|Motion: spatial variation of one or more observed or not observed objects in time. Problems arising in connection with attribution or withdrawal of predicates. See also change, temporal identity, process, flux, vectors.|
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Definition Problem of Quantities/S/R/Field: the representational theorems used for the generation of many numerical functors in physics (e.g. distance, relative velocity, acceleration) - they are not available for relativism because they depend on structural regularities of the space time which are lost when one discards those parts of the space time that are not completely occupied by matter as the space is - definition of distance without numbers by congruence and "between".
Law of movement/Nominalisation/Field: therefore we need the concepts trajectory and differentiation of the vector field - derivation: of scalars can be equated with differences of scalars - so also derivations of vectors with differences of vectors - problem: differences of vectors are themselves vectors - space time can be assumed to be infinite, but not temperature.
Law of movement/Nominalisation/Field: with the concept of the tangent on a trajectory - the trajectory can be differentiated if the tangent is not purely spatial - the accelerations of points (on one or more trajectories) are compared with the gradients of the gravitational potential at the points - Definition law of movement/Newtonian gravitational theory/Field: (if only gravitational forces are effective): for every such T, T-™,z,z-™,S,S-T™, y and y-™: there is a positive real number k so that a) the second directional derivative (ri-A) of the spatial separation (separation) of S from T to z i. Hbl. to zy> is taken twice k-times the gradient of the gravitational potential on z - b) the second ri-A of the r. Tr. from S-™ from T-™ to z-™ corresponding to the other coated symbols - nominalistic: one only has to use the second ri-A in (12-™).
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980