جستجوی مقالات مرتبط با کلیدواژه "منطق گرایی" در نشریات گروه "فلسفه و کلام"

In this paper, we intend to examine the controversy between Frege and Hilbert over geometry about abstract algebra; whether Frege's thinking about abstract algebra works out or Hilbert's? To this end, we first study the times when Frege and Hilbert were engaged in philosophy, to have an idea of the dominant intellectual atmosphere of that time and its influence on these two mathematicians. With this in mind, then we have pointed out some differences between Frege and Hilbert's approaches. We have concluded that their most important differences are the role of the subject in mathematics and the discussion about compatibility. After presenting the normative definition of algebra, we have investigated the points made by Hilbert and Frege, using the later Wittgenstein theories expressed in the books On Certainty and Philosophical Investigation. Finally, by considering all the aspects, we have concluded that what seems to be more useful in the philosophical study of algebra is a third approach, which is Wittgenstein's approach with some modifications, since it guarantees some important features. These features are meaningfulness, intersubjectivity, and rule-orientation, all of which are important features for mathematicians.

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.

Logicism is one of the important schools in philosophy of mathematics which reduce the concepts and propositions of mathematics into the concepts and propositions of logic. Bolzano was the pioneer mathematician who based mathematics on logic، and then Ferege continued this project through propounding a new version of logic. Ultimately، in the early decades of 20th century، this project was finalized by Russel and Withead. In this paper، I، attempt to review the historical development of logicism from Bolzano to Russel، and then through the examination of strengths and weaknesses of the project، I try to answer to this question: has logicism been satisfactory?

In the philosophy of mathematics, there are three important schools: intuitionism, formalism and logicism. Founded by Brouwer, intuitionism puts importance on mathematician's intuition, takes it as the basis, and try to free mathematics of the pure logical relations. Intuitionism takes mental processes as the basis of mathematics. In this part of his article, the author discusses intuitionism and its history.

In this essay, after short explanation, the effects of Godel’s first and second incompleteness theorems on philosophy of mathematics and philosophy of mind and against materialism and positivism is examined. The effect of Godel’s theorems on philosophy of mathematics has examined in three fields of logicism, formalism and nature of proof. in the area of philosophy of mind, the effect of Godel’s theorems on anti-mechanist proofs is pointed out.