Godel asserts that his philosophy falls under the category of conceptual realism. This paper gives a general picture of GOdel＇s conceptual realism＇s basic doctrines, and gives a way to understand conceptual realism ...Godel asserts that his philosophy falls under the category of conceptual realism. This paper gives a general picture of GOdel＇s conceptual realism＇s basic doctrines, and gives a way to understand conceptual realism in the background of Leibniz＇s and Kant＇s philosophies. Among philosophers of mathematics, there is a widespread view that Platonism encounters an epistemological difficulty because we do not have sensations of abstract objects. In his writings, Grdel asserts that we have mathematical intuitions of mathematical objects. Some philosophers do not think it is necessary to resort to intuition to defend Platonism, and other philosophers think that the arguments resorting to intuition are too naive to be convincing. I argue that the epistemic difficulty is not particular to Platonism; when faced with skepticism, physicalists also need to give an answer concerning the relationship between our experience and reality. Grdel and Kant both think that sensations or combinations of sensations are not ideas of physical objects, but that, to form ideas of physical objects, concepts must be added. However, unlike Kant, Grdel thinks that concepts are not subjective but independent of our minds. Based on my analysis of Grdel＇s conceptual realism, I give an answer to the question in the title and show that arguments resorting to intuition are far from naive, despite what some philosophers have claimed.展开更多
This paper compares Frege＇s philosophy of mathematics with a naturalistic and nominalistic philosophy of mathematics developed in Ye （2010a, 2010b, 2010c, 2011）, and it defends the latter against the former. The pa...This paper compares Frege＇s philosophy of mathematics with a naturalistic and nominalistic philosophy of mathematics developed in Ye （2010a, 2010b, 2010c, 2011）, and it defends the latter against the former. The paper focuses on Frege＇s account of the applicability of mathematics in the sciences and his conceptual realism. It argues that the naturalistic and nominalistic approach fares better than the Fregean approach in terms of its logical accuracy and clarity in explaining the applicability of mathematics in the sciences, its ability to reveal the real issues in explaining human epistemic and semantic access to objects, its prospect for resolving internal difficulties and developing into a full-fledged theory with rich details, as well its consistency with other areas of our scientific knowledge. Trivial criticisms such as ＂Frege is against naturalism here and therefore he is wrong＂ will be avoided as the paper tries to evaluate the two approaches on a neutral ground by focusing on meta-theoretical features such as accuracy, richness of detail, prospects for resolving internal issues, and consistency with other knowledge. The arguments in this paper apply not merely to Frege＇s philosophy. They apply as well to all philosophies that accept a Fregean account of the applicability of mathematics or accept conceptual realism. Some of these philosophies profess to endorse naturalism.展开更多
文摘Godel asserts that his philosophy falls under the category of conceptual realism. This paper gives a general picture of GOdel＇s conceptual realism＇s basic doctrines, and gives a way to understand conceptual realism in the background of Leibniz＇s and Kant＇s philosophies. Among philosophers of mathematics, there is a widespread view that Platonism encounters an epistemological difficulty because we do not have sensations of abstract objects. In his writings, Grdel asserts that we have mathematical intuitions of mathematical objects. Some philosophers do not think it is necessary to resort to intuition to defend Platonism, and other philosophers think that the arguments resorting to intuition are too naive to be convincing. I argue that the epistemic difficulty is not particular to Platonism; when faced with skepticism, physicalists also need to give an answer concerning the relationship between our experience and reality. Grdel and Kant both think that sensations or combinations of sensations are not ideas of physical objects, but that, to form ideas of physical objects, concepts must be added. However, unlike Kant, Grdel thinks that concepts are not subjective but independent of our minds. Based on my analysis of Grdel＇s conceptual realism, I give an answer to the question in the title and show that arguments resorting to intuition are far from naive, despite what some philosophers have claimed.
文摘This paper compares Frege＇s philosophy of mathematics with a naturalistic and nominalistic philosophy of mathematics developed in Ye （2010a, 2010b, 2010c, 2011）, and it defends the latter against the former. The paper focuses on Frege＇s account of the applicability of mathematics in the sciences and his conceptual realism. It argues that the naturalistic and nominalistic approach fares better than the Fregean approach in terms of its logical accuracy and clarity in explaining the applicability of mathematics in the sciences, its ability to reveal the real issues in explaining human epistemic and semantic access to objects, its prospect for resolving internal difficulties and developing into a full-fledged theory with rich details, as well its consistency with other areas of our scientific knowledge. Trivial criticisms such as ＂Frege is against naturalism here and therefore he is wrong＂ will be avoided as the paper tries to evaluate the two approaches on a neutral ground by focusing on meta-theoretical features such as accuracy, richness of detail, prospects for resolving internal issues, and consistency with other knowledge. The arguments in this paper apply not merely to Frege＇s philosophy. They apply as well to all philosophies that accept a Fregean account of the applicability of mathematics or accept conceptual realism. Some of these philosophies profess to endorse naturalism.
