Two short texts about mathematics and philosophy

In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings (alphanumeric sequences of symbols, usually as equations) using established manipulation rules. In Platonism, the truth-values of our mathematical assertions depend on facts involving Platonic entities that reside in a realm outside of space-time.在数学哲学领域，形式主义（formalism）主张，数学与逻辑陈述可被视作依照既定操作规则，对字符串（通常以等式形式呈现的字母数字符号序列）进行操作所产生结果的相关陈述。在柏拉图主义（Platonism）的视域中，我们的数学断言的真值取决于涉及柏拉图实体的事实——这些实体存在于时空之外的领域内。