Abstract: | Let = 〈X, ≧, R1, R2…〉 be a relational structure, 〈〉 be a Dedekind complete, totally ordered set, and n be a nonnegative integer. is said to satisfy n-point homogeneity if and only if for each x1,…, xn, y1,…, yn such that x1 ? x2 ? … ? xn and y1 ? y2 … ? yn, there exists an automorphism α of such that α(x1) = yi. is said to satisfy n-point uniqueness if and only if for all automorphisms β and γ of , if β and γ agree at n distinct points of , then β and γ are identical. It is shown that if satisfies n-point homogeneity and n-point uniqueness, then n ≦ 2, and for the case n = 1, is ratio scalable, and for the case n = 2, interval scalable. This result is very general and may in part provide an explanation of why so few scale types have arisen in science. The cases of 0-point homogeneity and infinite point homogeneity are also discussed. |