## 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 the
constituent words would find an obvious difference between the two
sets: whereas they might wonder about the truth or falsity of those of
set I, they would find themselves pretty quickly incapable of doubting
those of II. Unlike the former, these latter seem to be justifiable
automatically, "just by knowing what the words mean," as
many might spontaneously put it. Indeed, denials of any of them,
e.g.,



III.


(9)
#*Not all pediatricians are doctors - some aren't
at all!*
(10)
#*Not everyone who runs moves - some remain completely
still!*
 


would seem to be in some important way *unintelligible*, very
like contradictions in terms (the "#" indicates semantic
anomaly). Philosophers standardly refer to sentences of the first set
as "synthetic," those of the second as (at least
apparently) "analytic." (Members of set III. are sometimes
said to be "analytically false," although this term is
rarely used, and "analytic" is standardly confined to
sentences that are regarded as true.) We might call sentences such as
(5)-(10) part of the "analytic data" to which philosophers
and linguists have often appealed in invoking the distinction (without
prejudice, however, to whether such data might otherwise be
explained). Some philosophers might want to include in set III. what
are called *category mistakes* (q.v.) such as #*The number
three likes Tabasco sauce*, or #*Saturday is in bed* (cf.,
Ryle, 1949 [2009]), but these have figured less prominently in recent
discussions, being treated not as semantically anomalous, but as
simply false and silly (Quine 1960 [2013, p. 210]).



Many philosophers have hoped that the apparent necessity and *a
priori* status of the claims of logic, mathematics and much of
philosophy could be explained by their claims being analytic, our
understanding of the meaning of the claims explaining why they seemed
to be true "in all possible worlds," and knowable to be
so, "independently of experience." This view led many of
them to regard philosophy as consisting in large part in the
"analysis" of the meanings of the relevant claims, words
and
 concepts;[1]
 i.e., a provision of conditions that were individually necessary and
jointly sufficient for the application of a word or concept, in the
way that, for example, *being a female* and *being a
parent* are each necessary and together sufficient for *being a
mother*. Such a conception seemed to invite and support (although
we'll see it doesn't entail) the special methodology of
"armchair reflection" on concepts in which many
philosophers traditionally engaged, independently of any empirical
research.


### 1.1 Kant



Although there are precursors of the contemporary notion of the
analytic in Leibniz, and in Locke and Hume in their talk of
"relations of ideas," the conception that currently
concerns many philosophers has its roots in the work of Kant (1787
[1998]) who, at the beginning of his *Critique of Pure Reason*,
wrote:



> 
> 
> In all judgments in which the relation of a subject to the predicate
> is thought (if I only consider affirmative judgments, since the
> application to negative ones is easy) this relation is possible in two
> different ways. Either the predicate B belongs to the subject A as
> something that is (covertly) contained in this concept A; or B lies
> entirely outside the concept A, though to be sure it stands in
> connection with it. In the first case, I call the judgment analytic,
> in the second synthetic. (1787 [1998], B10)
> 
> 
> 



He provided as an example of an analytic judgment, "All bodies
are extended": in thinking of a body we can't help but
also think of it being extended in space; that would seem to be just
part of what is meant by "body." He contrasted this with
"All bodies are heavy," where the predicate ("is
heavy") "is something entirely different from that which I
think in the mere concept of body in general" (B11), and we must
put together, or "synthesize," the different concepts,
body and heavy (sometimes such concepts are called
"ampliative," "amplifying" a concept beyond
what is "contained" in it).



Kant tried to spell out his "containment" metaphor for the
analytic 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 of
the manifold that I always think in it, in order to encounter this
predicate therein" (B10). But then, picking up a suggestion of
Leibniz, he went on to claim:



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



As Jerrold Katz (1988) emphasized, this second definition is
significantly different from the "containment" idea, since
now, in its appeal to the powerful method of proof by contradiction,
the analytic would include all of the (potentially infinite) deductive
consequences of a particular claim, many of which could not be
plausibly regarded as "contained" in the concept expressed
in the claim. For starters, *Bachelors are unmarried or the moon is
blue* is a logical consequence of *Bachelors are
unmarried*--its denial contradicts the latter (a denial of a
disjunction is a denial of each disjunct)--but clearly nothing
about the color of the moon is remotely "contained in" the
concept *bachelor*. To avoid such consequences, Katz (e.g.,
1972, 1988) went on to try to develop a serious theory based upon only
the initial containment idea, as, along different lines, does Paul
Pietroski (2005, 2018).



One reason Kant may not have noticed the differences between his
different characterizations of the analytic was that his conception of
"logic" seems to have been confined to Aristotelian
syllogistic, and so didn't include the full resources of modern
logic, where, as we'll see, the differences between the two
characterizations become more glaring (see MacFarlane 2002). Indeed,
Kant demarcates the category of the analytic chiefly in order to
contrast it with what he regards as the more important category of the
"synthetic," which he famously thinks is not confined, as
one might initially suppose, merely to the
 empirical.[2]
 He argues that even so elementary an example in arithmetic as
*7+5=12* is synthetic, since the concept of *12* is not
contained in the concepts of *7*, *5*, or *+*,:
appreciating the truth of the proposition would seem to require some
kind of active "synthesis" by the mind uniting the
different constituent thoughts (1787 [1998], B15). And so we arrive at
the category of the "synthetic *a priori*," whose
very possibility became a major concern of his work. Kant tried to
show that the activity of synthesis was the source of the important
cases of *a priori* knowledge, not only in arithmetic, but also
in geometry, the foundations of physics, ethics, and philosophy
generally, a controversial view that set the stage for much of the
philosophical discussions of the subsequent centuries (see Coffa 1991,
pt. I).



Apart from geometry, Kant, himself, actually didn't focus much
on the case of mathematics. But, as mathematics in the 19th C. began
reaching new heights of sophistication, worries were increasingly
raised about its foundations. It was specifically in response to these
latter worries that Gottlob Frege (1884 [1980]) tried to improve upon
Kant's formulations of the analytic, and presented what is
widely regarded as the next significant discussion of the
 topic.[3]


### 1.2 Frege



Frege (1884 [1980], SSSS5,88) and others noted a number of
problems with Kant's "containment" metaphor. In the
first place, as Kant (1787 [1998], B756) himself would surely have
agreed, the criterion would need to be freed of
"psychologistic" suggestions, or claims about merely the
accidental thought processes of thinkers, as opposed to claims about
truth and justification that are presumably at issue with the
analytic. In particular, mere associations are not always matters of
meaning: many people in thinking about Columbus may automatically
think "the discoverer of America," or in thinking about
the number 7 they "can't help but also think" about
the numeral that denotes it, but it's certainly not analytic
that Columbus discovered America, or that a number is identical with a
numeral. Moreover, while it may be arguably analytic that a circle is
a closed figure of constant curvature (see Katz, 1972), someone could
fail to notice this and so think the one without the other.



Even were Kant to have solved this problem, it isn't clear how
his notion of "containment" would cover cases that seem to
be as "analytic" as any of set II, such as:



IV.


(11)
*Anyone who's an ancestor of an ancestor of Bob is an
ancestor of Bob.*
(12)
*If Bob is married to Sue, then Sue is married to
Bob.*
(13)
*If something is red, then it's colored.*
 


The transitivity of *ancestor* or the symmetry of
*married* are not obviously "contained in" the
corresponding thoughts in the way that the idea of *extension*
is plausibly "contained in" the notion of *body*,
or *male* in the notion of *bachelor*. (13) has seemed
particularly troublesome: what else besides *colored* could be
included in the analysis? The concept *red* involves color
- and what else? It is hard to see what else to
"add" - except *red* itself!



Frege attempted to remedy the situation by completely rethinking the
foundations of logic, developing what we now think of as modern
symbolic logic. He defined a perfectly precise "formal"
language, i.e., a language characterized by the "form"
- standardly, the shape--of its expressions, and he
carefully set out an account of the syntax and semantics of what are
called the "logical constants," such as "and,"
"or," "not," "all" and
"some," showing how to capture a very wide class of valid
inferences containing them. Saying precisely how the constants are
determined is a matter of controversy (see *Logical
Constants*), but, at least roughly and intuitively, they can be
thought of as those parts of language that don't
"point" or "function referentially," aiming to
refer 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, but
words like "or" and "all" don't seem to
function referentially at all. At any rate, it certainly isn't
clear that there are any *ors* and *alls* 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 truth
in a way that has become common (and will be particularly useful in
this entry) as *a sentence that is true no matter what non-logical
expressions occur in it* (cf. Tarski, 1936 [1983], Quine, 1956
[1976], Davidson 1980). Consequently (placing non-logical expressions
in bold, and re-numbering prior examples):



(14)
*All **doctors** that **specialize on
children** are **doctors**.*


counts as a (strict) logical truth: no matter what grammatical
expressions we put in for the non-logical terms "doctor",
"specialize on" and "children" in (14), the
sentence 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 shall
mean uniform substitution of one presumably univocal expression for
another in all its occurrences in a sentence.) But what about the
others 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 the
rest of the examples of II. (14) and (15) are patent logical truths;
their truth depends only upon the semantic values of their logical
particles. But *All pediatricians are doctors* and the other
examples, (6)-(8) and (11)-(13), are not *formal*
logical truths, specifiable by the logical *form* of the
sentence (or its pattern of logical particles) alone; nor are their
denials, e.g., (9) and (10), *formal* contradictions (i.e., of
the *form*, where '*p*' stands in for any
sentence: "*p* and it is *not* the case that
*p*"). How are we to capture them?



Here Frege appealed to the notion of "definition," or
--presuming that definitions preserve
"meaning"-- "synonymy": the non-logical
analytic truths are those that can be converted to formal logical
truths by substitution of definitions for defined terms, or synonyms
for synonyms. Since "mice" is not synonymous with
"pediatrician," (17) is not a substitution into (16) of
the required sort. We need, instead, a substitution of *the
definition* of "pediatrician," i.e., "doctor
that specializes on children," which would convert (16) into our
earlier purely formal logical truth:



(14)
*All doctors that specialize on children are doctors*.


Of course, these notions of *definition, meaning* and
*synonymy* would themselves need to be clarified, But they were
thought at the time to be sufficiently obvious notions whose
clarification didn't seem particularly urgent until W.V.O. Quine
(1953 [1980a]) raised serious questions about them much later (see
SS3.3ff below). Putting those questions to one side, Frege made
spectacularly interesting suggestions, offering a famous definition,
for example, of the "ancestral" relation involved in (11)
as a basis for his definition of *number* (see
*Frege's Theorem and Foundations for Arithmetic*), and
inspiring the program of "logicism" (or the reduction of
arithmetic to logic) that was pursued in Whitehead and Russell's
(1910-13) monumental *Principia Mathematica*, and the
(early) Ludwig Wittgenstein's (1922) *Tractatus
Logico-philosophicus*.



Frege was mostly interested in formalizing arithmetic, and so
considered the logical forms of a relative minority of natural
language sentences in a deliberately spare notation - he
didn't take on the likes of (12)-(13). But work on the logical
(or syntactic) structure of the full range of sentences of natural
language has blossomed since then, initially in the work of Bertrand
Russell (1905), in his famous theory of definite descriptions (see
*Descriptions*), which he (1912) combined with his views about
the knowledge by "acquaintance" with sense-data and
universals into a striking "fundamental principle in the
analysis of propositions containing descriptions":



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



an early version of a proposal pursued by Logical Positivists, to be
discussed in the next sections below. Frege's and
Russell's formalizations are also indirectly the inspiration for
the subsequent work of Noam Chomsky and other "generative"
linguists and logicians (see *supplement)*. Whether
Frege's criterion of analyticity will work for the rest of II
and other analyticities depends upon the details of these latter
proposals, some of which are discussed in the *supplement*,


## 2. High Hopes



Influenced by these developments in logic, many philosophers in the
first half of the Twentieth Century thought analyticity could perform
crucial epistemological work not only in accounting for our apparently
*a priori* knowledge of mathematics, but also --with a
little help from British empiricism--of our understanding of
claims about the spatiotemporal world as well. Indeed,
"analysis" and the "linguistic turn" (Rorty,
1992) soon came to constitute the very way many Anglophone
philosophers characterized their work, particularly since such
analyses of what we mean by our words seemed to be the sort of
enterprise available to "armchair reflection" that seemed
to many a distinctive feature of that work (see Haug, 2014). Many
thought this project would also perform the more *metaphysical*
work of explaining the *truth* and *necessity* of
mathematics, showing not only how it is we could *know* about
these topics independently of experience, but how they could be
*true 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 combining
the two projects:



> 
> 
> What I shall call a 'full-blooded theory of analytic
> truth' takes the analytic truths to be those that hold solely by
> virtue 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 then
contemporary philosophers.



This seemed like a grand unified plan until Saul Kripke (1972) and
Hilary Putnam (1975) drew attention to fundamental differences between
the metaphysical and epistemic modalities that had tended to be run
together throughout this period. They pointed out that, for example,
"water is H2O" might well be *necessarily* true,
but not knowable *a priori*, and "The meter stick in
Paris is one meter long" might be knowable *a priori* but
not be necessarily true (that very stick might have been broken and
never used for measurements; see *A Priori Justification and
Knowledge*).



Once the metaphysical and epistemic issues are separated, it becomes
less obvious that mere matters of meaning could really explain all
*necessities*. Recall that Frege's ambition had been to
reduce mathematics to logic by showing how, substituting synonyms for
synonyms, every mathematical truth could be shown to be a logical one.
He hadn't gone on to claim that the logical truths
*themselves* were true or necessary by virtue of meaning alone.
These were "Laws of Truth" (Frege, 1918/84:58), and it
wasn't clear what sort of explanation could be provided for
them. Obviously, appealing merely to further synonym substitutions
wouldn't suffice. As Michael Devitt (1993a) pointed out:



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



It was certainly not clear that the truth of "All unmarrieds are
unmarrieds" is based on the same sort of arbitrary synonymy
facts that underlie "All bachelors are unmarried." In any
event, a different kind of account seemed to be needed (see
 footnotes 9 and 16).



Jerrold Katz and Paul Postal (1991, pp. 516-7) did claim that
adequate linguistic theory should, *inter alia*, explain why,
if *John killed Bill* is true, then so is *Bill is
dead.* However, as David Israel (1991) pointed out in reply:
"there are facts about English, about what propositions are
expressed by certain utterances, and then there is a non-linguistic
fact: that one proposition entails another" (p. 571). Utterances
of *sentences* are one thing; the *propositions* (or
*thoughts*) many different sentences may *express*,
quite another, and the two shouldn't be confused:



> 
> 
> It is just not true that if the *proposition* expressed by [an
> utterance of *John killed Bill*] is true that, then "in
> virtue of [natural language] so, necessarily, is" the
> *proposition* expressed by [an utterance of *Bill is
> dead*]. Rather, if the proposition that, according to the grammar
> of English, is expressed by [an utterance of *John killed
> Bill*] is true, then, in virtue of the structure of the
> *propositions* concerned, the *proposition* that,
> according to the grammar of English, is expressed by [an utterance of
> *Bill is dead*] must also be true.--(D. Israel, 1991, p. 71,
> emphasis added)
> 
> 
> 



Providing the metaphysical basis for logical truth is a fine issue
(see *Logical Truth*), but as Devitt (1993a and b) and others
(e.g., Paul Boghossian, 1996, Williamson, 2007) went on to stress, it
has been the epistemological issues about justifying our
*beliefs* in necessary truths that have dominated philosophical
discussions 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 (SS1.2), Frege had developed formal logic to account
for our apparently *a priori* knowledge of mathematics. It is
worth dwelling on the interest of this problem. It is arguably one of
the oldest and hardest problems in Western philosophy, and is easy
enough to understand: ordinarily we acquire knowledge about the world
by using our senses. If we are interested, for example, in whether
it's raining outside, how many birds are on the beach, whether
fish sleep or stars collapse, we look and see, or turn to others who
do. It is a widespread view that Western sciences owe their tremendous
successes precisely to relying on just such "empirical"
(experiential, experimental) methods. However, it is also a patent
fact about all these sciences, and even our ordinary ways of counting
birds, fish and stars, that they depend on often immensely
sophisticated mathematics, and mathematics does not seem to be known
on the basis of experience. Mathematicians don't do experiments
in the way that chemists, biologists or other "natural
scientists" do. They seem simply to *think*, seeming to
rely precisely on the kind of "armchair reflection" to
which many philosophers also aspire. In any case, they don't try
to justify their claims by reference to experiments, arguing that
twice two is four by noting that pairs of pairs tend in all cases
observed so far to be quadruples.



But how could mere processes of thought issue in any knowledge about
the independently existing external world? The belief that it could
would 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 philosophers
like Plato, Descartes and Leibniz and, more recently, Katz (1988,
1990), George Bealer (1987) and Laurence Bonjour (1998), these all
seem no better off than appeals to "revelation" to
establish 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 the
foundations of mathematics by showing how the axioms of arithmetic
could all be derived from pure logic by substitution of synonyms,
perhaps it could also illuminate the foundations of the rest of our
knowledge by showing how its claims could similarly be derived from
some kind of combination of logic and experience. Such was the hope
and program of Logical Positivism (see *Logical Empiricism*)
championed by, e.g., Moritz Schlick, A.J. Ayer and, especially, Rudolf
Carnap from about 1915 in Vienna and Berlin to well into the 1950s in
England and America. Of course, such a proposal did presume that all
of our concepts were somehow "derived" either from logic
or experience, but this seemed in keeping with the then prevailing
presumptions of empiricism, which, they assumed, had been vindicated
by the immense success of the empirical sciences.



For the Positivists, earlier empiricists, such as Locke, Berkeley and
Hume, had erred only in thinking that the mechanism of construction
was mere association. But association can't account for the
structure of even a simple judgment, such as *Caesar is bald*.
This is not merely the excitation of its constituent ideas,
*Caesar*, *is*, and *bald*, along the lines of
the idea of *salt* exciting the idea of *pepper*, but,
as Frege had shown, involves combining the noun *Caesar* and
the predicate *is bald* in a very particular way, a fact that
was important in accounting for more complex judgments such as
*Caesar is bald or not bald*, or *Someone is bald*. Our
thoughts and claims about the world have some kind of *logical
structure*, of a sort that seems to begin to be revealed by
Frege's proposals. Equipped with his logic, it was possible to
provide a more plausible formulation of conceptual empiricism: our
claims about the empirical world were to be *analyzed* into the
(dis)confirming experiences out of which they must somehow have been
*logically* constructed.



But constructed out of *which* experiences? For the
Positivists, the answer seemed obvious: out of the experiential
*tests* that would standardly *justify*, *verify*
or *confirm* the claim. Indeed, as Ayer (1934, chap 1) made
plain, a significant motivation for the Positivists was to save
empirical knowledge from the predations of traditional sceptical
arguments about the possibility that all of life is a dream or the
deception of an evil demon: if meaning could be tied to verification,
such possibilities could be rendered "meaningless" because
unverifiable (see Jerry Fodor, 2001, pp. 3-5, for a penetrating
discussion of this motivation). In any event, interpreting
Wittgenstein's (1922) *Tractatus* claims about the nature
of language epistemologically along the lines of the American
philosopher, C.S. Peirce, they proposed various versions of their
"Verifiability Theory of Meaning," according to which the
meaning (or what they called the "cognitive significance")
of any sentence was *constituted* by the conditions of its
empirical
 (dis-)confirmation.[5]
 Thus, to say that the temperature of a liquid is of a certain
magnitude is to say, for example, that the mercury in a thermometer
immersed in the liquid would expand to a certain point marked by a
numeral representing that magnitude, a claim that would ordinarily be
disconfirmed if it didn't. Closer to "experience":
to say that there is a cat on a mat is just to say that certain
patterns of certain familiar visual, tactile and aural appearances are
to be expected under certain circumstances.



The project of providing analyses in this way of especially
problematic concepts like those concerning, for example, *material
objects, knowledge, perception, causation, expectation, freedom*,
and *the self*, was pursued by Positivists and other analytic
philosophers for a considerable period (see Carnap 1928 [1967] for
some 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 of
science, as "operationalism" ; and with regard to the
claims about people's mental lives, "analytical
behaviorism" (the relevant experiential basis of mental claims
being taken to be observations of others' behavior). Although
these programs became extremely influential, and some form of the
verifiability criterion was often (and sometimes still is) invoked in
physics and psychology to constrain theoretical speculation, they
seldom, if ever, met with any serious success. No sooner was an
analysis, say, of "material object" or
"freedom" or "expectation," proposed than
serious counterexamples were raised and the analysis revised, only to
be faced with still further counterexamples (see Roderick Chisholm
1957, and Fodor 1981, for discussion). Despite what seemed its initial
plausibility, philosophers came to suspect that the criterion, and
with it the very notion of analyticity itself, rested on some
fundamental 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 should
analyses be of any conceivable interest? After all, if an analysis
consists in providing the definition of an expression, then it should
be providing a synonym for it, and this, then, should be wholly
uninformative: if *brother* is analyzed as the presumably
synonymous *male sibling*, then the claim *Brothers are male
siblings* should be synonymous with *Brothers are
brothers*, and thinking the one should be no different from
thinking the other. But, aside from such simple cases as
*brother* and *bachelor*, proposed analyses, if
successful, often seemed quite non-obvious and philosophically
informative. The proposed reductions of, say, material object
statements to sensory ones (even where successful) were often fairly
complex, had to be studied and learned, and so could hardly be
uninformative. So how could they count as seriously
 analytic?[6]



This is "the paradox of analysis," which can be seen as
dormant in Frege's own move from his (1884) focus on definitions
to his more controversial (1892a) doctrine of "sense,"
where two senses are distinct if and only if someone can think a
thought containing the one but not other, as in the case of the senses
of "the morning star" and "the evening star."
If analyses or definitions preserved sense, then, unlike the case of
"morning star" and "evening star," whenever
one thought the definiendum, one should thereby be thinking the
definiens. And perhaps one can't think Bill is Bob's
brother without thinking Bill is Bob's male sibling. But few of
Frege's definitions of arithmetic concepts are nearly so simple
(see *Gottlob Frege*, SS2.5). In their case, it seems
perfectly possible to think the definiendum, say, *number*,
without thinking the elaborate definiens Frege provided (cf. Bealer
1982, Michael Dummett 1991, and John Horty 1993, 2007, for extensive
discussions 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, for
which further technical moves within the program might be made. For
example, one might make further distinctions within the theory of
sense between an expression's "content" and the
specific "linguistic vehicle" used for its expression, as
in Fodor (1990a) and Horty (1993, 2007); and perhaps distinguish
between the truth-conditional "content" of an expression
and its idiosyncratic role, or "character," in a language
system, along the lines of the distinction David Kaplan (1989)
introduced to deal with indexical and demonstrative expressions (such
as *I*, *now*, and *that*; see
*Demonstratives*, and *Narrow Mental Content*, as well
as Stephen White, 1982). Perhaps analyses could be regarded as
providing a particular "vehicle," having a specific
"character," that could account for why one could
entertain a certain concept without entertaining its analysis (cf.
Gillian Russell 2008, and Paul Pietroski 2002, 2005 and 2018 for
related suggestions).



However, the problems with the program seemed to many philosophers to
be deeper than merely technical. By far, the most telling and
influential of the criticisms both of the program, and then of
analyticity in general, were those of Quine, who began as a great
champion of the program (see esp. his 1934), and whose subsequent
objections therefore carry special weight. The reader is well-advised
to consult particularly his (1956 [1976], hereafter "CLT")
for as rich and deep a discussion of the issues up to that time as one
might find. The next two sections abbreviate some of that
discussion.


### 3.2 Problems with Logicism



Although pursuit of the logicist program produced a great many
insights into the nature of mathematics, there emerged a number of
serious difficulties with it. Right from the start there was, of
course, the problem of the logical truths themselves. Simply saying,
as Frege had, that they are "Laws of Truth" doesn't
seem to explain how we could know them *a priori*. But perhaps
they, too, are "analytic" involving perhaps some sort of
"implicit" acceptance of certain rules merely by virtue of
accepting certain patterns of reasoning. But any such proposal has to
account for people's frequent, often apparent violations of
rules of logic in fallacious reasoning and in ordinary speech, as well
as of disputes about the laws of logic of the sort that are raised,
for example, by mathematical intuitionists, who deny the Law of
Excluded Middle ("p or not p"), or, more recently, by
"para-consistent" logicians, who argue for the toleration
even 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 be
a reason for regarding them as "synthetic" in Kant's
sense (see Frege 1884 [1980], SS88, Katz 1988, pp. 58-9, and
MacFarlane 2002)?



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



> 
> 
> Consider...the logical truth "Everything is
> self-identical", "(x)(x = x)". We can say that it
> depends for its truth on traits of the language (specifically on the
> usage of "="), and not on traits of its subject matter;
> but we can also say, alternatively, that it depends on an obvious
> trait, viz., self-identity, of its subject matter, viz., everything.
> The tendency of [my] present reflections is that there is no
> difference. (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 is
> merely that the linguistic doctrine of elementary logical truth
> likewise leaves explanation unbegun. I do not suggest that the
> linguistic doctrine is false and some doctrine of ultimate and
> inexplicable insight into the obvious trait of reality is true, but
> only that there is no real difference between these two
> pseudo-doctrines. (CLT, p. 113)
> 
> 
> 



As we'll see, this is the seed for the challenge that continues
to haunt proposals about the analytic to this day: what explanatory
difference is there between "analytic" claims and simply
widely and firmly held beliefs, such as that *The earth has existed
for many years* or *There 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 no
difference can be sustained, then it's difficult to see the
significance 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 crucial
axioms, his *prima 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 predicate *x is not a member of
itself*? If there were a set for that predicate, that set itself
would be a member of itself if and only if it wasn't;
consequently, there could be no such set. Therefore Frege's
Basic Law V couldn't be true (but see *Frege's Theorem
and Foundations for Arithmetic* for ways to rescue something close
to logicism, discussed in SS5 below).



What was especially upsetting about Russell's paradox was that
there seemed to be no intuitively satisfactory way to repair set
theory in a way that could lay claim to being as obvious and/or merely
a matter of logic or meaning in the way that Frege and the Positivists
had hoped. Various proposals were made, but all of them seemed simply
tailor-made to avoid the paradox, and seemed to have little
independent appeal (although see Boolos, 1971, for a defense of the
"iterative" notion of set). Certainly none of them
appeared to be analytic. Indeed, as Quine notes:



> 
> 
> What we do [in set theory] is develop one or another set theory by
> obvious reasoning, or elementary logic, from unobvious first
> principles 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 the
analytic. After all, aren't matters of meaning, unlike matters
of fact, in the end really matters of arbitrary conventions about the
use of words? For example, someone could invest a particular word,
say, "schmuncle," with a specific meaning merely by
stipulating that it mean, say, unmarried uncle. Wouldn't that
afford a basis for claiming then that "A schmuncle is an
uncle" is analytic, or knowable to be true by virtue of the
(stipulated) meanings of the words alone?



Carnap (1956a) proposed setting out the "meaning
postulates" of a scientific language as just such conventional
stipulations. This had the further advantage of allowing terms to be
"implicitly defined" by their conventional roles in such
postulates, which might then serve as part of a theory's laws or
axioms. The strategy seemed especially appropriate for defining
logical constants, as well as for dealing with cases like (11)-(13)
above, e.g. "Red is a color," where mere substitution of
synonyms might not
 suffice.[9]
 So perhaps what philosophical analysis is doing is revealing the
tacit conventions of ordinary language, an approach particularly
favored by Ayer (1934/52).



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



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



If so, and if logic is established by convention, then one would need
a *meta*-meta-theory to establish the conventions for the use
of the logical particles of the meta-theory, and so on for what seemed
like an infinite regress of meta-theories. This is certainly an
argument that ought to give the proponents of the conventionality of
logic pause: for, indeed, how could one hope to set out the general
conventions for "all" or
"if...then..." without at some point using the
notions of "all" and "if...then..."
("ALL instances of a universal quantification are to be
true". "IF *p* is one premise, and *if p then
q* another, THEN conclude *q*")? (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 between
different, incompatible versions of set theory needed for mathematics
that were developed in the wake of Russell's paradox. Here:



> 
> 
> We find ourselves making deliberate choices and setting them forth
> unaccompanied by any attempt at justification other than in terms of
> elegance and convenience. (CLT, p. 117).
> 
> 
> 



But then it's hard to see the difference between mathematics and
the conventional "meaning postulates" Carnap had proposed
for establishing the rest of science --and then the difference
between them and any other claims of a theory. As Quine goes on to
argue, although stipulative definitions (what he calls
"legislative postulations")



> 
> 
> contribute truths which become integral to the corpus of truths, the
> artificiality of their origin does not linger as a localized quality,
> but suffuses the corpus. If a subsequent expositor singles out those
> once legislatively postulated truths again as postulates, this
> signifies nothing... He could as well choose his postulates from
> elsewhere in the corpus, and will if he thinks it this serves his
> expository ends. (CLT, pp. 119-20)
> 
> 
> 



Carnap's legislated "meaning postulates" should
therefore be regarded as just an arbitrary selection of sentences a
theory presents as true, a selection perhaps useful for purposes of
exposition, but no more significant than the selection of certain
towns in Ohio as "starting points" for a journey Quine
(1953 [1980a], p. 35).



Quine's observation certainly seems to accord with scientific
practice. Suppose, say, Newton, himself, had explicitly set out
"F=ma" as a stipulated definition of "F":
would "F=ma" be therefore justifiable by knowing the
meaning the words alone? Our taking such a stipulation seriously would
seem to depend upon our view of the plausibility of the surrounding
theory as a whole. After all, as Quine continues:



> 
> 
> [S]urely the justification of any theoretical hypothesis can, at the
> time of hypothesis, consist in no more than the elegance and
> convenience which the hypothesis brings to the containing bodies of
> laws and data. How then are we to delimit the category of legislative
> postulation, short of including under it every new act of scientific
> hypothesis? (CLT, p. 121)
> 
> 
> 



So conventional legislation of claims, such as Carnap's meaning
postulates, affords the claims no special status. As vivid examples,
Putnam (1965 [1975]) discusses in detail revisions of the definitions
of "straight line" and "kinetic energy" in the
light 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 and
> changes, through more or less arbitrary and deliberate revisions and
> additions of our own, more or less directly occasioned by the
> continuing stimulation of our sense organs. It is a pale grey lore,
> black with fact and white with convention. But I have found no
> substantial reasons for concluding that there are any quite black
> threads 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 expresses
a tremendously influential view of Quine's that led several
generations of philosophers to despair not only of the
analytic-synthetic distinction, but of the category of *a
priori* knowledge entirely. The view has come to be called
"confirmation holism," and Quine had expressed it more
shortly a few years earlier, in his widely read article, "Two
Dogmas of Empiricism" (1953 [1980a]):



> 
> 
> Our statements about the external world face the tribunal of sense
> experience 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 same
coin, the belief that "each statement, taken in isolation from
its fellows, can admit of confirmation or infirmation at all"
(p. 41), i.e., the very version of the Verifiability Theory of Meaning
we have seen the Positivists enlisted in their effort to
"analyze" the claims of science and
 commonsense.[12]



Quine bases his "confirmation holism" upon observations of
Pierre Duhem (1914 [1954]), who drew attention to the myriad ways in
which theories are supported by evidence, and the fact that an
hypothesis is not (dis)confirmed merely by some specific experiment
considered in isolation from an immense amount of surrounding theory.
Thus, a thermometer will be a good indication of ambient temperature
only if it's made of the right materials, calibrated
appropriately, and there aren't any other forces at work that
might disturb the measurement--and, of course, only if the
background laws of physics and other beliefs that have informed the
design of the measurement are sufficiently correct. A failure of the
thermometer to measure the temperature could be due to a failure of
any of these other conditions, which is, of course, why experimenters
spend so much time and money constructing experiments to
"control" for them. Moreover, with a small change in our
theories or background beliefs, or just in our understanding of the
conditions for measurement, we might change the tests on which we
rely, but often without changing the meaning of the sentences whose
truth we might be trying to establish (which, as Putnam 1965 [1975]
pointed out, is precisely what practicing scientists regularly
do).



What is novel--and highly controversial--about Quine's
understanding of these commonplace observations is his extension of
them to claims presumed by most people (e.g., by Duhem himself) to lie
outside their scope, viz., the whole of mathematics and even logic! It
is this extension that seems to undermine the traditional *a
priori* status of these latter domains, since it appears to open
the possibility of a revision of logic, mathematics and any supposed
analytic claims in the interest of the plausibility of the one,
overall resulting empirical theory--containing the empirical
claims *and* those of logic, mathematics and the analytic!
Perhaps this wouldn't be so odd should the revisability of such
claims permit their ultimately admitting of a justification that
didn't involve experience. But this is ruled out by
Quine's insistence that scientific theories, along with their
logic and mathematics, are confirmed "*only*" as
"corporate
 bodies."[13]



One might wonder why, though, there have historically been virtually
no revisions of mathematics on empirical grounds. A common example
offered is how Riemannian replaced Euclidean geometry in
Einstein's theory of General Relativity. But this mis-interprets
the history. Non-Euclidean geometries were purely conceptual
developments in the 19th C. by mathematicians such as Gauss, Riemann
and Lobechevsky. Einstein simply argued in 1916 that one of these
conceptual possibilities seemed to be better supported by physics than
was the traditional Euclidean one, and should therefore be taken to be
true of actual space(-time). It is only this latter claim that is
empirical.



Certainly, though, Quine's holism has been an epistemic
possibility that many have taken seriously. For example, influenced by
Quine's claim, Putnam (1968 [1975]) argued that one ought to
revise even elementary logic in view of the surprising results of
quantum mechanics (a proposal not without its critics, see *Quantum
Logic and Probability Theory*). And in his (1962 [1975] he also
argued that it isn't hard to imagine discovering that a
purported analytic truth, such as *Cats are animals*, could be
given up in light of discovering that the little things are really
cleverly disguised robots controlled from Mars (but see Katz, 1990,
pp. 216ff and G. Russell, 2008, for replies, and the
*supplement* SS3 for further discussion).


### 3.5 Quine on Meaning in Linguistics



Quine's discussion of the role of convention in science seems
right; but how about the role of meaning in ordinary natural language
(cf. Chomsky's 2000 cautions mentioned in
 footnote 10)?
 Is it really true that in the "pale grey lore" of all the
sentences we accept, there aren't some that are
"white" somehow "by virtue of the very meanings of
their 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 are
attorneys," or "A fortnight is a period of fourteen
days"? As Grice and Strawson (1956) and Putnam (1965 [1975])
pointed out, it is unlikely that so intuitively plausible a
distinction should turn out to have *no basis at all* in
fact.



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) and
related articles. In his (1953 [1980a]) he pressed his objection to
analyticity further to the very ideas of synonymy and the linguistic
meaning of an expression, on which, we saw, Frege's criterion of
analyticity crucially relied. His objection is that he sees no way to
make any serious explanatory sense of them. He explored plausible
explanations in terms of "definition,"
"intension," "possibility," and
"contradiction,", pointing out that each of these notions
seems to stand in precisely as much need of explanation as synonymy
itself (recall our observation in SS1.2 above regarding the lack
of any *formal* contradiction in "Some pediatricans
aren't doctors"). The terms seem to be mutually definable
in what seems to be a--viciously?--small "closed curve
in space" (Quine 1953 [1980a], p. 30). Though they might be
invoked to explain one another, they could not in the end answer the
challenge of how to distinguish an analytic claim from simply a
tenaciously held belief.



To take a recent example, David Chalmers (2012) revisits
Carnap's (1956b) proposal for basing synonymy on
"intension" by way of eliciting a person's judgments
about the extension of a term/concept in all possible
 worlds:[14]



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



But how are the informants to understand the questions they're
being asked? If they understand the term "possible" as
logicians do, as *truth in a set-theoretically specified
model*, then it will be too weak: there are obviously models in
which synonymous expressions e.g., "horse" and
"Pferd," or "bachelor" and "unmarried
male*"* are assigned non-overlapping sets (cf. Quine
[1953 [1980a], pp. 22-3), so that it's logically possible
for there be a horse that's not a Pferd, or a bachelor
that's married (again, "a married bachelor" is
formally contradictory only if one substitutes synonyms for synonyms;
but we certainly can't appeal to *synonymy* in trying to
*define* synonymy). But if "possible" is understood
(as it ordinarily would be) as merely *imaginable*, then it
will be far too strong, ruling out ideas that the scientifically
under-informed might find impossible, e.g., curved space-time,
something having the properties of both waves and particles, or
completely unconscious thoughts (which, at least, e.g., John Searle
1992, pp. 155-6, and Galen Strawson 1994, pp. 166-7 report
having trouble conceiving). As Quine (1953 [1980a]) famously argued,
such appeals to informant verdicts will only work if the informants
understand the questions as about *the very terms the proposed test
is supposed to define*, viz., "possible" as
constrained by synonymy or preservation of meaning. Although, as many
have noted (e.g., Williamson 2007, p. 50), there may be explanatory
circularities in the best of theories, the circularity here seems
particularly vicious, with the relevant ideas appearing not to perform
any explanatory work other than bringing in each other's
laundry.



Why was Quine so convinced of this last claim? Because he thought it
was possible to provide a satisfactory explanation of human language
without them, indeed, without any mentalistic notions at all. In his
(1953 [1980b], 1960 [2013] and 1974) he sketched a behavioristic
theory of language that doesn't rely on the postulation of
determinate meaning or reference, and argued that, indeed, translation
is "indeterminate": there is "no fact of the
matter" about whether two expressions do or do not have the same
meaning (see *Indeterminacy of Translation*). This would appear
to imply that there are pretty much no facts of the matter about
people's mental lives at all! For, if there is no fact of the
matter about whether two people mean the same thing by their words,
then there is no fact of the matter about the content of
anyone's thoughts. Quine himself took this consequence in
stride--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 showed
the "baselessness of intentional idioms and the emptiness of a
science of intention" (1960 [2013], p. 202). Needless to say,
many subsequent philosophers have not been happy with this view, and
have 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 to
explain *the appearance* of the analytic. It just seems an
empirical fact that most people would spontaneously distinguish our
original two sets of sentences (SS1) by saying that sentences of
the second set, such as "All pediatricians are doctors for
children" are "true by definition," or could be
known to be true just by knowing the meanings of the constituent
words. Moreover, they might agree about an indefinite number of
further 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's *nothing*
people are getting at in these judgments.


#### 3.6.1 Centrality



Quine's (1953 [1980a]) initial explanation of the appearance of
the analytic invoked his metaphor of the web of belief, claiming that
sentences are more or less revisable, depending upon how
"peripheral" or "central" their position is in
the web, the more peripheral ones being closer to experience. The
appearance of sentences being "analytic" is simply due to
their being, like the laws of logic and mathematics, comparatively
central, and so are given up, if ever, only under extreme pressure
from the peripheral forces of experience. But no sentence is
absolutely immune from revision; all sentences are thereby empirical,
and none is actually analytic.



There are a number of problems with this explanation. In the first
place, centrality and the appearance of analyticity don't seem
to be so closely related. As Quine (1960, p. 66) himself noted, there
are are plenty of central, unrevisable beliefs that don't seem
remotely 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 of
what seem analytic aren't seriously central: "Bachelors
are 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 and
Loomis, 2010, p. 118).



Secondly, it's not mere unrevisability that seems distinctive of
the analytic, but rather *a certain sort of unintelligibility*:
for all the unrevisability of "There have been black
dogs," it's perfectly possible to *imagine* it to
be false. In contrast, what's peculiar about analytic claims is
that their denials often seem peculiarly impossible to seriously
think: it seems distinctively impossible to imagine a married
bachelor. Now, of course, as we noted, this could be due simply to a
failure of imagination. But what's striking about about the
unrevisability of many apparently analytic cases is that they
don't appear to be like scientifically controversial cases such
as curved space-time or completely unconscious thoughts. The standard
cases about, e.g., bachelors or pediatricians seem entirely innocuous.
Far from unrevisability explaining analyticity, *it would seem to
be analyticity that explains this peculiar unrevisability*: the
only reason someone might balk at denying bachelors are unmarried is
that, well, that's just what the word "bachelor"
 means![15]
 The challenge, though, is to clarify the basis for this sort of
explanation.



It is important to note here a crucial change that Quine (and earlier
Positivists) casually introduced into the characterization of the
*a priori*, and consequently into much of the now common
understanding of the analytic. Where Kant and others had traditionally
assumed that the *a priori* concerned beliefs
"justifiable independently of experience," Quine and many
other philosophers of the time came to regard it as consisting of
beliefs "unrevisable in the light of experience." And, as
we have seen, a similar status is accorded the at least apparently
analytic. However, this would imply that people taking something to be
analytic or *a priori* would have to regard themselves as being
*infallible* about it, forever unwilling to revise it in light
of further evidence or argument. But this is a further claim that many
defenders of the traditional notions need not embrace (consider,
again, the disputes philosophers have about the proper analysis of
terms such as "knowledge" or "freedom").



Indeed, a claim might be in fact analytic and justifiable
independently of experience, but nevertheless perfectly well revised
in the light of it. Experience, after all, might mislead us, as it
(perhaps) misled Putnam when he suggested revising logic in light of
difficulties in quantum mechanics, or suggested revising "cats
are animals," were we to discover the things were robots. Just
which claims are genuinely analytic and *a priori* might not be
available in the "armchair" at the introspective or
behavioral surface of our lives in the way that Quine and much of the
philosophical tradition has assumed. Certainly the "dispositions
to 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" discussed
in SS4.1 below). Behavioral dispositions in general may have any
of a variety of aetiologies that aren't clearly distinguishable
in actual behavior (one wonders how much of Quine's seamless
epistemology went hand in hand with his mentalistically seamless
behavioristic psychology). The relevant dispositions might be hidden
more deeply in our minds, and our access to them as fallible as our
access to any other such facts about ourselves. The genuinely analytic
may be a matter of difficult reflective analysis or deep linguistic
theory (see Bealer, 1987, Bonjour 1998, Rey, 1998, and
*supplement*), a possibility to which we will return
shortly.


#### 3.6.2 One Criterion Concepts



In his expansion of Quine's point, Putnam (1962 [1975]) tried to
rescue what he thought were theoretically innocuous examples of
analytic truths by appeal to what he called
"one-criterion" concepts, or concepts like, e.g.,
*pediatrician, bachelor, widow*, where there seems to be only
one "way to tell" whether they apply. However, as Fodor
(1998) pointed out, so stated, this latter account won't suffice
either, since the notion of "criterion" seems no better
off than "meaning" or "analytic." Moreover, if
there were one way to tell what's what, there would seem,
trivially, to be indefinite numbers of other ways: look for some
reliable 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 so
now we would be faced with saying which of these ways is genuinely
"criterial," which would seem to leave us with the same
problem we faced in saying which way appears to be
"analytic."



Fodor (1998) tried to improve on Putnam's proposal by suggesting
that a criterion that appears to be analytic is the one on which all
the other criteria depend, but which does not depend upon them. Thus,
telling that someone is a bachelor by checking out his gender and
marriage status doesn't depend upon telling by asking his
friends, but telling by asking his friends does depend upon telling by
his gender and marriage status; and so we have an explanation of why
"bachelors are unmarried males" seems analytic, but, said
Fodor, without it's actually being so (perhaps somewhat
surprisingly, given his general "asymmetric dependence"
theory of content, see his 1990b and Rey, 2009, to be discussed
shortly, SSSS4.2-4.3).



However, such asymmetric dependencies among criteria alone will not
"explain (away)" either the reality or the appearance of
the analytic, since there would appear to be asymmetric dependencies
of the proposed sort in non-analytic cases. Natural kinds are dramatic
cases in point (see Putnam 1962 [1975], 1970 [1975], 1975). At some
stage in history probably the only way anyone could tell whether
something was a case of polio was to see whether there was a certain
constellation of standard symptoms, e.g. paralysis; other ways
(including asking others) asymmetrically depended upon that way. But
this wouldn't make "All polio cases exhibit
paralysis" remotely analytic--after all, the standard
symptoms for many diseases can sometimes be quite misleading. It
required serious empirical research to discover the proper definition
of a natural kind term like "polio." Precisely as Putnam
otherwise stressed, methods of testing are so variable it is doubtful
that even "single criterion" tests could provide a basis
for the identification of the stable meanings of words.



Indeed, as many philosophers in the wake of Quine's and
Putnam's work came to suspect, the recourse of philosophy in
general to *epistemology* to ground semantics may have been a
fundamental mistake. It was an enticing recourse: it seemed to offer a
way to dispatch philosophical disputes and secure empirical knowledge
from sceptical challenges regarding demons and dreams. But the above
difficulties suggested that those disputes and challenges would need
to be met in some other way, perhaps by looking not to words, but to
the world instead.


#### 3.6.3 The World, not Words



Indeed, another strategy that a Quinean can deploy to explain the
appearance of the analytic is to claim that analyses are really not of
the meanings of *words*, but of the actual *phenomena in the
world* to which they refer (see Fodor, 1990b, 1998). Thus, claims
that, e.g., cats are animals, triangles are three-sided, or that every
number has a successor should not be construed as claims about the
meanings of the words "cat", "triangle" or
"number," but about the *nature* of *cats,
triangles* and *numbers* themselves. Arguably, many such
claims, if they are true, are *necessarily* so (cf., Kripke,
1972; Putnam, 1975), and may be commonly understood to be, and this
might make them seem analytic. But then we would be faced with
precisely the challenge that Quine raised: how to distinguish claims
of analyticity from simply deeply held beliefs about "the
nature" of things.



This recourse to the world may, however, be a little too swift. Cases
of (arguably) deeply explanatory natural kinds such as *polio*
or *cats* contrast dramatically with cases of more superficial
kinds like *bachelor* or *fortnight*. whose natures are
not specified by any explanatory science, but are pretty much
exhausted by what would seem to be the meanings of the words. Again,
unlike the case of polio and its symptoms, the reason that gender and
marriage status are the best way to tell whether someone is a bachelor
is, again, that that's just what "bachelor" means.
Indeed, should a doctor propose revising the test for polio in the
light of better theory--perhaps reversing the dependency of
certain tests--this would not even begin to appear to involve a
change in the meaning of the term. Should, however, a feminist
propose, in the light of better politics, revising the use of
"bachelor" to include women, this obviously would. If the
appearance of the analytic is to be explained away, it needs to
account for such differences in our understanding of different sorts
of revisions in our beliefs, which don't *appear* to be
issues regarding the external world.


## 4. Post-Quinean Strategies



There has been a wide variety of responses to Quine's
challenges. Some, for example, Davidson (1980), Stich (1983) and
Dennett (1987), seem simply to accept it and try to account for our
practice of meaning ascription within its "non-factual"
bounds. Since they follow Quine in at least claiming to forswear the
analytic, we will not consider their views further here. Others, who
might be (loosely) called "neo-Cartesians," reject
Quine's attack as simply so much prejudice of the empiricism and
naturalism that they take to be his own uncritical dogmas (SS4.1
in what follows). Still others hope simply to find a way to break out
of the "intentional circle," and provide an account of at
least what it means for one thing (a state of the brain, for example)
to mean (or "carry the information about") another
external phenomenon in the world (SS4.2). Perhaps the most
trenchant reaction has been that of empirically oriented linguists and
philosophers, who look to a specific explanatory role the analytic may
play in an account of thought and talk (SS4.3). This role is
currently being explored in considerable detail in the now various
areas of research inspired by the important linguistic theories of
Noam Chomsky (SS4.4, and *supplement, Analyticity and Chomskyan
Linguistics*).


### 4.1 Neo-Cartesianism



The most unsympathetic response to Quine's challenges has been
essentially 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] is
> seemingly (a) direct or immediate, nondiscursive, and yet also (b)
> intellectual or reason-governed ... [It] depends upon nothing
> beyond an understanding of the propositional content itself....
> (p. 102)
> 
> 
> 



Bealer (1987, 1999) defends similar proposals. Neither Bonjour nor
Bealer are in fact particularly concerned to defend the analytic by
such claims, but their recourse to mere understanding of propositional
content is certainly what many defenders of the analytic have had in
mind. Katz (1998, pp. 44-5), for example, explicitly made the
very same appeal to intuitions on behalf of the analytic claims
supported by his semantic theory. Somewhat more modestly, Peacocke
(1992, 2004) claims that possession of certain logical concepts
requires that a person find certain inferences "primitively
compelling," or compelling not by reason of some inference that
takes "their correctness...as answerable to anything
else" (1992, p. 6; see also his 2004, p. 100 and the other
references in fn 9 above for the strategy, and fn 7, as well as
Harman, 1996 [1999], and Horwich, 2000, for qualms).



Perhaps the simplest reply along these lines emerges from a suggestion
of David Lewis (1972 [1980]), who proposes to implicitly define, e.g.,
psychological terms by conjoining the "platitudes" in
which they appear:



> 
> 
> Include only platitudes that are common knowledge among us -
> everyone knows them, everyone knows that everyone else knows them, and
> so on. For the meanings of our words are common knowledge, and I am
> going to claim that names of mental states derive their meaning from
> these platitudes. (1972 [1980], p. 212)
> 
> 
> 



Enlarging on this idea, Frank Jackson (1998) emphasizes the role of
intuitions about possible cases, as well as the need sometimes to
massage such intuitions so as to arrive at "the hypothesis that
best makes sense of [folk] responses" (p. 36; see also pp.
 34-5).[16]



The Quinean reply to all these approaches is, again, his main
challenge: how in the end are we to distinguish such claims of
"rational insight," "primitive compulsion,"
inferential practices or folk beliefs, from merely some deeply
entrenched empirical convictions, folk practices or, indeed, from mere
dogmas? Isn't the history of thought littered with what have
turned out to be deeply mistaken claims, inferences and platitudes
that 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 people
displaying to correction of the fallacies they commit in a surprising
range of ordinary thought (cf. fn 7 above); or in a more disturbing
vein, how the gifted mathematician, John Nash, claimed that his
delusional ideas "about supernatural beings came to me the same
way that my mathematical ideas did" (Nasar 1998, p. 11).
Introspected episodes, primitive compulsions, intuitions about
possibilities, or even tacit folk theories alone are not going to
distinguish the analytic, since these all may be due as much to
people's (possibly mad!) empirical theories as to any special
knowledge of meaning.



A particularly vivid way to feel the force of Quine's challenge
is afforded by a recent case that came before the Ontario Supreme
Court concerning whether laws that confined marriage to heterosexual
couples violated the equal protection clause of the constitution (see
Halpern *et al*. 2001). The question was regarded as turning in
part on the meaning of the word "marriage", and each party
to the dispute solicited affidavits from philosophers, one of whom
claimed that the meaning of the word *was* tied to
heterosexuality, another that it *wasn't*. Putting aside
the complex moral-political issues, Quine's challenge can be
regarded as a reasonably sceptical request to know how any serious
theory of the world might settle it. It certainly wouldn't be
sufficient merely to claim that marriage is/isn't necessarily
heterosexual on the basis of common "platitudes," much
less on "an act of rational insight [into] the propositional
content itself"; or because speakers found the inference from
marriage to heterosexuality "primitively compelling" and
couldn't imagine gay people getting
 married![17]



Indeed, some philosophers have offered some empirical evidence that
casts doubt on just how robust the data for the analytic might be. The
movement of "experimental philosophy" has pointed to
evidence of considerable malleability of subject's
"intuitions" with regard to the standard kinds of thought
experiments on which philosophical defenses of analytic claims
typically rely. Thus, Weinberg, Nichols and Stich (2001) found
significant cultural differences between responses of Asian and
Western students regarding whether someone counted as having knowledge
in a standard "Gettier" (1963) example of accidental
justified true belief; and Knobe (2003) found that
non-philosophers' judgments about whether an action is
intentional depended on the (particularly negative) moral qualities of
the action, and not, as is presumed by most philosophers, on whether
the action was merely intended by the agent. Questions, of course,
could be raised about these experimental results (How well did the
subjects understand the project of assessing intuitions? Did the
experiments sufficiently control for the multitudinous
"pragmatic" effects endemic to polling procedures? To what
extent are the target terms merely polysemous - see
*supplement*, SS3- allowing for different uses in
different contexts?) However, the results do serve to show how the
determination of meaning and analytic truths can be regarded as a far
more difficult empirical question than philosophers have traditionally
supposed (see Bishop and Trout, 2005, and Alexander and Weinberg,
2007, for further discussion).


### 4.2 Externalist Theories of Meaning



Developing the strategy of SS3.3C above, Externalist theories of
meaning (or "content") try to meet at least part of
Quine's challenge by considering how matters of meaning need not
rely on *epistemic*. or really *any* *internal*
connections among thoughts or beliefs, in the way that many
philosophers had traditionally supposed, but as involving largely
causal and social relations between uses of words and the phenomena in
the world that they pick out. This suggestion gradually emerged in the
work of Putnam (1962 [1975], 1965 [1975] and 1975), Kripke (1972
[1980]) and Burge (1979, 1986), but it took the form of positive
theories in, e.g., the work of Devitt (1981, 2015), Dretske (1988) and
Fodor (1990b), who tried to base meaning in various actual or
co-variational causal relations between states of the mind/brain and
external phenomena (see *Indicator Semantics*; as well as the
work on "teleosemantics" of Millikan, 1984), Papineau,
1987, and Neander, 1995, 2017, who look to mechanisms of natural
selection; see *Teleological Theories of Mental Content*).



Consider, for example, Fodor's proposal. Simplifying it
slightly, Fodor (1990b) claimed that



> 
> 
> a symbol *S* means *p* **if**
> 
> 
> 
> (i)
> under some conditions, C, it's a *law* that *S*
> is entokened iff *p*, and
> (ii)
> any other tokening of *S* synchronically depends upon (i),
> but not *vice versa*.
> 
> 



Thus, tokenings of "horse" mean *horse* because
there are (say, optimal viewing) conditions under which tokenings of
"horse" co-vary with horses, and tokenings of
"horse" caused by cows asymmetrically depend upon that
fact. The intuitive idea here is that what makes "horse"
mean *horse* 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 not *vice
versa*: getting things right doesn't depend upon getting
them wrong. The law in (i), so to say, "governs" the
tokenings of (ii). (Note that this condition is *metaphysical*,
appealing to *actual laws* of entokenings, and not upon
asymmetric dependencies between *epistemic* criteria suggested
by Fodor in his defense of Putnam we discussed in SS3.6.2.)



Fodor's and related proposals are not without their problems
(see Loewer, 1996, Rey, 2009 and *Causal Theories of Mental
Content*). Nevertheless, it's worth noting that,
*were* such theories to succeed in providing the kind of
explanatorily adequate, non-circular account of intentionality to
which they aspire, they would go some way towards saving at least
intentional psychology from Quine's attack, and provide at least
one *prima facie* plausible, naturalistic strategy for
distinguishing facts about meaning from facts about mere belief. The
proposals, unlike those in the traditions of Carnap or of
neo-Cartesians, have at least the *form* of a serious
reply.



However, even if such externalist strategies, either Fodor's or
teleosemantic ones, were to save intentionality and meaning, they
would do so only by forsaking the high hopes we noted in SS2
philosophers harbored for the analytic. For externalists are typically
committed to counting expressions as "synonymous" if they
happen to be linked in the right way to the same external phenomena,
even if a thinker couldn't realize that they are by *a
priori* (or, at any rate, "armchair") reflection
alone. By at least the Fregean substitution criterion (SS1.2),
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 Samuel
Clemens," since in each of these cases, something may co-vary in
the relevant way with tokenings of the expression on one side of the
identity if and only if it co-varies with tokenings of the one on the
other (similar problems and others arise for teleosemantics; see Fodor
1990b, pp. 72-73).



Of course, along the lines of the worldly turn we noted in
SS3.6.3, an externalist might cheerfully just allow that some
sentences, 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 an
older philosophical tradition less interested in the meanings of our
*words* and *concepts*, and more interested in the
"essences" of *the worldly phenomena they pick
out*. Locke (1690 [1975], II, 31, vi), for example, posited
"real" essences of things rather along the lines
resuscitated by Putnam (1975) and Kripke (1972 [1980]), the real
essences being the conditions in the world independent of our thought
that make something the thing it is. Thus, *being H2O* may be
what makes something *water*, and (to take the striking
examples of diseases noted by Putnam, 1962 [1975]) being the
activation of a certain virus is what makes something polio. But, of
course, such an external view would still dash the hopes of
philosophers looking to the analytic to explain *a priori*
knowledge (but see Bealer 1987 and Jackson 1998 for strategies to
assimilate such empirical cases to nevertheless *a priori*,
armchair analysis). Such a consequence, however, might not faze an
externalist like Fodor (1998), who is concerned only to save
intentional psychology, and might otherwise share Quine's
scepticism about the analytic and the *a priori*.



Two final problems, however, loom over any such externalist
strategies. One is how to provide content to
"response-dependent" terms, such as
"interesting," "amusing," "sexy,"
"worrisome," whose extensions vary greatly with users and
occasions. What seems crucial to the contents of such terms is not any
*externalia* that they might pick out, but simply some
*internal* reactions of thinkers that might vary among them
even under *all* conditions, but without difference in meaning.
At any rate, there's no reason to suppose there's any sort
of law that links the same phenomena to different people who find
different things "interesting," "funny," or
even "green" (cf. Russell, 1912; Hardin, 2008). The other
problem is how to distinguish necessarily *empty* terms that
purport to refer to (arguably) impossible phenomena such as perfectly
flat surfaces, Euclidean figures, fictional characters or immortal
souls. An externalist would seem to be committed to treating all such
terms as synonymous, despite, of course, the fact that thoughts about
them should obviously be distinguished (see Rey, 2009).


### 4.3 Internal Dependencies



A promising strategy for replying to these latter problems, as well as
to Quine's challenge in a way that might even begin to provide
what the neo-Cartesian wants, can be found in a proposal of Paul
Horwich (1998, 2005). He emphasizes how the meaning properties of a
term are the ones that play a "basic explanatory role"
with regard to the use of a term generally, the ones ultimately in
virtue of which a term is used with that meaning. For example, the use
of "red" to refer to the color of blood, roses, stop
signs, etc,. is arguably explained by its use to refer to certain
apparent colors in good light, but not *vice versa*: the latter
use is "basic" to all the other uses. Similarly, uses of
"and" explanatorily depend upon its basic use in
inferences to and from the sentences it conjoins, and number terms to
items 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, this
strategy offers a way to deal with response-dependent and necessarily
empty terms, and promises a way of distinguishing analyticities from
mere beliefs, there are still several further potential problems it
faces. The first is that merely appealing to a "basic
explanatory" condition for the use of a word doesn't
distinguish 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 often
met), and "the eye of a needle" by the shape of an animal
eye. In these latter cases, the words seem to be "frozen"
or "dead" metaphors, taking on meanings of their own.
While they are *explained* by original "basic"
uses, they are no longer "governed" by them.



Here it may be worth combining something of the Horwich view with
something of Fodor's aforementioned cousin suggestion of the
asymmetric counterfactual (SS4.2), along lines suggested by Rey
(2009; 2020a, SS10.3): the new "dead" uses of an idiom
or metaphor no longer *asymmetrically depend* upon the
explanatorily basic use. "Eye of a needle" would still
mean the hole at the end of a needle, even if "eye" no
longer referred to animal eyes. But "eye" used to refer
to, say, the drawing of an eye, would both asymmetrically and
explanatorily depend upon its being used to refer to actual eyes. And
describing a three-way correspondence as "triangular" may
asymmetrically and explanatorily depend upon thinking of certain
geometric figures as triangular, but not *vice versa* -
despite the impossibility of there ever being any actual triangles in
the external world (see Allott and Textor, 2022, for development of
this suggestion). Taking the asymmetric dependency to be
"internally" explanatory relieves it of the excessive
externalism with which Fodor burdened it, while avoiding the
etymologies and dead metaphors facing Horwich's view on its
own.



However, although such a proposal may offer a promising strategy for
meeting Quine's challenge about many ordinary terms, it
isn't clear it would work for highly theoretic ones. For if
Quine (1953 [1980a]) is right about even a limited holism involved in
the use of scientific terms, then there may be no sufficiently local
basic facts on which all other uses of a term asymmetrically and
explanatorily depend. To take the kind of case that most interested
Quine, it certainly seems unlikely that there is some small set of
uses of, say, "number," "positron,"
"space" or "biological species" that are
explanatorily basic, on which all other uses really depend. Such terms
often come with a large cluster of terms appearing in claims that come
as, so to say, a loose "package deal," and revision over
time may touch any particular claim in the interests of overall
explanatory adequacy. Uses of a term involved in the expression of
belief, either in thought or talk, will likely be justified and
explained by the same processes of holistic confirmation that led
Quine to his scepticism about the analytic in the first place (cf.
Gibbard, 2008). Of course, Quine might be wrong about taking the case
of theoretic terms in science to be representative of terms in human
psychology generally (cf. Chomsky, 2000,
 footnote 10
 above), and the above proposal might be confined to some restricted
portions of a speaker's psychology, e.g., to perception (as in
Fodor, 1983, 2000). But, to put it mildly, the verdict on these issues
is not quite in (see *supplement* SSSS4-5).



Lastly, a third (and, for some, a serious) possible drawback of this
strategy is that it still risks rendering matters of meaning far less
"transparent" and introspectively accessible than
philosophers have standardly supposed. There is little reason to
suppose that what is asymmetrically-explanatorily basic about
one's use of a term in thought or talk is a matter that is
available to introspection or armchair reflection. As in the case of
"marriage" mentioned earlier, but certainly with respect
to other philosophically problematic notions, just which properties,
if any, are explanatorily basic may not be an issue that is at all
easy to determine. What are the asymmetric-explanatorily basic uses of
"freedom" or "soul"? Do even people's
uses of animal terms really depend upon dubbings of species - or
of individual exemplars - or do they depend more upon an innate
disposition to think in terms of underlying biological kinds (cf. Keil
2014, pp. 327-333)? Do their uses of number words and concepts
really depend upon their grasp of Peano's axioms? Perhaps the
usage is grounded more in practices of (finite) counting, estimates
and noticing merely *finite* one-to-one correspondences; or
perhaps they lie in the general recursive character of
*language* (cf. Hauser et al 2002). Again, one may need the
resources of a psychology that delves into far more deeply into the
complex, internal causal relations in the mind than are available at
its introspective or behavioral surface.


### 4.4 Chomskyan Strategies



Such an interest in a deeper and richer *internal* psychology
emerged most dramatically in the 1950s in the work of Noam Chomsky. In
his (1957, 1965, 1968 [2006]) he began to revolutionize linguistics by
presenting substantial evidence and arguments for the existence of an
innate "generative" grammar in a special language faculty
in people's brains that he argued was responsible for their
underlying competence to speak and understand natural languages. This
opened 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 had
independently, empirically refuted (see Chomsky 1959, and Gleitman,
Gross and Reisberg 2011, chapter 7). Some of it also dovetails nicely
with ideas of Friedrich Waismann and the later Wittgenstein, as well
as with important recent work on polysemy. But the program Chomsky
initiated is complex, and its relation to the analytic quite
controversial, and so discussion of it is relegated to the following
*supplement* to this entry:



> 
> Supplement: Analyticity and Chomskyan Linguistics.
>  


## 5. Conclusion



Suppose, per the discussion of at least SS3 of the
*supplement*, that linguistics *were* to succeed in
delineating a class of analytic sentences grounded in the constraints
of a special language faculty in the way that some Chomskyans
sometimes seem to suggest. Would such sentences serve the purposes for
which we noted earlier (SS2) philosophers had enlisted them?
Perhaps some of them would. An empirical grounding of the analytic
might provide us with an understanding of what constitutes a
person's competence with specific words and concepts,
particularly logical or mathematical ones. Given that Quinean
scepticism about the analytic is a source of his scepticism about the
determinacy of cognitive states (see SS3.5 above), such a
grounding may be crucial for a realistic psychology, determining the
conditions under which someone has a thought with a specific
content.



Moreover, setting out the constitutive conditions for possessing a
concept might be of some interest to philosophers generally, since
many of the crucial questions they ask concern the proper
understanding of ordinary notions such as *material object, person,
action, freedom, god, the good*, or *the beautiful*.
Suppose, further, that a domain, such as perhaps ethics or aesthetics,
is "response dependent," *constituted* by the
underlying rules of our words and concepts; suppose, that is, that
these rules *constitute* the nature of, say, *the good, the
funny*, or *the beautiful*. If so, then it might not be
implausible to claim that successful conceptual analysis could provide
us with some *a priori* knowledge of such domains (although,
again, sorting out the rules may require empirical linguistic and
psychological theories not available to "armchair
reflection").



But, of course, many philosophers have wanted more than these
essentially psychological gains. They have hoped that analytic claims
might provide a basis for *a priori* knowledge of domains that
exist independently of us and are not exhausted by our concepts. An
important case in point would seem to be the very case of arithmetic
that motivated much of the discussion of the analytic in the first
place. Recent work of Crispin Wright (1983) and others on the logicist
program has shown how a version of Frege's program might be
rescued by appealing not to his problematic Basic Law V, but instead
merely to what is called "Hume's Principle," or the
claim that for *the number of Fs* to be equal to *the number
of Gs* is for there to be a "one-to-one
correspondence" between the Fs and the Gs (as in the case of the
fingers of a normal right and left hand), even in infinite cases.
According to what is now regarded as "Frege's
Theorem," the Peano axioms for arithmetic can be derived from
this principle in standard second-order logic (see *Frege's
theorem and foundations for arithmetic*).



Now, Wright has urged that Hume's Principle might be regarded as
analytic, and perhaps this claim could be sustained by an examination
of the language faculty along the lines of a Chomskyan linguistics set
out in the *supplement.* If so, then wouldn't that
vindicate the suggestion that arithmetic can be known *a
priori*? Not obviously, since Hume's Principle is a claim
not merely about *the concepts* F and G, but about the
presumably *concept-independent fact* about the number of
things that are F and the number of things that are G, and, we can
ask, 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 concepts
> they are numbers of are equinumerous, what guarantee do we have that
> every concept has a number? (p. 253)
> 
> 
> 



Indeed, as Edward Zalta (2013) observes,



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



The concept of a unique successor to every number might be a defining
feature of the lexical item, "number," but that
doesn't itself imply that *an infinity of numbers actually
exists*. Meanings and concepts are one thing; reality quite
another. Justification of such existential statements and, with them,
Hume's Principle would seem to have to involve something more
than appealing to merely the concept, but also --to recall
Quine's (CLT, p. 121, SS3.3 above) claim-- to
"the elegance and convenience which the hypothesis brings to the
containing bodies of laws and data," i.e., to our best overall
empirical theory of the world, irrespective of what constraints
language might impose (see Wright, 1999, and Horwich, 2000, for
further discussion).



The problem here becomes even more obvious in non-mathematical cases.
For example, philosophers have wanted to claim not merely that our
concepts of *red* and *green* exclude the possibility of
our thinking that something is both colors all over, but that this
possibility is ruled out for the *actual* colors,
***red*** and ***green***,
themselves (if such there be). It is therefore no accident that
Bonjour's (1998, pp. 184-5) defense of *a priori*
knowledge turns on resuscitating views of Aristotle and Aquinas,
according to which *the very properties of **red** and
**green*** *themselves* are constituents of
the propositions we grasp. But it is just such a wonderful coincidence
between merely our *concepts* and actual worldly
*properties* that a linguistic semantics alone obviously cannot
ensure.



But suppose, nevertheless, there *did* in fact exist a
correspondence between our concepts and the world, indeed, a deeply
reliable, counterfactual-supporting correspondence whereby it was in
fact *metaphysically impossible* for certain claims
constitutive of those concepts not to be true. This is, of course, not
implausible in the case of logic and arithmetic, and is entirely
compatible with, e.g., Boolos' reasonable doubts about them
(after all, it's always possible to doubt what is in fact a
necessary truth). Such necessary correspondences between thought and
the world might then serve as a basis for claims to *a priori*
knowledge in at least a reliabilist epistemology, where what's
important is not believers' abilities to *justify* their
claims, but merely the *reliability* of the processes by which
they arrive at them (see *Reliabilist Epistemology*). Indeed,
in the case of logic and arithmetic, the beliefs might be arrived at
by steps that were not only *necessarily reliable*, but might
also be taken to be so by believers, in ways that might in fact depend
in no way upon experience, but only on their competence with the
relevant words and concepts (Kitcher 1980; Rey 1998; and Goldman 1999
explore this strategy).



Such a reliabilist approach, though, might be less than fully
satisfying to someone interested in the traditional analytic *a
priori*. For, although someone might turn out in fact to have
analytic *a priori* knowledge of this sort, she might not
*know* that she does (reliabilist epistemologists standardly
forgo the "KK Principle," according to which if one knows
that p, one knows *that one knows* that p). Knowledge that the
relevant claims were knowable *a priori* might itself be only
possible by an empirically informed understanding of one's
language faculty and other cognitive capacities *a la*
Chomsky, and by its consonance with the rest of one's theory of
the world, *a la* Quine. One would only know *a
posteriori* that something was knowable *a priori*.



The trouble then is that claims that people do have a capacity for
*a priori* knowledge seem quite precarious. As we noted earlier
 (footnote 7),
 people are often unreliable at appreciating deductively valid
arguments; and appreciating the standard rules even of natural
deduction is for many people often a difficult intellectual
achievement. Consequently, people's general competence with
logical notions may not in fact consist in any grip on valid logical
rules; and so whatever rules do underlie that competence may well turn
out *not* to be the kind of absolutely reliable guide to the
world on which the above reliabilist defense of *a priori*
analytic knowledge seems to depend. In any case, in view merely of the
serious possibility that these pessimistic conclusions are true,
it's hard to see how any appeal to the analytic to establish the
truth of any controversial claim in any mind-independent domain could
have 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 the
semantic 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
(SS1). Consider, for example, the common puzzle about the
possibility that computers might actually think and enjoy a mental
life. In response to this puzzle some philosophers, e.g, Wittgenstein
(1953 [1967], SSSS111, 281), Ziff, 1959, and Hacker, 1990,
have suggested that it's analytic that a thinking thing must be
*alive*, a suggestion that certainly seems to accord with many
folk intuitions (many people who might cheerfully accept a
computational explanation of a thought process often balk at the
suggestion that an inanimate machine engaging in that computation
would actually be thinking). Now, as we noted in the
*supplement*, SS2, Chomsky (2000, p. 44) explicitly
endorses this suggestion. So suppose then this claim were in fact
sustained 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. Should
this really satisfy the person worried about the possibility of
artificial thought?



It's hard to see why. For the serious question that concerns
people worried about whether artifacts could think concerns whether
those artifacts could in fact share the genuine, *theoretically
interesting, explanatory properties* of a thinking thing (cf.
Jackson 1998, pp. 34-5). We might have no empirical, scientific
reason to suppose that genuine, biological *animacy* (n.b., not
merely the perhaps purely syntactic, *linguistic* feature
[+animate]!; see *supplement* SS2) actually figures among
them. And so we might conclude that, despite these supposed
constraints of natural language, inanimate computers could come to
"think" after all. Indeed, perhaps, the claim that
thinking things must be alive is an example of a claim that is
*analytic but false*, rather as the belief that cats are
animals would be, should it turn that the things are actually robots
from Mars; and so we should pursue the option of polysemy and
"open texture" that Chomsky also endorses, and proceed to
allow 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 were
nevertheless correct, other speakers could of course simply proceed to
define a new word "think\*" that lacks the animacy
constraint and applies to the explanatory kind that in fact turns out
to include, equally, humans and appropriately programmed artifacts.
The issue would reduce to merely a verbal quibble: so computers
don't "think"; they "think\*" instead.
Indeed, it's a peculiar feature of the entire discussion of the
analytic that it can seem to turn on what may in the end be mere
verbal quibbles. Perhaps the "linguist turn" of philosophy
that we sketched in SSSS1.2-3.3 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 minds
or or in the world to a large extent independently of language.



In any case, while the semantic conditions of a language might provide
a basis for securing *a priori* knowledge of claims about
mind-*dependent* domains, such as those of perhaps ethics and
aesthetics, in the case of mind-*independent* domains, such as
logic and mathematics, or the nature of worldly phenomena such as life
or thought, the prospects seem more problematic. There may be analytic
claims to be had here, but at least in these cases they would, in the
immortal words of Putnam (1965 [1975], p. 36), "cut no
philosophical ice...bake no philosophical bread and wash no
philosophical
 windows."[18]
 We would just have to be satisfied with theorizing about the
mind-independent domains themselves, without being able to justify our
claims about them by appeal to the meanings of our words alone.
Reflecting on the difficulties of the past century's efforts on
behalf of the analytic, it's not clear why anyone would really
want to insist otherwise.