Bertrand Russell in the Preface to his Introduction to Mathematical Philosophy writes:
Much of what is set forth in the following chapters is not properly to be called "philosophy," though matters concerned were included in philosophy so long as no satisfactory science of them existed. The nature of infinity and continuity, for example, belonged in former days to philosophy, but belongs now to mathematics.
Russell must be the right person to make such a statement, he was both a philosopher and mathematician.
But how does he justify the claim that philosophical infinity is now mathematical infinity.
I don't think these two can be reconciled. Philosophical infinity is something else and mathematical infinity is something else.
I'm still looking to find a satisfactory definition of the word infinite in mathematics.
