Discussion of verses posted so far ...

 Here the argument runs as follows:

 mAdhva:

  We may make a charge or partial siddha-sAdhana against you, the  advaitin, because the establishing of absence of sattva and absence  of asattva has a part, the establishing of absence of asattva with  regard to the world, that is already established by others.

 advaitin:

  Well, in that case, we can make the same charge against you  because your establishing of the difference and nondifference of a  quality from its possessor has a part, the establishing of difference  of a quality from its possessor, is already established by others such  as the bhATTas, naiyAyikas, sAMkhyas, etc., who admit the difference  of a quality from its possessor.

 mAdhva:

  Not so. You cannot establish such difference and nondifference  independently of each other. You have got to establish the conjunction of  the two conditions, namely difference and nondifference of a quality  from its possessor. The hetu here is "samAnAdhikR^itatva", which is  explained as being capable of being the content of a cognition of a  relation of nondifference in the same substratum where there is  difference. Or, we can explain the hetu, samAnAdhikR^itatva, as being  capable of being cognized as a qualifier (visheshhaNa) of the possessor  of the quality. In the cognition, "the pot is blue", (ghaTo nIlaH),  the blue color of the pot is cognized as the qualifier, visheshhaNa of  the pot which is the qualificand, visheshhya. The particular instance of  blue color of the pot is different and nondifferent  from the pot  (although the generic character of blue color is accepted to be only  different from the pot.) If we split the sAdhya into bheda (difference)  and abheda (nondifference), then we run into the following problem.  The sAdhya abheda in itself CANNOT be a necessary factor (prayojaka)  of the (sole) hetu. For example, there is no cognition of the form "the  pot is the jar", where the terms "pot" and "jar" are synonyms and the  hetu samAnAdhikR^itatva is present. Therefore, even though there is  abheda between "pot" and "jar" here, there is no hetu. And in the case  of the (erroneous) cognition "the pot is the cloth", there is bheda  between the pot and the cloth but again there is no hetu, samAnAdhi-  kR^itatva. Therefore, we need the conjunction of bheda and abheda  as the sAdhya so that the sAdhya becomes a prayojaka of the hetu.

  But, in your (advaitin's) case, things are different. You claim that  the world is unreal (mithyA) or has the absence of sattva and the  absence of asattva (or the difference from sattva and the difference  from asattva), because of the hetu, dR^ishyatva, perceptibility.  (What is perceptible or cognizable is mithyA.) Now, perceptibility  is a characteristic of everything other than Brahman, as per your  view. And Brahman is "sat". All you need to prove is absence of  sattva or difference from sattva with regard to the world. Proving  the absence of asattva (or difference from asattva) is redundant.   Hence the charge of partial siddha-sAdhana.

 advaitin:

  What you say is not justifiable. Just as in your case,  the conjunction of bheda and abheda is a necessary factor (prayojaka)  of the hetu, so in our case too the conjunction of absence of  sattva and the absence of asattva (or equivalently the conjunction  of difference from sattva and the difference from asattva) is the  prayojaka of the hetu, dR^ishyatva (perceptibility). Here is why.  If we make just the absence of sattva the sAdhya, then we run into a  problem in the case of a fictitious entity (a chimera). A fictitious  entity, such as the horn of a hare, has absence of sattva only. But  here the hetu, dR^ishyatva is NOT present. A fictitious entity is never  perceived. Again, if we make just the absence of asattva the sAdhya,  then we run into a problem in the case of Brahman. Here, we have  absence of asattva, but again the hetu, dR^ishyatva is NOT present in  Brahman. Therefore, we need to have the conjunction of absence of  sattva and absence of asattva as the sAdhya in order to make the  sAdhya a necessary factor (prayojaka) of the hetu. The charge of  siddha-sAdhana against us cannot be made.

 Notes:

  1)

  The thrust of the argument is that the hetu for the sAdhya in the  mAdhva's case as well as for the advaitin has to be a prayojaka,  a necessary factor of the hetu. In other words, the hetu must occur  exactly wherever the sAdhya occurs, no more no less. This is more  restrictive than the general form of vyApti, as may be recalled from  the introduction to nyAya in the third part of this series. When  the mountain has the hetu, smoke and we infer the sAdhya, fire, the  vyApti is less restrictive in the sense that we may allow the sAdhya  fire to occur without smoke, although the smoke must always be  accompanied by fire in order for the inference to be valid. But in the  present discussion, we cannot allow the sAdhya to occur where the  hetu is not found. The occurrences of sAdhya and hetu must exactly  coincide. Here, the sAdhya for the advaitin is sadbheda and asadbheda  and the hetu is dR^ishyatva. By defining a "tight" form of vyApti,  what the advaitin is saying is:

 Whatever is perceptible (cognizable) is different from sat AND  different from asat.

  The converse also holds.

   Whatever is different from sat AND different from asat is perceptible  (cognizable).

   Symbolically speaking, if H is the hetu, and the sAdhya is the logical  conjunction (AND) of S1 (sad-bheda) and S2 (asad-bheda), we may write:

    H -> S1 AND S2

   S1 AND S2 -> H

   where "->" means "implies"

  2) The mAdhvas' view here regarding the bheda-abheda of a quality from    the possessor of the quality is used here by MadhusUdana as an example    only. It does not necessarily mean that MadhusUdana endorses this view    of the mAdhvas in a broader context, as for example, with respect to    an exegetical context. Indeed, the mAdhvas seem to come under some    heavy attack from the VishishhTa-advaitins for not recognizing  the    bheda (difference) between dravya and adravya as RAmAnuja holds.    In his fourth volume titled "History of Indian Philosophy", Dasgupta    outlines the criticism of the mAdhvas by the vishishhTa-advaitin,    ParakAla Yati in his VijayIndra-parAjaya. Parakala Yati points out    how several texts in the upanishads become absurd if the mAdhva    position on dravya and adravya is held. Another major disagree-    ment between the two schools of Vaishnavism is the Ananda-tAratamya    position which is held by the mAdhvas but rejected by the    vishishhTa-advaitins. The latter cannot accept (nor can the advaitins)    that there is gradation in Bliss (Ananda) in the state of mokshha.    This position is also criticized by ParakAla Yati on exegetical    grounds as well. There is another vishishhTa-advaitin work named    Ananda-tAratamya-khaNDana that is also mentioned by Dasgupta.

    Nevertheless, it must be noted that the advaitin's use of the   mAdhva example on "guNa" and "guNI" is for illustration purposes only.   Any other example would also be fine.