论直觉主义学派的逻辑观

On the Intuitionism School's View of Logic

直觉主义学派奠基人布劳威尔在澄清科学、语言本质的基础上把逻辑规定为一门反映推理语言规律的科学,但他没有意识到:逻辑和数学一样,具有比其它科学更高的必然性。海丁把数学中使用的逻辑规则规定为一般化的数学定理,并构建了形式化的直觉主义逻辑。该学派强调构造性,对逻辑常项进行了构造性的解释,从而拒斥了排中律的普遍有效性,并质疑经典的间接证明方法。事实上,直觉主义的构造性证明与经典的间接证明体现了不同的推理方式,各自有不同的适用领域和应用价值,而兼容并蓄正是现代逻辑和现代科学的发展趋势。

On the basis of clarifying the nature of science and language , L. E. J. Brouwer, the founder of intuitionism school, defines logic as a science reflecting the laws of reasoning language. However, he does not realize that logic, like mathematics, has higher certainty than any other science. A. Heyting defines the logic rules used in mathematics as generalized mathematical theorems, and constructs the formal intuitionistic logic. The school emphasizes constructivity, constructively interprets the logical constants, thus rejects the u- niversal validity of law of excluded middle, and questions the classical indirect proof method. In fact, the con- structive proofs in intuitionism and the classical indirect proofs reflect different ways of reasoning, and they have different applicable fields and applied values, and all - inclusiveness is the trend of modern logic and modern science.