Three Aspects of the Effectiveness of Mathematics in Science

@inproceedings{Narens1990ThreeAO,
  title={Three Aspects of the Effectiveness of Mathematics in Science},
  author={L. Narens and R. Luce},
  year={1990}
}
Wigner (1960), in a widely read and cited article, articulated what had previously been recognized by many scientists, namely, the remarkable affinity between the basic physical sciences and mathematics, and he noted that it is by no means obvious why this should be the case. The remarkableness of this fact is obscured by the historical co-evolution of physics and mathematics, which makes their marriage appear to be natural and foreordained. But serious philosophical explanations for the… Expand
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References

SHOWING 1-10 OF 28 REFERENCES
A general theory of ratio scalability with remarks about the measurement-theoretic concept of meaningfulness
The role of mathematics in empirical science is puzzling, mysterious, and in my opinion has defied rational explanation. Why mathematics should be so enormously productive and effective in theExpand
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
There is a story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a reprint to hisExpand
Classification of concatenation measurement structures according to scale type
Abstract A relational structure is said to be of scale type ( M , N ) iff M is the largest degree of homogeneity and N the least degree of uniqueness ( Narens, Theory and Decision , 1981, 13 , 1–70;Expand
Measurement Scales on the Continuum
In a seminal article in 1946, S. S. Stevens noted that the numerical measures then in common use exhibited three admissible groups of transformations: similarity, affine, and monotonic. UntilExpand
Measurement structures with archimedean ordered translation groups
The paper focuses on three problems of generalizing properties of concatenation structures (ordered structures with a monotonic operation) to ordered structures lacking any operation. (1) What is theExpand
Uniqueness and homogeneity of ordered relational structures
Abstract There are four major results in the paper. (1) In a general ordered relational structure that is order dense, Dedekind complete, and whose dilations (automorphisms with fixed points) areExpand
A classification of all order-preserving homeomorphism groups of the reals that satisfy finite uniqueness
The only real relational structures of scale type (m, n) with 1 ≤ m ≤ n < ∞ are of scale type (1, 1), (1, 2), and (2, 2), and so are conjugate to structures whose automorphism groups are subgroups ofExpand
On the scales of measurement
Abstract Let X = 〈 X , ≧, R 1 , R 2 …〉 be a relational structure, 〈 X, ≧ 〉 be a Dedekind complete, totally ordered set, and n be a nonnegative integer. X is said to satisfy n -point homogeneity ifExpand
The unreauode efictivess of maUlcmatica in the Mturd sciences
  • Commum Pure Appl. Math
  • 1960
A ciausifidion of d l order-preserving homeomorphism proups of the reds thd satisfy finite uniqueness
  • J. Math Psyehdopy
  • 1987
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