Skip to main content
9 votes
Accepted

What are the origins of Galileo's paradox?

The answer depends on what "this" means. According to Mancosu's Measuring the Size of Infinite Collections of Natural Numbers (reprinted in his book Abstraction and Infinity): It is actually ...
Conifold's user avatar
  • 77.6k
6 votes

In which article/book chapter did Cantor, Hilbert, and Poincaré formally define or directly discusse the term “potential infinity”?

You have misinterpreted the article you refer to; nowhere does it say that "Cantor claimed that there would only be potential infinity, not actual infinity". In fact, it says the opposite: ...
Spencer's user avatar
  • 602
4 votes
Accepted

In which article/book chapter did Cantor, Hilbert, and Poincaré formally define or directly discusse the term “potential infinity”?

Hilbert devoted a whole paper to infinity, On the infinity, published in 1925 (1). Hilbert was one of the most tenacious defenders of the "paradise of the infinity" revealed by Cantor's ...
BakerStreet's user avatar
  • 1,065
3 votes

Is there a formal distinction between potential and actual infinities?

Not "formal" but quite precise: Aristotle and apeiron. See Meta, Book IX ($\Theta$), 1048b10: The infinite and the void and all similar things are said to exist potentially and actually in a ...
Mauro ALLEGRANZA's user avatar
2 votes

Did Leibniz use infinite numbers?

It appears that they are right in the "metaphysical" sense, here is a passage from Leibniz's letter to Bernoulli (1699):"I concede an infinite multitude, but this multitude forms neither a number nor ...
Conifold's user avatar
  • 77.6k
2 votes

Is there a formal distinction between potential and actual infinities?

The distinction between potential and actual infinities was Aristotle's clever solution to Zeno's paradoxes. The idea was that while we can mentally divide segments in half indefinitely actualizing ...
Conifold's user avatar
  • 77.6k
1 vote

History of Infinity: How does the idea of infinite set become widely accepted?

Quoting numerous sources, The German physicist Max Planck said that science advances one funeral at a time. Or more precisely: “A new scientific truth does not triumph by convincing its opponents and ...
Carl Witthoft's user avatar
1 vote

What is Newman's "infinite number of curves"?

As others have pointed it out, it's difficult to know what he meant. Remember that he was reporting on something he had been told which he probably hadn't fully comprehended at the time, or of which ...
Bence Mélykúti's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible