Berkeley Lecture 2013


The second Berkeley Lecture will be given by Professor Ivor Grattan-Guinness, Emeritus Professor of the History of Mathematics and Logic at Middlesex University.


Ménage à trois: Relations between Set Theory, Logic and Mathematics between 1890s and 1930s


Georg Cantor's set theory began to be developed on a large scale from the mid 1890s; for some mathematicians it became a dogma, the one and only foundation for mathematics. It also attracted some logicians, who absorbed it as part of their logical systems. However, it did not draw the two subjects together; the usual distance apart was maintained.

After a short exposition of the main traditions on the foundations of mathematics - metamathematics, logicism and set theory - I shall treat these three case studies:

  1. The overlooked limitations of membership for the generality of sets; did anyone notice?
  2. Kurt Gödel's incompletabilty theorems of 1931; the (lack of) reaction
  3. How did Alan Turing hear about logic?


Lecture Theatre 7, John Hume Building, North Campus, NUI Maynooth


Thursday, 4 April, 2013 at 4pm.

The Berkeley Lecture is an annual event at NUI Maynooth in which a talk in the general area of mathematics and philosophy will be given by a high-profile visiting speaker. It is sponsored by the Department of Mathematics and Statistics and the Department of Philosophy at NUI Maynooth.

This event is named after the famous Irish philosopher George Berkeley (1685-1753), who made major contributions to several areas of philosophy and had a keen interest in the philosophy of mathematics. Bishop Berkeley-1734 treatise The Analyst made a detailed criticism of the Calculus of Newton and Leibnitz. This caused a major headache for mathematics and over the next century, many great mathematicians tried and failed to overcome the problems highlighted by Berkeley. But, by highlighting problems that were eventually overcome, Berkeley's criticisms ultimately benefited mathematics by putting calculus on a firmer footing and making it safer for use by non-experts by eliminating the possibility of error through plausible but incorrect arguments. It also made the subject easier to teach, although it is still challenging material for students!