"By intuition is frequently understood perception, or the knowledge of actual reality, the apprehension of something as real. […] Intuition is the undifferentiated unity of the perception of the real and of the simple image of the possible. " (Benedetto Croce, "The Essence of Æsthetic", 1921)
"The objects of our perception invariably include places and times in combination. Nobody has ever noticed a place except at a time, or a time except at a place. But I still respect the dogma that both space and time have independent significance. A point of space at a point of time, that is a system of values x, y, z, t, I will call a world-point." (Hermann Minkowski, "The Principle of Relativity: A Collection of Original Memoirs on the, Special and General Theory of Relativity, Space and Time", Nature vol. 113, 1924)
"When a man of science speaks of his 'data', he knows very well in practice what he means. Certain experiments have been conducted, and have yielded certain observed results, which have been recorded. But when we try to define a 'datum' theoretically, the task is not altogether easy. A datum, obviously, must be a fact known by perception. But it is very difficult to arrive at a fact in which there is no element of inference, and yet it would seem improper to call something a 'datum' if it involved inferences as well as observation. This constitutes a problem [...]" (Bertrand Russell, The Analysis of Matter", 1927)
"At first sight the assimilative tendency shown by thought seems sufficient to secure stability in judgments. To assimilate, in psychology as in biology, is to reproduce oneself by means of the external world; it is to transform perceptions until they are identical with one’s own thought, i.e. with previous schemas. Assimilation is therefore preservation and, in a certain sense, identification." (Jean Piaget, "Judgement and Reasoning in the Child", 1928)
"Euclidean geometry can be easily visualized; this is the argument adduced for the unique position of Euclidean geometry in mathematics. It has been argued that mathematics is not only a science of implications but that it has to establish preference for one particular axiomatic system. Whereas physics bases this choice on observation and experimentation, i. e., on applicability to reality, mathematics bases it on visualization, the analogue to perception in a theoretical science. Accordingly, mathematicians may work with the non-Euclidean geometries, but in contrast to Euclidean geometry, which is said to be intuitively understood," these systems consist of nothing but 'logical relations' or 'artificial manifolds'. They belong to the field of analytic geometry, the study of manifolds and equations between variables, but not to geometry in the real sense which has a visual significance." (Hans Reichenbach, "The Philosophy of Space and Time", 1928)
"The different premises will possibly allow equally good explanations with respect to the imprecise nature of our sensory perception, because the sensory perception is, in fact, not concerned with issues of precision mathematics but of approximation mathematics." (Felix Klein, "Elementary Mathematics from a Higher Standpoint" Vol III: "Precision Mathematics and Approximation Mathematics", 1928)
"When we look at a very large number of small objects that are close together the idea of continuum arises within us. […] Even if we believe to perceive a continuum in front of us, a more accurate observation will often convince us that we are only observing a dense succession of small particles." (Felix Klein, "Elementary Mathematics from a Higher Standpoint" Vol III: "Precision Mathematics and Approximation Mathematics", 1928)
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