What are the seven great untenables?

What are the Seven Great Untenables? Prof. John Grimes seems to have a a book on it, and there seems to have been some discussion on advaitin mailing list on the same.

Answer: The following was posted in the advaitin mailing list.

THE SEVEN IMPOSSIBLE TENETS Ramanuja picks out what he sees as seven fundamental flaws in the Advaita philosophy for special attack: he sees them as so fundamental to the Advaita position that if he is right in identifying them as involving doctrinal contradictions, then Shankara's entire system collapses.

The post also says that they are the following:

1. The nature of Avidya.
   
2. The incomprehensibility of Avidya.
   
3. The grounds of knowledge of Avidya.
   
4. The locus of Avidya.
   
5. Avidya's obscuration of the nature of Brahman.
   
6. The removal of Avidya by Brahma-vidya.
   
7. The removal of Avidya.
   

Read the great post. It is very comprehensive and is a good example of the maturity of the systems, as well as the attack on existing systems, in ancient India.
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Continuation of the Sri Dakshinamurty Stotram in advaitin mailing list: In Part VI (first half) and Part VI (second half), Verse V of the stotram is discussed:

Deham praanamapi indriyaanyapi chalaam buddhim cha shunyam viduH
Stri-baala-andha-jadopamaastvahamiti bhraantaa bhrsham vaadinaH |
Maayaa-shakti-vilaasa-kalpita-mahaa-vyaamoha-samhaarine
Tasmai Srigurumurtaye nama idam Sridakshinamurtaye ||

Here is link to previous posts (parts I to V).

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Postscript (added on 03/27): Found the book The Seven Great Untenables by John. Grimes. Have a read a couple of chapters, but the attack of Sri Ramanujacharya on Sri Adi Shankara is amazing. The Seven Great Untenables form the first chapters of sri-bhashyam, a well known work of Sri Ramanuja, and as said above, attacks Adi Shankara's theory of Advaita (or non-duality) on the concept of avidya.

I advise to read the following post too.