Spór o uniwersalia

Anna Jaroszewska

doi:10.14746/fped.2012.1.2.9

Spór o uniwersalia

Filozofia Publiczna i Edukacja Demokratyczna ◽

10.14746/fped.2012.1.2.9 ◽

2018 ◽

Vol 1 (2) ◽

pp. 139-145

Author(s):

Anna Jaroszewska

Keyword(s):

Set Theory ◽

Conceptual Realism

The problem of universals has been taken over by the medieval philosophers through the commentators, especially by Porfiriusz. Medieval philosophers had united issues mentioned by Porfiriusz with response to Boecjusz, creating an alternative: “thing” or “ word”. The most staunch phase of the dispute took place in the XI and XII centuries around two positions: “a realistic” and “nominalistic”, there has been an attempt to reach a compromise by marginal discarding; then three concepts was developed: “conceptualism” (“sermonizm”), “moderate conceptual realism” or “set theory”.

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Gödel's Conceptual Realism

Bulletin of Symbolic Logic ◽

10.2178/bsl/1120231631 ◽

2005 ◽

Vol 11 (2) ◽

pp. 207-224 ◽

Cited By ~ 8

Author(s):

Donald A. Martin

Keyword(s):

Set Theory ◽

Bertrand Russell ◽

Sense Perception ◽

Sense Experience ◽

Mathematical Intuition ◽

Conceptual Realism ◽

Kurt Gödel ◽

Real Objects ◽

The Continuum

Kurt Gödel is almost as famous—one might say “notorious”—for his extreme platonist views as he is famous for his mathematical theorems. Moreover his platonism is not a myth; it is well-documented in his writings. Here are two platonist declarations about set theory, the first from his paper about Bertrand Russell and the second from the revised version of his paper on the Continuum Hypotheses.Classes and concepts may, however, also be conceived as real objects, namely classes as “pluralities of things” or as structures consisting of a plurality of things and concepts as the properties and relations of things existing independently of our definitions and constructions.It seems to me that the assumption of such objects is quite as legitimate as the assumption of physical bodies and there is quite as much reason to believe in their existence.But, despite their remoteness from sense experience, we do have something like a perception also of the objects of set theory, as is seen from the fact that the axioms force themselves upon us as being true. I don't see any reason why we should have less confidence in this kind of perception, i.e., in mathematical intuition, than in sense perception.The first statement is a platonist declaration of a fairly standard sort concerning set theory. What is unusual in it is the inclusion of concepts among the objects of mathematics. This I will explain below. The second statement expresses what looks like a rather wild thesis.

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