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Proof vs Provability: On Brouwer’s Time Problem
History and Philosophy of Logic ( IF 0.5 ) Pub Date : 2020-01-15 , DOI: 10.1080/01445340.2019.1702264
Palle Yourgrau 1
Affiliation  

Is a mathematical theorem proved because provable, or provable because proved? If Brouwer’s intuitionism is accepted, we’re committed, it seems, to the latter, which is highly problematic. Or so I will argue. This and other consequences of Brouwer’s attempt to found mathematics on the intuition of a move of time have heretofore been insufficiently appreciated. Whereas the mathematical anomalies of intuitionism have received enormous attention, too little time, I’ll try to show, has been devoted to some of the temporal anomalies that Brouwer has invited us to introduce into mathematics.

中文翻译:

证明与可证明性:关于布劳威尔的时间问题

数学定理是因为可证明而被证明,还是因为被证明而可证明?如果 Brouwer 的直觉主义被接受,我们似乎就倾向于后者,这是非常有问题的。或者我会争论。迄今为止,布劳威尔试图根据时间移动的直觉发现数学的这一结果和其他结果尚未得到充分重视。尽管直觉主义的数学异常受到了极大的关注,但我将尝试表明,用于讨论 Brouwer 邀请我们引入数学的一些时间异常的时间太少了。
更新日期:2020-01-15
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