The object of this paper is to give a satisfactory account of the Foundations of Mathematics in accordance with the general method of Frege, Whitehead and Russell. Following these authorities, I hold that mathematics is part of logic, and so belong to what may be called the logical school as opposed to the formalist and intuitionist schools. I have therefore taken Principia Mathematica as a basis for discussion and ammendment; and believe myself to have discovered how, by using the work of Mr Ludwig Wittgenstein, it can be rendered free from the serious objections which have caused its rejection by the majority of German authorities, who have deserted altogether its line of approach.
Frank P. RamseyRelated topics
account approach authorities believe following formalist free general hold line mathematics paper principia satisfactory school take using whitehead work RussellRelated quotes
We set ourselves the ultimate aim of abolishing the state, i. e., all organized and systematic violence, all use of violence against people in general. We do not expect the advent of a system of society in which the principle of subordination of the minority to the majority will not be observed.
In striving for socialism, however, we are convinced that it will develop into communism and, therefore, that the need for violence against people in general, for the subordination of one man to another, and of one section of the population to another, will vanish altogether since people will become accustomed to observing the elementary conditions of social life without violence and without subordination.
Vladimir Lenin
Isaac Newton's Philosophae Naturalis Principia Mathematica abstracted time from events, establishing its tractability to scientific calculation. Conceived as pure, absolute duration, without qualities, it conforms perfectly to its mathematical idealization (as the real number line). Since time is already pure, its reality indistinguishable from its formalization, a pure mathematics of change – the calculus – can be applied to physical reality without obstruction. The calculus can exactly describe things as they occur in themselves, without straying, even infinitesimally, from the rigorous dictates of formal intelligence. In this way natural philosophy becomes modern science.
Nick Land
No honest man or woman in Germany feels responsible for these things. Good Germans took Nazism as a new religion. These people are shocked by the revelations which have shown that Nazism was not idealism, but a means to the performance of criminal acts...
In war a German feels bound to join the ranks without question. Three of my sons were called up. I could not hold back. I wrote from the concentration camp to Admiral Raeder, C. in C. of the Navy, asking to be allowed to return to the submarine service or to do any other service in the Navy. I heard nothing for several months, and then a reply came, not from Raeder but from Keitel, head of the Wehrmacht. He thanked me, but regretted I could not be employed on active service.
Martin Niemöller
By following entirely the guidance of lust, in the manner of fools, man loses his intellectual energy, injures his body, and perishes before his natural time; sighs and cares multiply; there is an increase of envy, hatred, and warfare, for the purpose of taking what another possesses. The cause of all this is the circumstance that the ignorant considers physical enjoyment as an object to be sought for its own sake. God in His wisdom has therefore given us such commandments as would counteract that object, and prevent us altogether from directing our attention to it, and has debarred us from everything that leads only to excessive desire and to lust. This is an important thing included in the objects of our Law.
Maimonides
NATO foreign ministers met several days ago to support the US position. According to media reports, they did this after Washington presented certain irrefutable documents confirming that the treaty was violated. If this is so, we have not received any such documents from the US side. This is what we have been asking the US to do for a long time. We are still ready for a serious and professional discussion. Instead, the Americans resort to unfounded accusations, and again and again, from high rostrums, make allegations for the entire international community to hear about things that should first be clarified with the other party to the treaty. This would be a more appropriate, polite and correct approach.
Sergey Lavrov