Without that proportionality assumption, the quam proxime biconditional collapses into a one-directional inference, undermining the 'if and only if' structure of the original claim.

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Key Terms

Biconditional(in formal logic): A logical statement that says two things are true if and only if each other is true; it's a two-way relationship (like saying 'you can vote if and only if you're 18').
if and only if(in logic and philosophical definitions): A logical phrase meaning both directions must be true: A happens exactly when B happens, and if B happens, then A must happen. It's a two-way requirement, not just one direction.
one-directional inference(in logic): A logical connection that only works one way—like 'if it's raining, the ground is wet,' but wet ground doesn't necessarily mean it's raining.
proportionality assumption(in logic and argumentation): The idea that two things relate to each other in a balanced, matching way—like if one thing causes another, the strength of the cause should match the strength of the effect.

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quam proxime(Newton uses quam proxime forms of exact propositions to apply idealized mathematical results to real physical observations that only approximately satisfy the exact conditions)

A Latin phrase meaning 'as nearly as possible' or 'approximately'; used by Newton to denote that a proposition holds in an approximate or limiting sense rather than exactly

Without that proportionality assumption, the quam proxime biconditional collapses into a one-directional inference, undermining the 'if and only if' structure of the original claim.

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