“Some forms of Kantianism put great weight on “what we can imagine” holding that this can be a source of insight into necessary connections. Thus various of Kant’s arguments about space and time depend on the purported fact that it is impossible for us to imagine certain things: we can know, Kant claims, a priori that space has only three dimensions because we cannot imagine it as having more than three dimensions. History in the form of non-Euclidean geometry and modern physics has put paid to that particular line of argument, but in general we should beware of depending too much on “What we can imagine?,” especially in politics. As Nietzsche puts it somewhere, sometimes the fact that you can’t imagine a situation in which things are very different from the way they are now is not an especially good argument for the claim that they must be as they now are, but, rather, represents a failure of your powers about which you should feel mildly apologetic.”

— Raymond Geuss , book Philosophy and Real Politics

Source: Philosophy and Real Politics (2008), pp. 48-49.

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Raymond Geuss 38

British philosopher 1946

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“The triangles that we can measure are not large enough… to detect the curvature. Fortunately, however, we are, in a way, able to communicate with the fourth dimension. The theory of relativity has given us an insight into the structure of the real universe: …a four-dimensional structure. The study of the way in which the three space-dimensions are interwoven with the time-dimension affords a kind of outside point of view of the three-dimensional space… from this outside point of view we might be able to perceive the curvature of the three-dimensional world.”

Willem de Sitter (1872–1934) Dutch cosmologist

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“If time is treated in modern physics as a dimension on a par with the dimensions of space, why should we a priori exclude the possibility that we are pulled as well as pushed along its axis? The future has, after all, as much or as little reality as the past, and there is nothing logically inconceivable in introducing, as a working hypothesis, an element of finality, supplementary to the element of causality, into our equations. It betrays a great lack of imagination to believe that the concept of "purpose" must necessarily be associated with some anthropomorphic deity.”

Arthur Koestler (1905–1983) Hungarian-British author and journalist

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“Whereas the conception of space and time as a four-dimensional manifold has been very fruitful for mathematical physicists, its effect in the field of epistemology has been only to confuse the issue. Calling time the fourth dimension gives it an air of mystery. One might think that time can now be conceived as a kind of space and try in vain to add visually a fourth dimension to the three dimensions of space. It is essential to guard against such a misunderstanding of mathematical concepts. If we add time to space as a fourth dimension it does not lose any of its peculiar character as time. …Musical tones can be ordered according to volume and pitch and are thus brought into a two dimensional manifold. Similarly colors can be determined by the three basic colors red, green and blue… Such an ordering does not change either tones or colors; it is merely a mathematical expression of something that we have known and visualized for a long time. Our schematization of time as a fourth dimension therefore does not imply any changes in the conception of time. …the space of visualization is only one of many possible forms that add content to the conceptual frame. We would therefore not call the representation of the tone manifold by a plane the visual representation of the two dimensional tone manifold.”

Hans Reichenbach (1891–1953) American philosopher

The Philosophy of Space and Time (1928, tr. 1957)

“If we wished to relate the space of the [Cubist] painters to geometry, we should have to refer it to the non-Euclidean mathematicians; we should have to study, at some length, certain of Riemann's theorems.”

Jean Metzinger (1883–1956) French painter

Du Cubisme (1912)

Albert Gleizes (1881–1953) French painter

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“Some philosophers have believed that a philosophical clarification of space also provided a solution of the problem of time. Kant presented space and time as analogous forms of visualization and treated them in a common chapter in his major epistemological work. Time therefore seems to be much less problematic since it has none of the difficulties resulting from multidimensionality. Time does not have the problem of mirror-image congruence, i. e., the problem of equal and similarly shaped figures that cannot be superimposed, a problem that has played some role in Kant's philosophy. Furthermore, time has no problem analogous to non-Euclidean geometry. In a one-dimensional schema it is impossible to distinguish between straightness and curvature. …A line may have external curvature but never an internal one, since this possibility exists only for a two-dimensional or higher continuum. Thus time lacks, because of its one-dimensionality, all those problems which have led to philosophical analysis of the problems of space.”

Hans Reichenbach (1891–1953) American philosopher

The Philosophy of Space and Time (1928, tr. 1957)

“We are saved the difficulty of imagining how the processes of life can go on in two dimensions, because nothing goes on.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

Space, Time and Gravitation (1920)
Context: It is of interest to inquire what happens when the aviator's speed... approximates to the velocity of light. Lengths in the direction of flight become smaller and smaller, until for the speed of light they shrink to zero. The aviator and the objects accompanying him shrink to two dimensions. We are saved the difficulty of imagining how the processes of life can go on in two dimensions, because nothing goes on. Time is arrested altogether. This is the description according to the terrestrial observer. The aviator himself detects nothing unusual; he does not perceive that he has stopped moving. He is merely waiting for the next instant to come before making the next movement; and the mere fact that time is arrested means that he does not perceive that the next instant is a long time coming.<!--p.26

“No matter how much experience we may gather in life, we can never in life get the dimension of experience that the imagination gives us. Only the arts and sciences can do that, and of these, only literature gives us the whole sweep and range of human imagination as it sees itself.”

Northrop Frye (1912–1991) Canadian literary critic and literary theorist

"Quotes", The Educated Imagination (1963), Talk 4: The Keys To Dreamland

“…the differential element of non-Euclidean spaces is Euclidean. This fact, however, is analogous to the relations between a straight line and a curve, and cannot lead to an epistemological priority of Euclidean geometry, in contrast to the views of certain authors.”

Hans Reichenbach (1891–1953) American philosopher

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“[Experimental Physicist] Phys. I cannot imagine myself perceiving non-Euclidean space!
Math. Look at the reflection of the room in a polished doorknob, and imagine yourself one of the actors in what you see going on there.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

p, 125
Space, Time and Gravitation (1920)

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Raymond Geuss 38

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