“The concept of space, therefore, is a pure intuition, being a singular concept, not made up by sensations, but itself the fundamental form of all external sensation.”

—  Immanuel Kant

Kant's Inaugural Dissertation (1770), Section III On The Principles Of The Form Of The Sensible World

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German philosopher 1724–1804

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“What is reality? What is space? And what is time? These are the three questions that we want to investigate taking into account the knowledge that we have gained by modern physics. Our intuitive prescientific conception of the world in relation with these three concepts is not very precise but could be summarised as follows.
- Reality is everything that exists now in the present. The past has been real but is not anymore and the future is what shall become real but is not yet.
- Space is the theatre where reality is in. It englobes all of reality.
Till the birth of relativity theory all physical theories where compatible with this intuitive scheme. But when relativity theory entered the scene, these intuitive conceptions of space and time, and what is less recognised even till today, also the conception of reality, has got into problems.”

Diederik Aerts (1953) Belgian theoretical physicist

Diederik Aerts (2001) " Time, space and reality : an analysis from physics. http://www.vub.ac.be/CLEA/aerts/publications/2001TimeSpaceReality.pdf"

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“The main objection to the theory of pure visualization is our thesis that the non-Euclidean axioms can be visualized just as rigorously if we adjust the concept of congruence. This thesis is based on the discovery that the normative function of visualization is not of visual but of logical origin and that the intuitive acceptance of certain axioms is based on conditions from which they follow logically, and which have previously been smuggled into the images. The axiom that the straight line is the shortest distance is highly intuitive only because we have adapted the concept of straightness to the system of Eucidean concepts. It is therefore necessary merely to change these conditions to gain a correspondingly intuitive and clear insight into different sets of axioms; this recognition strikes at the root of the intuitive priority of Euclidean geometry. Our solution of the problem is a denial of pure visualization, inasmuch as it denies to visualization a special extralogical compulsion and points out the purely logical and nonintuitive origin of the normative function. Since it asserts, however, the possibility of a visual representation of all geometries, it could be understood as an extension of pure visualization to all geometries. In that case the predicate "pure" is but an empty addition, since it denotes only the difference between experienced and imagined pictures, and we shall therefore discard the term "pure visualization."”

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“The use of the intellect in the sciences whose primitive concepts as well as axioms are given by sensuous intuition is only logical, that is, by it we only subordinate cognitions to one another according to their relative universality conformably to the principle of contradiction, phenomena to more general phenomena, and consequences of pure intuition to intuitive axioms. But in pure philosophy, such as metaphysics, in which the use of the intellect in respect to principles is real, that is to say, where the primary concept of things and relations and the very axioms are given originally by the pure intellect itself, and not being intuitions do not enjoy immunity from error, the method precedes the whole science, and whatever is attempted before its precepts are thoroughly discussed and firmly established is looked upon as rashly conceived and to be rejected among vain instances of mental playfulness.”

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“The concepts which now prove to be fundamental to our understanding of nature—a space which is finite; a space which is empty, so that one point [of our 'material' world] differs from another solely in the properties of space itself; four-dimensional, seven- and more dimensional spaces; a space which for ever expands; a sequence of events which follows the laws of probability instead of the law of causation—or alternatively, a sequence of events which can only be fully and consistently described by going outside of space and time—all these concepts seem to my mind to be structures of pure thought, incapable of realisation in any sense which would properly be described as material.”

James Jeans book The Mysterious Universe

Source: The Mysterious Universe (1930), p. 122, 1937 ed.

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