Meaningfulness as a “Principle of Theory Construction”

In 1959, Duncan Luce published the famous paper entitled “On the possible psychophysical laws.” The results presented here were inspired by that paper and by the ensuing controversy centered on the invariance concept of “meaningfulness.” We give a formal definition of this concept. As we define it, the condition of meaningfulness is quite potent. In its context, relatively weak additional conditions may suffice for the derivation of precise scientific or geometric laws. We give several examples of such derivations, including the Pythagorean Theorem and Beer's Law.