It is well known that tests are not 100% accurate at classifying individuals. The actual condition of an individual(e.g. diseased, or not diseased) does not coincide with her test result (positive, or negative). Nevertheless, it is often presupposed, as a rule of thumb, that individuals with negative results can be “ruled out” if screening test is highly sensitive and “ruled in” if screening...
We prove a characterization theorem for filters, proper filters and ultrafilters which is a kind of converse of Łoś's theorem. It is more natural than the usual intuition of these terms as large sets of coordinates, which is actually unconvincing in the case of ultrafilters. As a bonus, we get a very simple proof of Łoś's theorem.
I discuss the Pythagorean law of small numbers and its use in interpretations of our sensory discriminations of consonance vs. dissonance. It seems that the fact of non-western musical traditions contradicts the law and forces us to interpret the discriminations as acquired and subjective. I would like to show that this is a wrong interpretation, because it is based on the irrelevant empirical evidence...
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