Proof. Assume n > 2, 2 divides n and n is prime. Therefore, 2 is a prime factor of n. But since every prime number only has one prime factor, itself, then n = 2. But n = 2 contradicts n > 2. Therefore, no prime numbers greater than 2 exist. QED.
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Claim. There is no beer in the fridge. Argument. I opened the fridge, there was no beer in the fridge.
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p is a proposition. ~p is its negation. Take q = ~p. Proving p is the same as proving ~q.
Seems to me you can most certainly prove "negatives".
Fine. One can't necessarily prove a negative. Only if you can prove the negation of the assertion can you "prove the negative".
Now apply that logic to: <Musk> I can reduce the cost of boring by an order of magnitude.
Can you prove that he can't? The gp was (over)simply stating that just because no other digging project has done what Musk claims to be able to do doesn't necessarily mean that Musk can't do it.
One can't prove a negative.
Musk can access great people and large amounts of capital, thinks things out from first principles, doesn't believe in "safety first", and thinks tunnels could be of great value. Traffic (on car and trains) is killing our cities and nothing is being done about it. No new transportation infrastructure built in the Bay Area since 1980 except a few small BART extensions. We could put anything in these tunnels. Not sure why people are so worried that he is going to get some people together and try.