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The law of inertia is a problem in teaching due to the impossibility of showing the proposition experimentally As we cannot do an experiment to verify the law, we cannot know if it is correct On the other hand, we know that the science based upon it is successful A study in the history of mechanics has shown that there are different foundations for the law but also that the law plays the same role in the science since Newton To avoid a statement of which we cannot be sure, the present paper proposes to understand the law through its function in the theory In this case, we do not have to say how a free body moves, but rather that the rectilinear and uniform motion is the motion of reference in Newtonian mechanics

The Law of Inertia: How Understanding its History can Improve Physics Teaching

Each predicate of the Aristotelian square of opposition includes the word “is”. Through a twofold interpretation of this word the square includes both classical logic and non-classical logic. All theses embodied by the square of opposition are preserved by the new interpretation, except for contradictories, which are substituted by incommensurabilities. Indeed, the new interpretation of the square of opposition concerns the relationships among entire theories, each represented by means of a characteristic predicate. A generalization of the square of opposition is achieved by not adjoining, according to two Leibniz’ suggestions about human mind, one more choice about the kind of infinity; i.e., a choice which was unknown by Greek’s culture, but which played a decisive role for the birth and then the development of modern science. This essential innovation of modern scientific culture explains why in modern times the Aristotelian square of opposition was disregarded.

The Square of Opposition and the Four Fundamental Choices

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Different formulations of Newton's first law are compared. A proposal for a real body-fixed inertial reference frame and for a corresponding separate formulation of the law of inertia is given.

https://iopscience.iop.org/article/10.1088/0143-0807/7/2/011/pdf

Newton's first law

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Newton's first law