Algebra, Number Theory and Mathematical Logic

How can we possibly test, or improve upon the truth of a theory if it is built in such a manner then any conceivable event can be described, and explained, in terms of its principles? The only way of investigating such all-embracing principles would be to compare them with a different set of equally all embracing principles- but this procedure has been excluded from the very beginning.

The successful development of science requires a proper balance between the method of building up from observations and the method of deducing by pure reasoning from speculative assumptions...

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!'