《大莊嚴論經》卷1:「善知僧佉論衛世師論若提碎摩論」(CBETA, T04, no. 201, p. 258, c16-17)
僧佉 is sāṃkhya.
衛世師論 is vaiśeṣika
若提碎摩論 is curious. Logically it would be nyāya as Namdrol suggests.
The character 若 has an ancient Japanese on-yomi reading of
nya, such as in 般若
han'nya, which is preserved Chinese reading from the Sui-Tang.
Looking at the on-yomi readings for this might be helpful (they preserve the old pronunciation of characters used to transliterate Sanskrit better than modern Mandarin does).
若
jyaku /
nya提
tei /
chou /
dai碎
sai摩
mo /
ma碎摩 looks more like a verb, to smash and scatter something -- otherwise "refute"? Like 破.
I wonder if this isn't a translation for something like nyāya tarka-vidyā ?
"Tarka" meaning the following:
(H2) tarka [p= 439,3] [L=83342] m. conjecture MBh. &c
[L=83343] reasoning , speculation , inquiry Kat2hUp. ii , 9 Pa1rGr2. ii , 6 , 5 Gaut. Mn. xii , 106 MBh. &c
[L=83344] doubt W.
[L=83345] system or doctrine founded on speculation or reasoning , philosophical system (esp. the nyāya system , but applicable also to any of the six darśana q.v.) BhP. ii , vii f. Prab. Vop. Caran2. Madhus.
The 提 character might have had a "-k" consonant ending in the fifth century.
This is the reconstructed reading according to Baxter-Sagart. See page 127.
http://crlao.ehess.fr/docannexe.php?id=1202提 tí dej (MC) (d- + -ej A) (MC) *dˤe {*[d]ˤe} (OC) lift, grasp
The middle Chinese reading was
dej. The old Chinese reading might not be so important because that's many centuries prior to when Kumarajiva was alive.
So do you think 提 could be for tarka given that 若 is probably nyāya and that 碎摩 is not a transliteration, but a Chinese translation meaning "debate"?
This is just my speculation, but what do you think?