Boethius, in his commentaries on the aforementioned translation, says that a universal, if it were to exist, has to apply to several particulars entirely. He also specifies that they apply simultaneously at once and not in a temporal succession. He reasons that they cannot be mind-independent, i.e. they do not have a real existence, because a quality cannot be both one thing and common to many particulars in such a way that it forms part of a particular's substance, as it would then be partaking of universality and particularity. However, he also says that universals can't also be of the mind since a mental construct of a quality is an abstraction and understanding of something outside of the mind. He concludes that either this representation is a true understanding of the quality, in which case we revert to the earlier problem faced by those who believe universals are real; or, if the mental abstractions were not a true understanding, then 'what is understood otherwise than the thing is false'.
boEThius, in his coMmeNtarieS on thE AforemenTionED trANsLAtion, sAys thaT a uNiversAl, IF It were to eXisT, has to aPply TO several paRtIcuLars enTIrely. hE also speciFiEs THat they aPply simulTaneously at once And not in a tempoRal sUCCeSsion. he reaSOnS that They caNnot be miNd-InDepeNdeNt, i.e. they do not have a real ExistenCe, becauSe A quaLIty CAnNot be BOTH One tHing and commON tO mANy PArTiculArS IN suCh a Way tHAt iT formS pARt of A paRticulAr's SuBstaNcE, aS It would thEN BE partakING of UnIversalIty aND parTiCulaRItY. however, hE also Says THAt UnivErsals cAn't AlSo bE Of tHe mind sinCe a meNtAL COnStruct Of A qualiTY IS AN aBstracTion aND uNdeRSTandinG OF sOmething outside of ThE mind. he coNcLudeS That eIthER thIs ReprESeNtAtion is A True understaNDiNg of the QUality, In WHich case we REvErT tO The EARliEr prObLEm facEd By tHOse who bElieve uNiversAls aRe REal; oR, if tHe Mental absTractIonS WERe NoT a tRUe undersTanDing, tHeN 'whAt iS unDerSToOd otHerWISe ThaN thE thiNg iS FAlse'.