A Short History of Modern Philosophy: From Descartes to Wittgenstein, Second Edition (38 page)

There was a particular consequence of this overthrow which Frege did not at first foresee. The old logic had taken its cue from the grammar of ordinary language. It was this that made it so difficult to represent the difference between ‘Socrates exists’ and ‘Socrates is alive’. The difference is in fact so radical that we are forced to conclude that grammatical form in ordinary language is no guide to logical behaviour. To put it in Russell’s way, the true logical form of the sentence ‘Socrates exists’ is not reflected in its grammar. How then should we represent this sentence? The natural answer is to seek for a system of symbols that would allow expression only to the true ‘logical form’ of any sentence. This intrusion of mathematical method into the foundations of logic was the first of many. Since logic itself governs much of philosophical argument, the process can be continued further; eventually it resulted in the almost entirely mathematised philosophies of atomism and positivism which I shall mention in the final chapter.

There are more specific ways in which Frege’s adoption and extension of mathematical ideas changed the nature of philosophy. This can be seen in Frege’s theory of the nature of language. It was clear to Frege, as it had been to Leibniz, that statements of identity are different in form from statements which predicate a property of an object. The ‘is’ of identity and the ‘is’ of predication are logically distinct. If I say ‘Venus is the Morning Star’ then I make a statement of identity. The statement remains true (or, if false, false), when the names are reversed: the Morning Star is as much Venus as Venus is the Morning Star. In the sentence ‘Socrates is wise’ the terms cannot be reversed in the same way. The whole sense of the sentence depends upon my ascribing a different role to the subject term ‘Socrates’ and the predicate term ‘wise’.

Now the distinction between subject and predicate is basic to thought. A creature who could not understand it, who spoke only of identities, would know nothing of his world; he would know only the arbitrary determinations of his own usage, whereby he is able to substitute one name for another. But he would know nothing about the things that he thereby names. It behoves us, therefore, to try to understand the relation between subject and predicate—in so far as anything so basic will yield itself to logical investigation.

Frege’s analysis of this relation is contained in a series of articles among which the most important is ‘On Sense and Reference’. Frege there advances various theses, some of which had already proved important in describing the nature of arithmetic. Two theses of particular interest are these: first, that it is only in the context of a whole sentence that a word has a definite meaning; secondly, that the meaning of any sentence must be derivable from the meanings of its parts. These seem to be, but are not, contradictory. The first (an application of which is found in Frege’s contextual definition of number) says that the meaning of a word does not belong to it in isolation, but consists in its potentiality to contribute to a completed ‘thought’. It is because sentences can express thoughts that the words which compose them have a meaning. The second thesis states that the meaning of the whole sentence (or of any other composite linguistic entity) must be wholly determined by the various ‘potentialities’ belonging to its parts. Thus the word ‘man’ has the meaning it has because we use it to talk about men. Equally, the sentences with which we talk about men derive their meaning in part from that of ‘man’. This mutual dependence of part on whole and whole on part is characteristic of language. As linguists have begun to realise, it is what makes language learnable. If the meaning of the sentence is determined by the meaning of its parts, then, knowing only a finite vocabulary, I may yet understand indefinitely many sentences. My language-use is automatically ‘creative’, and gives me the capacity for unlimited thought.

How then do we proceed to describe the component parts of a subject-predicate sentence? Consider the sentence ‘Socrates is wise’. Frege argues that, for the purpose of clearer representation, we can assume this to be composed of two parts, a name and a predicate. Names may seem to be more intelligible than predicates: we understand them because they stand for objects, and if we know which objects they stand for we seem already to know what they mean. But, Frege argues, matters are more complicated than that. Consider the sentence ‘Hesperus is Phosphorus’. This uses two names, only one in fact the name of the Evening Star. Surely I could understand it without knowing it to be true? But if to understand ‘Hesperus’ is to know to which object it refers, then I ought to know that the sentence is true just as soon as I understand it. But I do not. Frege took this example as proving that there is a general distinction in language between that which we understand (the sense of a term) and that which a term refers to or ‘picks out’ (the reference of the term). The sense of a term directs us towards the reference: but it is not identical with it.

In the case of a name the sense is something like a complex description—‘the planet which...’ or ‘the man who...’. The reference, on the other hand, is an object. This may seem intuitively acceptable— although in fact it is now widely devoted. But what about predicates? And what about the sentence taken as a whole?

In discussing Frege’s theory of arithmetic I wrote loosely of concepts, properties and predicates, wishing to postpone the question of the interpretation of these terms. But now it is necessary to be more precise. A predicate has as its reference a particular concept: in understanding the predicate ‘is wise’ I am ‘led to’ the concept of wisdom, by its sense or meaning. What then can we say, from the philosophical point of view, about the nature of concepts? Frege was clear about one thing: concepts are public, and belong as much to the publicly recognisable aspect of language as do the words which express them. The ‘senses’ of predicates are therefore equally public. Otherwise the meaning of words could not be taught, and language would cease to be a form of communication. Senses are to be distinguished from private associations, from images and from every other merely ‘inner’ episode. They are determined by rules of usage which are available to every speaker.

Embodied in the idea of the publicity of ‘sense’, is a rejection of the traditional empiricist theories of meaning. All these theories confuse meaning and association, since they identify the meaning of a term with some subjective idea aroused in the mind of a person who either uses or hears it. Frege also, through his theory of reference, develops the basis for a novel metaphysical rejection of idealism.

How do predicates refer? How is their reference distinct from their sense? Frege argued that, unlike names, predicates are ‘unsaturated’. Their reference can be understood not as a complete object, but only as an operation which needs to be completed before any object is determined by it. Borrowing a mathematical idea, he called this operation a function. Consider, for example, the mathematical function
()
²
+ 2
(or, using the symbol for a variable,
x
²
+
2). This yields a value for any particular number: the value
3
for x =
1, 6
for x =
2,
and so on. And its significance lies wholly in that. The mathematical function transforms one number into another.

Likewise the predicate,
‘x
is wise’ should be conceived as determining a function which yields a value for each individual object that is referred to by the name substituted for ‘x’. What is this ‘value’ to which the sentence refers? Frege argued that it can be nothing more nor less than the reference of the sentence as a whole. For having combined the reference of the subject with that of the predicate, we must obtain the reference of their combination.

To what then do sentences refer? Frege’s answer to this question constitutes what is perhaps the most original part of his philosophy. It is tempting to think that if a sentence refers to anything it is to a fact, or to a state of affairs, or to some such thing. ‘Socrates is wise’ refers to the fact that Socrates is wise. But then to what do false sentences refer? And how many states of affairs are there? If you try to answer the second question, you soon realise that the
only
way to count states of affairs is by counting either sentences, or their meanings. In which case your idea of the
reference
of a sentence has been confused with your idea either of the sentence itself, or of its sense. By a series of extremely subtle and persuasive arguments Frege was able to conclude that in fact the only possible answer to the question, ‘To what does a sentence refer?’ is: ‘To its truth value’. That is, to truth, or to falsehood. Truth and falsehood stand to sentences as objects do to names. And predicates refer to concepts which determine functions yielding truth or falsehood according to the objects to which they are applied.

The analysis of the subject-predicate sentence is completed by answering the question: what is the
sense
of a completed sentence? Frege argued that the sense is a thought: the thought, in our example, that Socrates is wise. A thought, like a concept, is a public thing, not to be confused with any private penumbra or ‘tone’. It is to be identified in terms of the conditions which make a sentence true. Anyone who supposes that Socrates is wise, supposes that certain conditions are fulfilled, in virtue of which the sentence ‘Socrates is wise’ is true (or, to put it more formally, in virtue of which the sentence refers to the truth value: true). The final analysis of the subject-predicate sentence thus attributes to it two complete levels of meaning, in the following way:

Just as the sense of the whole sentence is determined by the sense of its parts, so too is the truth-value determined by the reference of the individual words.

The significance for philosophy of this quasi-mathematical analysis of linguistic structure is enormous. If Frege is right, then the old distinction between extension and intension can be applied to sentences. The extension of a sentence is its truth-value, and the intension its truth-conditions. The extension of a term is detachable from it, and identifiable in other ways. It can therefore be accorded an independent existence. We can think of a sentence as
standing for
the true or the false. The notion of a logical relation between sentences now becomes completely clear. The complex sentence ‘p and q’ for example, is true if and only if
p
is true and
q
is true. Hence the inference from ‘p and q’ to ‘q’ is valid: it takes us from truth to truth. Other ‘logical connectives’ such as ‘if’ and ‘or’ can be clarified in the same way and their logic explained. The principle of extensionality— that every term stands for its extension—can now be used to construct a complete logic of the relations between sentences. It was this idea which revolutionised philosophy, leading first to the ‘logical atomism’ of Russell and Wittgenstein, and then to the new forms of analytical metaphysics which gradually came to replace it.

Moreover, if Frege’s theory of language is right, the fundamental notion involved in understanding words is that of truth. Some have wished to argue thus: a sentence has meaning because people use it to make assertions. It is therefore the peculiar function performed in assertion that we ought to analyse. It is this ‘assertion’ that provides the essence of linguistic communication, and hence must be isolated as the basic subject matter of any philosophy of language. But consider the following argument: (1)
p
implies q; (2) p; therefore (3)
q.
In (1) the sentence ‘q’ is not asserted; in (3) it is: yet the argument is valid. Hence ‘
q
’ must mean the same in each occurrence, otherwise there would be a fallacy through equivocation. It follows, Frege argues, that ‘assertedness’ cannot be part of the meaning of a sentence. If we ask ourselves what we understand in understanding a sentence, or an argument, then the answer always leads back, not to assertion, but to truth. What we understand is either a relation among truth-values, or the conditions which make a sentence true. Frege also believed that the relation of a sentence to its truth-conditions must be objectively determined. Hidden within the very logic of discourse we discover a metaphysical assumption. This is the assumption of an objective truth, at which all our utterances are aimed, and from which they take their sense.

These thoughts of Frege’s have been slowly, and somewhat erratically, incorporated into the framework of modern analytical philosophy. Some thinkers object to Frege’s idea that truth-conditions determine meaning. Others object to the specifically ‘realistic’ or ‘anti-idealistic’ interpretation which Frege gave to this idea. In this way, discussion of Frege has reactivated the fundamental question posed by Kant’s metaphysics. How do we steer the middle course between ‘transcendental realism’ and ‘empirical idealism’? This question has now become: ‘What is fundamental to understanding language; truth considered independently of our ability to assess it, or assertion considered as an act circumscribed by our own epistemological powers?’

Other philosophers object to Frege’s description of the nature of predicates, and his characterisation of the logic of ordinary language in quasi-mathematical terms. Whatever position is adopted, however, whether in the theory of meaning, or in metaphysics, we can be sure that, if the position belongs to the tradition of ‘analytic’ philosophy, it will have tacitly relied on Frege’s ideas, if not to provide its arguments, at least to provide the terminology in which they are expressed.