With regards to your comment that "physicists seem to confuse the mathematical description of a thing with the thing itself", I'd have to say that is not correct. Rather, they are confusing the attributes (properties) of the mathematical description of a thing with the attributes (properties) of the thing itself.
The distinction is important. Since you mention having an interest in Philosophy, allow me to remind you that Plato frequently depicts Socrates reminding people to bear in mind this distinction between a thing and its attributes. Socrates then proceeds to get them to contradict themselves, by inducing them to ignore this distinction. Unfortunately for the physicists, they have managed to confuse themselves, without requiring any help from Socrates.
Color is an example of such a phenomenon, that has been debated for centuries. Is it an attribute of a thing? No. It is an attribute of the relationship between a thing and an observer. For example, red and green light together, like the pixels on your computer screen, will be perceived as yellow, since a pair of cone cells in the retina of your eye produce the same amplitude ratio, on the output of a pair of filters, as described in my essay. (See attached figure. I hope this works, this is the first time I have tried to attach a file to one these this posts.)
In your essay, you mention thought experiments. The most famous thought experiment in Quantum Mechanics is Schrodinger's Cat. As with all thought experiments, it lacks the virtue of being tested experimentally - if it were to be tested, it would no longer be a thought experiment. But it has other even less virtuous attributes. Physicists have simply assumed that the wavefunction in question, that describes the relationship between the cat and the observer, can be determined, at least in principle. But it cannot.
The reason is, the wavefunction is based on Fourier Transforms. Computing a transform that is a function of time requires an integration over all time. This can only be accomplished when the function being integrated is known at all times.
Since the past can be known, at least in principle, integrating over the past is not a problem. But what about integrating over the future? The future of the dead cat is known. It will remain in the constant state of being dead forever, unless you believe in the resurrection of cats. But the same is not the case for the observer, since he or she is not yet dead.
If the future of the human observer could be predicted perfectly, then you could integrate over the predicted future. But that cannot be done, for the reasons I discussed in the blog for Dan Bruiger's essay.
So no knowable wavefunction can exist for any living observer. It is important to note that this argument does not apply to things, like elementary particles, that QM was designed to describe. This is true, because, as described in my essay, they are all characterized by the attribute of being nearly devoid of information. As a direct result, their future, unlike a human observer, can be predicted; an undisturbed particle will remain in its constant state. And the future of a constant is easily predictable. That, by the way, is the sole significance of all the conservations laws in physics.Attachment #1: Gaussian_Filters.jpg