@erosalie
The error in that line of thought is the absolutism you've introduced. When something's ruled out, you don't go putting it back in, because it's definitively OUT...for the time being, and it's time that would change that, pending new evidence to the contrary.
It's absolutism that provides any given "smart" criminal the loopholes he seeks to avoid prosecution because he's thoroughly convinced that, by your own rules, you cannot prove his guilt.
Thus we arrive at the value of Venn, which covers those shades of gray between ruling in and ruling out, which it will do but dependent on conditions.
You can still rule things out that don't fit any of those conditions.
@ClaraListensprechen4
I would both agree and disagree, agreeing that in practice this is treated as proving a negative but disagreeing in the absolute sense.
In forensic science, the assertion "this person's DNA is not at the crime scene" is grounded in the analysis of specific, finite samples. This does not conclusively prove the person's DNA was absent from the entire scene, as uncollected or untested areas might contain it. Thus, this is a probabilistic conclusion rather than an absolute disproof of the negative. It's also a probabilistic conclusion that is probably wise to make since we could not function if we demanded the latter.
Although in practice, such conclusions are treated as if they prove a negative, it's more accurate to consider them as effective probabilities based on available evidence. For instance, stating "this person's DNA was not at the scene" generally refers to the tested samples, serving as a practical shorthand. This approach is valid because it relies on specific, constrained claims and established methods for DNA testing.
We have similar principles in medicine and public health where the dynamic is the same. If we test someone for HIV (let's assume a highly effective test) and it comes back negative, we "rule it out" but the test could technically be wrong. Operating on that assumption however is not practical or even advisable.
When we rule something out we're shorthanding a fuller statement: based upon the available evidence from the sample examined, we rule this out because it's extremely unlikely to be the culprit based upon these results.
Critically, in the context I raise, this type of assertion tends to be a demand for that which we cannot prove even if functionally we can rule something out.