The challenge you have here is that aspartame isn't just one of most widely studied substances in the food chain, but that it's also one of the most widely and vigorously consumed. People drink a lot of diet soda; a lot of people drink it to the exclusion of all other liquids. So it's going to be tricky to get the epidemiology to match up with the claim here: if aspartame is meaningfully carcinogenic (meaning: more t…
If someone tried to prove an airplane design can fly 1,300 times and all it did was come off the ground for a centimeter for half a second, would you say "this airplane design can possibly fly"? I doubt any reasonable person would. But with aspartame there is an idea in people's heads that it's harmful and should be avoided therefore people continue to go with the theory that even though they've failed to prove it's harmful 1,300 times they may do so in the future.