逻辑学研究
邏輯學研究
라집학연구
Supplement to the Journal of Sun Yatsen University
2012年
1期
50~67
,共null页
数学证明 计算机 证据 哲学意义 四色定理 经验性
數學證明 計算機 證據 哲學意義 四色定理 經驗性
수학증명 계산궤 증거 철학의의 사색정리 경험성
有论者认为以电脑辅助进行之数学证明其实包含了经验性之前提,因此要接受此类证明,就得修改传统的“数学证明”的概念。本文审视此说法;以讨论Thomas Tymoczko的一篇关于四色定理得哲学意义的论文为发端,进而论及TylerBurge等人的相关观点,并由此对上述说法提出质疑。
有論者認為以電腦輔助進行之數學證明其實包含瞭經驗性之前提,因此要接受此類證明,就得脩改傳統的“數學證明”的概唸。本文審視此說法;以討論Thomas Tymoczko的一篇關于四色定理得哲學意義的論文為髮耑,進而論及TylerBurge等人的相關觀點,併由此對上述說法提齣質疑。
유론자인위이전뇌보조진행지수학증명기실포함료경험성지전제,인차요접수차류증명,취득수개전통적“수학증명”적개념。본문심시차설법;이토론Thomas Tymoczko적일편관우사색정리득철학의의적논문위발단,진이론급TylerBurge등인적상관관점,병유차대상술설법제출질의。
It has been claimed that computer-assisted proof utilizes empirical evidence in a manner unheard of in traditional mathemalics and therefore its cmployment forces us to modify our conception of proof. This paper provides a critical survey of strait arguments for this claim. It starts by revisiting a well known paper by Thomas Tymoczko on the comptuter proof of the Four-Color Theorem. Drawing on some ideas from the works of Tyler Burgc and olhers, il then considers a way to see the philosophical significance of computcr proof that oasis doubts on the claim.