Na cha asatiativyapti,
Just because, the eternal non-existence of something is being discussed, one should not levy a charge of ativyapti against the Advaitin. Why? The revered author clarifies this:
It is not that here the knowledge takes place without any corresponding cognition(pratite) of existence. In the definition we have to accept “sattwenpratitiarhatwa” as an adjective. Mithya objects unlike asat objects appear to be existent though they are actually adjuncts of absolute non-existence in their locus of appearance.
The dualist now raises a new objection:
Na chatadaiyke ahu asatevamidamagreasititishrutyaasatasattwapratitetatraativyaptidushpariharaitivachyam.
According to the follower of the Madhwa School, even addition of “satwenpartitiarhatwang”-that which appears to be existent, to the definition of revered Chitsulkhacharya does not solve the problem of a too broad definition (ativyapti). This is because shruti itself says “asatamidamagreasit”- prior to creation there was only non-existence (and that was cognizable). So even absolute non-existence can be cognized as existence and thus it cannot be meaning fully distinguished from mihyatwa. However,MadhusudanaSaraswatiji says- na cha vachyam-don’t say like this as it is not logical.
The shruti says itself that whatever exists is nothing but existence. So if the interpretation of the dualist is accepted then shruti would become contradictory. Thus “asat” in the first sentence quoted above does not imply absolute non-existecne but only apparent absence of Existence, and is thus equivalent to mithyatwa.
atonaativyaptisarvam cha nyatpurvauktamevaanusandhyemitiuparamyate.
Thus there is no ativyaptidosha. All other remaining doubts has been clarified in the second definition of falsity.
Here ends the discussion on the fourth definition of falsity.
Sadviviktamvamithyatwam. Sattwang cha pramanasiddhatwam.Pramang cha doshasahakritajnankaranatwam, tenswapnadivatpramanasiddhabhinatwammithyatwamsidhyati.
This is the fifth and the final definition of falsity.Sadviviktatwam-that which is different from sat is what is mithya. Here sat means that which is having sattwa(existence ness) and that is which is –pramanasiddhatwam. Nyayamritakara had given various definitions of sat in this context, and had refuted them. MadhusudanaSaraswatiji , does not accept any of those definitions and says that which is sat is –pramanasiddhatwam- that which is proved through pramanas. Pramana cha doshaasahakritamjnanakaranatwam- Pramana is that which is the means of knowledge and does not have any fault in them. So, that which is associated with error, like nidradoshha, cannot be a pramana, like the knowledge gained through dreams. So mithyatwa is doshasahakrita jnana karanatwam.
Pramanasiddhyatwam cha avadhyavypyamitianyat.
Moreover pramanasiddhyatwa is avadhyatwavapyam. Whatever is known by means of right knowledge that has avadhyatwa- non-negtability.
Atrapiasatinirdharmakabrahmani cha ativyaptivaranayasattwenpratiyamanatwamvisheshanamdeyam, tayosattwaprkarakpratitivishyatwaabhavat.
Now Brahman does not have existence as attribute, but is nirdharmaka-without any attributes. So in that sense it is also satviviktwam and hence becomes mithya. Moreover asat-absolute non existence is also different from existence and thus would get incorporated within the category of mithyatwa. To remove Brahman and ast from the category of mithya, an adjective of “sattwenpratitiarhatwang” should be added to the definition “sat viviktwam”. This is because there is no sattwapratitiprakara in Brahman and asat as they never appear to be sattwa.
Nyaymritakara asks in His text, that whetehr it has sattajati in the adhikarana that is being discussed, or issatta that which is non-negatable, or is satta identical to Brahman.
In pot etc it is accepted, that the class that exists is avidyaka-jati-a class characterised by avidya. So here sattwajati cannot be there. However, this argument is not correct. It is not because of the pot existence is there, but it is on Existence the pot has been superimposed. The second point was avadytwa-If one accepts satwa to be avadytwa, then finally it will be reduced to vadytwa, as jagat is mithya and hence vadya. If the third poition is accepted then there is siddhasadhanadosha as Brahman is already accepted to be different from jagat.
So all these three positions are not accepted by Advaitins but pramnasiddhatwam is accepted to be definition of the falsity.
All the discussions that took place while analysing the first definition of falsity, sad-asadvilakshanatwam (not beng the locus of existence and non-existence) can be incorporated here to answer the relevant doubts raised by Nyayamritakara. If some doubt still persists, those will be clarified (MadhusudanaSaraswatiji says) on the chapter on drishtanta-the example.
Here ends the discussion on the fifth definition of falsity.
In the text called Shatadushani, seven definitions for falsity/mithyatwa was chosen and all of them were condemned. Among them only five definitions of falsity that have been discussed above are considered to be error free by the knowers of tradition.
 Since these definitions are very similar.
Because Brahman is often referred as sat-chid-ananda.
 In advaita Vedanta existence is not simply an attribute.
PancaMithyatve (the five definitions of Mithya-ness) my Dream / Pet project written by Shri Rajit Biswas who wrote these after listening the Lectures comes to an end.