统计学是科学吗？ 第1页

我是来反对高票答案的，以及所有强调可证伪性的答案。

可证伪性(falsifiability)是波普尔提出的，而他的理论只是针对于经验科学(empirical science)，其中经验科学只是科学的一个分支。

科学还有一个分支叫形式科学(formal science)。数学，统计学，逻辑学，理论计算机学都属于形式科学。

参见

这里附上一张wikipedia 里的插图。

补充，关于数学是否具有可证伪性。参见

Many philosophers believe that mathematics is not experimentally falsifiable, and thus not a science according to the definition of Karl Popper. However, in the 1930s Gödel's incompleteness theorems proved that there does not exist a set of axioms for mathematics which is both complete and consistent. Karl Popper concluded that "most mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently. Other thinkers, notably Imre Lakatos, have applied a version of falsificationism to mathematics itself.

哥德尔的不完备定理表明任何一个允许定义自然数的体系必定是不完全的，它包含了既不能证明为真也不能证明为假的命题。也就是说，表面上单独一个数学命题可能看似不具有可证伪性时，但它所在的数学体系是具有可证伪性的。