Abstract
The measurement of force is based on a formal law of additivity, which characterizes the effects of two or more configurations on the equilibrium of a material point. The representing vectors (resultant forces) are additive over configurations. The existence of a tight interrelation between the force vector and the geometric space, in which motion is described, depends on observations of partial (directional) equilibria; an axiomatization of this interrelation yields a proof of part two of Newton's second law of motion. The present results (which were derived from a curious and deep isomorphism between force measurement and trichromatic color measurement) yield a kind of subunit, which needs to be incorporated into more complete axiomatizations of mechanics that would fulfill the Mach–Kirchhoff program.
Keywords
Motion (physics)Space (punctuation)Point (geometry)MathematicsClassical mechanicsCentral forceIsomorphism (crystallography)Additive functionLawMathematical analysisPhysicsComputer scienceGeometry
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Publication Info
- Year
- 1973
- Type
- article
- Volume
- 40
- Issue
- 4
- Pages
- 481-495
- Citations
- 13
- Access
- Closed
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Cite This
David H. Krantz
(1973).
Fundamental Measurement of Force and Newton's First and Second Laws of Motion.
Philosophy of Science
, 40
(4)
, 481-495.
https://doi.org/10.1086/288560
Identifiers
- DOI
- 10.1086/288560