You know what the absolutely key thing about "possibly carcinogenic" is? Dose/quantity.
Many things that are normally consumed and considered harmless can be very harmful in large(r) quantitites. As far as I know, aspartame has never been reliably proven to cause any health issues (it also wouldn't be used if it did). The only (and still inconclusive) evidence about it possibly being harmful I recall was always tied to large doses many times over a normally used limit.
Also, as pointed out, there are *many* things in the same 2B category ("There is some evidence that it can cause cancer in humans but at present it is far from conclusive"), including (as metioned) ginkgo biloba or aloe vera.
And then there's also the 2A category ("There is strong evidence that it can cause cancer in humans, but at present it is not conclusive"), classified as "probably carcinogenic" (as opposed to "possibly"). You know what is considered part of that category? Eating red meat, night shift work, working as a barber/hairdresser or drinking beverages above 65°C.
So, you know, if you happen to be a barber or work nights, it might be prudent to limit your aloe vera exposure. You might still get cancer, because cancer is far more complicated than exposure to specific things and, in a way, it's also inherent to advances in medicine and health care (because many people who nowadays get cancer would simply not live long enough to get it before), but if you're worried about aspartame being carcinogenic, I guess it might make you feel better.
