CONTENTS

1   INTRODUCTION

2   EXPOSITION

3   THE HIERARCHY OF REFERENCE

4   THE NEUTRALITY OF LANGUAGE

5   CONCLUSIONS

1   INTRODUCTION

In searching for a formulation of logic sufficiently rigorous and sufficiently powerful to be used as a basis for arithmetic, Frege concluded that the forms of natural languages are seriously defective. Their structure is a poor reflection of the logical structure of the senses they attempt to express. In place of natural language forms, Frege proposed a regimented language (a Begriffsschrift), based upon two sorts of complete expression: the sentence and the name, and a hierarchy of incomplete expressions, formed iteratively by removing expressions already constructed from sentences or names. In what follows, the word "language" will be used to refer specifically to this regimented structure discovered by Frege, and not to the generality of natural languages.

The notion of an incomplete expression, and the hierarchy based upon it, are described in more detail in another essay, along with the semantics Frege built upon this syntactic structure. The purpose of the present essay is to explore the ontological implications of Frege's theory of language. For this purpose it is convenient to restrict attention to only a part of the full hierarchy:

sentence
1-place predicate        2-place predicate      ....
name

truth-value
concept        relation      ....
object.

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