And what would, according to you, be a proper way to say whether the names for the numbers in a language are Indo-European in origin or not?
The only way is to show systematic sound changes/correspondences in a large sample of vocabulary items. If the numbers fit into that pattern then they probably also have the same origin. (But individual items can be exceptions, so there's really no way to be absolutely certain.)
Remember, you can't prove anything in science. You can just provide evidence that is consistent with a hypothesis and
falsify alternative hypotheses by showing evidence that is inconsistent with those.
Etruscan names for the numbers 1-10 don't particularly resemble that in Indo-European languages, but they aren't much more different than the Armenian and Albanian ones are from other Indo-European languages.
That's untrue because you are using the wrong methodology. The numbers in Armenian and Albanian can be traced back via regular sound changes to PIE roots. You're approaching this the wrong way, asking whether something is "different" or "similar", instead of asking whether there is a predictable path of development. There is no way to know just by looking at words whether they're related or not, regardless of how similar or different they are.
Armenian and Albanian names for the numbers 1-10 are supposed to be derived from the Proto-Indo-European ones by some counter-intuitive sound changes.
Sound changes are not "intuitive" (or "counter-intuitive"). They are facts of history, shown by recurring patterns. I won't argue about this with you, because this has been known and accepted for about 200 years. The validity of a specific change is based on whether it can be shown to consistently apply to and explain the vocabulary of a given language. Grimm's Law for example might seem "counter-intuitive" to you (it's certainly not especially transparent) but it's well established and explains a huge amount of Germanic vocabulary. Your intuition is irrelevant. (Mine too.)
Therefore, on the first glance, regular sound correspondences don't exist in the numbers...
No, no, no!
1) "First glance" is irrelevant. That's not science. On first glance I can't see gravity, but it's there because I can observe it experimentally (such as by dropping a bowling ball on my foot).
2) "Regular" in this context means
rule-based, not "obvious" or "intuitive" or "simple". Look for consistency, not transparency. That's how this works.
How do we know that the same is not true for Etruscan?
We do not know that it isn't true. But we also should not assume it is until there is evidence to support it. The reason we do not currently accept that it is true is because there are no consistent patterns of sound change (=rules, =regularity) that derive those words. It does not matter whether it looks like it might (or might not) be true to you. It matters whether we can identify consistent patterns.
After all, the Etruscan names for 2 and 10 start with a similar sound
Again, "similar sound" is irrelevant and arguably meaningless. That's just your impression. What matters is not whether it's the same or different, but whether that pattern fits.
A big mistake people often make when trying to imagine distant relationships over large time depths is to say "look, these sounds are the same (or similar)!" when in fact, over enough time, it's unlikely the sounds would be the same. For example, trying to relate PIE and Proto-Afro-Asiatic some people have pointed to fairly transparent "cognates" in Latin and a Semitic language. The odds of those being real cognates are low, however, because over that much time, real cognates probably would have shifted farther apart rather than inexplicably not changing. Therefore the only way to identify real cognates is to show the same sound correspondences across a large number of vocabulary items, regardless of whether the sounds are the same/similar/different.
and the Etruscan names for 6 and 7 start with the same sound (and the same is true for most of the Indo-European languages).
An interesting coincidence is that "six" is quite similar in a lot of languages, some of them unrelated. This is just a coincidence (or possibly borrowing in some cases), though, and it shows that "it looks the same" isn't a good argument.
In other words, isn't the fact that there appear to be two sound correspondences (each with two examples) between Etruscan and Indo-European names for the numbers 1-10 a much stronger argument that the Etruscan numbers are related to the Indo-European ones than "they don't look similar" is against it?
No, because neither of those arguments is how sound change works, see above.
"They don't look similar" is not the reason that trained linguists give for the lack of a relationship between PIE and Etruscan: it is because we have no evidence for regular sound changes (=
patterns!).
"There appear to be two sound correspondences (each with two examples)" is not nearly sufficient evidence to establish consistent patterns across the vocabulary. When you have several dozen examples, reconsider this. And it won't be accepted until you can show many such patterns, and also don't find an overwhelming number of exceptions to the proposed patterns.
Search online for "Regularity of sound change" for background information on this. There are also some good discussions of how to avoid bias from coincidental similarities.
