>You cannot confirm the effects of "artificial sweeteners" as a category with an experiment that is based on saccharin. //
Hmm. Yes you can, you just can't generalise the result.
If you want to test the hypothesis that "artificial sweeteners cause ..." then you start by testing if something from that category causes whatever effect. That shows that "artificial sweeteners cause the effect" but as you note it doesn't show that "all artificial sweeteners cause the effect".
Of course you follow up by looking at other sweeteners as this feeds in to understanding of the underlying mechanisms.
Logical analogy: Do birds sit on telephone wires? Yes, I saw one. Does that mean all birds sit on telephone wires, no. Indeed it's demonstrable that some birds never even see a telephone wire.
When you conclude the <category> has <trait> you are implicitly assuming that the elements of that category are somewhat representative.
If you only saw some pigeons sitting an the wire it would be better to conclude that pigeons sit on wires because the assumption that those pigeons are representative of pigeons is much more reasonable than assuming that those pigeons are representative of birds.
For a more contrived example I could do a study and conclude that liquids are poisonous. Technically true but extremely misleading.
When it comes to health effects, it's not necessary to prove that all members of a category share those effects. Simply showing that at least one member of the group is dangerous can be enough to recommend that people alter their behavior.
For example, not all snakes have venom that's harmful to humans. But some do and that's enough to assume than an unknown snake is venomous until it's been shown to be otherwise. Similarly, your "liquids are poisonous" study is enough to conclude that we shouldn't be ingesting liquids that haven't been shown to be safe.
Similarly, if we can conclude that one or more artificial sweeteners are harmful to our health, we can and should be consuming unsweetened foods until such time as individual artificial sweeteners are shown to be safe.
> it's not necessary to prove that all members of a category share those effects
You're assuming "artificial sweeteners" is a meaningful category, of the same kind as "snakes" or "liquids". Since the various substances in question are very different, chemically, I think that assumption requires more justification than just a bare assertion.
With pharmaceuticals the FDA customarily insists that "class effects", meaning adverse effects and black-box warnings, apply to all drugs considered to belong to a category. It doesn't even matter if a brand new drug is far less likely to produce certain "class effects" than prior drugs in the same category, the exact same warnings must still be listed.
In other words, the implicit rule is that drugs or additives in a class are "guilty" of potentially causing an adverse effect unless thorough study provides evidence that a member of a class does not produce particular negative effects. It's a high bar for manufacturers to get over and it's seldom attempted.
The FDA can assume serious adverse effects of one artificial sweetener apply to others, if the others are officially in the same class of substances as the first.
Hmm. Yes you can, you just can't generalise the result.
If you want to test the hypothesis that "artificial sweeteners cause ..." then you start by testing if something from that category causes whatever effect. That shows that "artificial sweeteners cause the effect" but as you note it doesn't show that "all artificial sweeteners cause the effect".
Of course you follow up by looking at other sweeteners as this feeds in to understanding of the underlying mechanisms.
Logical analogy: Do birds sit on telephone wires? Yes, I saw one. Does that mean all birds sit on telephone wires, no. Indeed it's demonstrable that some birds never even see a telephone wire.