If error is corrected whenever it is recognized as such, the path of error is the path of truth.

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.

If the definition of simultaneity is given from a moving system, the spherical surface will result when Einstein’s definition with є = 1/2 is used, since it is this definition which makes the velocity of light equal in all directions.

Although it is admitted that certain differences cannot be verified by experiment, we should not infer from this fact that they do not exist. …we are accused of having confused subjective inability with objective indeterminacy.

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.” Instead we shall speak of the normative function of the thinking process, which can guide the pictorial elements of thinking into any logically permissible structure.

Related posts:

  1. Can a human function with only half a brain? A human being cannot function to ‘full capacity’ with the corpus callosum severed, let alone an entire hemisphere removed. This said, more than 60 epileptic children have undergone an operation formerly known as a hemispherectomy, and survived. So depending on...
  2. The Basic Conventions of Moral Philosophy. Moral philosophy is the study of ethics in relation to the ultimate questions of morality. There are two main branches of thought being Metaethics and Normative Ethics. Metaethics: Question: What is the nature and methodology of moral judgement? The study...
  3. Private Institutions and Poverty So long as power remains privately concentrated, everybody, everybody, has to be committed to one overriding goal: and that’s to make sure that the rich folk are happy — because unless they are, nobody else is going to get anything....
  4. Antonio Gramsci Quotes I’m a pessimist because of intelligence, but an optimist because of will. The crisis consists precisely in the fact that the old is dying and the new cannot be born; in this interregnum a great variety of morbid symptoms appear....