“Analytic” sentences, such as “Pediatricians aredoctors,” have historically been characterized as ones that aretrue by virtue of the meanings of their words alone and/or can beknown to be so solely by knowing those meanings. They are contrastedwith more usual “synthetic” sentences, such as“Pediatricians are rich,” (knowledge of) whose truthdepends also upon (knowledge of) the worldly fortunes ofpediatricians. Beginning with Frege, many philosophers hoped to showthat the truths of logic and mathematics and other apparentlyapriori domains, such as much of philosophy and the foundations ofscience, could be shown to be analytic by careful “conceptualanalysis” of the meanings of crucial words. Analyses ofphilosophically important terms and concepts, such as “materialobject,” “cause,” “freedom,” or“knowledge” turned out, however, to be far moreproblematic than philosophers had anticipated, and some, particularlyQuine and his followers, began to doubt the reality of thedistinction. This in turn led him and others to doubt the factualdeterminacy of claims of meaning and translation in general, as wellas, ultimately, the reality and determinacy of mental states. Therehave been a number of interesting reactions to this scepticism, inphilosophy and linguistics (this latter to be treated in thesupplement, Analyticity and Chomskyan Linguistics); but,while the reality of mental states might be saved, it has yet to beshown that appeals to the analytic will ever be able to ground“analysis” and thea priori in quite the way thatphilosophers had hoped. (Note that all footnotes are substantive, butinessential to an initial reading, and are accessed in a separate fileby clicking on the bracketed superscript. The mention vs. use of aterm will be indicated either by quotation marks or italics, dependingupon which is most easily readable in the context.)

• 1. The Intuitive Distinction
  • 1.1 Kant
  • 1.2 Frege
• 2. High Hopes
  • 2.1 Mathematics
  • 2.2 Science and Beyond
• 3. Problems with the Distinction
  • 3.1 The Paradox of Analysis
  • 3.2 Problems with Logicism
  • 3.3 Convention?
  • 3.4 Verificationism and Confirmation Holism
  • 3.5 Quine on Meaning in Linguistics
  • 3.6 Explaining Away the Appearance of the Analytic
    • 3.6.1 Centrality
    • 3.6.2 One Criterion Concepts
    • 3.6.3 The World, Not Words
• 4. Post-Quinean Strategies
  • 4.1 Neo-Cartesianism
  • 4.2 Externalist Theories of Meaning
  • 4.3 Internal Dependencies
  • 4.4 A Chomskyan Strategy
• 5. Conclusion
• Supplement: Analyticity and Chomskyan Linguistics
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. The Intuitive Distinction

Compare the following two sets of sentences:

I.

(1)

All doctors that specialize on children are rich.

(2)

All pediatricians are rich.

(3)

Everyone who runs damages their bodies.

(4)

If Holmes killed Sikes, then Watson must be dead.

II.

(5)

All doctors that specialize on children are doctors.

(6)

All pediatricians are doctors.

(7)

Everyone who runs moves.

(8)

If Holmes killed Sikes, then Sikes must be dead.

Most competent English speakers who know the meanings of all theconstituent words would find an obvious difference between the twosets: whereas they might wonder about the truth or falsity of those ofset I, they would find themselves pretty quickly incapable of doubtingthose of II. Unlike the former, these latter seem to be justifiableautomatically, “just by knowing what the words mean,” asmany might spontaneously put it. Indeed, denials of any of them,e.g.,

III.

(9)

#Not all pediatricians are doctors – some aren’tat all!

(10)

#Not everyone who runs moves – some remain completelystill!

would seem to be in some important wayunintelligible, verylike contradictions in terms (the “#” indicates semanticanomaly). Philosophers standardly refer to sentences of the first setas “synthetic,” those of the second as (at leastapparently) “analytic.” (Members of set III. are sometimessaid to be “analytically false,” although this term israrely used, and “analytic” is standardly confined tosentences that are regarded as true.) We might call sentences such as(5)-(10) part of the “analytic data” to which philosophersand linguists have often appealed in invoking the distinction (withoutprejudice, however, to whether such data might otherwise beexplained). Some philosophers might want to include in set III. whatare calledcategory mistakes (q.v.) such as #The numberthree likes Tabasco sauce, or #Saturday is in bed (cf.,Ryle, 1949 [2009]), but these have figured less prominently in recentdiscussions, being treated not as semantically anomalous, but assimply false and silly (Quine 1960 [2013, p. 210]).

Many philosophers have hoped that the apparent necessity andapriori status of the claims of logic, mathematics and much ofphilosophy could be explained by their claims being analytic, ourunderstanding of the meaning of the claims explaining why they seemedto be true “in all possible worlds,” and knowable to beso, “independently of experience.” This view led many ofthem to regard philosophy as consisting in large part in the“analysis” of the meanings of the relevant claims, wordsand concepts;^[1] i.e., a provision of conditions that were individually necessary andjointly sufficient for the application of a word or concept, in theway that, for example,being a female andbeing aparent are each necessary and together sufficient forbeing amother. Such a conception seemed to invite and support (althoughwe’ll see it doesn’t entail) the special methodology of“armchair reflection” on concepts in which manyphilosophers traditionally engaged, independently of any empiricalresearch.

1.1 Kant

Although there are precursors of the contemporary notion of theanalytic in Leibniz, and in Locke and Hume in their talk of“relations of ideas,” the conception that currentlyconcerns many philosophers has its roots in the work of Kant (1787[1998]) who, at the beginning of hisCritique of Pure Reason,wrote:

In all judgments in which the relation of a subject to the predicateis thought (if I only consider affirmative judgments, since theapplication to negative ones is easy) this relation is possible in twodifferent ways. Either the predicate B belongs to the subject A assomething that is (covertly) contained in this concept A; or B liesentirely outside the concept A, though to be sure it stands inconnection with it. In the first case, I call the judgment analytic,in the second synthetic. (1787 [1998], B10)

He provided as an example of an analytic judgment, “All bodiesare extended”: in thinking of a body we can’t help butalso think of it being extended in space; that would seem to be justpart of what is meant by “body.” He contrasted this with“All bodies are heavy,” where the predicate (“isheavy”) “is something entirely different from that which Ithink in the mere concept of body in general” (B11), and we mustput together, or “synthesize,” the different concepts,body and heavy (sometimes such concepts are called“ampliative,” “amplifying” a concept beyondwhat is “contained” in it).

Kant tried to spell out his “containment” metaphor for theanalytic in two ways. To see that any of set II is true, he wrote,“I need only to analyze the concept, i.e., become conscious ofthe manifold that I always think in it, in order to encounter thispredicate therein” (B10). But then, picking up a suggestion ofLeibniz, he went on to claim:

I merely draw out the predicate in accordance with the principle ofcontradiction, and can thereby at the same time become conscious ofthe necessity of the judgment. (B11)

As Jerrold Katz (1988) emphasized, this second definition issignificantly different from the “containment” idea, sincenow, in its appeal to the powerful method of proof by contradiction,the analytic would include all of the (potentially infinite) deductiveconsequences of a particular claim, many of which could not beplausibly regarded as “contained” in the concept expressedin the claim. For starters,Bachelors are unmarried or the moon isblue is a logical consequence ofBachelors areunmarried—its denial contradicts the latter (a denial of adisjunction is a denial of each disjunct)—but clearly nothingabout the color of the moon is remotely “contained in” theconceptbachelor. To avoid such consequences, Katz (e.g.,1972, 1988) went on to try to develop a serious theory based upon onlythe initial containment idea, as, along different lines, does PaulPietroski (2005, 2018).

One reason Kant may not have noticed the differences between hisdifferent characterizations of the analytic was that his conception of“logic” seems to have been confined to Aristoteliansyllogistic, and so didn’t include the full resources of modernlogic, where, as we’ll see, the differences between the twocharacterizations become more glaring (see MacFarlane 2002). Indeed,Kant demarcates the category of the analytic chiefly in order tocontrast it with what he regards as the more important category of the“synthetic,” which he famously thinks is not confined, asone might initially suppose, merely to the empirical.^[2] He argues that even so elementary an example in arithmetic as7+5=12 is synthetic, since the concept of12 is notcontained in the concepts of7,5, or+,:appreciating the truth of the proposition would seem to require somekind of active “synthesis” by the mind uniting thedifferent constituent thoughts (1787 [1998], B15). And so we arrive atthe category of the “synthetica priori,” whosevery possibility became a major concern of his work. Kant tried toshow that the activity of synthesis was the source of the importantcases ofa priori knowledge, not only in arithmetic, but alsoin geometry, the foundations of physics, ethics, and philosophygenerally, a controversial view that set the stage for much of thephilosophical discussions of the subsequent centuries (see Coffa 1991,pt. I).

Apart from geometry, Kant, himself, actually didn’t focus muchon the case of mathematics. But, as mathematics in the 19th C. beganreaching new heights of sophistication, worries were increasinglyraised about its foundations. It was specifically in response to theselatter worries that Gottlob Frege (1884 [1980]) tried to improve uponKant’s formulations of the analytic, and presented what iswidely regarded as the next significant discussion of the topic.^[3]

1.2 Frege

Frege (1884 [1980], §§5,88) and others noted a number ofproblems with Kant’s “containment” metaphor. In thefirst place, as Kant (1787 [1998], B756) himself would surely haveagreed, the criterion would need to be freed of“psychologistic” suggestions, or claims about merely theaccidental thought processes of thinkers, as opposed to claims abouttruth and justification that are presumably at issue with theanalytic. In particular, mere associations are not always matters ofmeaning: many people in thinking about Columbus may automaticallythink “the discoverer of America,” or in thinking aboutthe number 7 they “can’t help but also think” aboutthe numeral that denotes it, but it’s certainly not analyticthat Columbus discovered America, or that a number is identical with anumeral. Moreover, while it may be arguably analytic that a circle isa closed figure of constant curvature (see Katz, 1972), someone couldfail to notice this and so think the one without the other.

Even were Kant to have solved this problem, it isn’t clear howhis notion of “containment” would cover cases that seem tobe as “analytic” as any of set II, such as:

IV.

(11)

Anyone who’s an ancestor of an ancestor of Bob is anancestor of Bob.

(12)

If Bob is married to Sue, then Sue is married toBob.

(13)

If something is red, then it’s colored.

The transitivity ofancestor or the symmetry ofmarried are not obviously “contained in” thecorresponding thoughts in the way that the idea ofextensionis plausibly “contained in” the notion ofbody,ormale in the notion ofbachelor. (13) has seemedparticularly troublesome: what else besidescolored could beincluded in the analysis? The conceptred involves color– and what else? It is hard to see what else to“add” – exceptred itself!

Frege attempted to remedy the situation by completely rethinking thefoundations of logic, developing what we now think of as modernsymbolic logic. He defined a perfectly precise “formal”language, i.e., a language characterized by the “form”– standardly, the shape—of its expressions, and hecarefully set out an account of the syntax and semantics of what arecalled the “logical constants,” such as “and,”“or,” “not,” “all” and“some,” showing how to capture a very wide class of validinferences containing them. Saying precisely how the constants aredetermined is a matter of controversy (seeLogicalConstants), but, at least roughly and intuitively, they can bethought of as those parts of language that don’t“point” or “function referentially,” aiming torefer to something in the world, in the way that ordinary nouns,verbs, adjectives, adverbs and prepositions seem to do.“Socrates” refers to Socrates, “dogs” to dogs,“(is) clever” to cleverness and/or clever things, butwords like “or” and “all” don’t seem tofunction referentially at all. At any rate, it certainly isn’tclear that there are anyors andalls in the world,along with Socrates, the dogs, and sets or properties of them.

This distinction between non-logical, “referring”expressions and logical constants allows us to define a logical truthin a way that has become common (and will be particularly useful inthis entry) asa sentence that is true no matter what non-logicalexpressions occur in it (cf. Tarski, 1936 [1983], Quine, 1956[1976], Davidson 1980). Consequently (placing non-logical expressionsin bold, and re-numbering prior examples):

(14)

Alldoctors thatspecialize onchildren aredoctors.

counts as a (strict) logical truth: no matter what grammaticalexpressions we put in for the non-logical terms “doctor”,“specialize on” and “children” in (14), thesentence will remain true. For example, substituting“cats” for “doctors”, “chase” for“specialize on” and “mice” for“children,” we get:

(15)

All cats that chase mice are cats.

(Throughout this discussion, by “substitution” we shallmean uniform substitution of one presumably univocal expression foranother in all its occurrences in a sentence.) But what about theothers of set II? Substituting “cats” for“doctors” and “mice” for“pediatricians” in

(16)

All pediatricians are doctors.

we get:

(17)

All mice are cats.

which is obviously false, as would many such substitutions render therest of the examples of II. (14) and (15) are patent logical truths;their truth depends only upon the semantic values of their logicalparticles. ButAll pediatricians are doctors and the otherexamples, (6)–(8) and (11)–(13), are notformallogical truths, specifiable by the logicalform of thesentence (or its pattern of logical particles) alone; nor are theirdenials, e.g., (9) and (10),formal contradictions (i.e., oftheform, where ‘p’ stands in for anysentence: “p and it isnot the case thatp”). How are we to capture them?

Here Frege appealed to the notion of “definition,” or—presuming that definitions preserve“meaning”— “synonymy”: the non-logicalanalytic truths are those that can be converted to formal logicaltruths by substitution of definitions for defined terms, or synonymsfor synonyms. Since “mice” is not synonymous with“pediatrician,” (17) is not a substitution into (16) ofthe required sort. We need, instead, a substitution ofthedefinition of “pediatrician,” i.e., “doctorthat specializes on children,” which would convert (16) into ourearlier purely formal logical truth:

(14)

All doctors that specialize on children are doctors.

Of course, these notions ofdefinition, meaning andsynonymy would themselves need to be clarified, But they werethought at the time to be sufficiently obvious notions whoseclarification didn’t seem particularly urgent until W.V.O. Quine(1953 [1980a]) raised serious questions about them much later (see§3.3ff below). Putting those questions to one side, Frege madespectacularly interesting suggestions, offering a famous definition,for example, of the “ancestral” relation involved in (11)as a basis for his definition ofnumber (seeFrege’s Theorem and Foundations for Arithmetic), andinspiring the program of “logicism” (or the reduction ofarithmetic to logic) that was pursued in Whitehead and Russell’s(1910–13) monumentalPrincipia Mathematica, and the(early) Ludwig Wittgenstein’s (1922)TractatusLogico-philosophicus.

Frege was mostly interested in formalizing arithmetic, and soconsidered the logical forms of a relative minority of naturallanguage sentences in a deliberately spare notation – hedidn’t take on the likes of (12)-(13). But work on the logical(or syntactic) structure of the full range of sentences of naturallanguage has blossomed since then, initially in the work of BertrandRussell (1905), in his famous theory of definite descriptions (seeDescriptions), which he (1912) combined with his views aboutthe knowledge by “acquaintance” with sense-data anduniversals into a striking “fundamental principle in theanalysis of propositions containing descriptions”:

Every proposition which we can understand must be composed wholly ofconstituents with which we are acquainted (1912:58),

an early version of a proposal pursued by Logical Positivists, to bediscussed in the next sections below. Frege’s andRussell’s formalizations are also indirectly the inspiration forthe subsequent work of Noam Chomsky and other “generative”linguists and logicians (seesupplement). WhetherFrege’s criterion of analyticity will work for the rest of IIand other analyticities depends upon the details of these latterproposals, some of which are discussed in thesupplement,

2. High Hopes

Influenced by these developments in logic, many philosophers in thefirst half of the Twentieth Century thought analyticity could performcrucial epistemological work not only in accounting for our apparentlya priori knowledge of mathematics, but also —with alittle help from British empiricism—of our understanding ofclaims about the spatiotemporal world as well. Indeed,“analysis” and the “linguistic turn” (Rorty,1992) soon came to constitute the very way many Anglophonephilosophers characterized their work, particularly since suchanalyses of what we mean by our words seemed to be the sort ofenterprise available to “armchair reflection” that seemedto many a distinctive feature of that work (see Haug, 2014). Manythought this project would also perform the moremetaphysicalwork of explaining thetruth andnecessity ofmathematics, showing not only how it is we couldknow aboutthese topics independently of experience, but how they could betrue in this and in all possible worlds, usually, though,without distinguishing this project from the epistemic one. Thus,Gilbert Harman (1967 [1999] begins his review of the topic combiningthe two projects:

What I shall call a ‘full-blooded theory of analytictruth’ takes the analytic truths to be those that hold solely byvirtue of meaning or that are knowable solely by virtue of meaning.(p. 119, see also p. 127),

taking himself to be expressing the views of a number of other thencontemporary philosophers.

This seemed like a grand unified plan until Saul Kripke (1972) andHilary Putnam (1975) drew attention to fundamental differences betweenthe metaphysical and epistemic modalities that had tended to be runtogether throughout this period. They pointed out that, for example,“water is H2O” might well benecessarily true,but not knowablea priori, and “The meter stick inParis is one meter long” might be knowablea priori butnot be necessarily true (that very stick might have been broken andnever used for measurements; seeA Priori Justification andKnowledge).

Once the metaphysical and epistemic issues are separated, it becomesless obvious that mere matters of meaning could really explain allnecessities. Recall that Frege’s ambition had been toreduce mathematics to logic by showing how, substituting synonyms forsynonyms, every mathematical truth could be shown to be a logical one.He hadn’t gone on to claim that the logical truthsthemselves were true or necessary by virtue of meaning alone.These were “Laws of Truth” (Frege, 1918/84:58), and itwasn’t clear what sort of explanation could be provided forthem. Obviously, appealing merely to further synonym substitutionswouldn’t suffice. As Michael Devitt (1993a) pointed out:

the sentence ‘All bachelors are unmarried’ is not truesolely in virtue of meaning and so is not analytic in the…sense[of true in virtue of meaning alone]. The sentence is indeed truepartly in virtue of the fact that ‘unmarried’ must referto anything that ‘bachelor’ refers to but it is also truepartly in virtue of the truth of ‘All unmarrieds areunmarried.’ (Devitt 1993a, p. 287; cf., Quine 1956 [1976], p.118)

It was certainly not clear that the truth of “All unmarrieds areunmarrieds” is based on the same sort of arbitrary synonymyfacts that underlie “All bachelors are unmarried.” In anyevent, a different kind of account seemed to be needed (seefootnotes 9 and 16).

Jerrold Katz and Paul Postal (1991, pp. 516–7) did claim thatadequate linguistic theory should,inter alia, explain why,ifJohn killed Bill is true, then so isBill isdead. However, as David Israel (1991) pointed out in reply:“there are facts about English, about what propositions areexpressed by certain utterances, and then there is a non-linguisticfact: that one proposition entails another” (p. 571). Utterancesofsentencesare one thing; thepropositions (orthoughts) many different sentences mayexpress,quite another, and the two shouldn’t be confused:

It is just not true that if theproposition expressed by [anutterance ofJohn killed Bill] is true that, then “invirtue of [natural language] so, necessarily, is” theproposition expressed by [an utterance ofBill isdead]. Rather, if the proposition that, according to the grammarof English, is expressed by [an utterance ofJohn killedBill] is true, then, in virtue of the structure of thepropositions concerned, theproposition that,according to the grammar of English, is expressed by [an utterance ofBill is dead] must also be true.--(D. Israel, 1991, p. 71,emphasis added)

Providing the metaphysical basis for logical truth is a fine issue(seeLogical Truth), but as Devitt (1993a and b) and others(e.g., Paul Boghossian, 1996, Williamson, 2007) went on to stress, ithas been the epistemological issues about justifying ourbeliefs in necessary truths that have dominated philosophicaldiscussions of the analytic in the last seventy years.^[4] Consequently, we will focus primarily on this more modest,epistemological project in the remainder of this entry.

2.1 Mathematics

As we noted (§1.2), Frege had developed formal logic to accountfor our apparentlya priori knowledge of mathematics. It isworth dwelling on the interest of this problem. It is arguably one ofthe oldest and hardest problems in Western philosophy, and is easyenough to understand: ordinarily we acquire knowledge about the worldby using our senses. If we are interested, for example, in whetherit’s raining outside, how many birds are on the beach, whetherfish sleep or stars collapse, we look and see, or turn to others whodo. It is a widespread view that Western sciences owe their tremendoussuccesses precisely to relying on just such “empirical”(experiential, experimental) methods. However, it is also a patentfact about all these sciences, and even our ordinary ways of countingbirds, fish and stars, that they depend on often immenselysophisticated mathematics, and mathematics does not seem to be knownon the basis of experience. Mathematicians don’t do experimentsin the way that chemists, biologists or other “naturalscientists” do. They seem simply tothink, seeming torely precisely on the kind of “armchair reflection” towhich many philosophers also aspire. In any case, they don’t tryto justify their claims by reference to experiments, arguing thattwice two is four by noting that pairs of pairs tend in all casesobserved so far to be quadruples.

But how could mere processes of thought issue in any knowledge aboutthe independently existing external world? The belief that it couldwould seem to involve some kind of mysticism; and, indeed, many“naturalistic” philosophers have felt that the appeals of“Rationalist” philosophers to some special faculty of“rational intuition,” such as one finds in philosopherslike Plato, Descartes and Leibniz and, more recently, Katz (1988,1990), George Bealer (1987) and Laurence Bonjour (1998), these allseem no better off than appeals to “revelation” toestablish theology. The program of logicism and “analysis”seemed to many to offer a more promising, “naturalistic”alternative.

2.2 Science and Beyond

But why stop at arithmetic? If logical analysis could illuminate thefoundations of mathematics by showing how the axioms of arithmeticcould all be derived from pure logic by substitution of synonyms,perhaps it could also illuminate the foundations of the rest of ourknowledge by showing how its claims could similarly be derived fromsome kind of combination of logic and experience. Such was the hopeand program of Logical Positivism (seeLogical Empiricism)championed by, e.g., Moritz Schlick, A.J. Ayer and, especially, RudolfCarnap from about 1915 in Vienna and Berlin to well into the 1950s inEngland and America. Of course, such a proposal did presume that allof our concepts were somehow “derived” either from logicor experience, but this seemed in keeping with the then prevailingpresumptions of empiricism, which, they assumed, had been vindicatedby the immense success of the empirical sciences.

For the Positivists, earlier empiricists, such as Locke, Berkeley andHume, had erred only in thinking that the mechanism of constructionwas mere association. But association can’t account for thestructure of even a simple judgment, such asCaesar is bald.This is not merely the excitation of its constituent ideas,Caesar,is, andbald, along the lines ofthe idea ofsalt exciting the idea ofpepper, but,as Frege had shown, involves combining the nounCaesar andthe predicateis bald in a very particular way, a fact thatwas important in accounting for more complex judgments such asCaesar is bald or not bald, orSomeone is bald. Ourthoughts and claims about the world have some kind oflogicalstructure, of a sort that seems to begin to be revealed byFrege’s proposals. Equipped with his logic, it was possible toprovide a more plausible formulation of conceptual empiricism: ourclaims about the empirical world were to beanalyzed into the(dis)confirming experiences out of which they must somehow have beenlogically constructed.

But constructed out ofwhich experiences? For thePositivists, the answer seemed obvious: out of the experientialtests that would standardlyjustify,verifyorconfirm the claim. Indeed, as Ayer (1934, chap 1) madeplain, a significant motivation for the Positivists was to saveempirical knowledge from the predations of traditional scepticalarguments about the possibility that all of life is a dream or thedeception of an evil demon: if meaning could be tied to verification,such possibilities could be rendered “meaningless” becauseunverifiable (see Jerry Fodor, 2001, pp. 3–5, for a penetratingdiscussion of this motivation). In any event, interpretingWittgenstein’s (1922)Tractatus claims about the natureof language epistemologically along the lines of the Americanphilosopher, C.S. Peirce, they proposed various versions of their“Verifiability Theory of Meaning,” according to which themeaning (or what they called the “cognitive significance”)of any sentence wasconstituted by the conditions of itsempirical (dis-)confirmation.^[5] Thus, to say that the temperature of a liquid is of a certainmagnitude is to say, for example, that the mercury in a thermometerimmersed in the liquid would expand to a certain point marked by anumeral representing that magnitude, a claim that would ordinarily bedisconfirmed if it didn’t. Closer to “experience”:to say that there is a cat on a mat is just to say that certainpatterns of certain familiar visual, tactile and aural appearances areto be expected under certain circumstances.

The project of providing analyses in this way of especiallyproblematic concepts like those concerning, for example,materialobjects, knowledge, perception, causation, expectation, freedom,andthe self, was pursued by Positivists and other analyticphilosophers for a considerable period (see Carnap 1928 [1967] forsome rigorous examples, Ayer 1934 [1952] for more accessible ones).With regard to material object claims, the program came to be known as“phenomenalism”; with regard to the theoretical claims ofscience, as “operationalism” ; and with regard to theclaims about people’s mental lives, “analyticalbehaviorism” (the relevant experiential basis of mental claimsbeing taken to be observations of others’ behavior). Althoughthese programs became extremely influential, and some form of theverifiability criterion was often (and sometimes still is) invoked inphysics and psychology to constrain theoretical speculation, theyseldom, if ever, met with any serious success. No sooner was ananalysis, say, of “material object” or“freedom” or “expectation,” proposed thanserious counterexamples were raised and the analysis revised, only tobe faced with still further counterexamples (see Roderick Chisholm1957, and Fodor 1981, for discussion). Despite what seemed its initialplausibility, philosophers came to suspect that the criterion, andwith it the very notion of analyticity itself, rested on somefundamental mistakes.

3. Problems with the Distinction

3.1 The Paradox of Analysis

One problem with the entire program was raised by C.H. Langford (1942)and discussed by G.E. Moore (1942 [1968], pp. 665–6): why shouldanalyses be of any conceivable interest? After all, if an analysisconsists in providing the definition of an expression, then it shouldbe providing a synonym for it, and this, then, should be whollyuninformative: ifbrother is analyzed as the presumablysynonymousmale sibling, then the claimBrothers are malesiblings should be synonymous withBrothers arebrothers, and thinking the one should be no different fromthinking the other. But, aside from such simple cases asbrother andbachelor, proposed analyses, ifsuccessful, often seemed quite non-obvious and philosophicallyinformative. The proposed reductions of, say, material objectstatements to sensory ones (even where successful) were often fairlycomplex, had to be studied and learned, and so could hardly beuninformative. So how could they count as seriously analytic?^[6]

This is “the paradox of analysis,” which can be seen asdormant in Frege’s own move from his (1884) focus on definitionsto his more controversial (1892a) doctrine of “sense,”where two senses are distinct if and only if someone can think athought containing the one but not other, as in the case of the sensesof “the morning star” and “the evening star.”If analyses or definitions preserved sense, then, unlike the case of“morning star” and “evening star,” wheneverone thought the definiendum, one should thereby be thinking thedefiniens. And perhaps one can’t think Bill is Bob’sbrother without thinking Bill is Bob’s male sibling. But few ofFrege’s definitions of arithmetic concepts are nearly so simple(seeGottlob Frege, §2.5). In their case, it seemsperfectly possible to think the definiendum, say,number,without thinking the elaborate definiens Frege provided (cf. Bealer1982, Michael Dummett 1991, and John Horty 1993, 2007, for extensivediscussions of this problem, as well as of further conditions, e.g.,fecundity, that Frege placed on serious definitions).

These problems, so far, can be regarded as relatively technical, forwhich further technical moves within the program might be made. Forexample, one might make further distinctions within the theory ofsense between an expression’s “content” and thespecific “linguistic vehicle” used for its expression, asin Fodor (1990a) and Horty (1993, 2007); and perhaps distinguishbetween the truth-conditional “content” of an expressionand its idiosyncratic role, or “character,” in a languagesystem, along the lines of the distinction David Kaplan (1989)introduced to deal with indexical and demonstrative expressions (suchasI,now, andthat; seeDemonstratives, andNarrow Mental Content, as wellas Stephen White, 1982). Perhaps analyses could be regarded asproviding a particular “vehicle,” having a specific“character,” that could account for why one couldentertain a certain concept without entertaining its analysis (cf.Gillian Russell 2008, and Paul Pietroski 2002, 2005 and 2018 forrelated suggestions).

However, the problems with the program seemed to many philosophers tobe deeper than merely technical. By far, the most telling andinfluential of the criticisms both of the program, and then ofanalyticity in general, were those of Quine, who began as a greatchampion of the program (see esp. his 1934), and whose subsequentobjections therefore carry special weight. The reader is well-advisedto consult particularly his (1956 [1976], hereafter “CLT”)for as rich and deep a discussion of the issues up to that time as onemight find. The next two sections abbreviate some of thatdiscussion.

3.2 Problems with Logicism

Although pursuit of the logicist program produced a great manyinsights into the nature of mathematics, there emerged a number ofserious difficulties with it. Right from the start there was, ofcourse, the problem of the logical truths themselves. Simply saying,as Frege had, that they are “Laws of Truth” doesn’tseem to explain how we could know thema priori. But perhapsthey, too, are “analytic” involving perhaps some sort of“implicit” acceptance of certain rules merely by virtue ofaccepting certain patterns of reasoning. But any such proposal has toaccount for people’s frequent, often apparent violations ofrules of logic in fallacious reasoning and in ordinary speech, as wellas of disputes about the laws of logic of the sort that are raised,for example, by mathematical intuitionists, who deny the Law ofExcluded Middle (“p or not p”), or, more recently, by“para-consistent” logicians, who argue for the tolerationeven of contradictions to avoid certain paradoxes.^[7] Moreover, given that the infinitude of logical truths needs to be“generated” by rules of inference, wouldn’t that bea reason for regarding them as “synthetic” in Kant’ssense (see Frege 1884 [1980], §88, Katz 1988, pp. 58–9, andMacFarlane 2002)?

Much more worrisome is a challenge raised by Quine (CLT, §II):even if certain logical truths seemed undeniable, how does claimingthem to be analytic differ from claiming them to be simply “obvious”?^[8]

Consider…the logical truth “Everything isself-identical”, “(x)(x = x)”. We can say that itdepends for its truth on traits of the language (specifically on theusage of “=”), and not on traits of its subject matter;but we can also say, alternatively, that it depends on an obvioustrait, viz., self-identity, of its subject matter, viz., everything.The tendency of [my] present reflections is that there is nodifference. (CLT, p. 113)

Pressing the point more deeply:

I have been using the vaguely psychological word “obvious”non-technically, assigning it no explanatory value. My suggestion ismerely that the linguistic doctrine of elementary logical truthlikewise leaves explanation unbegun. I do not suggest that thelinguistic doctrine is false and some doctrine of ultimate andinexplicable insight into the obvious trait of reality is true, butonly that there is no real difference between these twopseudo-doctrines. (CLT, p. 113)

As we’ll see, this is the seed for the challenge that continuesto haunt proposals about the analytic to this day: what explanatorydifference is there between “analytic” claims and simplywidely and firmly held beliefs, such as thatThe earth has existedfor many years orThere have been black dogs?We’ll consider some proposals —and their problems—in due course, but it’s important to bear in mind that, if nodifference can be sustained, then it’s difficult to see thesignificance of the logicist program or of the claims of (strictly)“analytic” philosophy generally.

The most immediately calamitous challenge to Logicism was, however,the famous paradox Russell raised for one of Frege’s crucialaxioms, hisprima facie plausible “Basic Law V”(sometimes called “the unrestricted Comprehension Axiom”),which had committed him to the existence of a set for every predicate.But what, asked Russell, of the predicatex is not a member ofitself? If there were a set for that predicate, that set itselfwould be a member of itself if and only if it wasn’t;consequently, there could be no such set. Therefore Frege’sBasic Law V couldn’t be true (but seeFrege’s Theoremand Foundations for Arithmetic for ways to rescue something closeto logicism, discussed in §5 below).

What was especially upsetting about Russell’s paradox was thatthere seemed to be no intuitively satisfactory way to repair settheory in a way that could lay claim to being as obvious and/or merelya matter of logic or meaning in the way that Frege and the Positivistshad hoped. Various proposals were made, but all of them seemed simplytailor-made to avoid the paradox, and seemed to have littleindependent appeal (although see Boolos, 1971, for a defense of the“iterative” notion of set). Certainly none of themappeared to be analytic. Indeed, as Quine notes:

What we do [in set theory] is develop one or another set theory byobvious reasoning, or elementary logic, from unobvious firstprinciples which are set down, whether for good or for the time being,by something like convention. (CLT, p. 111)

3.3 Convention?

Convention, indeed, would seem to be at the very heart of theanalytic. After all, aren’t matters of meaning, unlike mattersof fact, in the end really matters of arbitrary conventions about theuse of words? For example, someone could invest a particular word,say, “schmuncle,” with a specific meaning merely bystipulating that it mean, say, unmarried uncle. Wouldn’t thatafford a basis for claiming then that “A schmuncle is anuncle” is analytic, or knowable to be true by virtue of the(stipulated) meanings of the words alone?

Carnap (1956a) proposed setting out the “meaningpostulates” of a scientific language as just such conventionalstipulations. This had the further advantage of allowing terms to be“implicitly defined” by their conventional roles in suchpostulates, which might then serve as part of a theory’s laws oraxioms. The strategy seemed especially appropriate for defininglogical constants, as well as for dealing with cases like (11)-(13)above, e.g. “Red is a color,” where mere substitution ofsynonyms might not suffice.^[9] So perhaps what philosophical analysis is doing is revealing thetacit conventions of ordinary language, an approach particularlyfavored by Ayer (1934/52).

Quine is sceptical such a strategy could work for the principles oflogic itself. Drawing on his earlier discussion (1936 [1976]) of theconventionality of logic, he argues that logic itself could not beentirely established by such conventions, since:

the logical truths, being infinite in number, must be given by generalconventions rather than singly; and logic is needed then in themeta-theory, in order to apply the general conventions to individualcases (CLT, p. 115)

If so, and if logic is established by convention, then one would needameta-meta-theory to establish the conventions for the useof the logical particles of the meta-theory, and so on for what seemedlike an infinite regress of meta-theories. This is certainly anargument that ought to give the proponents of the conventionality oflogic pause: for, indeed, how could one hope to set out the generalconventions for “all” or“if…then…” without at some point using thenotions of “all” and “if…then…”(“ALL instances of a universal quantification are to betrue”. “IFp is one premise, andif p thenq another, THEN concludeq”)? (See Warren, 2017,however, for a reply, exploiting the resources of implicit definition;cf. fns 9 and 16.)

As we noted, Quine sees more room for convention in choosing betweendifferent, incompatible versions of set theory needed for mathematicsthat were developed in the wake of Russell’s paradox. Here:

We find ourselves making deliberate choices and setting them forthunaccompanied by any attempt at justification other than in terms ofelegance and convenience. (CLT, p. 117).

But then it’s hard to see the difference between mathematics andthe conventional “meaning postulates” Carnap had proposedfor establishing the rest of science —and then the differencebetween them and any other claims of a theory. As Quine goes on toargue, although stipulative definitions (what he calls“legislative postulations”)

contribute truths which become integral to the corpus of truths, theartificiality of their origin does not linger as a localized quality,but suffuses the corpus. If a subsequent expositor singles out thoseonce legislatively postulated truths again as postulates, thissignifies nothing… He could as well choose his postulates fromelsewhere in the corpus, and will if he thinks it this serves hisexpository ends. (CLT, pp. 119–20)

Carnap’s legislated “meaning postulates” shouldtherefore be regarded as just an arbitrary selection of sentences atheory presents as true, a selection perhaps useful for purposes ofexposition, but no more significant than the selection of certaintowns in Ohio as “starting points” for a journey Quine(1953 [1980a], p. 35).

Quine’s observation certainly seems to accord with scientificpractice. Suppose, say, Newton, himself, had explicitly set out“F=ma” as a stipulated definition of “F”:would “F=ma” be therefore justifiable by knowing themeaning the words alone? Our taking such a stipulation seriously wouldseem to depend upon our view of the plausibility of the surroundingtheory as a whole. After all, as Quine continues:

[S]urely the justification of any theoretical hypothesis can, at thetime of hypothesis, consist in no more than the elegance andconvenience which the hypothesis brings to the containing bodies oflaws and data. How then are we to delimit the category of legislativepostulation, short of including under it every new act of scientifichypothesis? (CLT, p. 121)

So conventional legislation of claims, such as Carnap’s meaningpostulates, affords the claims no special status. As vivid examples,Putnam (1965 [1975]) discusses in detail revisions of the definitionsof “straight line” and “kinetic energy” in thelight of Einstein’s theories of relativity.^[10]

This appeal to “the containing bodies of laws and data”essentially invokes Quine’s famous holistic metaphor of the“web of belief” with which CLT eloquently concludes:

the lore of our fathers is a fabric of sentences [which] develops andchanges, through more or less arbitrary and deliberate revisions andadditions of our own, more or less directly occasioned by thecontinuing stimulation of our sense organs. It is a pale grey lore,black with fact and white with convention. But I have found nosubstantial reasons for concluding that there are any quite blackthreads in it, or any white ones (CLT, p. 132)^[11]

3.4 Verification and Confirmation Holism

The picture presented in this last and many similar passages expressesa tremendously influential view of Quine’s that led severalgenerations of philosophers to despair not only of theanalytic-synthetic distinction, but of the category ofapriori knowledge entirely. The view has come to be called“confirmation holism,” and Quine had expressed it moreshortly a few years earlier, in his widely read article, “TwoDogmas of Empiricism” (1953 [1980a]):

Our statements about the external world face the tribunal of senseexperience not individually, but only as a corporate body. (1953[1980a], p. 41)

Indeed, the “two dogmas” that the article discusses are(i) the belief in the intelligibility of the “analytic”itself, and (ii), what Quine regards as the flip side of the samecoin, the belief that “each statement, taken in isolation fromits fellows, can admit of confirmation or infirmation at all”(p. 41), i.e., the very version of the Verifiability Theory of Meaningwe have seen the Positivists enlisted in their effort to“analyze” the claims of science and commonsense.^[12]

Quine bases his “confirmation holism” upon observations ofPierre Duhem (1914 [1954]), who drew attention to the myriad ways inwhich theories are supported by evidence, and the fact that anhypothesis is not (dis)confirmed merely by some specific experimentconsidered in isolation from an immense amount of surrounding theory.Thus, a thermometer will be a good indication of ambient temperatureonly if it’s made of the right materials, calibratedappropriately, and there aren’t any other forces at work thatmight disturb the measurement—and, of course, only if thebackground laws of physics and other beliefs that have informed thedesign of the measurement are sufficiently correct. A failure of thethermometer to measure the temperature could be due to a failure ofany of these other conditions, which is, of course, why experimentersspend so much time and money constructing experiments to“control” for them. Moreover, with a small change in ourtheories or background beliefs, or just in our understanding of theconditions for measurement, we might change the tests on which werely, but often without changing the meaning of the sentences whosetruth we might be trying to establish (which, as Putnam 1965 [1975]pointed out, is precisely what practicing scientists regularlydo).

What is novel—and highly controversial—about Quine’sunderstanding of these commonplace observations is his extension ofthem to claims presumed by most people (e.g., by Duhem himself) to lieoutside their scope, viz., the whole of mathematics and even logic! Itis this extension that seems to undermine the traditionalapriori status of these latter domains, since it appears to openthe possibility of a revision of logic, mathematics and any supposedanalytic claims in the interest of the plausibility of the one,overall resulting empirical theory—containing the empiricalclaimsand those of logic, mathematics and the analytic!Perhaps this wouldn’t be so odd should the revisability of suchclaims permit their ultimately admitting of a justification thatdidn’t involve experience. But this is ruled out byQuine’s insistence that scientific theories, along with theirlogic and mathematics, are confirmed “only” as“corporate bodies.”^[13]

One might wonder why, though, there have historically been virtuallyno revisions of mathematics on empirical grounds. A common exampleoffered is how Riemannian replaced Euclidean geometry inEinstein’s theory of General Relativity. But this mis-interpretsthe history. Non-Euclidean geometries were purely conceptualdevelopments in the 19th C. by mathematicians such as Gauss, Riemannand Lobechevsky. Einstein simply argued in 1916 that one of theseconceptual possibilities seemed to be better supported by physics thanwas the traditional Euclidean one, and should therefore be taken to betrue of actual space(-time). It is only this latter claim that isempirical.

Certainly, though, Quine’s holism has been an epistemicpossibility that many have taken seriously. For example, influenced byQuine’s claim, Putnam (1968 [1975]) argued that one ought torevise even elementary logic in view of the surprising results ofquantum mechanics (a proposal not without its critics, seeQuantumLogic and Probability Theory). And in his (1962 [1975] he alsoargued that it isn’t hard to imagine discovering that apurported analytic truth, such asCats are animals, could begiven up in light of discovering that the little things are reallycleverly disguised robots controlled from Mars (but see Katz, 1990,pp. 216ff and G. Russell, 2008, for replies, and thesupplement §3 for further discussion).

3.5 Quine on Meaning in Linguistics

Quine’s discussion of the role of convention in science seemsright; but how about the role of meaning in ordinary natural language(cf. Chomsky’s 2000 cautions mentioned infootnote 10)? Is it really true that in the “pale grey lore” of all thesentences we accept, there aren’t some that are“white” somehow “by virtue of the very meanings oftheir words”? What about our examples in our earlier set II?What about sentences of the sort that interest Juhl and Loomis (2010)that merely link patent synonyms, as in “Lawyers areattorneys,” or “A fortnight is a period of fourteendays”? As Grice and Strawson (1956) and Putnam (1965 [1975])pointed out, it is unlikely that so intuitively plausible adistinction should turn out to haveno basis at all infact.

Quine addressed this issue, first, in his (1953 [1980a], chapter 3),and then in a much larger way in his (1960, chapter 2, and 1974) andrelated articles. In his (1953 [1980a]) he pressed his objection toanalyticity further to the very ideas of synonymy and the linguisticmeaning of an expression, on which, we saw, Frege’s criterion ofanalyticity crucially relied. His objection is that he sees no way tomake any serious explanatory sense of them. He explored plausibleexplanations in terms of “definition,”“intension,” “possibility,” and“contradiction,”, pointing out that each of these notionsseems to stand in precisely as much need of explanation as synonymyitself (recall our observation in §1.2 above regarding the lackof anyformal contradiction in “Some pediatricansaren’t doctors”). The terms seem to be mutually definablein what seems to be a—viciously?—small “closed curvein space” (Quine 1953 [1980a], p. 30). Though they might beinvoked to explain one another, they could not in the end answer thechallenge of how to distinguish an analytic claim from simply atenaciously held belief.

To take a recent example, David Chalmers (2012) revisitsCarnap’s (1956b) proposal for basing synonymy on“intension” by way of eliciting a person’s judgmentsabout the extension of a term/concept in all possible worlds:^[14]

Carnap’s key idea is that we can investigate the intension thata subject associated with an expression by investigating thesubject’s judgments about possible cases. To determine theintension of an expression such as ‘Pferd’ for a subject,we present the subject with descriptions of various logically possiblecases, and we ask the subject whether he or she is willing to applythe term ‘Pferd’ to objects specified in these cases. Ifwe do this for enough cases, then we can test all sorts of hypothesesabout the intension of the expression. (Chalmers 2012, p. 204)

But how are the informants to understand the questions they’rebeing asked? If they understand the term “possible” aslogicians do, astruth in a set-theoretically specifiedmodel, then it will be too weak: there are obviously models inwhich synonymous expressions e.g., “horse” and“Pferd,” or “bachelor” and “unmarriedmale” are assigned non-overlapping sets (cf. Quine[1953 [1980a], pp. 22–3), so that it’s logically possiblefor there be a horse that’s not a Pferd, or a bachelorthat’s married (again, “a married bachelor” isformally contradictory only if one substitutes synonyms for synonyms;but we certainly can’t appeal tosynonymy in trying todefine synonymy). But if “possible” is understood(as it ordinarily would be) as merelyimaginable, then itwill be far too strong, ruling out ideas that the scientificallyunder-informed might find impossible, e.g., curved space-time,something having the properties of both waves and particles, orcompletely unconscious thoughts (which, at least, e.g., John Searle1992, pp. 155–6, and Galen Strawson 1994, pp. 166–7 reporthaving trouble conceiving). As Quine (1953 [1980a]) famously argued,such appeals to informant verdicts will only work if the informantsunderstand the questions as aboutthe very terms the proposed testis supposed to define, viz., “possible” asconstrained by synonymy or preservation of meaning. Although, as manyhave noted (e.g., Williamson 2007, p. 50), there may be explanatorycircularities in the best of theories, the circularity here seemsparticularly vicious, with the relevant ideas appearing not to performany explanatory work other than bringing in each other’slaundry.

Why was Quine so convinced of this last claim? Because he thought itwas possible to provide a satisfactory explanation of human languagewithout them, indeed, without any mentalistic notions at all. In his(1953 [1980b], 1960 [2013] and 1974) he sketched a behavioristictheory of language that doesn’t rely on the postulation ofdeterminate meaning or reference, and argued that, indeed, translationis “indeterminate”: there is “no fact of thematter” about whether two expressions do or do not have the samemeaning (seeIndeterminacy of Translation). This would appearto imply that there are pretty much no facts of the matter aboutpeople’s mental lives at all! For, if there is no fact of thematter about whether two people mean the same thing by their words,then there is no fact of the matter about the content ofanyone’s thoughts. Quine himself took this consequence instride—he was, after all, a behaviorist– regarding it as“of a piece” with Franz Brentano’s (1874 [1995])famous thesis of the “irreducibility of the intentional”;it’s just that for him, unlike for Brentano, it simply showedthe “baselessness of intentional idioms and the emptiness of ascience of intention” (1960 [2013], p. 202). Needless to say,many subsequent philosophers have not been happy with this view, andhave wondered where Quine’s argument went wrong.

3.6 Explaining Away the Appearance of the Analytic

One problem many have had with Quine’s argument is about how toexplainthe appearance of the analytic. It just seems anempirical fact that most people would spontaneously distinguish ouroriginal two sets of sentences (§1) by saying that sentences ofthe second set, such as “All pediatricians are doctors forchildren” are “true by definition,” or could beknown to be true just by knowing the meanings of the constituentwords. Moreover, they might agree about an indefinite number offurther examples, e.g., that ophthalmologists are eye doctors,grandfathers are parents of parents, sauntering a kind of movement,pain and beliefs mental states, and promising an intentional act.Again, as Grice and Strawson (1956) and Putnam (1965 [1975]) stressed,it’s implausible to suppose that there’snothingpeople are getting at in these judgments.

3.6.1 Centrality

Quine’s (1953 [1980a]) initial explanation of the appearance ofthe analytic invoked his metaphor of the web of belief, claiming thatsentences are more or less revisable, depending upon how“peripheral” or “central” their position is inthe web, the more peripheral ones being closer to experience. Theappearance of sentences being “analytic” is simply due totheir being, like the laws of logic and mathematics, comparativelycentral, and so are given up, if ever, only under extreme pressurefrom the peripheral forces of experience. But no sentence isabsolutely immune from revision; all sentences are thereby empirical,and none is actually analytic.

There are a number of problems with this explanation. In the firstplace, centrality and the appearance of analyticity don’t seemto be so closely related. As Quine (1960, p. 66) himself noted, thereare are plenty of central, unrevisable beliefs that don’t seemremotely analytic, e.g., “There have been black dogs,”“The earth has existed for more than five minutes,”“Mass-energy is conserved”; and many standard examples ofwhat seem analytic aren’t seriously central: “Bachelorsare unmarried,” “A fortnight is two weeks” or“A beard is facial hair” are pretty trivial verbal issues,and could easily be revised if people really cared (cf., Juhl andLoomis, 2010, p. 118).

Secondly, it’s not mere unrevisability that seems distinctive ofthe analytic, but rathera certain sort of unintelligibility:for all the unrevisability of “There have been blackdogs,” it’s perfectly possible toimagine it tobe false. In contrast, what’s peculiar about analytic claims isthat their denials often seem peculiarly impossible to seriouslythink: it seems distinctively impossible to imagine a marriedbachelor. Now, of course, as we noted, this could be due simply to afailure of imagination. But what’s striking about about theunrevisability of many apparently analytic cases is that theydon’t appear to be like scientifically controversial cases suchas curved space-time or completely unconscious thoughts. The standardcases about, e.g., bachelors or pediatricians seem entirely innocuous.Far from unrevisability explaining analyticity,it would seem tobe analyticity that explains this peculiar unrevisability: theonly reason someone might balk at denying bachelors are unmarried isthat, well, that’s just what the word “bachelor” means!^[15] The challenge, though, is to clarify the basis for this sort ofexplanation.

It is important to note here a crucial change that Quine (and earlierPositivists) casually introduced into the characterization of thea priori, and consequently into much of the now commonunderstanding of the analytic. Where Kant and others had traditionallyassumed that thea priori concerned beliefs“justifiable independently of experience,” Quine and manyother philosophers of the time came to regard it as consisting ofbeliefs “unrevisable in the light of experience.” And, aswe have seen, a similar status is accorded the at least apparentlyanalytic. However, this would imply that people taking something to beanalytic ora priori would have to regard themselves as beinginfallible about it, forever unwilling to revise it in lightof further evidence or argument. But this is a further claim that manydefenders of the traditional notions need not embrace (consider,again, the disputes philosophers have about the proper analysis ofterms such as “knowledge” or “freedom”).

Indeed, a claim might be in fact analytic and justifiableindependently of experience, but nevertheless perfectly well revisedin the light of it. Experience, after all, might mislead us, as it(perhaps) misled Putnam when he suggested revising logic in light ofdifficulties in quantum mechanics, or suggested revising “catsare animals,” were we to discover the things were robots. Justwhich claims are genuinely analytic anda priori might not beavailable in the “armchair” at the introspective orbehavioral surface of our lives in the way that Quine and much of thephilosophical tradition has assumed. Certainly the “dispositionsto assent or dissent from sentences” on which Quine (1960[2013], chapter 2) standardly relied are likely very dubious guides(see the findings of “experimental philosophy” discussedin §4.1 below). Behavioral dispositions in general may have anyof a variety of aetiologies that aren’t clearly distinguishablein actual behavior (one wonders how much of Quine’s seamlessepistemology went hand in hand with his mentalistically seamlessbehavioristic psychology). The relevant dispositions might be hiddenmore deeply in our minds, and our access to them as fallible as ouraccess to any other such facts about ourselves. The genuinely analyticmay be a matter of difficult reflective analysis or deep linguistictheory (see Bealer, 1987, Bonjour 1998, Rey, 1998, andsupplement), a possibility to which we will returnshortly.

3.6.2 One Criterion Concepts

In his expansion of Quine’s point, Putnam (1962 [1975]) tried torescue what he thought were theoretically innocuous examples ofanalytic truths by appeal to what he called“one-criterion” concepts, or concepts like, e.g.,pediatrician, bachelor, widow, where there seems to be onlyone “way to tell” whether they apply. However, as Fodor(1998) pointed out, so stated, this latter account won’t sufficeeither, since the notion of “criterion” seems no betteroff than “meaning” or “analytic.” Moreover, ifthere were one way to tell what’s what, there would seem,trivially, to be indefinite numbers of other ways: look for somereliable correlate (living alone, frequenting singles bars for“bachelor”), or, just ask someone who knows the one way;or ask someone who knows someone who knows; or…, etc., and sonow we would be faced with saying which of these ways is genuinely“criterial,” which would seem to leave us with the sameproblem we faced in saying which way appears to be“analytic.”

Fodor (1998) tried to improve on Putnam’s proposal by suggestingthat a criterion that appears to be analytic is the one on which allthe other criteria depend, but which does not depend upon them. Thus,telling that someone is a bachelor by checking out his gender andmarriage status doesn’t depend upon telling by asking hisfriends, but telling by asking his friends does depend upon telling byhis gender and marriage status; and so we have an explanation of why“bachelors are unmarried males” seems analytic, but, saidFodor, without it’s actually being so (perhaps somewhatsurprisingly, given his general “asymmetric dependence”theory of content, see his 1990b and Rey, 2009, to be discussedshortly, §§4.2–4.3).

However, such asymmetric dependencies among criteria alone will not“explain (away)” either the reality or the appearance ofthe analytic, since there would appear to be asymmetric dependenciesof the proposed sort in non-analytic cases. Natural kinds are dramaticcases in point (see Putnam 1962 [1975], 1970 [1975], 1975). At somestage in history probably the only way anyone could tell whethersomething was a case of polio was to see whether there was a certainconstellation of standard symptoms, e.g. paralysis; other ways(including asking others) asymmetrically depended upon that way. Butthis wouldn’t make “All polio cases exhibitparalysis” remotely analytic—after all, the standardsymptoms for many diseases can sometimes be quite misleading. Itrequired serious empirical research to discover the proper definitionof a natural kind term like “polio.” Precisely as Putnamotherwise stressed, methods of testing are so variable it is doubtfulthat even “single criterion” tests could provide a basisfor the identification of the stable meanings of words.

Indeed, as many philosophers in the wake of Quine’s andPutnam’s work came to suspect, the recourse of philosophy ingeneral toepistemology to ground semantics may have been afundamental mistake. It was an enticing recourse: it seemed to offer away to dispatch philosophical disputes and secure empirical knowledgefrom sceptical challenges regarding demons and dreams. But the abovedifficulties suggested that those disputes and challenges would needto be met in some other way, perhaps by looking not to words, but tothe world instead.

3.6.3 The World, not Words

Indeed, another strategy that a Quinean can deploy to explain theappearance of the analytic is to claim that analyses are really not ofthe meanings ofwords, but of the actualphenomena in theworld to which they refer (see Fodor, 1990b, 1998). Thus, claimsthat, e.g., cats are animals, triangles are three-sided, or that everynumber has a successor should not be construed as claims about themeanings of the words “cat”, “triangle” or“number,” but about thenature ofcats,triangles andnumbers themselves. Arguably, many suchclaims, if they are true, arenecessarily so (cf., Kripke,1972; Putnam, 1975), and may be commonly understood to be, and thismight make them seem analytic. But then we would be faced withprecisely the challenge that Quine raised: how to distinguish claimsof analyticity from simply deeply held beliefs about “thenature” of things.

This recourse to the world may, however, be a little too swift. Casesof (arguably) deeply explanatory natural kinds such aspolioorcats contrast dramatically with cases of more superficialkinds likebachelor orfortnight. whose natures arenot specified by any explanatory science, but are pretty muchexhausted by what would seem to be the meanings of the words. Again,unlike the case of polio and its symptoms, the reason that gender andmarriage status are the best way to tell whether someone is a bacheloris, again, that that’s just what “bachelor” means.Indeed, should a doctor propose revising the test for polio in thelight of better theory—perhaps reversing the dependency ofcertain tests—this would not even begin to appear to involve achange in the meaning of the term. Should, however, a feministpropose, in the light of better politics, revising the use of“bachelor” to include women, this obviously would. If theappearance of the analytic is to be explained away, it needs toaccount for such differences in our understanding of different sortsof revisions in our beliefs, which don’tappear to beissues regarding the external world.

4. Post-Quinean Strategies

There has been a wide variety of responses to Quine’schallenges. Some, for example, Davidson (1980), Stich (1983) andDennett (1987), seem simply to accept it and try to account for ourpractice of meaning ascription within its “non-factual”bounds. Since they follow Quine in at least claiming to forswear theanalytic, we will not consider their views further here. Others, whomight be (loosely) called “neo-Cartesians,” rejectQuine’s attack as simply so much prejudice of the empiricism andnaturalism that they take to be his own uncritical dogmas (§4.1in what follows). Still others hope simply to find a way to break outof the “intentional circle,” and provide an account of atleast what it means for one thing (a state of the brain, for example)to mean (or “carry the information about”) anotherexternal phenomenon in the world (§4.2). Perhaps the mosttrenchant reaction has been that of empirically oriented linguists andphilosophers, who look to a specific explanatory role the analytic mayplay in an account of thought and talk (§4.3). This role iscurrently being explored in considerable detail in the now variousareas of research inspired by the important linguistic theories ofNoam Chomsky (§4.4, andsupplement, Analyticity and ChomskyanLinguistics).

4.1 Neo-Cartesianism

The most unsympathetic response to Quine’s challenges has beenessentially to stare him down and insist upon an inner faculty of“intuition” whereby the truth of certain claims is simply“grasped” directly through, as Bonjour (1998) puts it:

an act of rational insight or rational intuition … [that] isseemingly (a) direct or immediate, nondiscursive, and yet also (b)intellectual or reason-governed … [It] depends upon nothingbeyond an understanding of the propositional content itself….(p. 102)

Bealer (1987, 1999) defends similar proposals. Neither Bonjour norBealer are in fact particularly concerned to defend the analytic bysuch claims, but their recourse to mere understanding of propositionalcontent is certainly what many defenders of the analytic have had inmind. Katz (1998, pp. 44–5), for example, explicitly made thevery same appeal to intuitions on behalf of the analytic claimssupported by his semantic theory. Somewhat more modestly, Peacocke(1992, 2004) claims that possession of certain logical conceptsrequires that a person find certain inferences “primitivelycompelling,” or compelling not by reason of some inference thattakes “their correctness…as answerable to anythingelse” (1992, p. 6; see also his 2004, p. 100 and the otherreferences in fn 9 above for the strategy, and fn 7, as well asHarman, 1996 [1999], and Horwich, 2000, for qualms).

Perhaps the simplest reply along these lines emerges from a suggestionof David Lewis (1972 [1980]), who proposes to implicitly define, e.g.,psychological terms by conjoining the “platitudes” inwhich they appear:

Include only platitudes that are common knowledge among us –everyone knows them, everyone knows that everyone else knows them, andso on. For the meanings of our words are common knowledge, and I amgoing to claim that names of mental states derive their meaning fromthese platitudes. (1972 [1980], p. 212)

Enlarging on this idea, Frank Jackson (1998) emphasizes the role ofintuitions about possible cases, as well as the need sometimes tomassage such intuitions so as to arrive at “the hypothesis thatbest makes sense of [folk] responses” (p. 36; see also pp. 34–5).^[16]

The Quinean reply to all these approaches is, again, his mainchallenge: how in the end are we to distinguish such claims of“rational insight,” “primitive compulsion,”inferential practices or folk beliefs, from merely some deeplyentrenched empirical convictions, folk practices or, indeed, from meredogmas? Isn’t the history of thought littered with what haveturned out to be deeply mistaken claims, inferences and platitudesthat people at the time have found “rationally” and/or“primitively compelling,” say, with regard to God, sin,disease, biology, sexuality, or even patterns of reasoning themselves?Again, consider the resistance Kahneman (2011) reports peopledisplaying to correction of the fallacies they commit in a surprisingrange of ordinary thought (cf. fn 7 above); or in a more disturbingvein, how the gifted mathematician, John Nash, claimed that hisdelusional ideas “about supernatural beings came to me the sameway that my mathematical ideas did” (Nasar 1998, p. 11).Introspected episodes, primitive compulsions, intuitions aboutpossibilities, or even tacit folk theories alone are not going todistinguish the analytic, since these all may be due as much topeople’s (possibly mad!) empirical theories as to any specialknowledge of meaning.

A particularly vivid way to feel the force of Quine’s challengeis afforded by a recent case that came before the Ontario SupremeCourt concerning whether laws that confined marriage to heterosexualcouples violated the equal protection clause of the constitution (seeHalpernet al. 2001). The question was regarded as turning inpart on the meaning of the word “marriage”, and each partyto the dispute solicited affidavits from philosophers, one of whomclaimed that the meaning of the wordwas tied toheterosexuality, another that itwasn’t. Putting asidethe complex moral-political issues, Quine’s challenge can beregarded as a reasonably sceptical request to know how any serioustheory of the world might settle it. It certainly wouldn’t besufficient merely to claim that marriage is/isn’t necessarilyheterosexual on the basis of common “platitudes,” muchless on “an act of rational insight [into] the propositionalcontent itself”; or because speakers found the inference frommarriage to heterosexuality “primitively compelling” andcouldn’t imagine gay people getting married!^[17]

Indeed, some philosophers have offered some empirical evidence thatcasts doubt on just how robust the data for the analytic might be. Themovement of “experimental philosophy” has pointed toevidence of considerable malleability of subject’s“intuitions” with regard to the standard kinds of thoughtexperiments on which philosophical defenses of analytic claimstypically rely. Thus, Weinberg, Nichols and Stich (2001) foundsignificant cultural differences between responses of Asian andWestern students regarding whether someone counted as having knowledgein a standard “Gettier” (1963) example of accidentaljustified true belief; and Knobe (2003) found thatnon-philosophers’ judgments about whether an action isintentional depended on the (particularly negative) moral qualities ofthe action, and not, as is presumed by most philosophers, on whetherthe action was merely intended by the agent. Questions, of course,could be raised about these experimental results (How well did thesubjects understand the project of assessing intuitions? Did theexperiments sufficiently control for the multitudinous“pragmatic” effects endemic to polling procedures? To whatextent are the target terms merely polysemous – seesupplement, §3– allowing for different uses indifferent contexts?) However, the results do serve to show how thedetermination of meaning and analytic truths can be regarded as a farmore difficult empirical question than philosophers have traditionallysupposed (see Bishop and Trout, 2005, and Alexander and Weinberg,2007, for further discussion).

4.2 Externalist Theories of Meaning

Developing the strategy of §3.3C above, Externalist theories ofmeaning (or “content”) try to meet at least part ofQuine’s challenge by considering how matters of meaning need notrely onepistemic. or reallyanyinternalconnections among thoughts or beliefs, in the way that manyphilosophers had traditionally supposed, but as involving largelycausal and social relations between uses of words and the phenomena inthe world that they pick out. This suggestion gradually emerged in thework of Putnam (1962 [1975], 1965 [1975] and 1975), Kripke (1972[1980]) and Burge (1979, 1986), but it took the form of positivetheories in, e.g., the work of Devitt (1981, 2015), Dretske (1988) andFodor (1990b), who tried to base meaning in various actual orco-variational causal relations between states of the mind/brain andexternal phenomena (seeIndicator Semantics; as well as thework on “teleosemantics” of Millikan, 1984), Papineau,1987, and Neander, 1995, 2017, who look to mechanisms of naturalselection; seeTeleological Theories of Mental Content).

Consider, for example, Fodor’s proposal. Simplifying itslightly, Fodor (1990b) claimed that

a symbolS meanspif

(i)

under some conditions, C, it’s alaw thatSis entokened iffp, and

(ii)

any other tokening ofS synchronically depends upon (i),but notvice versa.

Thus, tokenings of “horse” meanhorse becausethere are (say, optimal viewing) conditions under which tokenings of“horse” co-vary with horses, and tokenings of“horse” caused by cows asymmetrically depend upon thatfact. The intuitive idea here is that what makes “horse”meanhorse is that errors and other tokenings of“horse” in the absence of horses (e.g., dreaming of them)depend upon being able to get things right, but notviceversa: getting things right doesn’t depend upon gettingthem wrong. The law in (i), so to say, “governs” thetokenings of (ii). (Note that this condition ismetaphysical,appealing toactual laws of entokenings, and not uponasymmetric dependencies betweenepistemic criteria suggestedby Fodor in his defense of Putnam we discussed in §3.6.2.)

Fodor’s and related proposals are not without their problems(see Loewer, 1996, Rey, 2009 andCausal Theories of MentalContent). Nevertheless, it’s worth noting that,were such theories to succeed in providing the kind ofexplanatorily adequate, non-circular account of intentionality towhich they aspire, they would go some way towards saving at leastintentional psychology from Quine’s attack, and provide at leastoneprima facie plausible, naturalistic strategy fordistinguishing facts about meaning from facts about mere belief. Theproposals, unlike those in the traditions of Carnap or ofneo-Cartesians, have at least theform of a seriousreply.

However, even if such externalist strategies, either Fodor’s orteleosemantic ones, were to save intentionality and meaning, theywould do so only by forsaking the high hopes we noted in §2philosophers harbored for the analytic. For externalists are typicallycommitted to counting expressions as “synonymous” if theyhappen to be linked in the right way to the same external phenomena,even if a thinker couldn’t realize that they are byapriori (or, at any rate, “armchair”) reflectionalone. By at least the Fregean substitution criterion (§1.2),they would seem to be committed to counting as “analytic”many patently empirical sentences as “Water is H2O,”“Salt is NaCl” or “Mark Twain is SamuelClemens,” since in each of these cases, something may co-vary inthe relevant way with tokenings of the expression on one side of theidentity if and only if it co-varies with tokenings of the one on theother (similar problems and others arise for teleosemantics; see Fodor1990b, pp. 72–73).

Of course, along the lines of the worldly turn we noted in§3.6.3, an externalist might cheerfully just allow that somesentences, e.g., “water is H20,” are in fact analytic,even though they are “external” and subject to empirical(dis)confirmation. Such a view would actually comport well with anolder philosophical tradition less interested in the meanings of ourwords andconcepts, and more interested in the“essences” ofthe worldly phenomena they pickout. Locke (1690 [1975], II, 31, vi), for example, posited“real” essences of things rather along the linesresuscitated by Putnam (1975) and Kripke (1972 [1980]), the realessences being the conditions in the world independent of our thoughtthat make something the thing it is. Thus,being H2O may bewhat makes somethingwater, and (to take the strikingexamples of diseases noted by Putnam, 1962 [1975]) being theactivation of a certain virus is what makes something polio. But, ofcourse, such an external view would still dash the hopes ofphilosophers looking to the analytic to explaina prioriknowledge (but see Bealer 1987 and Jackson 1998 for strategies toassimilate such empirical cases to neverthelessa priori,armchair analysis). Such a consequence, however, might not faze anexternalist like Fodor (1998), who is concerned only to saveintentional psychology, and might otherwise share Quine’sscepticism about the analytic and thea priori.

Two final problems, however, loom over any such externaliststrategies. One is how to provide content to“response-dependent” terms, such as“interesting,” “amusing,” “sexy,”“worrisome,” whose extensions vary greatly with users andoccasions. What seems crucial to the contents of such terms is not anyexternalia that they might pick out, but simply someinternal reactions of thinkers that might vary among themeven underall conditions, but without difference in meaning.At any rate, there’s no reason to suppose there’s any sortof law that links the same phenomena to different people who finddifferent things “interesting,” “funny,” oreven “green” (cf. Russell, 1912; Hardin, 2008). The otherproblem is how to distinguish necessarilyempty terms thatpurport to refer to (arguably) impossible phenomena such as perfectlyflat surfaces, Euclidean figures, fictional characters or immortalsouls. An externalist would seem to be committed to treating all suchterms as synonymous, despite, of course, the fact that thoughts aboutthem should obviously be distinguished (see Rey, 2009).

4.3 Internal Dependencies

A promising strategy for replying to these latter problems, as well asto Quine’s challenge in a way that might even begin to providewhat the neo-Cartesian wants, can be found in a proposal of PaulHorwich (1998, 2005). He emphasizes how the meaning properties of aterm are the ones that play a “basic explanatory role”with regard to the use of a term generally, the ones ultimately invirtue of which a term is used with that meaning. For example, the useof “red” to refer to the color of blood, roses, stopsigns, etc,. is arguably explained by its use to refer to certainapparent colors in good light, but notvice versa: the latteruse is “basic” to all the other uses. Similarly, uses of“and” explanatorily depend upon its basic use ininferences to and from the sentences it conjoins, and number terms toitems in a sequence respecting Peano’s axioms (Horwich,1998:45,129; see also Devitt 1996, 2002 for a similar proposal).

Although by allowing for purely internal explanatory conditions, thisstrategy offers a way to deal with response-dependent and necessarilyempty terms, and promises a way of distinguishing analyticities frommere beliefs, there are still several further potential problems itfaces. The first is that merely appealing to a “basicexplanatory” condition for the use of a word doesn’tdistinguish misuses and metaphors from etymologies, derived idioms and“dead metaphors”: saying “Juliet is the sun”can be explained by the use of “sun” to refer to the sun,but so can “lobbying” be explained by the use of“lobby” for lobbies of buildings (where politicians oftenmet), and “the eye of a needle” by the shape of an animaleye. In these latter cases, the words seem to be “frozen”or “dead” metaphors, taking on meanings of their own.While they areexplained by original “basic”uses, they are no longer “governed” by them.

Here it may be worth combining something of the Horwich view withsomething of Fodor’s aforementioned cousin suggestion of theasymmetric counterfactual (§4.2), along lines suggested by Rey(2009; 2020a, §10.3): the new “dead” uses of an idiomor metaphor no longerasymmetrically depend upon theexplanatorily basic use. “Eye of a needle” would stillmean the hole at the end of a needle, even if “eye” nolonger referred to animal eyes. But “eye” used to referto, say, the drawing of an eye, would both asymmetrically andexplanatorily depend upon its being used to refer to actual eyes. Anddescribing a three-way correspondence as “triangular” mayasymmetrically and explanatorily depend upon thinking of certaingeometric figures as triangular, but notvice versa –despite the impossibility of there ever being any actual triangles inthe external world (see Allott and Textor, 2022, for development ofthis suggestion). Taking the asymmetric dependency to be“internally” explanatory relieves it of the excessiveexternalism with which Fodor burdened it, while avoiding theetymologies and dead metaphors facing Horwich’s view on itsown.

However, although such a proposal may offer a promising strategy formeeting Quine’s challenge about many ordinary terms, itisn’t clear it would work for highly theoretic ones. For ifQuine (1953 [1980a]) is right about even a limited holism involved inthe use of scientific terms, then there may be no sufficiently localbasic facts on which all other uses of a term asymmetrically andexplanatorily depend. To take the kind of case that most interestedQuine, it certainly seems unlikely that there is some small set ofuses of, say, “number,” “positron,”“space” or “biological species” that areexplanatorily basic, on which all other uses really depend. Such termsoften come with a large cluster of terms appearing in claims that comeas, so to say, a loose “package deal,” and revision overtime may touch any particular claim in the interests of overallexplanatory adequacy. Uses of a term involved in the expression ofbelief, either in thought or talk, will likely be justified andexplained by the same processes of holistic confirmation that ledQuine to his scepticism about the analytic in the first place (cf.Gibbard, 2008). Of course, Quine might be wrong about taking the caseof theoretic terms in science to be representative of terms in humanpsychology generally (cf. Chomsky, 2000,footnote 10 above), and the above proposal might be confined to some restrictedportions of a speaker’s psychology, e.g., to perception (as inFodor, 1983, 2000). But, to put it mildly, the verdict on these issuesis not quite in (seesupplement §§4–5).

Lastly, a third (and, for some, a serious) possible drawback of thisstrategy is that it still risks rendering matters of meaning far less“transparent” and introspectively accessible thanphilosophers have standardly supposed. There is little reason tosuppose that what is asymmetrically-explanatorily basic aboutone’s use of a term in thought or talk is a matter that isavailable to introspection or armchair reflection. As in the case of“marriage” mentioned earlier, but certainly with respectto other philosophically problematic notions, just which properties,if any, are explanatorily basic may not be an issue that is at alleasy to determine. What are the asymmetric-explanatorily basic uses of“freedom” or “soul”? Do even people’suses of animal terms really depend upon dubbings of species – orof individual exemplars – or do they depend more upon an innatedisposition to think in terms of underlying biological kinds (cf. Keil2014, pp. 327–333)? Do their uses of number words and conceptsreally depend upon their grasp of Peano’s axioms? Perhaps theusage is grounded more in practices of (finite) counting, estimatesand noticing merelyfinite one-to-one correspondences; orperhaps they lie in the general recursive character oflanguage (cf. Hauser et al 2002). Again, one may need theresources of a psychology that delves into far more deeply into thecomplex, internal causal relations in the mind than are available atits introspective or behavioral surface.

4.4 Chomskyan Strategies

Such an interest in a deeper and richerinternal psychologyemerged most dramatically in the 1950s in the work of Noam Chomsky. Inhis (1957, 1965, 1968 [2006]) he began to revolutionize linguistics bypresenting substantial evidence and arguments for the existence of aninnate “generative” grammar in a special language facultyin people’s brains that he argued was responsible for theirunderlying competence to speak and understand natural languages. Thisopened up the possibility of a response to Quine’s (1960)scepticism about the analytic within his own naturalistic framework,simply freed of its odd behaviorism, which Chomsky and others hadindependently, empirically refuted (see Chomsky 1959, and Gleitman,Gross and Reisberg 2011, chapter 7). Some of it also dovetails nicelywith ideas of Friedrich Waismann and the later Wittgenstein, as wellas with important recent work on polysemy. But the program Chomskyinitiated is complex, and its relation to the analytic quitecontroversial, and so discussion of it is relegated to the followingsupplement to this entry:

Supplement: Analyticity and Chomskyan Linguistics.

5. Conclusion

Suppose, per the discussion of at least §3 of thesupplement, that linguisticswere to succeed indelineating a class of analytic sentences grounded in the constraintsof a special language faculty in the way that some Chomskyanssometimes seem to suggest. Would such sentences serve the purposes forwhich we noted earlier (§2) philosophers had enlisted them?Perhaps some of them would. An empirical grounding of the analyticmight provide us with an understanding of what constitutes aperson’s competence with specific words and concepts,particularly logical or mathematical ones. Given that Quineanscepticism about the analytic is a source of his scepticism about thedeterminacy of cognitive states (see §3.5 above), such agrounding may be crucial for a realistic psychology, determining theconditions under which someone has a thought with a specificcontent.

Moreover, setting out the constitutive conditions for possessing aconcept might be of some interest to philosophers generally, sincemany of the crucial questions they ask concern the properunderstanding of ordinary notions such asmaterial object, person,action, freedom, god, the good, orthe beautiful.Suppose, further, that a domain, such as perhaps ethics or aesthetics,is “response dependent,”constituted by theunderlying rules of our words and concepts; suppose, that is, thatthese rulesconstitute the nature of, say,the good, thefunny, orthe beautiful. If so, then it might not beimplausible to claim that successful conceptual analysis could provideus with somea priori knowledge of such domains (although,again, sorting out the rules may require empirical linguistic andpsychological theories not available to “armchairreflection”).

But, of course, many philosophers have wanted more than theseessentially psychological gains. They have hoped that analytic claimsmight provide a basis fora priori knowledge of domains thatexist independently of us and are not exhausted by our concepts. Animportant case in point would seem to be the very case of arithmeticthat motivated much of the discussion of the analytic in the firstplace. Recent work of Crispin Wright (1983) and others on the logicistprogram has shown how a version of Frege’s program might berescued by appealing not to his problematic Basic Law V, but insteadmerely to what is called “Hume’s Principle,” or theclaim that forthe number of Fs to be equal tothe numberof Gs is for there to be a “one-to-onecorrespondence” between the Fs and the Gs (as in the case of thefingers of a normal right and left hand), even in infinite cases.According to what is now regarded as “Frege’sTheorem,” the Peano axioms for arithmetic can be derived fromthis principle in standard second-order logic (seeFrege’stheorem and foundations for arithmetic).

Now, Wright has urged that Hume’s Principle might be regarded asanalytic, and perhaps this claim could be sustained by an examinationof the language faculty along the lines of a Chomskyan linguistics setout in thesupplement. If so, then wouldn’t thatvindicate the suggestion that arithmetic can be knownapriori? Not obviously, since Hume’s Principle is a claimnot merely aboutthe concepts F and G, but about thepresumablyconcept-independent fact about the number ofthings that are F and the number of things that are G, and, we canask, what justifies any claim about them? As George Boolos (1997)asked in response to Wright:

If numbers are supposed to be identical if and only if the conceptsthey are numbers of are equinumerous, what guarantee do we have thatevery concept has a number? (p. 253)

Indeed, as Edward Zalta (2013) observes,

The basic problem for Frege’s strategy, however, is that for hislogicist project to succeed, his system must at some point include(either as an axiom or theorem) statements that explicitly assert theexistence of certain kinds of abstract entities and it is not obvioushow to justify the claim that we know such explicit existentialstatements. (2013, Section 6.2)

The concept of a unique successor to every number might be a definingfeature of the lexical item, “number,” but thatdoesn’t itself imply thatan infinity of numbers actuallyexists. Meanings and concepts are one thing; reality quiteanother. Justification of such existential statements and, with them,Hume’s Principle would seem to have to involve something morethan appealing to merely the concept, but also —to recallQuine’s (CLT, p. 121, §3.3 above) claim— to“the elegance and convenience which the hypothesis brings to thecontaining bodies of laws and data,” i.e., to our best overallempirical theory of the world, irrespective of what constraintslanguage might impose (see Wright, 1999, and Horwich, 2000, forfurther discussion).

The problem here becomes even more obvious in non-mathematical cases.For example, philosophers have wanted to claim not merely that ourconcepts ofred andgreen exclude the possibility ofour thinking that something is both colors all over, but that thispossibility is ruled out for theactual colors,red andgreen,themselves (if such there be). It is therefore no accident thatBonjour’s (1998, pp. 184–5) defense ofa prioriknowledge turns on resuscitating views of Aristotle and Aquinas,according to whichthe very properties ofred andgreenthemselves are constituents ofthe propositions we grasp. But it is just such a wonderful coincidencebetween merely ourconcepts and actual worldlyproperties that a linguistic semantics alone obviously cannotensure.

But suppose, nevertheless, theredid in fact exist acorrespondence between our concepts and the world, indeed, a deeplyreliable, counterfactual-supporting correspondence whereby it was infactmetaphysically impossible for certain claimsconstitutive of those concepts not to be true. This is, of course, notimplausible in the case of logic and arithmetic, and is entirelycompatible with, e.g., Boolos’ reasonable doubts about them(after all, it’s always possible to doubt what is in fact anecessary truth). Such necessary correspondences between thought andthe world might then serve as a basis for claims toa prioriknowledge in at least a reliabilist epistemology, where what’simportant is not believers’ abilities tojustify theirclaims, but merely thereliability of the processes by whichthey arrive at them (seeReliabilist Epistemology). Indeed,in the case of logic and arithmetic, the beliefs might be arrived atby steps that were not onlynecessarily reliable, but mightalso be taken to be so by believers, in ways that might in fact dependin no way upon experience, but only on their competence with therelevant words and concepts (Kitcher 1980; Rey 1998; and Goldman 1999explore this strategy).

Such a reliabilist approach, though, might be less than fullysatisfying to someone interested in the traditional analyticapriori. For, although someone might turn out in fact to haveanalytica priori knowledge of this sort, she might notknow that she does (reliabilist epistemologists standardlyforgo the “KK Principle,” according to which if one knowsthat p, one knowsthat one knows that p). Knowledge that therelevant claims were knowablea priori might itself be onlypossible by an empirically informed understanding of one’slanguage faculty and other cognitive capacitiesà laChomsky, and by its consonance with the rest of one’s theory ofthe world,à la Quine. One would only knowaposteriori that something was knowablea priori.

The trouble then is that claims that people do have a capacity fora priori knowledge seem quite precarious. As we noted earlier (footnote 7), people are often unreliable at appreciating deductively validarguments; and appreciating the standard rules even of naturaldeduction is for many people often a difficult intellectualachievement. Consequently, people’s general competence withlogical notions may not in fact consist in any grip on valid logicalrules; and so whatever rules do underlie that competence may well turnoutnot to be the kind of absolutely reliable guide to theworld on which the above reliabilist defense ofa priorianalytic knowledge seems to depend. In any case, in view merely of theserious possibility that these pessimistic conclusions are true,it’s hard to see how any appeal to the analytic to establish thetruth of any controversial claim in any mind-independent domain couldhave any special justificatory force without a sufficiently detailed,empirical psychological theory to back it up.

Moreover, even if we did have a true account of our minds and thesemantic rules afforded by our linguistic and conceptual competence,it’s not clear it would really serve the “armchair”purposes of traditional philosophy that we mentioned at the outset(§1). Consider, for example, the common puzzle about thepossibility that computers might actually think and enjoy a mentallife. In response to this puzzle some philosophers, e.g, Wittgenstein(1953 [1967], §§111, 281), Ziff, 1959, and Hacker, 1990,have suggested that it’s analytic that a thinking thing must bealive, a suggestion that certainly seems to accord with manyfolk intuitions (many people who might cheerfully accept acomputational explanation of a thought process often balk at thesuggestion that an inanimate machine engaging in that computationwould actually be thinking). Now, as we noted in thesupplement, §2, Chomsky (2000, p. 44) explicitlyendorses this suggestion. So suppose then this claim were in factsustained by linguistic theory, showing that the lexical item“think” is, indeed, constrained by the feature [+animate],and so is not felicitously applied to artifactual computers. Shouldthis really satisfy the person worried about the possibility ofartificial thought?

It’s hard to see why. For the serious question that concernspeople worried about whether artifacts could think concerns whetherthose artifacts could in fact share the genuine,theoreticallyinteresting, explanatory properties of a thinking thing (cf.Jackson 1998, pp. 34–5). We might have no empirical, scientificreason to suppose that genuine, biologicalanimacy (n.b., notmerely the perhaps purely syntactic,linguistic feature[+animate]!; seesupplement §2) actually figures amongthem. And so we might conclude that, despite these supposedconstraints of natural language, inanimate computers could come to“think” after all. Indeed, perhaps, the claim thatthinking things must be alive is an example of a claim that isanalytic but false, rather as the belief that cats areanimals would be, should it turn that the things are actually robotsfrom Mars; and so we should pursue the option of polysemy and“open texture” that Chomsky also endorses, and proceed toallow that artifacts could think.

Of course, a speaker could choose not to go along with, so to say,opening the texture this far. But if the explanatory point werenevertheless correct, other speakers could of course simply proceed todefine a new word “think*” that lacks the animacyconstraint and applies to the explanatory kind that in fact turns outto include, equally, humans and appropriately programmed artifacts.The issue would reduce to merely a verbal quibble: so computersdon’t “think”; they “think*” instead.Indeed, it’s a peculiar feature of the entire discussion of theanalytic that it can seem to turn on what may in the end be mereverbal quibbles. Perhaps the “linguist turn” of philosophythat we sketched in §§1.2–3.3 led into a blind alley,and it would be more fruitful to explore, so far as possible,conceptual and/or explanatory connections that may exist in our mindsor or in the world to a large extent independently of language.

In any case, while the semantic conditions of a language might providea basis for securinga priori knowledge of claims aboutmind-dependent domains, such as those of perhaps ethics andaesthetics, in the case of mind-independent domains, such aslogic and mathematics, or the nature of worldly phenomena such as lifeor thought, the prospects seem more problematic. There may be analyticclaims to be had here, but at least in these cases they would, in theimmortal words of Putnam (1965 [1975], p. 36), “cut nophilosophical ice…bake no philosophical bread and wash nophilosophical windows.”^[18] We would just have to be satisfied with theorizing about themind-independent domains themselves, without being able to justify ourclaims about them by appeal to the meanings of our words alone.Reflecting on the difficulties of the past century’s efforts onbehalf of the analytic, it’s not clear why anyone would reallywant to insist otherwise.

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Acknowledgements

I’m grateful to many readers for calling attention to errors inprevious editions of this entry, and to Nicholas Allott, John Collins,Alexander Williams and anonymous referees for generous comments ondrafts of the present one.