Set Theory Quotes (5 quotes)
No one shall expel us from the paradise which Cantor has created for us.
Expressing the importance of Cantor's set theory in the development of mathematics.
In George Edward Martin, The Foundations of Geometry and the NonEuclidean Plane (1982), 33.
Since the examination of consistency is a task that cannot be avoided, it appears necessary to axiomatize logic itself and to prove that number theory and set theory are only parts of logic. This method was prepared long ago (not least by Freges profound investigations); it has been most successfully explained by the acute mathematician and logician Russell. One could regard the completion of this magnificent Russellian enterprise of the axiomatization of logic as the crowning achievement of the work of axiomatization as a whole.
Address (11 Sep 1917), 'Axiomatisches Denken' delivered before the Swiss Mathematical Society in
Zόrich. Translated by Ewald as 'Axiomatic Thought', (1918), in William Bragg Ewald, From Kant to Hilbert (1996), Vol. 2, 1113.
To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.
In Axiomatic Set Theory (1971), 915. In Thomas Tymoczko, New Directions in the Philosophy of Mathematics: an Anthology (), 1112.
[Cantors set theory:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.
As quoted in Constance Reid, Hilbert (1970), 176.
~~[No known source]~~ Later generations will regard Mengenlehre [set theory] as a disease from which one has recovered.
Webmaster finds zero support for the authenticity of this quote. Speculations on how it may have evolved include reference to a
beau cas pathologique (a beautiful pathological case) in a very different quote which begins I think, and I am not the only one
. (See the
Henri Poincarι Quotes web page of this site.) More details readily available with a Google search (for example): Did Poincarι say set theory is a disease. The quote is included here to provide this caution.
In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) 
Carl Sagan
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