etymology - Are "money" and "mind" cognates?

Wiktionary gives me these pieces of information:

[money] [1]

From Middle English moneie, moneye, from Old French moneie (“money”), from Latin monēta, from the name of the temple of Juno Moneta in Rome, where a mint was.

Displaced native Middle English schat (“money, treasure”) (from Old English sceatt (“money, treasure, coin”)), Middle English feoh (“money, property”) (from Old English feoh (“money, property, cattle”)).

[mint-2] [3]

From Middle English mynt, münet (“money, coin”), from Old English mynet (“coin, money”), from Proto-Germanic *munitan, *munitō (“coin”), from Latin monēta (“place for making coins, coined money”), from the temple of Juno Moneta (named for Monēta mother of the Muses), where coins were made; akin to Dutch munt (“currency, coin, mint”), German Münze (“coin, coinage, mint”), Danish mønt (“coin”), and to Russian монета (“coin”).

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[mint-1] [2]

From Middle English minten, from Old English myntan (“to mean, intend, purpose, determine, resolve”), from Proto-Germanic *muntanan, *muntijanan (“to think, consider”), from Proto-Indo-European *men-, *mnā- (“to think”).

Cognate with Eastern Frisian mintsje, muntsje (“to aim, target”), Dutch munten (“to aim at, target”), Dutch monter (“cheerful, gladsome, spry”), Gothic 𐌼𐌿𐌽𐍃 (muns, “thought, opinion”), Old English munan (“to be mindful of, consider, intend”). More at mind.

[mind] [4]

From Middle English minde, from Old English ġemynd (“memory, remembrance, memorial, thought”), from Proto-Germanic *gamundiz, *mundiz (“memory, remembrance”), from Proto-Indo-European *men- (“to think”).

Cognate with Gothic 𐌼𐌿𐌽𐌳𐍃 (munds, “memory, mind”), Old English myntan (“to mean, intend, purpose, determine, resolve”), Latin mens,mentis (“mind, reason”), Albanian mënd (“mind, reason”). More at mint.

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There are two etymologies, mint-2 and mint-1 provided for mint, referring respectively to two meanings: "a coin/place making coins" and "intent to do".

(Q1)So are mint-1 (intent to do) and mint-2 (a coin) cognates or not?

If they are not cognates, given that money is cognate with mint-2 (a coin) while mind is cognate with mint-1,

(Q2)can we draw the conclusion that money and mind are not cognates?

Answer

Yes, they're all related.

The Latin name Monēta comes from the verb moneō, monēre, monuī, monitus, 'to warn'. "Juno the Warner" was a cognomen of the goddess Juno; there's a story about geese in the link. The fact that the Roman mint was located (and named) at the temple of Juno Moneta is a coincidence. That's where a lot of names come from.

But, to return to the question, the etymology of moneō is very interesting. It turns out to be an O-grade ablaut variant of the PIE *men- 'mind' root, same as the other ones. But it's a Causative. Warn is a causative in PIE because it meant 'cause to think (of)'. And they had a way to indicate this.

PIE was highly inflected, like Sanskrit, and it had a causative aspect, which was a suffix -i- or -iy- before the person/tense inflection. The PIE would have been something like mon-iy-, and by Latin that had become mon-ē-.

This "yodated causative" -iy- suffix came down into English too, surviving as a fossil palatalization in words like drench, which comes from older drink-y-an and meant 'cause to drink'. Thus, at some point in English history, you could lead a horse to water, but you couldn't drench him.

Many English verbs that end in [tʃ] or [dʒ] can be paired off with an non-causative verb like drink/drench. For instance, milk/milch, dike/ditch, make/match, blank/blanch, wring/wrench, and the like (vowel changes happen often, but consonants tend to linger).