Okay, so I think the differences is the third term are somewhat significant, so I’ll comment on that.
The term is itikira. It is a compound of two particles, iti meaning “thus, such”, and used to mark a direct quote; and kira meaning “so it seems”, “they say”, “it appears”. Kira is often used in a dubitative sense, such as saccaṃ kira tumhe “Is it really true that you …”. Like several of these terms, it only appears in this passage in the early texts, so nailing an exact meaning is difficult. But I think it is related to itihītiha in a similar sense, also a name for ancient texts or knowledge, and meaning something like “They say it was like such and such”. I suspect this means “legends”, and is possibly a reference to such myths as the Mahabharata, etc (in their archaic forms). Thus in the list of traditional brahmanical lore we find itihāsa, “So it was”. Also compare the well known itivuttaka. These are idiomatic expressions for a kind of traditional lore or knowledge. Whereas Ven Bodhi has “hearsay”, to me this is too casual. It’s not talking about something that gets randomly passed down as gossip. I used the translation “testament”, as this conveys a similar sense of reporting another’s truth, but has a formal religious connotation.
The next one is takkahetu. I guess Ven Bodhi included the word “reasoning” in this entry and the next because the second element in these compounds is hetu, “cause, reason”. However, I don’t think hetu in this sense means “reasoning” as such. In these two terms, the instrumental case is lacking, and I believe the hetu has a purely syntactical role here. If we translate the other items literally as “don’t go by oral transmission”, etc., these two terms might be rendered, “don’t rely on logic”, etc. Such nuances are usually smoothed over in translation, but perhaps they shouldn’t be.
In any case, takka (Skt. tarka) is a standard Buddhist term for “logic”, and will be very familiar to the Tibetans!
Naya means something like “inference, drawing out a conclusion”. It’s not used much in the early texts, but the sense can be seen in such sentences as Mil 6.3.10:
sakkā pana tassa nibbānassa rūpaṃ vā saṇṭhānaṃ vā vayaṃ vā pamāṇaṃ vā opammena vā kāraṇena vā hetunā vā nayena vā upadassayitun
But is it possible to show that nibbana’s form or shape or age or measure by means of simile or reason or logic (hetu) or inference (naya)?
Or in Mil 1:
Nāgasenakathā citrā opammehi nayehi ca*
Nagasena’s speech is fancy with both simile and inference (naya)
After reflecting more on the grammatical nuances of the passage, I have revised my translation to better reflect the richness in phrasing.
Don’t go by oral transmission, don’t go by lineage, don’t go by testament, don’t go by canonical authority, don’t rely on logic, don’t rely on inference, don’t go by reasoned contemplation, don’t go by the acceptance of a view after consideration, don’t go by the appearance of competence, and don’t think “The ascetic is our respected teacher.”