Essays | Books

Do the Terms 'Analytic' and 'Synthetic' Have any Meaning?

Quine's Attack on the Dogma of Empiricism

In this essay we shall examine the notions of synthetic and analytic truth and ask whether they are clear and distinct ideas or whether in fact, as some have claimed, all statements are ultimately synthetic. Firstly, we must explore the various attempts to distinguish between synthetic and analytic statements and examine the inherent shortcomings of these definitions. Problems over finding convincing definitions will lead us to question the very possibility of such a priori knowledge. In particular we explore the famously sceptical arguments of W.V.O. Quine. These arguments lead logically to a scepticism about the nature of meaning and understanding in language and in particular to the possibility of discovering metaphysical truths about the world. Finally we shall propose some responses to Quine’s position which seek to restore, or at least patch up, the shaky foundations of metaphysics.

Firstly then, what do we mean by the terms analytic and synthetic? Hume recognised that human knowledge can be classified as either ‘relations of ideas’ or ‘matters of fact’. It is Kant, in Critque of Pure Reason , who first uses the term analytic to denote statements which are necessarily true in all possible worlds. The truth of an analytic statement can be seen purely by virtue of reflecting on the meaning of the ideas (concepts) contained within it. In contrast, the truth of a synthetic statement depends upon both the meaning of the concepts and on the state of the world – synthetic statements are only contingently true and must be established by empirical observation. For example, the statement ‘all triangles have 3 sides’ is clearly an analytic truth that is valid in all possible worlds by virtue of the meaning of ‘triangle’. However, my claim that ‘this triangle is blue’ is a matter of contingent fact that must be investigated through experiment.

The notion of analyticity seems at first sight to be a clear and coherent concept. Human beings normally have no apparent difficulty in recognising the analyticity of a statement expressed in natural language. Can we provide then a simple decision procedure which would allow us to determine the analyticity or otherwise of any statement? Is there a clear and unambiguous definition of analyticity to be had?

Kant’s initial definition introduced the notion of ‘containment’, saying that an analytic statement does not attribute to its subject any more than its already contained within the subject concept. To Kant, the statement ‘all bachelors are unmarried males’ is analytic because the concept of ‘bachelor’ contains the concept ‘unmarried male’. But surely this does not get us very far for Kant’s ‘conceptual containment’ is only a loose term which is itself as much in need of explanation as the notion of analyticity. In addition, this simple definition only appears applicable to sentences of the subject-predicate form: x is P. But natural language is capable of expressing higher order logics containing modal operators such as necessarily. For example, the sentence ‘Caesar murders those whose life he takes illegally’ is true purely by virtue of the meaning of the words without any need to observe Caesar’s behaviour over time. And yet, how are the concepts of ‘murder’ and ‘illegal killing’ contained within the concept of Caesar? Kant’s first definition of analyticity is too narrow to apply to analytic sentences in general.

Kant broadens his definition by declaring a statement as analytic if its denial results in a self-contradiction. But once again, we have replaced one contentious term (analyticity) with an equally broad and ill-defined concept that requires the same level of clarification. What exactly do we mean by self-contradiction? In strictly logical terms, a self-contradictory statement must reduce syntactically to the tautology: (P L ØP). A statement such as ‘a dog is not a dog’ is obvious but what about ‘all bachelors are married’? Here the syntactic form of the statement is ("x: Px), whereas the self-contradiction arises internally from the meanings of the concepts involved. We need a notion of self-contradiction which is broader than this narrow syntactic sense. But surely this is virtually equivalent to our original quest to find a definition for analyticity?

Kant then does not provide an adequate explanation of ‘analytic’ which is clearly and unambiguously applicable to all statements in human language. Can we appeal to logic to provide a set of defining criteria for analyticity? Frege proposed that analytic statements are those which can be reduced to purely logical truths. Logical truths are those that remain true regardless of the interpretation of their component predicates – providing the interpretation of the logical operators (AND, OR, NOT, IF..THEN etc.) remain constant. For example, “all red widgets are red” remains true however ‘red’ and ‘widget’ are interpreted (whatever their meaning).

More formally, we can say that an analytic statement must be either:

Type 1: a logical law, or
Type 2: derivable from logical laws using only definitions as premises.

Thus, ‘all unmarried men are unmarried’ is type (1) analytic whereas ‘all bachelors are unmarried’ is type (2) analytic by virtual of them definition of ‘bachelor’.

This seems at first sight to provide a clear decision rule for analyticity. Analytic statements of type (1) are no problem sense they rely purely on syntactic form and not on the meanings of the predicate terms. The analyticity of statements of type (2) however hinges on the correctness of the definitions of the constituent terms. For example, the statement ‘all paperweights are unmarried’ is analytic under Frege’s framework provided we define ‘paperweight’ as ‘unmarried man’. Once more we have replaced our original problem, defining analyticity, with the equivalent problem of determining rules for deciding the correctness of definitions. Is it possible to say that a definition is correct or incorrect without pre-supposing an answer to our original question about analyticity?

In his seminal paper ‘Two Dogmas of Empiricism’, A.V.O. Quine argues that the notion of analyticity is unintelligible - that it is not possible, even in principle, to give an adequate account of analyticity which does not rely upon circularly related terms such as synonomy, definition, self-contradiction, semantical rule, and the like. However, the radical nature of Quine’s attack results in a deeply sceptical view of meaning itself.

Quine begins by reviewing Kant and Frege’s attempts to define analyticity; raising the problems noted above. Quine however takes the argument further to attack the narrow logical positivist theory of meaning. Frege’s framework requires that an analytic statement can be reduced to a logical truth by the application of correct definitions. In other words, a complex statement can be simplified by replacing complex concepts by synonyms which have the same meaning but which use more atomic constituents. A definition then is correct if the defined and defining terms are synonymous. Thus, by replacing ‘bachelor’ with its synonym ‘unmarried man’, the statement ‘all bachelors are unmarried’ is immediately reduced to a logical truth, and is thus seen as analytic.

But now we have the problem of accounting for synonymy. One possible approach would be to say that P and Q are synonymous if they are interchangeable within a statement without changing its truth value (i.e. intersubstitutable salva veritate). If this is a valid move then it provides a sound definition for synonymy, which then provides us with a means of deciding the correctness of definitions, which in turn provide the basis for analyticity.

But, as Quine points out, this notion of synonymy is hopelessly inadequate because it relies completely on reference while leaving out entirely the sense, or meaning, of the terms judged to be synonymous. Two predicates may apply simultaneously to the same set of objects (i.e. have the same extension) and may thus be intersubstituted salva veritate while having wildly different meanings. The classic example involves the terms ‘renate’ (creature with kidneys) and ‘cordate’ (creature with a heart). For most purposes, they may be interchanged in statements without changing the overall truth value since, in this world, the same objects share both properties. However these terms are clearly not synonymous in any intuitive sense - we can easily image possible worlds where hearty creatures are bereft of kidneys.

Simple intersubstitution then is clearly not a strong enough condition for synonymy . Can we use the notion of necessity to escape from the accidental co-extension of our candidate synonyms? We could propose that terms P and Q are synonyms if they are necessarily intersubstitutable salva veritate. Thus ‘renate’ and ‘cordate’ are not synonymous because we can easily conceive of worlds where they have different extensions – it is only an accident of nature that they have the same extension in this world. But once again we have merely replaced one troublesome term with another – what does it mean to say that ‘necessarily P’? As Quine points out, this is merely a restatement of the proposition that ‘P is analytic’ – the starting point of our original quest.

To summarise then, to define analyticity within Frege’s system we need to explain the notion of correct definitions. This then requires explanation of synonymy through intersubstitution which must in turn rest on the notion of a necessary truth. But a necessary truth is one which is true in all possible worlds – i.e. is analytic. We have come full circle. Quine clearly argues that all attempts to define analyticity must either pre-suppose the notion of analyticity itself or rest upon terms which are either just as unclear as analyticity or in turn reduce to analyticity. To the extent that there is no clear and non-circular characterisation of the nature of an analytic truth, then how can we distinguish between analytic and synthetic truths? For Quine, there is no such distinction - the acceptance of any sentence depends both on the conventions of language users and on facts about the world.

To accept Quine’s conclusions is to accept that there is something fundamentally wrong with our intuitive understanding of meaning. How can we ever agree between ourselves on the meaning of a statement if, ultimately, meaning is grounded in definitions which rely on a number of axioms which are analytic truths. If the very notion of ‘true in all possible worlds’ is rendered incoherent by Quine’s argument, then we have no fixed axioms upon which to base our definitions and hence our shared meanings. If we allow that all statements must have an empirical component then language has no foundation – the bedrock of analyticity has been cut from beneath our feet. Once one starts to question synonymy so fundamentally, then surely it becomes questionable to talk about sentences having meaning at all? Grice and Strawson, in their reply to ‘Two Dogmas’, point out that once sentence-synonymy is denied, then we must also deny the possibility of being able to answer the question ‘what does this sentence mean?’ Quine’s attack is so radical that, taken to its extreme implications, it denies the very possibility of philosophical argument at all!

While the logic of Quine’s position is coherent, it nevertheless denies the evident truth that there are in fact analytic truths and that human language users have no difficulty in detecting and appreciating their analyticity. Furthermore, we clearly can attribute a meaning to a sentence that is shared among all users of the common language. So what response can be made to counter Quine’s sceptical argument and restore our ability to communicate meaningfully?

As a starting point, consider the assumptions underlying Quine’s argument. Quine appears to have no problem with the concept of a logical truths. His argument asserts however that there is no basis for using them to characterise a class of analytic truths in a way that does not rely implicitly upon analyticity as a given axiom. But surely Quine’s own argument against analyticity also applies equally to the notion of logical truths – thus undermining the validity of the argument? For example, ‘for all green banks are green’ is syntactically a logical truth. However, this is only the case if the instances of syntactically identical terms (e.g. bank) are synonymous. If the token occurrences of ‘bank’ actually have different meanings then this is no longer a logical truth. Hence Quine’s argument relies implicitly on the soundness of our concept of logical truths – but this very concept is susceptible to Quine’s own argument against definition and synonymy.

In essence, Quine’s argument reduces to the impossibility of finding a intelligible meaning for analyticity which is not based upon a circular definition. An explicit definition for concept P is the set of conditions necessary for the instantiation of P: x is P iff Fx. Quine’s argument imposes the strict condition that either P or any concept which relies upon P cannot appear in the definition of F. But surely this is far too strong a condition to impose on P being intelligible? There are many real world examples of concepts which are perfectly well understood but which have no definition satisfying Quine’s condition. Consider the concept of colour for example. There are clearly no necessary and sufficient conditions available to judge the correct application of the terms ‘red’ or ‘green’, and yet we have a perfect understanding of sentences containing these concepts.

Taking the argument to extremes, Quine would appear to say that a language is only intelligible if there exists a complete set of explicit and non-circular definitions for each of its component expressions. This would require an infinite set of linguistic axioms or atomic primitives upon which compound concepts within the language are based. Not only would such a language be un-learnable in principle, it would be totally unlike all known human languages which, subject to experience, clearly support intelligible meaning. Quine’s tight constraints on the validity of definition cannot then be globally applicable to the entirety of language since, if so, then Quine’s own argument loses its meaning. If however, we take Quine to mean that his constraints apply only to some local subset of language that includes the concept of analyticity, then we must ask for his justification as to what the particular problem is with ‘analyticity’. Quine’s hesitation to render the term ‘analyticity’ intelligible should thus apply equally to the use of terms such as ‘red’ or ‘green’ since these equally fail to meet his criteria for intelligibility.

Grice and Strawson, responding to Quine in ‘In Defence of a Dogma’, contend that notions such as meaning, synonymy, analyticity and necessity form a set or "family" of inter-definable concepts that are useful, in spite of the fact that there appears to be no way of underpinning them with unambiguous, non-circular definitions meeting Quine’s criteria for intelligibility. Quine argues that the analytic / synthetic distinction is illusory and people are actually confusing obvious with analytic. But, argue Grice and Strawson, we have no difficulty in distinguishing between analytic and synthetic statements - there is no illusion. Why are we required to have a formal logistic definition of analyticity in order to have meaning? Just as logic relies upon a few axiomatic primitives which are not defined ‘inside’ the system, so language and knowledge rely on a set of ill-defined but readily understood concepts (such as analyticity) which are axiomatic to meaning. The meaning of such primitives arises from their usage within language, rather than from some extra-logical definition expressed in a formal meta-language.

Quine’s attack on analyticity in ‘Two Dogmas’ seems to be both too narrow and restrictive to be plausible and to be based implicitly on what it seeks to discredit. However, Quine’s own preference for a ‘holistic’ theory of meaning has much which seems intuitively true. Language can be seen as a single conceptual framework within which our beliefs form a vast interconnected network (the ‘web of beliefs’). In the light of experience we revise our beliefs in order to maintain the consistency of the system as a whole. Each belief faces the ‘tribunal of experience’ and is adjusted so as to maintain a conceptual equilibrium. If we consider this web of beliefs as a whole then there appears no clear distinction between those beliefs which are necessarily true (and which are therefore immune from revision) and those that are contingently true (and may be revised in the light of experience). The only distinction we can make relies upon a fuzzy decision procedure which determines which beliefs remain inviolate in the face of contrary evidence and those that we readily revise to accord with experience. The former we may term ‘ersatz analytic’. The distinction then is one merely of attitude to a homologous body of beliefs and not of two characteristically different categories of truth. Because experience can be interpreted in a way that maintains our core beliefs, there is no single belief associated with a single sense experience. In other words, the smallest unit of meaning becomes the whole language.

In summary, the notions of analytic and synthetic truths remain impossible to pin down in strict terms whereby any statement can be characterised as one or the other according to a mechanistic procedure. While this remains, it is also undoubtedly true that these concepts have a clear and consistent meaning that is intelligible to humans and allows them to distinguish between them on an intuitive basis. Where Quine succeeds is in his attack on the verificationist principles of the logical positivists and their atomic sense of meaning routed in experiential verification. Quine has I believe failed to make the case that it is actually meaningless to attempt to distinguish between synthetic and analytic categories of truth since, if true, then we clearly lose meaning itself, and hence all of metaphysics and philosophy.


1. Grice, H. P., and Strawson, P. F., "In Defense of a Dogma", in Philosophical Review 65, 1956.
2. Kant, Immanuel, Critique of Pure Reason, translated by Norman Kemp Smith, 1929.
3. Quine, W. V. O., "Two Dogmas of Empiricism" (1951) in From a Logical Point of View, 1953.