"For of an image one requires some kind of sameness with the pictured object, of a statue sameness of form, of a delineation sameness of perspective projection in the visual field, of a painting also sameness of color. " (Heinrich Hertz, "The Facts in Perception", 1878)
"As for everything else, so for a mathematical theory: beauty can be perceived but not explained." (Arthur Cayley, [president's address] 1883)
"It is difficult to give an idea of the vast extent of modern mathematics. The word 'extent' is not the right one: I mean extent crowded with beautiful details - not an extent of mere uniformity such as an objectless plain, but of a tract of beautiful country seen at first in the distance, but which will bear to be rambled through and studied in every detail of hillside and valley, stream, rock, wood and flower. But, as for everything else, so for a mathematical theory - beauty can be perceived but not explained." (Arthur Cayley, [address before the meeting of the British Association at Southport] 1883)
"While all that we have is a relation of phenomena, a mental image, as such, in juxtaposition with or soldered to a sensation, we can not as yet have assertion or denial, a truth or a falsehood. We have mere reality, which is, but does not stand for anything, and which exists, but by no possibility could be true. […] the image is not a symbol or idea. It is itself a fact, or else the facts eject it. The real, as it appears to us in perception, connects the ideal suggestion with itself, or simply expels it from the world of reality. […] you possess explicit symbols all of which are universal and on the other side you have a mind which consists of mere individual impressions and images, grouped by the laws of a mechanical attraction." (Francis H Bradley, "Principles of Logic", 1883)
"Mathematics stands forth as that which unites, mediates between Man and Nature, inner and outer world, thought and perception, as no other subject does." (Julius Froebel, 1893)
"Experience is the collecting of what is similar in different particular perceptions." (Heinrich Hertz, "The Principles of Mechanics Presented in a New Form", 1894)
"It is a mistake to reduce mater to the perception which we have of it, a mistake also to make of it a thing able to produce in us perceptions, but in itself is of another nature than they. Matter, in our view, is an aggregate of ‘images’. And by ‘image‘ we mean a certain existence which is more than that which the idealist calls a representation, but less than that which the realist calls a thing - an existence placed halfway between the ‘thing‘ and the ‘representation’. This conception of matter is simply that of common sense. [...] For common sense, then, the object exists in itself, and, on the other hand, the object is, in itself, pictorial, as we perceive it image it is, but a self-existing image." (Henri Bergson,"Matter and Memory", 1896)
"We call that psychical process, which is operative in the clear perception of a narrow region of the content of consciousness, attention." (Wilhelm M Wundt,"Outlines of Psychology", 1897)
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