I am more closely aligned with this understanding.
I should clarify that Thieme is mainly Trichotomous = Body, Soul, Spirit - and his view of the dead human spirit is really not Classic Dichotomy = Body, Soul/Spirit. He's known for a militaristic precision and his system is mostly unique. Free Grace Dispensationalism is close but not the same.
Over time I came to have an issue with the dead human spirit concept and I'm not even sure how much it matters. When I searched and studied all the spirit, soul, heart, mind, words it was very hard much of the time to strictly separate them. As I understand, this is part of the what makes for the soul/spirit viewpoint.
Rather than "Death of the Human Spirit — Fallen man is Dichotomous = body and soul", I see it as body and soul + spirit without the presence of the Holy Spirit (as I explained at Post 7627). Functionally, it is closely aligned with dichotomous, but I think if we remove spirit altogether, do we then contradict verses in Scripture which speak of the spirit of man? Could it be that rather than "spiritually dead" what occurred in Adam was more in line with "spiritually disabled" ... or "spiritually incapacitated" ... "spiritual paralysis" ... we see people who have physical disabilities ... could Adam and Eve's sin result spiritual paralysis ... the part is there, just functioning so far below what God initially created due to God having removed His Spirit?
The heart of man is what God desires ... the whole heart. Could it be that when Adam sinned and God removed His presence from the heart of Adam what remained was the work of the law being written in [the] heart (Rom 2:15) without the presence of the Holy Spirit to direct and guide the actions?
Under New Covenant, God creates a new heart within upon which is not written the work of the law ... God writes His law upon our hearts and puts His law in our minds (Heb 8:10) ... the mind of Christ which is also part of the new birth (1 Cor 2:16) is designed to hold all God gives.
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I looked at that linked post and your following closing made me smile:
"... just a few thoughts on the matter ..."
Just a few!?
You'd have to show me how you get to the concept of Adam originally having the Holy Spirit. I'm not requesting you do this work, BTW. I'm not sure how much I'll be giving all of this more attention. Reading all the varied views of so many different systems leaves me with my face in my hands wondering why.
Back to my original issue of terminology, Thieme IMO is a good example of using phrases like "spiritual death". Unless it's defined who would know he sees it as essentially meaning no human spirit until regeneration? So, any time we read Scripture that may seem to speak of fallen man having a spirit, we'd have to know Thieme may be seeing something differently. And since the fall and the meaning of death are applicable all the way through the resolutions, it's not a small matter IMO if we want to understand how this all works down to the details.
In closing this, in case anyone else reads it, I will say that looking at all of this again and including Augustine and Calvin in all the modeling, is just more and more reason for me to have strong disagreements with the Reformed system at nearly every turn.