ABSTRACT

(Click here to go to the full essay.)

The essence of Fregean 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.

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.

Assertion C is actually an aspiration rather than a fact. It has to be weakened to take account of things which can not be expressed in language. The first of these is Fregean ontology itself. 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.

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.

Now let us look in more detail at the three levels of reference identified above.

Object      To understand the concept of object as it appears in Fregean ontology, one must above all grasp its generality. All prejudices, for example, about material objects in space and time should be put aside. These are parts of a putative account of the ontology of the actual world, the contingent furniture built into the necessary framework of Fregean ontology. The generality of the Fregean framework has a great liberating effect. One need not, for example, be afraid a priori of postulating a Platonic account of the ontology of numbers. There is still work to be done to justify such and account, but it can not be rejected out of hand on the grounds that the numbers are not physical objects. Another prejudice to be rejected is that while concepts are to do with perception, objects are the underlying ground of being. In the Fregean picture, concepts and objects are equally part of objective reality.

Concept    When Frege speaks of a concept (in the original German, "Begriff"), in spite of the subjective, mentalistic flavour of the word, he intends to refer to an objective, although incomplete, feature of the world. This is a second liberation for realists; we can sustain an ontological commitment to concepts without worrying that the objectivity of our account of the world is thereby compromised. To sustain this position we must indicate what counts as the existence or non-existence of a concept (strictly speaking the reference or failure to refer of a predicate-sense). The existence condition can not be extensional; it can not be that the concept is true of at least one object. For us truthfully to say: there is no x such that f(x), then the predicate "f(x)" must have a reference. Instead the existence criterion for a concept is something along the lines of the possibility that it be true of some object. Likewise we should not use an extensional identity criterion for concepts. It may be that two distinct concepts happen to be true of exactly the same set of objects. Concept identity is when this sameness is necessary.

Truth-Value   To substantiate Frege's account of truth-values as the two possible referents of any sentence, we have to answer at least the following questions.

1. Why do we ascribe to sentences a duality of truth-values?
   
   
2. Why should we describe the ascription of truth-values to sentences as being the reference of sentences?
   
   
3. Why should we not think of sentences as referring to something other than truth-values (the prime candidates for the "something other" being states of affairs)?

The argument for the two-fold nature of truth-values invokes the primary role of sentences as being used to make assertions. The only distinction we can make simply by asserting the sentence (as opposed to choosing the details of its contents) is a two-fold one. Truth-values are identified as being the referents of sentences because they are what is preserved when one component of the sentence is replaced by another with the same referent, and truth-value is what fails if a sentence component fails to refer. (It is more difficult to show that if all components refer, then the sentence must have a truth-value.) An alternative account of sentence reference (for example in the opening passages of the Tractatus) invokes states of affairs as the sentence referents. Although there are intuitive merits to adding states of affairs to the ontology, they would have to be in addition to, rather than replacing, truth-values.

The problem with attempting to build a realist ontology on top of Frege's theory of reference seems therefore to be trying to have one's cake and eat it too. It aspires to the certainty of the logic and yet the substance of ontology. These two can be brought together only at the cost of infecting ontology with the structures of language, an infection which threatens to be fatal to the claims of realism. The realist counter to this is to argue that the Fregean framework is ontologically neutral and unconstraining. It allows the world to be whatever it wants to be.

It appears, however, that this claim is too strong. While the Fregean framework is largely unconstraining, there exist features of the world which are accessible to us but can not be expressed in language. Fregean ontology itself is a (necessary) feature of the world with this property. The classic example of an unsayable contingent feature is time - McTaggart's paradox shows that we can not capture within language what we experience of temporal becoing. This is in fact good news for realism. It shows that our view of the world is not contaminated by the shortcomings of the mechanism of saying. The realities of the world, in this case temporal phenomena, force themselves upon us regardless of these shortcomings.

1. to establish as clearly as possible what assertions are involved in Fregean Ontology;
   
   
2. to show that the assertions are strong ones, being non-trivial and difficult, and to point out where some of the difficulties lie;
   
   
3. to establish nevertheless a sufficient degree of prima facie plausibility of the assertions for them to be adopted as a provisional basis on which the rest of philosophical analysis can be built.
   

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