In Gaudiya vaishnava sAmpradAya, often the three words are referred to represent three different entities, namely "nirguna(impersonal) Brahman, all-pervading consciousness, Personality of Godhead". Let us examine the correctness of this notion.

vadanti tat tattva-vidaH tattvam yat jn~Anam advayam |

bramha iti paramAtma iti bhagavAn iti SabdyatE ||

( Srimad Bhagavatha Purana 1.2.11 )

The following is the summary of what has been rightly explained by the SrI VaishNava AchArya SrI VIrarAghavAchArya :

The previous verse

".....jIvasya tattva-jijn~AsA na arthaH ...." (1.2.10)

states that, the objective of a jIvAtma is "tattva-jijn~Asa" ie.Knowledge of the "Tattva" / Enquiry into Tattva. The next verse (1.2.11), states as to which "Tattva" it is.

< Note: Basically it is the Bramhan. The very first sUtra in VEdAnta SUtras state about the "athAso Bramha jijn~Asa" >

tattva-vidaH = Wise-Men knowledged about this Tattva;

vadanti = say;

tattvam = tattvam <The jijn~Asa of which is a jIvAtman's objective>;

tat : as that

advayam : <advayam : jn~Anam a-dvayam = advitIyam => No equal Or Superior ;

a-avayam = No avaya-bhEda => No internal distinctions through various parts {ie.No distinctions in its essential nature <svarUpa> anywhere ; ex:Not like a body which has various distinctions like ear,nose,hand, etc};> <jn~Anam : jn~Ana svarUpa (DivyAtma-SvarUpa) possesing jn~Ana (dharma-bhUta-jn~Ana)> advayam jn~Anam => jn~Anam which is advayam yat : which is SabdyatE : sounded so

bramha iti : as Bramha <Not the four-headed bramha>;

paramAtma iti : as ParamAtman bhagavAn iti :

and as BhagavAn.

anvayam in Sanskrit : yat advayam jn~Anam bramha iti paramAtma iti bhagavAn iti SabdyatE tat tattvavidaH tattvam vadanti

This verse states that the Tattva- The Supreme Entity, is the "advayam-jn~Anam" , which is denoted by the Sabdas Or words ParamAtman, Bramhan and BhagavAn. These three words are the SAmAnya (General) and ViSEsha (Particular) Sabdas for denoting the Supreme Reality which is the "advayam jn~Anam".

For instance, in Upanishad statements like "sat Eva sOmya idam agra aaseet", "bramhavA idam agra aaseet", "aatmavA idam agra aaseet" and "ekO ha vai nArAyaNa aaseet", which state about the Jagad-KAraNa entity {which existed before PraLaya}, the words Sat, Bramha, aatma and nArAyaNa denote the same entity which is the Supreme Reality

{Note: Bramhan is defined in the sUtra "janmAdyasya yataH" -Brahman as that from which proceeds the jagat, gets maintained and dissolved}. "sat" which means "Existence" can refer God,chit and achit. Hence, it is a "sAmAnya" {General} Sabda. The word "Bramhan" can denote any of the three entities while primarily it refers to Supreme Entity.

"Aatma" can refer both jIvAtma and God-the ParamAtma, and also manas {mind}. Hence, it is a sAmAnya Sabda. NArAyaNa Sabda is a ViSEsha Sabda, since it denotes only the Supreme Reality-God.

Similarly, in this verse, the Sabdas Bramhan,ParamAtman and BhagavAn have the sAmAnya-ViSEsha sambandha, with one being more specific to the other. This verse has nothing to do with the existence of three separate features Bramhan, ParamAtman and BhagavAn as various aspects of the one supreme-reality, which is defined as the "advayam jn~Anam". Upanishads refer the Supreme-Reality as "Bramhan" in many places and IthihAsa-purANas, pAn~charAtra refer the supreme-reality as "ParamAtman" and "BhagavAn" too. This fact is used in this verse.

It is clearly stated to be "iti SabdyatE" denoting that the same entity [advayam jn~Anam] is referred by three different words (Sabdas). Now that the Supreme-Reality is "advayam jn~Anam", what is the distinction spoken off between BhagavAn, ParamAtman and Impersonal Bramhan by the GauDiyas ?

If Brahman is held as attributeless and ParamAtma as mere all-pervading consciousness , how can this nirviSEsha Bramhan be same as BhagavAn and ParamAtman, as held so fundamentally ? How is this nirviSEsha Bramhan related to BhagavAn? If it is related, then it ceases to be nirviSEsha / nirguNa !

If it is unrelated, it becomes a distinct entity apart from BhagavAn and hence they can't be same. Ultimate reality is immutable since it is "jn~Anamaya" - One can't cut it into pieces. Even assuming that somehow it is cut to form the Impersonal Bramhan, it will still be pratyak having the notion of "I" - It can't be nirviSEsha. Also, there is nothing called nirviSEsha Bramhan in reality - please refer SrI-BhAshya and SrI VEdAnta DESika's SatadUshaNI.

Sometimes, gaudiyas also say that Impersonal Bramhan is the effulgence of BhagavAn. Actually, the light emanating from Lord's divine body is a property of the Suddha-Sattva tattva {in being luminous}. But that light by itself is not a part of the "Bramha tattva / Supreme Tattva". Hence they can't be fundamentally same. Also, what is then the relationship between this sort of Impersonal Bramhan and BhagavAn ? If they are non-different in all aspects, then one should not speak of the other as the different feature of BhagavAn. Also, Ultimate relaity is actually all-pervading. Effulgence is something which "flows" - Basically it contradicts the all pervading nature of the Ultimate reality.

Conclusion: Brahman is not attributeless, ParamAtma is not without all kalyana (auspicious) gunas(attributes), and they are one and the same as Bhagavan. But the sabdas (words) emphasise the sense of Ishvara(personal God) in asending order.