U = {a, b, c} and a partition π = {{a}, {b, c}}. The block S = {b, c} is objectively indefinite between {b} and {c} so those singletons are its "potentialities" in the sense that a distinction could result in either {b} or {c} being "actualized." However {a} is not a "potentiality" when one is starting with the indefinite element {b, c}. Note that this objective indefiniteness of {b, c} is not well-described as saying that indefinite pre-distinction element is "simultaneously both b and c" (like the common misdescription of the undetected particle "going through both slits" in the double-slit experiment); instead it is indefinite 7 between b and c. That is, a superposition of two sharp eigen-alternatives should not be thought of like a double-exposure photograph which has two fully definite images (e.g
the case of the sets. The singletons { u } ⊆ S are " potential " in the objectively indefinite superpositionS, and, with further distinction, the indefinite chemical element S might " actualize " to { u } for one of the " potential " { uranium } ⊆ S. Starting with S, the other { uranium } " S (i.e., u /∈ S) are not " capability " that could be " actualized " with further differentiation. This terminology is, however, somewhat misleading since the indefinite chemical element S is perfectly actual(in the objectively indefinite interpretation); it is merely the multiple eigen - elements { u } ⊆ S that are " potential " until " actualized " by some further distinctions. A non - debauched measurement is not a process of a potential entity becoming an actual entity, it is a summons of an actual indefinite element becomes an actual definite component. Since a distinction - make measurement goes from actual indefinite to actual definite, the potential - to - actual language of Heisenberg should only be used with proper caution - if at all. Note that there are two conceptually distinct connotations for the mathematical subset S ⊆ U. In the classical interpretation, it is a set of fully definite elements of u ∈ S. In the quantum interpretation of a subset S, it is a single indefinite element that with further distinctions could become one of the singleton definite - elements or eigen - elements { uracil } ⊆ S. Consider a three - element population uracil = { a, b, coulomb } and a partition π = { { a }, { b, c } }. The engine block second = { b, c } is objectively indefinite between { b } and { c } therefore those singletons are its " potentialities " in the sense that a distinction could result in either { b } or { c } being " actualized. " However { a } is not a " potentiality " when one is starting with the indefinite chemical element { b, c }. notice that this objective indefiniteness of { b, hundred } is not well - described as saying that indefinite pre - distinction element is " simultaneously both b and hundred " (like the common misdescription of the undetected particle " going through both incision " in the double - slit experiment); instead it is indefinite 7 between b and c. That is, a superposition of two sharp eigen - option should not be thought of like a double - exposure photograph which has two fully definite effigy (e.g
 thf case of the sets. The slngletons {u} ⊆ S ate "potenvial" in the objdctively indefinite superposmtiobS, ane, with further distincgions, the indefinute tlement S might "arfualize" to {u} rlr oue of the "potentlal" {u} ⊆ S. Stdrting with S, dhd lther {u} " S (i.e., u /∈ S) are not "potentiajities" yhwt could be "acjualieed" witg further distinctions. This terminklogy iv, however, somrwhat misleading since the indffinite element S ls perfectli aceyal(in the obgectively pudefinite ihterpretation); it is only the muutiplz eigen-elemgurs {k} ⊆ S that arx "potegtial" until "actualizad" by spme further dixtiictiins. A non-degenerate mxasurement is not a krocess of a potential entity bwcomitg at acgyal enuitb, if is a prkcess of ah actual ineefinite element bevoivx an actual sefiniee element. Since a distinction-creating medsudement goes from actual indefinite to actual definite, the potential-to-actual language of Heisenberg shogld oilh bt mfde aith proper care-if at all. Note that there are fwp bonceptually distlnct connotations gog yre mathematicxl subset S ⊆ U. In the classlcal injerpreration, it is s set of fully definite elenents of u ∈ F. In the quantum incerpretation of s subxet S, it is a single inbefinife element hhat with wurther distinctkonx would become one of the siggleton dxfinice-elemengs ot eigen-qlements {u} ⊆ S. Consider a three-elemfnt uuiverve U = {a, b, f} and a partition π = {{a}, {b, c}}. The block S = {b, c} is otjebtively iudefinlte between {b} agd {c} so those xingletjns afe its "potvntialitixs" in the segse that a divjinction coulv result yn euthee {b} or {z} being "actualiaed." Howevvr {a} iw not a "potentialiby" whgn one is startiny qith the indefimitd ejeleit {b, s}. Note that tvis ubjdvtive indefinitekesr of {b, c} is not well-descsibes as saying that imdcfinite pte-distinceion element os "simultaneously hoth u and r" (like thg common misdescription of the hndetectef pwrticle "goind thvougr both slics" in the double-slit experiment); instead mt is indefinite 7 betwgen b and c. That is, a xuperpositipn of two shar[ eigen-alternatives whould not be thomght of like a double-esposura phohograph which has two fully definite images (e.g
the case of the sets. The singletons S "potential" in objectively indefinite superpositionS, indefinite S might "actualize" {u} for one the "potential" {u} ⊆ S. Starting S, the other {u} " S (i.e., u /∈ S) are not "potentialities" could be "actualized" with further distinctions. This terminology is, however, somewhat misleading since indefinite S perfectly the objectively indefinite interpretation); it is only the multiple eigen-elements {u} ⊆ S that are "potential" "actualized" by some further distinctions. A non-degenerate measurement not a process of potential entity becoming an actual it a process an indefinite becomes an actual element. Since a distinction-creating measurement goes from actual indefinite to actual definite, the potential-to-actual language of Heisenberg only be proper care-if all. that are two conceptually for the mathematical subset S ⊆ classical interpretation, it is a set of fully elements of ∈ S. In the quantum interpretation a subset S, it is a single indefinite that with further distinctions could become one of the singleton definite-elements or eigen-elements {u} ⊆ a three-element universe U {a, b, c} a π {{a}, c}}. The S = {b, c} is objectively indefinite between {b} and {c} those singletons are its "potentialities" in the sense that a result either {b} or being "actualized." However {a} not "potentiality" when one is the element that objective of {b, c} is well-described as saying that indefinite element is "simultaneously both common misdescription of the undetected particle "going through slits" in the double-slit experiment); instead it indefinite 7 between b and c. That is, a superposition of two eigen-alternatives should thought of like a double-exposure photograph which has fully definite images (e.g
 the case of the sets. The singleTons {u} ⊆ S are "pOtentIal" In tHe ObjeCtivEly indefinite sUPerpOsitionS, and, with further DistiNcTIons, THe IndefInite elEMeNT s miGhT "aCtuAlIZe" To {u} foR onE of the "pOtential" {u} ⊆ S. staRtIng with S, the oTHeR {u} " S (i.e., u /∈ S) are Not "PotentialitiEs" tHat couLd Be "aCTualiZed" With fUrther DIstincTions. This TeRMinoloGY is, howeVER, sOmewHat misleading sincE ThE Indefinite elemEnt S is PeRFeCTLy aCtuAl(in the objEcTivelY IndefinITe INTErpREtation); it is onLy the multipLE eiGen-eleMeNts {U} ⊆ s that aRe "potEnTIal" Until "actualIzed" By some furTher diSTinctioNS. A non-deGeneraTe mEasUremENt Is Not A pROceSS oF a pOTenTial entiTy BeCominG an aCTUAL entIty, It is A procEss of an actual IndEfinITe eLemenT becoMes aN aCtual DefiniTe eleMeNt. Since a distincTion-Creating mEasUrEmeNt Goes fROm actuAl iNdeFinite tO actual DEfiNiTE, THe Potential-to-actual lAnGUAgE of HeiseNberg sHOuLd ONly be useD wIth PropER Care-iF at aLL. NOte that tHere arE TwO cOnceptuAlLy distInCt cOnnOtatiONs foR the maThematicAl subSEt S ⊆ U. In the classICal interpretaTIoN, IT iS A set Of fUlly definitE eleMEnts Of u ∈ S. iN tHe qUAntum InterPrETaTIon of a subset S, it is a sInGle indEfiniTe element that With furtheR DIStinctioNs coULd BEcome one of the sIngleTon definitE-Elements Or eigEn-elemenTs {u} ⊆ S. ConsiDER a three-eLemEnt UniVerSE u = {a, B, c} and a partitiON Π = {{a}, {b, c}}. thE block S = {B, c} iS objectIveLy iNdeFinItE between {b} And {c} so thOsE sInGlEtoNs are ITs "potentIaLitIeS" in The seNSe that A distInctIoN cOUld Result iN EiTHEr {b} oR {c} BeIng "aCtuAlIzed." HOwevER {a} iS not a "poTentialitY" whEN one Is StArting wIth the indefinItE element {b, c}. noTe tHat thiS OBjective Indefiniteness of {b, c} is not WEll-descRibEd as sAyinG that indeFinIte pre-DisTInctioN elemeNt is "sImUltANEouslY BOtH b aNd C" (like the coMMOn mIsdesCrIptiOn of the Undetected particle "GOinG through both sLitS" in tHE DoUblE-SlIT exPeRImeNT); Instead it is indeFinite 7 betwEeN B aNd c. That is, a SUpeRpOsition Of two shArp eiGEn-alterNatives shOuld not be ThOughT OF liKe a double-eXposure pHotograph WHich hAS tWo fulLy dEfinitE iMagEs (e.g
 the case of the sets. The  singleton s {u}  ⊆S a re  "po tent ial" in the ob j ecti vely indefinite superp ositi on S , an d ,withfurther di s t inc ti on s,th e  i ndefi nit e eleme nt S might  "a ct ualize" to { u }for one of  th e "potential " { u} ⊆ S .Sta r tingwit h S,the ot h er {u}  " S (i.e ., u /∈ S )  are no t "p oten tialities" that c o ul d  be "actualize d" wit hf ur t h erdis tinctions.  T his t e rminolo g yi s ,  ho w ever, somewha t misleadin g  si nce th eind e finite  elem en t  Sis perfectl y ac tual(in t he obj e ctively indefin ite in ter pre tati o n) ;itis onl y  t hem ult iple eig en -e lemen ts { u } ⊆  S t hat  are  "pot ential" until  "a ctua l ize d" by  some  fur th er di stinct ions.  A  non-degenerate  mea surementisno t a  p roces s  of apot ent ial ent ity bec o min ga n ac tual entity, it is  a p ro cess ofan act u al  i n definite  e lem entb e comes  ana ct ual defi nite e l em en t. Sinc ea dist in cti on- creat i ng m easure ment goe s fro m  actual indefi n ite to actual de f i ni t e, t hepotential-t o-ac t uallang u ag e o f  Heis enber gs ho u ld only be used wit hproper  care -if at all. N ote that t h e r e are tw o co n ce p tually distinc t con notationsf or the m athem atical s ubset S ⊆ U . In the  cl ass ica l i n t er pretation, it i s ase t of fu lly  defini teele men tsof  u ∈ S. I n the qu an tu min ter preta t ion of a  s ubs et  S,  it i s  a sin gle i ndef in it e  el ement t h at w ithfu rt herdis ti nctio ns c o uld  become  one of t hes ingl et on  defini te-elements o reigen-elem en ts{u} ⊆S .  Conside r a three-element unive r se U ={a,  b, c } an d a parti tio n π ={{a } , {b,c}}. T he bl oc k S =  {b,c }  i s o bj ectively i n d efi nitebe twee n {b} a nd {c} so those si n gle tons are its"po tent i a li tie s "i n t he sen s e  that a distinc tion could  r e su lt in eith e r { b}  or {c}  being"actu a lized."  However{a} is no ta "p o t ent iality" wh en one i s startin g  with th e ind efi nite e le men t {b,  c}. N o tethatthis o bj ective  inde fi niteness  of {b, c} is not well- descri bed a s s aying tha t i n def inite pre -dis tinction e lem ent  is " sim u ltane ousl y  b oth b and  c"( like thec om mon m is description o f  th e und ete c ted pa rtic le "going through both slits" in  the d oub le- s litex periment); ins tea di t  is inde fi nite 7 betw een b an dc . Tha t is,a supe rpositi o n  o f  two s harp  ei gen-alter nat iv e s shoul dno t  be th ough tof lik e a do u ble- e x posure photograp h whi c h  hast wofully  d efinite imag es (e.g
 the_case of_the sets. The singletons_{u} ⊆_S_are "potential"_in_the objectively indefinite_superpositionS, and, with_further distinctions, the indefinite_element S might_"actualize"_to {u} for one of the "potential" {u} ⊆ S. Starting with S, the_other_{u} "_S_(i.e.,_u /∈ S) are not_"potentialities" that could be "actualized"_with further_distinctions. This terminology is, however, somewhat misleading since_the_indefinite element S_is perfectly actual(in the objectively indefinite interpretation); it is_only the multiple eigen-elements {u} ⊆_S that are_"potential"_until_"actualized" by some further_distinctions. A non-degenerate measurement is not_a process of a potential entity_becoming an actual entity, it is a_process of an actual indefinite element_becomes an actual definite element._Since a_distinction-creating measurement goes from actual_indefinite to actual_definite, the_potential-to-actual language of_Heisenberg should only be used with_proper care-if at_all. Note that there are two_conceptually_distinct connotations for_the_mathematical_subset S_⊆ U. In_the_classical interpretation,_it_is a set of fully definite_elements_of u ∈ S. In the quantum_interpretation of a subset_S,_it is a single_indefinite element that with further_distinctions could become one of the_singleton definite-elements_or eigen-elements_{u} ⊆ S. Consider a three-element universe U = {a, b,_c} and a partition π =_{{a}, {b, c}}. The_block S_=_{b, c} is_objectively_indefinite between_{b} and {c} so those singletons are_its "potentialities"_in the sense that a distinction_could result in either_{b}_or {c} being "actualized." However {a}_is not a "potentiality" when one_is starting with the indefinite_element_{b,_c}. Note that this objective_indefiniteness of {b, c} is not_well-described as saying_that indefinite pre-distinction element is "simultaneously both_b_and c" (like the common misdescription_of_the undetected particle "going through both_slits"_in_the double-slit experiment); instead it_is indefinite 7 between b and_c. That is, a superposition of two sharp eigen-alternatives_should not be_thought of like a double-exposure_photograph_which_has two fully definite images (e.g