[deleted]
RLO, You wrote:"in science [the kind that was practiced in 1905−1925,
not untestable postmodern pseudoscience]".
I am not sure. Could it not be possible that very basic mistakes can be attributed to just in this time or even to some decades before it? What about the methods to save and even teach until now (!) what contemporaries called untenable and naive? More recently Ebbinghaus called it an error but nonetheless a valuable truth. Yes, I know the risk being suspected unqualified or stupid because I do not pretend believing in aleph_2 and related phantasm. Those who do not like basic corrections, because they envision a huge heap of rubble, do not even respect Galilei who concluded that the relations larger, equal, and smaller are not valid for infinite quantities. For instance, "Anglin (1949- )" who left the year of his dead open when he proudly quoted himself wrote: (Galileo) "did not contribute to mathematics".
Galilei did still understand infinity as something that cannot be enlarged:
oo anything = oo. 2^oo=oo.
Believing in an actually infinite God, Medieval thinker like Gregory of Rimini (1300-1358) were not limited to Aristotele's potential infinity, i.e., to the property of being unlimited. While Albert of Saxony (1350) correctly understood that a part of infinity is not smaller than infinity itself, Bolzano (1781-1848) was only correct in that a bijection between infinite series does not imply that they have the same number of elements. However, he did not understand that there are not differently large infinities. His obvious influence on Weierstrass and G. Cantor misled mathematics.
Cantor tried in 1886 in vain to convince cardinal Franzelin that there is an Infinitum creatum sive Transfinitum. Rather average mathematicians and G. Cantor's friends like Mittag-Leffler, Hurwitz, and Hadamard enthusiastically celebrated G. Cantor's admittedly stunning proofs. Alfred Nobel did not like Mittag-Leffler and decided "let be no price for mathematics". Cantor himself might have almost understood the impossibility to tame the infinite when he described it as an abyss. In 1884 he got insane for the first time. Nonetheless he got famous, and he successfully attacked Kronecker who died in 1891.
Hilbert's speech on infinity in memoriam of Weierstrass reveals a lot, e.g. when it refers to simple "Hinueberzaehlen" (counting in excess of infinity). The German term for uncountable is ueberabzaehlbar (more than countable).
The Cantor story is an ongoing series of fiercely defended mistakes with benign consequences for physics. Apparently nobody objected against the less spectacular but presumably worse joint influence of Cantor's friend Dedekind who already in 1872 replaced the understanding of numbers as pieces of a line by points.
Eckard Blumschein