CONTENTS

1   INTRODUCTION

2   EXPOSITION

3   THE HIERARCHY OF REFERENCE

4   THE NEUTRALITY OF LANGUAGE

5   CONCLUSIONS

2  EXPOSITION

The essence of Fregean realism, as opposed to naive realism, is that it takes the reference of sentences and of incomplete expressions seriously as being part of ontology. Each level in the hierarchy of expressions refers out to the world in its own way. Fregean ontology is concerned as much with the truth-value of sentences as with the existence of objects. Indeed the existence of objects is a special case of the truth-value of sentences.

The hierarchy of referents constitutes therefore the basic framework of ontology. Because it is based on the nature of language (the real thing, and not the various human constructions striving to approximate to it), it is a logically necessary framework. Contingent ontology - the description of the actual world - consists in filling out the Fregean categories, saying what objects there are and what concepts and relations they fall under.

2.1 Three Assertions

To establish reference as the underlying framework of a realist ontology, one must establish three key assertions.

 

A	The structure of language is determined by the needs of saying. As such it is unique and objective - it is a human discovery rather than a human invention.
B	It makes sense to speak of the different levels in Frege's syntactic hierarchy as referring to the objective world, each in its own way, but nevertheless in a manner which is broadly analogous to the way in which names refer to objects.
C	The objective structure of language is ontologically neutral, able to express any reality without contamination or distortion.

A consequence of the last of these assertions is that, strictly speaking, it is a misnomer to speak of "Fregean ontology". Because of its neutrality, the hierarchy of categories is not part of ontology. Rather it is a meta-ontology, a non-ontological structure within which ontology must be carried out. The term "Fregean ontology" refers not to the hierarchy itself, but the discipline of ontology carried out using the hierarchy as its boundary condition.

2.2 The Inexpressibility of Fregean Ontology

An immediate difficulty with Fregean Ontology is that attempts completely to describe it fail. Because this affects all our subsequent attempts to describe and defend the theory, it is best that this problem be confronted and delineated right away.

We can approach the problem through the following question. Are objects all there is in the world (or indeed in any possible world)? The answer (to both questions) is tautologically yes. Everything is an object. The predicate "... is an object" is trivial in the sense that it can not be false of anything. If the name put in the argument place has a referent, then the resulting sentence is true. If the name lacks a referent then (as always happens) so does the sentence containing it.

However let us pose the question in a different way. Is name-reference the only way in which language refers to the world? Now the answer is no. There are the modes of reference relevant to the incomplete expressions and to sentences. Given this answer we ask a third question. Are all the modes of reference the subject matter of ontology? The thesis of the present essay is that the answer here is yes. It makes no sense to isolate name-reference as the subject-matter of a self-contained discipline.

Returning to the first question, we encounter one of the major problems with discussing Fregean ontology. We have no way of quantifying over all the types of referent. This in fact means we can not even state the previous sentence. We try to use words like "referent" or "entity" or whatever to try to capture the totality of what is referred to by language, and, in a realist theory, what there is in the world. But this attempt fails. Part of an understanding of what Fregean ontology is all about is an understanding of why it fails, and why attempts even to express the failure in words must fail.

In order to make headway with describing Fregean ontology, we have to use a "sayable model". This replaces all the other referents with objects, and we have new concepts in the meta-language:

... is an object
... is a concept
... is a truth-value.

Here it is no longer trivially true (in fact it is false) that everything is an object. In the model we can have a predicate, for example:

... is a referent

which is trivially true of everything. We can use this model to say everything sayable about the Fregean hierarchy. But then the explanation has to be completed by saying that the reality of Fregean ontology is different from the model, and different in ways which cannot be expressed in language.

At any level in the hierarchy we can speak about the referents in terms of a (trivial) expression of the next higher level. The concept analogue of "x is an object" can be expressed using a second-order predicate CxF(x), which in (tortured) English is something like

To say F(x) is to attribute to x a concept.

This is trivially true of all concepts - a true sentence results from inserting in the argument place any first-order predicate which refers. What we can not have is any expression which does this job for all the referents across different levels of the hierarchy.

This discussion of inexpressibility deepens the understanding of the fundamental thesis of this essay, namely:

there is more to ontology than simply to say what things there are.

The immediate response to this is to say that however many new categories one introduces, there will be some overarching notion of "thing" which covers all of the categories, and that if you say, for example, that as well as objects there are concepts and truth-values and relations, these are all sub-categories of a general category, call it "entity" or "referent" or what you will. It is essential to the understanding of Fregean Ontology to grasp that there is no such overarching category, even though, to talk about Fregean Ontology, we have to pretend that there is. We have to create an expressible model to point in the general direction of Fregean Ontology, the pointing then being completed by saying that this model is not the thing pointed out. The most we can say about the real thing is negatively that it is not the model.

It might be thought that inexpressibility is the reductio ad absurdum of Fregean Ontology, a demonstration that the whole idea is incoherent. This may ultimately turn out to be the case. However the desire to maintain a realist account of linguistic reference motivates persisting with Fregean Ontology as a working hypothesis. Doing this entails rejecting the thesis that:

the mechanism of saying is omnipotent.

Instead we must allow that there are true things which are inexpressible. This is a theme to which we return in Section 4.3 below.

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