Algebra, Number Theory and Mathematical Logic

All men are mortal. Socrates was mortal. Therefore, all men are Socrates.

Never call yourself a philosopher, nor talk a great deal among the unlearned about theorems, but act conformably to them.

It is clear that the arm of criticism cannot replace the criticism of arms. Material force can only be overthrown by material force, but theory itself becomes a material force when it has seized the masses. Theory is capable of seizing the masses when it demonstrates ad hominem, and it demonstrates ad hominem as soon as it becomes radical. To be radical is to grasp things by the root. But for man the root is man himself. What proves beyond doubt the radicalism of German theory, and thus its practical energy, is that it begins from the resolute positive abolition of religion. The criticism of religion ends with the doctrine that man is the supreme being for man. It ends, therefore, with the categorical imperative to overthrow all those conditions in which man is an abased, enslaved, abandoned, contemptible being—conditions which can hardly be better described than in the exclamation of a Frenchman on the occasion of a proposed tax upon dogs: 'Wretched dogs! They want to treat you like men!'