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Physics quantities and laws, especially some fundamental laws and quantities, show property of tautology. For instance, mass and Newton's second law.

My question is why physics quantities and laws with such a property are applied? Are invariant of physics quantities and laws under transformations the reason?

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Eugene Wigner asked the question about the unreasonable effectiveness of mathematics in physics. Both, in my opinion, are the expression of what the greeks would have called ananke or neccessity. In Plato's Timeus, where he described his cosmology, he described the origin of the world as a blending of nous (intellect) and ananke (neccessity). In more modern philosophical language it is as I've already said translated as neccessity, but also logical neccessity and physical laws.

Since tautologies are those truths that are neccessarily true we see that physics and mathematics attempts to reduce their field of study to tautologies but with an irreducible minimum that distinguishes from tautologies per se. After all, mathematics and physics is not logic, they refer to the world and in the world, there is always a degree of freedom.

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There is nothing wrong with tautologies. A tautology is just something that is true by definition. So any time that you define things you will have tautologies.

In physics we define many quantities that are convenient in different situations. So you will find many tautologies. The important thing is that the theory makes experimental predictions that accurately predict the results of physical experiments, not to avoid tautologies in the process.

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