皮尔士如何成为逻辑学中的“弗雷格革命”?
How Peircean was the "'Fregean' Revolution" in Logic?
摘要:
逻辑史学设想了一场弗雷格革命,在这场革命中,现代数理逻辑(也称为符号逻辑)已经取代了亚里士多德逻辑。这一概念的杰出倡导者是Jean van Heijenoort(1912-1986)和Donald Angus Gillies。构成数理逻辑并使之区别于亚里士多德逻辑的创新和特征,根据这一概念,由弗雷格从虚无中创造出来(1848-1925)在他1879年的《Begriffsschrift》中,(1872年至1970年)作为其首席这一立场同样理解代数逻辑的奥古斯都德摩根(1806年至1871年),乔治布尔(1815年至1864年),查尔斯桑德斯皮尔士(1838年至1914年),和恩斯特施罗德(1841年至1902年)属于阿伦特传统。从这个有利的角度来看,“布尔”被理解为仅仅是在代数的伪装下重写了阿斯特丽德的三段论。最详细的清单和阐述弗雷格的创新,以及特点,区分数理逻辑从阿斯特丽德逻辑,提出了范Heijenoort。我考虑了凡·海杰努特的清单中的每一个要素,并注意到皮尔士在多大程度上也发展了逻辑的每一个方面。我也认为在何种程度上皮尔士和弗雷格都知道,并可能影响,对方的逻辑著作。
英文摘要:
The historiography of logic conceives of a Fregean revolution in which modern mathematical logic (also called symbolic logic) has replaced Aristotelian logic. The preeminent expositors of this conception are Jean van Heijenoort (1912-1986) and Donald Angus Gillies. The innovations and characteristics that comprise mathematical logic and distinguish it from Aristotelian logic, according to this conception, created ex nihlo by Gottlob Frege (1848-1925) in his Begriffsschrift of 1879, and with Bertrand Russell (1872-1970) as its chief This position likewise understands the algebraic logic of Augustus De Morgan (1806-1871), George Boole (1815-1864), Charles Sanders Peirce (1838-1914), and Ernst Schröder (1841-1902) as belonging to the Aristotelian tradition. The "Booleans" are understood, from this vantage point, to merely have rewritten Aristotelian syllogistic in algebraic guise. The most detailed listing and elaboration of Frege's innovations, and the characteristics that distinguish mathematical logic from Aristotelian logic, were set forth by van Heijenoort. I consider each of the elements of van Heijenoort's list and note the extent to which Peirce had also developed each of these aspects of logic. I also consider the extent to which Peirce and Frege were aware of, and may have influenced, one another's logical writings.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。