Is Intuition Necessary for Defending Platonism?

G?del asserts that his philosophy falls under the category of conceptual realism. This paper gives a general picture of G?del’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, G?del 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 na?ve 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. G?del 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, G?del thinks that concepts are not subjective but independent of our minds. Based on my analysis of G?del’s conceptual realism, I give an answer to the question in the title and show that arguments resorting to intuition are far from na?ve, despite what some philosophers have claimed.     

On Field’s Epistemological Argument Against Platonism

Hartry Field’s formulation of an epistemological argument against platonism requires knowledge to be causally constrained. Contrary to recent claims (e.g. in [6], [7]), it thus fails the very same criterion usually taken to discredit Benacerraf’s earlier version.     

How Gödel Relates Platonism to Mathematics

It is well known that Gödel takes his realistic world view as closely related to mathematics, especially to his own work in the foundations of mathematics. He reports, publicly as well as privately, that Platonism is fundamental to his major work in logic and set theory, and suggests that this philosophical position can be seen as a product of reflections on mathematics. These views of Gödel, however, are often regarded as being insufficiently formulated or argued for. In this article, the author tries to consider some points which are related to the understanding of the Gödelian mode of the interaction between mathematics and philosophy.     

Platonism and laws: A reply to Demetra Sfendoni‐Mentzou

This paper is a reply to Demetra Sfendoni‐Mentzou; it defends a realist—indeed a platonist—account of laws of nature.     

Toward the “overthrow of Platonism”: Processist critical social ontology and ameliorative discourse

In this article, I argue that, for the purpose of developing an effective critical social ontology about gender groups, it is not simply sufficient to carve gender groups at their joints: one must have in view whether the metaphysical categories we use to make sense of gender groups are prone to ideological distortion and vitiation. The norms underpinning a gender group's constitution as a type of social class and the norms involved in gender identity attributions, I propose, provide compelling reason to think critical social ontological discourse is more processist-orientated, rather than substantival-orientated. The advantages of a processist critical social ontology of gender groups are that, unlike substance-discourse, process-discourse recognizes how gender group talk and gender identity talk are often messy and therefore require a conceptual scheme that can transform vocabulary for the emancipatory purpose of ending oppression, domination, and marginalization.     

Platonism and metaphor in the texts of mathematics: Gödel and Frege on mathematical knowledge

In this paper, I challenge those interpretations of Frege that reinforce the view that his talk of grasping thoughts about abstract objects is consistent with Russell's notion of acquaintance with universals and with Gödel's contention that we possess a faculty of mathematical perception capable of perceiving the objects of set theory. Here I argue the case that Frege is not an epistemological Platonist in the sense in which Gödel is one. The contention advanced is that Gödel bases his Platonism on a literal comparison between mathematical intuition and physical perception. He concludes that since we accept sense perception as a source of empirical knowledge, then we similarly should posit a faculty of mathematical intuition to serve as the source of mathematical knowledge. Unlike Gödel, Frege does not posit a faculty of mathematical intuition. Frege talks instead about grasping thoughts about abstract objects. However, despite his hostility to metaphor, he uses the notion of ‘grasping’ as a strategic metaphor to model his notion of thinking, i.e., to underscore that it is only by logically manipulating the cognitive content of mathematical propositions that we can obtain mathematical knowledge. Thus, he construes ‘grasping’ more as theoretical activity than as a kind of inner mental ‘seeing’.

     

Platonism and metaphor in the texts of mathematics: G?del and Frege on mathematical knowledge

In this paper, I challenge those interpretations of Frege that reinforce the view that his talk of grasping thoughts about abstract objects is consistent with Russell's notion of acquaintance with universals and with Gödel's contention that we possess a faculty of mathematical perception capable of perceiving the objects of set theory. Here I argue the case that Frege is not an epistemological Platonist in the sense in which Gödel is one. The contention advanced is that Gödel bases his Platonism on a literal comparison between mathematical intuition and physical perception. He concludes that since we accept sense perception as a source of empirical knowledge, then we similarly should posit a faculty of mathematical intuition to serve as the source of mathematical knowledge. Unlike Gödel, Frege does not posit a faculty of mathematical intuition. Frege talks instead about grasping thoughts about abstract objects. However, despite his hostility to metaphor, he uses the notion of grasping as a strategic metaphor to model his notion of thinking, i.e., to underscore that it is only by logically manipulating the cognitive content of mathematical propositions that we can obtain mathematical knowledge. Thus, he construes grasping more as theoretical activity than as a kind of inner mental seeing.     

The Dynamic Association of Being and Non-Being: Heidegger’s Thoughts on Plato’s <Emphasis Type="Italic">Sophist</Emphasis> Beyond Platonism

This article examines Heidegger’s interpretation of Plato’s Sophist, focusing on his attempts to grasp Plato’s original thinking of being and non-being. Some contemporary thinkers and commentators argue that Heidegger’s view of Plato is simply based on his criticism against the traditional metaphysics of Platonism and its language. But a close reading of his lecture on the Sophist reveals that his view of Plato is grounded in Plato’s questioning struggle with the ambiguous nature of human speech or language (logos). For Heidegger, Plato’s way of philosophizing is deeper than the metaphysical understanding of Platonism which sees only fixed ideas of being. In the Sophist, dialectical thinking of Plato constantly confronts the questionable force of the logos which betrays the natural possibility of non-being based on the tension between movement and rest. Thus, from Plato’s original insight Heidegger uncovers the dynamic association (koinōnia) of being and non-being as a natural ground of everyday living with others. However, although Heidegger’s understanding of the Sophist powerfully demonstrates the lively possibility (dunamis) of being beyond the customary perspective of Platonic metaphysics, his interpretation fails to further disclose Plato’s political question of being emerging in the Sophist, which seeks the true associative ground of human beings.