Set Theory and Nominalization, Part I

  title={Set Theory and Nominalization, Part I},
  author={Fairouz Kamareddine},
  journal={J. Log. Comput.},
This paper argues that the basic problems of nominalisation are those of set theory. We shall therefore overview the problems of set theory, the various solutions and assess the influence on nominalisation. We shall then discuss Aczel's Frege structures and compare them with Scott domains. Moreover, we shall set the ground for the second part which demonstrates that Frege structures are a suitable framework for dealing with nominalisation. 

A type free theory and collective/distributive predication

A simple type-free set theory is provided which can be used to give the various readings of collective/distributive sentences.

Paradoxes, Self-Reference and Truth in the 20th Century

  • A. Cantini
  • Philosophy
    Logic from Russell to Church
  • 2009

Semantics and the Liar Paradox

The semantical paradoxes are not a scientific subject like Inductive Definitions, Algebraic Geometry or Plasma Physics. At least not yet. On the other hand the paradoxes exert a strong fascination

Chapter 9 – Types

Are Types Needed for Natural Language

Mixing type freeness and logic leads to contradictions. This can be seen by taking the following simple example.

A System at the Cross-Roads of Functional and Logic Programming

Are types needed for natural languages

The final author version and the galley proof are versions of the publication after peer review that features the final layout of the paper including the volume, issue and page numbers.



Nominalization and Scott's domains. II

  • R. Turner
  • Linguistics
    Notre Dame J. Formal Log.
  • 1985
/ Introduction In Turner [17] we developed a semantics for nominalized predicates within the general framework of Montague Grammar. We offered an extension of Montague's PTQ which sanctioned the

Semantics in a frege structure

A perspective in which the semantics of natural language constructs are unpacked in terms of Peter Aczel's Frege structures is offered and is shown to provide promising results for both nominalisation and intensionality.

Philosophical Perspectives on Formal Theories of Predication

Predication has been a central, if not the central, issue in philosophy since at least the time of Plato and Aristotle. Different theories of predication have in fact been the basis of a number of

Three theories of nominalized predicates

It is the aim of this work to provide a model-theoretic interpretation for a formal language which admits the occurrence of such abstract singular terms.

Toward Useful Type-Free Theories. I

The informal argument that the paradoxes are blocked in ZF is that its axioms are true in the cumulative hierarchy of sets where (i) unlike the theory of types, a set may have members of various (ordinal) levels, but (ii) the level of a set is greater than that of each of its members.

A Theory of Properties

Much room is available for the development of theories of truth which meet almost all of Tarski's desiderata, as demonstrated by the work of Gilmore, Feferman, and Aczel.

Frege's double correlation thesis and quine's set theories NF and ML

In particular, in [5] I have explained how Frege's view of classes in the logical sense can be reconstructed without paradox by modifying in either of two ways what I there referred to as Frege’s double correlation thesis.

A Formulation of the Simple Theory of Types

A formulation of the simple theory oftypes which incorporates certain features of the calculus of λ-conversion into the theory of types and is offered as being of interest on this basis.

Non-well-founded sets

  • P. Aczel
  • Philosophy
    CSLI lecture notes series
  • 1988
If the lesson of the paradoxes of set theory is that a predicate need no more have a set as extension than the name "Santa Claus" need denote someone, then perhaps the lessons of the liar paradox is that nothing answers to a liar sentence.