“Leibniz believed not only that it was a metaphysical fact that all truths are reducible to primary logical truths, but also that, given an appropriate formal language, all truths should be capable of a priori proof. The means of carrying out such proofs was the subject of one of Leibniz's earliest works, his dissertation De Arte Combinatoria (On the Art of Combinations) written in 1666... In it Leibniz reveals his vision of a Characteristica Universalis, or universal characteristic, that would operate as a formal logic through which all true propositions would be demonstrable, merely through adherence to syntactical rules...”
“These doubts did not halt mathematical creation. Technicians working on the superstructure did not drop their tools and scurry down to the basement because some of their underpinning needed reinforcin...”
Foundations of mathematics
“The truth is that the mathematical sciences are growing in complete security and harmony. The ideas of Dedekind, Poincare, and Hilbert have been systematically developed with great success, without an...”
Foundations of mathematics
“As soon as I have put it into order I intend to write and if possible to publish a work on parallels. At this moment, it is not yet finished, but the way which I have followed promises me with certain...”
Foundations of mathematics
“I should regard it as a great misfortune if you were to allow yourself to be deterred by the 'clamors of the Bœotians' from explaining your views of geometry. From what Lambert has said and [Ferdinand...”
Foundations of mathematics
“The world is totally connected. Whatever explanation we invent at any moment is a partial connection, and its richness derives from the richness of such connections as we are able to make. ...mathemat...”
Foundations of mathematics