Mediate Quotes (4 quotes)
Genes make enzymes, and enzymes control the rates of chemical processes. Genes do not make ‘novelty seeking’ or any other complex and overt behavior. Predisposition via a long chain of complex chemical reactions, mediated through a more complex series of life’s circumstances, does not equal identification or even causation.
If it were always necessary to reduce everything to intuitive knowledge, demonstration would often be insufferably prolix. This is why mathematicians have had the cleverness to divide the difficulties and to demonstrate separately the intervening propositions. And there is art also in this; for as the mediate truths (which are called lemmas, since they appear to be a digression) may be assigned in many ways, it is well, in order to aid the understanding and memory, to choose of them those which greatly shorten the process, and appear memorable and worthy in themselves of being demonstrated. But there is another obstacle, viz.: that it is not easy to demonstrate all the axioms, and to reduce demonstrations wholly to intuitive knowledge. And if we had chosen to wait for that, perhaps we should not yet have the science of geometry.
Mathematic stands forth as that which unites, mediates between Man and Nature, Inner and Outer world, Thought and Perception, [as no other subject does].
Mathematics is the language of languages, the best school for sharpening thought and expression, is applicable to all processes in nature; and Germany needs mathematical gymnasia. Mathematics is God’s form of speech, and simplifies all things organic and inorganic. As knowledge becomes real, complete and great it approximates mathematical forms. It mediates between the worlds of mind and of matter.