Quote: Russell's paradox shook the foundations of Frege's arithmetic; substitution of equality is not always valid

Quotation Skeleton

[Frege's response to Russell's letter] Your discovery of the contradiction caused me … which I intended to build arithmetic. It seems, … is not always permitted, that my Rule V … to ensure that my combinations of signs have … more serious since, with the loss of my … arithmetic, seem to vanish. Yet, I should think, … equality into an equality of courses-of-value such that … will perhaps result in a great advance in …   Google-1   Google-2

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