It is not. We do it day in and day out in science and in real life. It is a fallacy and high-school debating line to say what you did. Those of you who make this false argument are in dire need of reading this short article from professor Steven Hales: https://www.cambridge.org/core/serv...f/thinking-tools-you-can-prove-a-negative.pdf
"But there is one big, fat problem with all this. Among professional logicians, guess how many think that you can't prove « a negative? That's right: zero. Yes, Virginia, you can prove a negative, and it's easy, too."
I enjoy reading many of the sources you provide, but this one I don't care for too much. I will very
briefly state my concerns (don't want to derail the thread). The author plays fast and loose with the meaning of proofs and totally misrepresents proofs in science. As you well know, the scientific method does not prove a theory, all it does is test the null hypothesis. Philosophy of science is filled with examples of scientific advancement being affected by perceptions, dominant perceptions, and paradigm shifts. This PC study is another apt example. You can study as many cables as you want, but in the end, all we can accomplish is show that there is no evidence to suggest the contrary. When "believers" dream up stupifying theories to support their views, then we can develop hypotheses to test their theories, and determine if their "theory" is able to explain any of the data available to us. However, as @JanesJr1
already stated, Popper noted that all it would take is one contrary incident to disprove years of accumulated data and study. So no, science does not absolutely prove the existence of things, but it is able to provide us with the means to study and understand our experienced reality by providing us with many tools to circumvent our human filters/limitations (please note that there is value to having filters, it provides us with the means to interact with each other as a community).
Not being able to prove the negative is problematic since the subject proposing the stance can continue down a path of "infinite" absurdum, the very nature of the claim does not allow for reasonable proof (e.g. the listener must
be able to view the equipment being tested, otherwise they are under too much stress to evaluate the equipment); that is why individuals making extraordinary claims are generally expected to provide strong evidence to support their claim (sadly in the history of science, sometimes this has led to the perpetuation of poor theories until sufficient non-explainable data was gathered to destabilize the old predominant theory).
2 examples of extraordinary claims:
1. One of Descartes' arguments suggested that we may be living in a fantasy world created by super powerful being (yes, hundreds of yrs before the Wachowski brothers (they were brothers at that time) created The Matrix, Descartes had already conjectured about the possibility of living in a fictional realm) controls all of our experience, then nothing is real (in a "Platonic" sense). All experience is subject to the creation of the superbeing (or as some in the field you used to work in have contemplated, you/I/we could be nothing more than the result of an algorithm created by a complex computer program/AI. None of these can be disproven, we can merely attempt to develop theories and test hypotheses to examine how the above noted claims of fictional reality may be "proven" if "real".
2. We are all under the mind control of powerful aliens, and the thoughts we think we have are the result of controls they have implemented in our thinking process to make us believe and experience in a particularly specific way to serve their needs. Oh... and the reason people can hear the difference between cables is that they are momentarily able to break from the control of such aliens, but the aliens have forced particular ways of thinking into our reasoning process to be able to "disprove" those actual moments of lucidity.
As you can see, the power of the negative is that it can always be stretched beyond the realm of our ability to prove the contrary. The debate about God's existence has been going on for over millennia, and brilliant people on both sides have attempted to prove their claims. I don't need to tell you how that is going.