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Theory reduction is the process by which a more general theory absorbs a special theory.<ref name=":0" /> For example, both [[Johannes Kepler|Kepler's]] laws of the motion of the [[planet]]s and [[Galileo Galilei|Galileo]]'s theories of motion formulated for terrestrial objects are reducible to Newtonian theories of mechanics because all the explanatory power of the former are contained within the latter. Furthermore, the reduction is considered beneficial because [[Newtonian mechanics]] is a more general theory—that is, it explains more events than Galileo's or Kepler's. Besides scientific theories, theory reduction more generally can be the process by which one explanation subsumes another.

Theory reduction is the process by which a more general theory absorbs a special theory.<ref name=":0" /> For example, both [[Johannes Kepler|Kepler's]] laws of the motion of the [[planet]]s and [[Galileo Galilei|Galileo]]'s theories of motion formulated for terrestrial objects are reducible to Newtonian theories of mechanics because all the explanatory power of the former are contained within the latter. Furthermore, the reduction is considered beneficial because [[Newtonian mechanics]] is a more general theory—that is, it explains more events than Galileo's or Kepler's. Besides scientific theories, theory reduction more generally can be the process by which one explanation subsumes another.

== 在科学中 ==

== 在科学中 ==

In [[mathematics]], reductionism can be interpreted as the philosophy that all mathematics can (or ought to) be based on a common foundation, which for modern mathematics is usually [[axiomatic set theory]]. [[Ernst Zermelo]] was one of the major advocates of such an opinion; he also developed much of axiomatic set theory. It has been argued that the generally accepted method of justifying mathematical [[axioms]] by their usefulness in common practice can potentially weaken Zermelo's reductionist claim.<ref name=":19">{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref>

In [[mathematics]], reductionism can be interpreted as the philosophy that all mathematics can (or ought to) be based on a common foundation, which for modern mathematics is usually [[axiomatic set theory]]. [[Ernst Zermelo]] was one of the major advocates of such an opinion; he also developed much of axiomatic set theory. It has been argued that the generally accepted method of justifying mathematical [[axioms]] by their usefulness in common practice can potentially weaken Zermelo's reductionist claim.<ref name=":19">{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref>

在数学中，还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学，而对于现代数学来说，这个基础通常是公理化集合论。策梅洛（Ernst Zermelo）是这种观点的主要倡导者之一，他也对公理化集合论做出了许多发展。有人认为，用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法，可能会削弱泽梅洛的还原论主张<ref name=":19" />。

在数学中，还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学，而对于现代数学来说，这个基础通常是公理化集合论。'''<u>策梅洛（Ernst Zermelo）</u>'''是这种观点的主要倡导者之一，他也对公理化集合论做出了许多发展。有人认为，用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法，可能会削弱'''<u>泽梅洛</u>'''的还原论主张<ref name=":19" />。

Jouko Väänänen has argued for [[second-order logic]] as a foundation for mathematics instead of set theory,<ref name=":20">{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> whereas others have argued for [[category theory]] as a foundation for certain aspects of mathematics.<ref name=":21">{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref name=":22">{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref>

Jouko Väänänen has argued for [[second-order logic]] as a foundation for mathematics instead of set theory,<ref name=":20">{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> whereas others have argued for [[category theory]] as a foundation for certain aspects of mathematics.<ref name=":21">{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref name=":22">{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref>