What is the best way to explain the concept of analyticity?

Consider the following two sets of sentences:

Column 1

Column 2

All baseball players catch balls. All baseball players catch thieves.
All bachelors are males. All bachelors are gay.
Hesperus is Hesperus. Hesperus is Phosphorus.
If Holmes killed Moriarty, then Moriarty died. If Holmes killed Moriarty, then Watson died.
All ophthalmologists are doctors. All ophthalmologists are bald.
Whatever is red all over is not blue all over. Snow is white.

Most people would agree that most of the statements in Column 1 are "True in virtue of the meaning of the words involved" - at least in some vague and loosely understood sense of that phrase.   Most people would also agree that most of the statements in Column 2 seem to require additional information about the world before a judgement can be made of whether they are true or false.   Additionally, it seems obvious to most people that the negation of statements like those on the left are more than just false, they are in some significant sense self-contradictory.   Whereas, the negation of true(false) statements like those on the right do not seem to be at all contradictory, merely false(true).   Moreover, given any random (properly grammatical) English sentence, most of us would have little difficulty in agreeing on whether the statement ought to be grouped in Column 1 or in Column 2 (as long as we know what the words mean, of course).  

Statements like those in Column 1 are usually called "analytic", while those in Column 2 are usually called "Synthetic".   So it appears quite obvious that despite the protestations of some philosophers (notably Quine), there must indeed be something to the analyticity.   The question, of course, is how to formalize (i.e. "explain") what it is that we intuitively recognize so easily.   And therein arises the controversy.

The specific terms "analytic" and "Synthetic" were initially introduced by Kant in his Critique of Pure Reason (1781) -

"In all judgments in which the relation of a subject to the predicate is thought (if I only consider affirmative judgments, since the application to negative ones is easy) this relation is possible in two different ways. Either the predicate B belongs to the subject A as something that is (covertly) contained in this concept A; or B lies entirely outside the concept A, though to be sure it stands in connection with it. In the first case, I call the judgment analytic, in the second synthetic."(1a)  

According to Kant, all analytic judgments rest on the principle of non-contradiction.   "For since the predicate of an affirmative analytic judgment is already thought beforehand in the concept of the subject, it cannot be denied of the subject without contradiction."(1b)   And "analytic judgments are therefore those in which the connection is through identity."(1c)

Kant's "containment" theory works well for statements drawn primarily from syllogistic logic.   If one is dealing with statements of the sort "{All/Some/No} A {predicate verb} {not} B" - then it is relatively easy to conceive of analyticity as involving the containment of the concept B within the concept A.   Of course, not many statements of English correspond (or can be re-phrased into) sentences this easy to deal with.   So Kant's definition of the concept of analyticity is clearly not sufficient to explain what it is that we recognize with our intuitive ability.

The next advance in our understanding of the concept of analyticity was provided by Frege as a consequence of his efforts to develop what we now think of as modern symbolic logic (1884-1892)(2).   In the process of carefully specifying the details of a "formal" language of logic (what we now call the axiomatic predicate calculus), he set down an account of what are called "logical constants" - "and", "or", "not", "all", and the like.   Separating the logical constants from "referring expressions" - words, unlike the logical constants, that refer to things in the world - he permitted the classification of "logical truths".   Logical truths are those statements that are true in virtue of the meaning of the logical constants, no matter what referring expressions appear in the statement.   Hence "all X are X" (eg. "all doctors are doctors") is a logical truth - it is true regardless of what referring expression replaces the X.   Unfortunately, Frege's concept of a logical truth does not cover such common statements as "all X are Y" (eg. "all ophthalmologists are doctors").  

So Frege appealed to the idea of definitions, assuming that a definition preserves meaning between the definiendum and the definiens.   With this addition, Frege explains non-logical analyticity as statements that can be converted into strict logical truth by replacing definienda with the appropriate definiens - or synonyms for synonyms.

As set out by Frege for the predicate calculus, the rules of the formal language(s) of symbolic logic are established by stipulation.   All true statements of symbolic logic are based on a few key axioms, and inferences by specified inferential steps from those axioms.   The meanings of the logical constants employed in symbolic logic are likewise established either by direct stipulation, or by implicit definition through their use in the axioms.   So statements of symbolic logic that are true only in virtue of the stipulations on which the language is based, can be called "analytic".   These are the "logically true" statements - they are true regardless of the contents of the free variables.   So any English statement that can be readily re-phrased into a "logically true" statement of symbolic logic can also be called "analytic".

By treating a definition as a stipulation of what is synonymous with what, we can greatly expand the scope of English sentences that can be called analytic.   We can add to the body of analytic English sentences all those that we can translate into a logically true statement of symbolic logic by replacing synonym for synonym.   This is especially so if we expand the scope of acceptable definitions beyond the direct stipulations of an explicit definition, to include ostensive, implicit, and conventional definitions.   This seems to cover most of the examples in the table of statements above quite nicely.  

Frege's theory of analyticity seems to nicely capture the intuitive feel of "True in virtue of the meaning of the words".   It also, by way of synonymy, captures much of the "cognitive containment" theory of Kant.   And in those cases where it seems to stumble, an argument could be made that it is due to an indeterminacy in the meaning of the words involved, or an insufficiency in the formal language(s) of modern symbolic logic, but not any inadequacy in the notion of synonymous translation.

And thus things stood until 1951 and Quine's "Two Dogmas of Empiricism"(3).  


In this brief essay, Quine presents what has become accepted as the definitive critique of the Analytic-Synthetic Dichotomy.   The focus of Quine's attack on the notion of analyticity is the claim that Frege's concept of the analytic depends on a prior understanding of synonymy, and that there is no acceptable explanation of synonymy.

"Our problem ΓΆ‚¬¦ is analyticity; and here the major difficulty lies not in the first class of analytic statements, the logical truths, but rather in the second class, which depends on the notion of synonymy."   Quine, "Two Dogmas of Empiricism"(3)

Quine has no difficulty with the class of analytic statements called "logical truths".   Nor, as we will see later, does he have a difficulty with explicitly stipulated synonymy.   His problem lies with that class of statements that are claimed to be analytic but depend for that classification on an unacceptable presupposition of synonymy.   A presupposition the he argues is not supportable.

In sections 1 thru 4 of his essay, Quine attacks a series of possible explanations of how analyticity can be explained.   Each of these, he argues, is flawed in some fundamental way.   Hence, he reasons there is no satisfactory explanation for analyticity.   And therefore, analyticity is an illusory classification.   In section 5 of his essay, Quine offers his own theory of meaning - "meaning holism" - and argues that such a theory of meaning cannot support a distinction between analytic and synthetic sentences.

What we have at the end of Quine's analysis is that the notion of "analyticity" is dependent on the notion of "Synonomy" which in turn is dependent on the notion of "analyticity".   The same argument can be made for the circularity of the relationship between "analyticity" and "Self-contradictory", "definition" (in the broader sense), "necessity", and (perhaps) "Semantical rule".   Hence, Quine's conclusion that the notion of analyticity is sufficiently ill understood that it makes no sense to employ the classification for sentences that are not analytic in virtue of being a logical truth, or in virtue of a stipulated synonymy.   Analyticity, in other words, is an unnecessary fiction.

In the last sections of his essay, Quine   argues that no sentence can be considered "unrevisable" in the face of evidence from facts of the world.   No sentence can be considered any more "True come what may", or "True in all possible worlds", or "True in virtue of meaning alone" than any other sentence.   No sentence can be considered any more immune from disconfirmation by evidence than any other.   Hence, there can in principle be no basis for a distinction between "analytic" and "Synthetic".

Countering Quine's critique must remain the empirical observation, as noted at the start of this essay, that people can and do use the classifications of "analytic" and "Synthetic" with a high degree of consistency.  

'they apply the term "analytic" to more or less the same cases, withhold it from more or less the same cases, and hesitate over more or less the same cases.   ΓΆ‚¬¦   In short, "analytic" and "Synthetic" have a more or less established philosophical use; and this seems to suggest that it is absurd, even senseless, to say that there is no such distinction."   Grice & Strawson, Pg 143.

If, as Quine claims, there is no coherent and determinate property that is picked out by the classifying label "analytic" (or, since Quine has demonstrated their correlativity, the label "Synonymous"), then that can only be because there are no facts of the matter as to whether a sentence is analytic (synonymous) or not.

"But, now, how can there fail to be facts about whether any two expressions mean the same -- even where these are drawn from within a single speaker's idiolect, so that no questions of interlinguistic synonymy arise? Wouldn't this have to entail that there are no facts about what each expression means individually? Putting the question the other way: Could there be a fact of the matter about what each expression means, but no fact of the matter about whether they mean the same?"   Boghossian, Pg 370

Because Quine finds no acceptable basis from which to understand what property it is that he is seeking, he concludes that there is no such property.   But in order to support his conclusion that synonymy is not possible, he must maintain that while there is a fact of the matter about what each sentence means, no two sentences can ever possibly mean the same thing.   This position only works on the assumption that the meaning of any one sentence is given by the entirety of ones belief network (the first of any pair of sentence appearing in the belief-network of the second, and vice versa).   Given the undisputed philosophical usage of "analytic", Quine's critique of the analytic-synthetic distinction can be viewed as a reductio ad absurdum proof that meaning-holism is the wrong theory of meaning.   Or, more leniently, one can view his critiques of the specific explanations of "analyticity" that he examined as showing that they are flawed in some fashion, without demonstrating that no explanation of analyticity is possible.

If one rejects meaning-holism, as most philosophers do, then one must find a way out of the circle (network?) of inter-dependence between "analyticity", "Synonymy", "Self-contradictory", "definition" (in the broader sense), "necessity", and (perhaps) "Semantical rule".   Once one rejects Quine's conclusion that a way out is not possible in principle, there are two avenues to explore.   One can maintain that there must be a way out.   Or one can maintain that a way out is not needed.

We clearly make use of all of these terms with a fair degree of consistency.   So it is reasonable to suppose that there is an explanation for why our use of these terms does show such consistency.   And because these terms are used to classify sentences, it is reasonable to suppose that whatever explanation is eventually deemed satisfactory will be couched in concepts relevant to a theory of the meaning of these sentences.   When we add to this the observation that there is not yet any generally accepted theory of the meaning of sentences, it is perhaps not too surprising that there is no generally accepted explanation for analyticity.   The failure of philosophers to have discovered an acceptable theory of meaning is not interpreted as a demonstration that no such theory is possible.   So neither should the failure of philosophy to offer a generally acceptable explanation of analyticity be interpreted as entailing that no such explanation is possible.

It is also possible that we already have just such an explanation, even if we do not generally recognize it as such.   A network of inter-dependence among a number of fundamental terms is not necessarily vicious.   As is frequently argued by coherence theorists, reasoning in a circle does not have to be circular reasoning.   The coherence theory of knowledge maintains that our claims to knowledge are justified on the basis of a statement's coherence with other statements in our belief-network.   Even a correspondence theorist (of truth) will allow that our judgments of the truth of a statement are made on the basis of the coherence of the statement with (a relevant portion of) the rest of our belief-network.   Is there then something in principle wrong with the notion of claiming knowledge and truth for our classification of some statements as "analytic" on the basis of the coherence of that classification scheme with the rest of our belief-network - without our being able to provide a specific "if and only if" definition of how and why we make that classification?   Perhaps Quine's search for such a philosophically precise definition of the term is unnecessary.

If one insists on a more informative explanation of analyticity, then one must first establish a suitable theory of meaning within which to discuss the issue.   Quine has demonstrated that meaning-holism is probably not the appropriate theory.   What is needed is a theory of meaning that will provide a suitable explanation for "Synonymy" that is not as strict as Quine demands.   For example, Quine's concept of synonymy is too strict to permit Kant's notion of "cognitive containment" - it does not permit an explanation of why such sentences as "anything green is extended" are deemed analytic.   There is no sense of "Sameness of meaning" that will allow us to translate that statement into a logical truth.   What is necessary then, is a looser conception of synonymy that will allow for both the notion of "containment", and for a broader acceptance of the role of definitions in the establishment of acceptable synonymy.

The conclusion of all of this exposition is that a modified version of Frege's explanation of "analyticity" remains the best available.   Although it is readily acknowledged that analyticity is not yet satisfactorily explained, in the sense of a generally accepted set of necessary and sufficient conditions for the identification of all and only analytic sentences.  

Quine's "definitive critique" of the analytic-synthetic distinction is driven by his prior commitment to meaning-holism.   An alternative theory of meaning, like a set-theoretic rendition of an intentional description-cluster theory of meaning similar to that of Searle's theory of proper names(4), offers hope of providing a satisfactory explanation of analyticity in terms of meanings.

Despite its admitted inadequacies, the best way to explain the concept of analyticity remains -

A sentence S is analytic iff

(a)   it can be readily re-phrased into a logical truth (using the formalisms of modern symbolic logic); or

(b)   it can be readily translated in to a logical truth by replacing "cognitive synonyms" for "cognitive synonyms" - where a "cognitive synonym" for one term is another that "means the same thing" in a general sense; or

(c)   it can be shown that the concept of the subject "contains" the concept of the predicate - where "containment" is to be interpreted in a set-theoretic fashion of set-membership and set-membership criteria.

Notes & References

(1a)   Kant, I.   The Critique of Pure Reason, trans. by P. Guyer and A.W.Wood.   Cambridge University Press, Cambridge, England. 1781/1998. §:6-7.

(1b)   Kant, I.   Prolegomena to Any Future Metaphysics. The Library of Liberal Arts / Bobbs-Merrill Educational Publishing, Indianapolis, Indiana. 1950. ISBN 0-672-60487-7. pg 27

(1c)   Kant, I.   The Critique of Pure Reason, trans. by P. Guyer and A.W.Wood.   Cambridge University Press, Cambridge, England. 1781/1998. §:7 & B:11.

(2)   Frege, G.    

The Foundations of Arithmetic, 2nd revised ed., Blackwell Publishing, London, England. 1884/1980

"On Sense and Reference," in P.Geach and M. Black (eds.), Translations from the Works of Gottlob Frege, Blackwell Publishing, Oxford, England. 1892a/1966. pp56-78.  

"On Concept and Object," in P.Geach and M. Black (eds.), Translations from the Works of Gottlob Frege, Blackwell Publishing, Oxford, England. 1892b/1966. pp42-55.

(3)   Quine, V.O.   Two Dogmas of Empiricism;   downloaded from the Internet August 8, 2008 from URL=<http://www.ditext.com/quine/quine.html>   [Originally published in The Philosophical Review 60 (1951): 20-43. Reprinted in W.V.O. Quine, From a Logical Point of View (Harvard University Press, 1953; second, revised, edition 1961)]

(4)   Searle, J. R.

                      "Proper Names", Mind, New Series, Vol 67, No 226, (Apr 1958), pp 166-173.

                      Speech Acts: An Essay in the Philosophy of Langauge. Cambridge: Cambridge University Press. 1969.

                      Intentionality: An Essay in the Philosophy of Mind. Cambridge: Cambridge University Press. 1983.

Boghossian, P.   "Analyticity Reconsidered"   Nous, Vol. 30, No. 3 (Sep., 1996), pp. 360-391, downloaded from the Internet   Sept 20, 2008. URL=<http://www.jstor.org/stable/2216275>

P.F.Grice, H.P. & Strawson, P.F.     "In Defence of a Dogma", The Philosophical Review, Vol. 65, No. 2.   Apr. 1956, Pgs 141-158   downloaded from the Internet Sept 20, 2008, URL=<http://www.jstor.org/stable/2182828>

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