Vectors
How do we know that the formulas that deal with physical vectors are correct and describe reality? These are formulas that were invented and their relevance was tested in experiments and found to describe what happens in the world when forces are applied to objects?
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I didn’t understand the question. Everything is tested in experiments just like any other physical law. Vector calculus is a mathematical theory, but once it is applied to physical phenomena (like forces or velocities) it should withstand empirical experiments.
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Is this supposed to stand up to empirical tests since we rely on induction?
Yes. Like any other scientific law.
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