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Hierarchies ontological and ideological

By Øystein Linnebo and A. Rayo


Gödel claimed that Zermelo-Fraenkel set theory is ‘what becomes of the theory of types if certain superfluous restrictions are removed’. The aim of this paper is to develop a clearer understanding of Gödel's remark, and of the surrounding philosophical terrain. In connection with this, we discuss some technical issues concerning infinitary type theories and the programme of developing the semantics for higher-order languages in other higher-order languages

Topics: phil
Publisher: Oxford Journals
Year: 2012
OAI identifier:

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  2. (2006). Beyond Plurals. doi
  3. (2006). Circularity and paradox. doi
  4. (1995). Collected Works, volume III.
  5. (2000). Cumulative higher-order logic as a foundation for set theory. doi
  6. (1935). Der Wahrheitsbegriff in den formalisierten Sprachen. Studio Philosophica, 1:261–405. English translation in (Tarski,
  7. (2000). Foundations without Foundationalism: A Case for Second-Order Logic. doi
  8. (1967). From Frege to Go¨del, doi
  9. (1996). From Kant to Hilbert: A Source Book
  10. (1997). How we learn mathematical language. doi
  11. (1995). Introductory note to *1933o. In
  12. (1998). Logic, Logic, and Logic. doi
  13. (1983). Logic, Semantics, Metamathematics. doi
  14. (1934). Logische Syntax der Sprache. doi
  15. (1983). Mathematics in Philosophy. doi
  16. (1952). Negative types. doi
  17. (2001). Nominalism through De-Nominalization. doi
  18. (1985). Nominalist Platonism. doi
  19. (2007). On quantifying into predicate position.
  20. (1991). Parts of Classes. doi
  21. (1986). Philosophy of Logic, Second Edition. doi
  22. (1983). Philosophy of Mathematics: Selected Readings, Cambridge. doi
  23. (1987). Principles of reflection and second-order logic. doi
  24. (1944). Russell’s Mathematical Logic. In (Benacerraf and Putnam, doi
  25. (1933). The present situation in the foundations of mathematics. In
  26. (1984). To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables). doi
  27. (1999). Toward a Theory of Second-Order Consequence. doi
  28. (1926). U¨ber das Unendliche. doi
  29. (1930). U¨ber Grenzzahlen und Mengenbereiche. Fundamenta Mathematicae,
  30. (1888). Was Sind und Was Sollen die Zahlen? doi
  31. (1977). What Is the Iterative Conception of Set? doi

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