7) He (Leibniz) was prevented from succeeding by respect for the authority of Aristotle, whom he could not believe guilty of definite, formal fallacies; but the subject which he had desired to create now exists, in spite of the patronising contempt with which his schemes have been treated by all superior persons.
Interessant. So etwas gibt es also.
8) The solutions, for those acquainted with mathematics, are so clear as to leave no longer the slightest doubt of difficulty. This achievement is probably the greatest of which our age has to boast.
9) The proofs favourable to infinity, on the other hand, involved no principle that had evil consequences.
Nanu? Er erwàhnt doch selbst Tristram Shandy etwas spàter im Text! Er bemerkt aber nicht, dass allein der mathematische Grenzwert der Kardinalitàten über das Ergebnis entscheidet? This is an instance of the amazing power of desire in blinding even very able men to fallacies which would otherwise be obvious at once." [Bertrand Russell: "What I believe" aus "Why I Am Not A Christian and Other Essays on Religion and Related Subjects", (Paul Edwards, ed.), London: George Allen & Unwin (1957)]
10) There are exactly as many fractions as whole numbers.
In der Mathematik ist das beweisbar falsch. Siehe: Not enumerating all positive rational numbers (formal approach) in https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf
11) There is a greatest of all infinite numbers, which is the number of things altogether, of ever sort and kind. It is obvious that there cannot be a greater number than this, because, if everything has been taken, there is nothing left to add. Cantor has a proof that there is no greatest number, and if this proof were valid, the contradictions of infinity would reappear in a sublimated form. But in this one point, the master has been guilty of a very subtle fallacy, which I hope to explain in some future work.
Natürlich. Cantor verschiebt das potentiell Unendliche lediglich aus dem Bereich der natürlichen Zahlen in den Bereich der transfiniten Ordinalzahlen. Alle Probleme, die dem potentiell Unendlichen (zu Unrecht) angedichtet werden, müssen so "am Ende" wieder erscheinen. Russell war wàhrend der Niederschrift des Artikels noch in einem rational gepràgten Zustand.
12) Note added in 1917: Cantor was not guilty of a fallacy in this point.
Schade. Nun hatte er einmal etwas Richtiges erkannt und widerruft es.
13) But if Achilles were to overtake the tortoise, he would have been in more places than the tortoise, but we saw that he must, in any period, be in exactly as many places as the tortoise.
14) This paradoxical but perfectly true proposition depends upon the fact that the number of days in all time is no greater than the number of years.
Falsch: Der Faktor betràgt ungefàhr 365 für jedes Zeitintervall, das man überprüfen kann. Unüberprüfbare Resultate, sogenannte Glaubenssàtze gehören allenfalls zur schmutzigen Mathematik, niemals zur reinen.