مباني «برنهاد منطق رياضي» راسل

Foundations of Russell’s “Logicist Thesis

با در نظر گرفتن دو جريان فراگير فلسفي قرن نوزدهم يعني ايده‌آليسم و رئاليسم، آنچه در اين مقاله مورد بررسي قرار مي­ گيرد اين است كه راسل بر پايه­ كدام نظام فلسفي منطق ­گرايي خود را بنا كرد. طرح منطق­ گرايي راسل در سه دوره­ فكري بررسي مي ­شود. در دوره­ اوّل راسل در بررسي ­هاي منطقي خويش رويكرد ايده‌آليستي دارد. در دوره­ دوّم با پايه­ ريزي فلسفه­ رئاليستي خود نسخه­ اوّليه­ منطق­ گرايي ­اش را در اصول مي­ آورد. در دوره­ سوّم به دليل پارادوكس ­هاي برخواسته از جريان منطق ­گرايي، راسل به ايده‌آليسم اصلاح يافته­ اي روي مي­ آورد و با ارائه­ «نظريه طبقات» نسخه­ كاملي از منطق­ گرايي خود را در كتاب مباني رياضي ارائه مي ­دهد. امّا راسل همچنان در ارائه­ عموميتي معتبر كه براي منطق و رياضيات اساسي است با موانعي مواجه مي­شود. نهايتا راسل دو «اصل موضوع تحويل­ پذيري» و «اصل موضوع بي­ نهايت» را براي برداشتن اين موانع مطرح مي­ كند تا بتواند نظام منطقي خود را به درستي بنا كند

This paper is concerned with a general account of logicism as developed within Russell’s philosophy of mathematics. At first Russell’s approach in metaphysic was idealistic and he relied on this point of view for extending his platonic atomism. To expound this account it will be demonstrated that after developing platonic atomism, Russell attempted to present his logicism in The Principles of Mathematics as a view opposed to an idealistic account of mathematics. However, a number of paradoxes arose had their roots deep in Russell’s metaphysical views. At this point he was forced to moderate his realistic extreme approach. Afterward it is shown that to evade these paradoxes, Russell adopts a view that allows for ontological distinctions and then introduces a full-fledged theory of types in Principia Mathematica. Nevertheless, the new framework yields problems of its own that pose a threat to Russell’s object-centered metaphysics but also deprives him of handling truths of unrestricted generality. Then to present a final version of his logicism, Russell’s way out of these issues will be set forth which comes in form of axioms of reducibility and infinity. Although these axioms represent a solution to remove paradoxes, actually those are too complicated to use.