Quine on Analyticity

Quine’s First Dogma of Empiricism: Analyticity

The problem of analyticity goes back at least as far as Leibniz. It has become the victim of a series of “sign substitutions” (to use Derrida’s term). The essential distinction we can now make is between synthetic and analytic statements (to opt, essentially, for Kant’s terms). Hume, for one, made the following distinction between

relations of ideas

and

matters of fact

The former are a question of what goes on in the mind (the “play of ideas”), regardless of what goes on in the outside world. Hume would have given as an example of this the statement

1+1=2

We do not need to look out of the window, or anywhere else, to determine the truth of that statement. So “matters of fact” are of course matters of the external world. A statement like

Tony Blair is the Prime Minister of the UK.

will fit the bill nicely. I cannot determine the truth of this statement simply by analysing the contents of my own mind. (Unless, an experience of Tony Blair being the Prime Minister is already part of the content of my own mind.)

Instead of talking about “relations of ideas”, Leibniz, before Hume, talked about “truths of reason”. According to Leibniz

truths of reason are true in all possible worlds.

Hume’s “matters of fact” may be true in only one possible world (perhaps our own).

According to both Leibniz and Hume, all statements fall into these two categories. Hume went further and said that all statements that didn’t fall into these two categories should be “assigned to the flames” as nonsense (e.g., those of Scholastic metaphysics).

Kant is known not for making this distinction, but for clarifying what he deemed to be an analytic statement. He said that analytic statements

attribute to their subjects nothing more than is already conceptually contained in the subjects.

An example of this would be:

Prime Minister Tony Blair is a politician.

To use Kant’s terms here. The attribute

is a politician

is already conceptually contained in the subject

Prime Minister Tony Blair.

In contemporary speak, the second phrase “is a politician” would be classed as the “predicate” rather than the “attribute”. To gloss on the Tony Blair example, we can say that if the subject is an existent (that Tony Blair is Prime Minister), then the attribute must be true (that he is a politician).

To generalise. A analytic statement is true

by virtue of meanings [alone] and independently of fact.

I the subject-term is true, then the predication must be true. The meaning of “Prime Minister Tony Blair” makes the meaning of “is a politician” true. It can be deemed true without recourse to experience, providing we accept the actuality of the subject-term.

Meaning and Essence

Quine then moves away from analyticity itself and has something to say about meaning. His first point is that extensions or references (or objects or denotata) cannot determine the meaning of a word or phrase. He gives the examples of the term

‘9’

and the phrase

‘the number of planets’

Both the term and the phrase designate the same abstract entity, namely, the number 9. However, we cannot say that the term “9” and the phrase “the number of planets” have the same meaning. There is a possible world where the number of planets is not nine; whereas

in every possible world “9” will designate the number 9.

Quine points out that astronomical observation was required to determine the number of planets in our world; but astronomy isn’t needed to determine the referent of “9”. This means that we need to distinguish the meanings of general terms, rather than particular terms, from their extensions. Quine gives the examples of

creature with a kidney

and

creature with a heart

as having the same extension. This means the collection of objects that are the extension of the former are also the extension of the latter. The meanings of these two examples are clearly not the same. Extensions alone do not provide us with the meanings of terms. Saying something has a heart is clearly not the same as saying that something has a kidney.

Quine then goes in for a bit of historical exegesis. According to him, the concept [essence] is historically related to the concept [meaning]. More precisely,

essence was the forerunner…of the modern notion of intension or meaning.

Quine rejects the whole notion of essence. He says that

it makes no sense to say of the actual individual, who, is at once a man and a biped, that his rationality is essential and his two-leggedness accidental or vice versa.

 (That is, the class of men and the class of bipeds both include the same extension.)

Quine doesn’t see why this distinction between essential and contingent properties is made. It appears in essence to be entirely arbitrary and seems to serve no real purpose. Why is rationality essential and two-leggedness contingent (or vice versa)? For example:

i) Is an irrational man not a man?

ii) If an elephant were rational, would it be a man?

What is the connection Quine is making between essence and meaning?

Traditionally, according to Quine, only things had essences. And, of course, only linguistic forms had meanings. Somewhere along the line, essences became meanings. As Quine puts it:

Meaning is what essence becomes when it is divorced from the object of reference and wedded to the word.

That is, the essence of a thing is passed onto the essential meanings of the word that refer to that thing. We now look for the essence, or the essential, in the meaning of a word. Essence

is divorced from the object

and then it is found again by being

wedded to the word.

The word or the linguistic expression is not the essence; it is the meaning prior to or behind the word. Meanings provide us with essences. The old show carries on under a series of “sign substitutions”. Formerly we had the essences of things and their contingent properties. (For example, rationality as the essence of man and two-leggedness as a contingent property.). Now we have the essences of words and their contingent properties. (That is, the meaning of a word is its essence. And the linguistic expression or notation of it, i.e. the word, is merely a contingent property.)

Quine wants to jettison this traditional view of meanings as mental entities behind or prior to their expression. All he now wants from meaning is

simply the synonymy of linguistic forms and the analyticity of statements.

This means that when someone asks for the meaning of a statement, we do not refer to abstract mental entities or even mention them; we simply offer a synonym of that statement. As for the analyticity of statements, the subject and predicate of an analytic statement are not synonyms because they both contain the same meanings, but because they are both mutually inter-translatable. Meanings

as obscure intermediary entities may well be abandoned.

Quine shows us what he means by giving us an example of a “logically true” statement. Take the following:

No unmarried man is married.

This statement is “logically true”. Why? Because

under any and all reinterpretations of ‘man’ and ‘married’ it remains true.

The logical particles “no”, “un-“, “not”, “if”, “then” and “and”, would remain the same in all reinterpretations, even if we substitute “bloke” for “man” or “heterosexual” and “gay” for “unmarried” and “married”, as in:

No heterosexual bloke is gay.

However, that statement is problematic and vague in this context. Despite what has been said, the above is not a logical truth, it is an analytic truth. And an analytic truth, by virtue of being an analytic truth, can be turned into a logical truth “by putting synonyms for synonyms”. The above can be turned into

No non-gay is gay.

(It could, strictly speaking, be said that non-gay is not a synonym of heterosexual, if a non-gay is not, again strictly speaking, heterosexual either.)

A less contentious substitution would be Quine’s own example, in which

No bachelor is married.

becomes

No unmarried man is married.

Because of the similarity of terms, Quine’s substitution seems clearer than my own.

Not we begin to see why Quine believes that analytic statements are not fully distinguishable, or distinguishable at all, from synthetic statements. Take

No heterosexual is gay.

again. Can we really know this to be true independently of experience (or Humean “matters of fact”)? It is indeed true that “bachelor” is defined as “unmarried man”. How do we find this out? We can look at a dictionary. But, according to Quine, the lexicographer “is an empirical scientist”. That means that he has found out certain matters of fact. Namely, that among English speakers “unmarried man” is deemed the definition of “bachelor”. More correctly and relevantly, “unmarried man” is not the meaning of “bachelor”; it is a synonym of that word. Again, there is no need to advert to entities called “meanings”. Not only does

No bachelor is married.

not depend on meanings for it truth, it may not be truly analytic either. Why is that? Because we depend on the “general or preferred usage” of the terms involved in the statement. And they exist prior to our own articulation of it.

Definitions

Quine goes into more detail about the exact nature of definitions. His first point is that a relation of synonymy (say, between “bachelor” and “unmarried man”) is stipulated, or created “by fiat”, to use Quine’s term, between the definiendum (“bachelor”) and the definiens (“an unmarried man”). This relation of synonymy, according to Quine, “did not hold before”. That’s why it is stipulated or created “by fiat”. The

definiendum becomes synonymous with the definiens simply because it has been created expressly for the purpose of being synonymous with the definiens.

This is Quine’s way of saying that these synonyms are the result of convention, or human will, rather than the matching up of both terms with pre-existing mental or Platonic entities (i.e., meanings). We decide that “bachelor” and “unmarried man” are synonyms. They aren’t made so by prior meanings. The synonymy

is created by definition

not by abstract meanings.

What makes two linguistic forms synonymous? According to Quine, it is because both synonymous terms are interchangeable

in all contexts without change of truth value.

They are interchangeable salva veritate. What does that mean? It means that

All bachelors are unmarried

can have its terms substituted for

All unmarried men are unmarried

without a change in truth-value. We could also, in this context, substitute “men without wives” for “bachelors” salva veritate. The stipulative synonyms could be, I suppose, indefinite.

Quine then goes into greater detail about the nature of synonymy. He talks about two forms of synonymy between words or statements. Firstly there is psychological synonymy. That is a

complete identity in psychological associations or poetic quality

between words or statements. This kind of synonymy does not concern Quine here. The kind of synonymy he is concerned with he calls “cognitive synonymy”. What is cognitive synonymy? This is a synonymy that can be created by turning an analytic statement into a logical truth by putting synonyms for synonyms. So again we turn

No bachelor is married.

into Quine’s

All and only bachelors are unmarried men.

What is Analyticity?

But Quine still has a problem. And that problem is: What is “analyticity”? (Rather than “What does ‘analytic’ mean?”) Quine explains his problem. To say

Necessarily all and only bachelors are unmarried men.

is true is to say that

All and only bachelors are unmarried men.

is analytic. So we are back with the term “analytic”. We are saying that “bachelor” and “unmarried man” are cognitively synonymous (or analytic). We class that which is synonymous by saying that it is ‘analytic’. And that which is analytic by saying that it is that which is ‘synonymous with…’  We are arguing in a circle. Again, what is “analyticity”?

Here Quine recaps on the notion of extensionality. He says that two predicates are extensional when they are true of the same object. From there we can move to synonymy or analyticity. The two predicates just mentioned can be interchangeable salva veritate (i.e., while retaining truth). The two predicates used within the same statement will guarantee synonymy and therefore analyticity. But Quine says that in an

extensional language…interchangeability salva veritate is no assurance of cognitive synonymy.

What’s Quine’s problem? Well, to be cognitively synonymous is to say that a statement must be a logical truth, not an analytic truth. A logical truth is

No unmarried man is married.

whereas an analytic truth is

All and only bachelors are unmarried men.

They clearly aren’t identical. To guarantee an analytic truth’s independence from syntheticity (Humean “matters of fact”) would require it to be, well, a logical rather than an analytical truth. Quine goes on and says that

‘bachelor’ and ‘unmarried man’ are interchangeable salva veritate in an extensional language assures us

of this. That is

All and only bachelors are unmarried men.

is true. So we are back to analyticity, which hasn’t been adequately explained.

There is a synthetic, rather than an analytic, component to the statement above. There is no

assurance here that the extensional agreement of ‘bachelor’ and ‘unmarried man’ rests on meaning [analyticity] rather than merely on accidental matters of fact.

If “creature with a heart” and “creature with kidneys” have extensional agreement without sameness of meaning, then “bachelor” and “unmarried man” may have extensional agreement without sameness of meaning. So let’s forget about sameness of meaning altogether. Or, more completely, let’s forget about meaning simpliciter. Let’s just concern ourselves with extensional agreement or sameness. According to Quine:

extensional agreement is the nearest approximation to synonymy we need care about.

Analyticity appears to be a mere ‘will-o’-the-wisp’. Quine went through a whole series of stages to try and find analyticity. Firstly

1) Analyticity…seemed most naturally definable by appeal to a realm of meanings.

then

2) On refinement, the appeal to meanings gave way to an appeal to synonymy or definition.

And then

3) …definition turned out to be a will-o’-the-wisp, and synonymy turned out to be best understood only by dint of a prior appeal to analyticity itself.

As Quine put it,

we are back at the problem of analyticity.

We have delineated a circle of terms, all mutually interdependent and inter-definable.

Quine then changes his tune a little by forgetting about bachelors and unmarried men to focus on what is a well known example of an analytically true statement:

Everything green is extended.

Is that statement analytic? Intuitively it seems to be analytically true (or simply analytic). How can anything be green and not also be extended? Greenness needs something to be green; it doesn’t just float in the air. (What about rainbows?) And if the colour green needs an object to be green, it can’t exist apart from an object. So everything green must be extended. What’s Quine’s problem with the analyticity of “Everything green is extended”? He doesn’t have a problem with the meanings of “green” and “extended”. He knows what “green” and “extended” mean. No; the trouble is with that term again – “analytic”. He may accept that everything green is extended, but he doesn’t accept that “Everything green is extended” is an analytic statement. What does analyticity add to the truth of that statement? More precisely, again, what is analyticity? Is there something over and above that statement’s being true? Where it? What is it?

Semantical Rules

Carnap offered another take on analyticity. He too said that analyticity is a question of meanings. But he said that the analyticity is generated by semantical rules. Quine goes into detail about Carnap’s alternative but rejects this too. Carnap said that you formulate an artificial language. Call it L^o. The semantical rules of L^o tell us which statements of the language are analytic. After this account of Quine’s position on analyticity, we should be able to guess Quine’s problem with this approach. I wrote earlier that L^o tells us which statements should be taken as analytic. Yes, but we don’t understand the word “analytic” in the first place. How do the stipulations of L^o solve our problems with analyticity? To use Quine’s own words, we

understand what expressions the rules attribute analyticity to, but we do not understand what the rules attribute to those expressions.

L^o tells us what statements are analytic, and perhaps why they are analytic, but it does not tell us what “analyticity” is. We are back with analyticity again. Quine thinks that Carnap would have been forced back to un-interpreted analyticity thus

A statement S is analytic for language L^o, if and only if… (It is analytic)

More to the point, by

saying what statements are analytic for L^o, we explain ‘analytic-for-L’ but not ‘analytic’ but analytic for…

Instead of explaining the word “analytic”, we could explain “semantical rule” instead. Now Quine makes a holist point about this and the other explications of analyticity. (Quine is very big on holisms of various descriptions.) He would say, Yes; of course analytic can be accepted or defined within a system or a system of terms. (We mentioned the analyticity circle earlier one.) In terms of what postulates are, he says:

Relative to a given set of postulates, it is easy to say what a postulate is: it is a member of the set [the set of postulates].

And the same is true of semantical rules:

Relative to a given set of semantical rules, it is equally easy to say what a semantical rule is.

Yes; it is a member of the set. Why not fill in the blanks here?

Q) What is an analytic statement?

A) Relative to a given set of analytic statements, it is easy to say what an analytic statement is: it is a member of the set.

But, you guessed it, we are told which statements are analytic, but not what analyticity is! To get back to semantical rules. Quine said that semantical rules are

determining the analytic statements of an artificial language are of interest only in so far as we already understand the notion of analyticity; they are of no help in gaining that understanding.

Why spend so much time on the notion of analyticity? Well, for a start, the belief that

in general…the truth of a statement is somehow analyzable into a linguistic component and a factual component.

is what Quine is arguing against. In fact, this is the first dogma of empiricism. If you take the linguistic/factual dualism to be true, then one will believe that a statement in which there is no factual element will be analytic. Quine has argued that no such division can be made. The so-called “analytic” statements he analysed contained both a factual and a linguistic element. As he puts it:

…a boundary between analytic and synthetic statements simply has not been drawn.

Such a belief in analytic statements is an

unempirical dogma of empiricists, a metaphysical article of faith.

Overview

In a Quinian spirit, perhaps we could have said to Hume that his ideas, and their ‘relations’ to each other, though not immediately dependent on matters of fact, are nevertheless still dependent upon them. We do not need to consult the world now that

1+1=2

but we did need to consult the world to learn arithmetic; to learn the symbols and their designations and so on. We can agree with Kant here. Kant said:

All knowledge begins with experience; but not all knowledge belongs to experience.

Numbers may well exist without minds and certainly without experience. But Hume, in his relations of ideas, wasn’t talking about abstract numbers but of the psychological relations of ideas. 1+1 equals 2 regardless of minds. This would not be anything to do with relations of ideas, which was what Hume was talking about. It may be a metaphysically necessary truth, but epistemically it is not necessary or a priori in that it depends on our learning arithmetical languages, etc. The same goes for Leibniz’s “truths of reason”. We had to learn via experience that 1+1=2; regardless of its metaphysical status as a necessary truth. Again, Hume was talking about the relations of ideas not the mind-independent status of that arithmetical equation.

And we can play a similar game with the supposedly synthetic statement

Tony Blair is Prime Minister and is therefore a politician.

We do not need to consult experience to clarify this if we already know it. Now this may seem like a cheap trick. However, the same can be said about 1+1=2 – we don’t need to consult experience because we have already consulted experience. It’s the same argument for both! Now I carry around with me in my head Tony Blair being a politician and therefore also being a politician. The analytic statement was learnt from experience in the manner the synthetic statement was learnt from experience.

Truths of reason seem a little different, at least prima facie. But how could we have a theory of possible worlds without experience of certain chaps talking and explaining possible worlds theories? Perhaps

 ‘the relation of ideas’

isn’t a synonym for

‘truths of reason’

Hume is talking explicitly about empirical psychological processes. However, when a philosopher talks about reason one can’t be that sure. As a rationalist, Leibniz wasn’t talking about mental processes. We know, therefore, that 1+1=2 from birth. Perhaps not only the numbers but also the equation is innate. This can’t be true. What about the equations that even as adults we don’t know the answer to (at least not straight away)? We can’t discount them just because they are difficult. Why shouldn’t they be innate too? Why isn’t the answer to Goldbach’s theorem known innately? Where is the line drawn when it comes to innate or a priori knowledge (though, of course, they are distinguishable)?

Of course when we say that

The words ‘is a politician’ is ‘conceptually contained’ in ‘is Prime Minister’

we are being metaphorical. How should we take it? How is the predicate “contained”? Does Kant mean that

Part of the meaning of ‘Prime Minister’ is ‘politician’?

Is that true? In another possible world there could be a Prime Minister who is not a politician. It’s a very hard metaphor to pin down. For a start, in terms of pure psychology, someone may understand the meaning of “Prime Minister” and not understand the meaning of “politician” (say, a young child).

There is another way in which an analytic statement is not strictly analytic. Take

Prime Minister Tony Blair is a politician.

again. If the subject-phrase is true, that is, that the Prime Minister is Tony Blair, then Tony Blair will indeed be a politician. But that’s only if we know that the subject-phrase is true. Surely there is a synthetic part to this statement. Fair enough, if you simply take the subject-expression to be true, then, yes, the predicate will be true too. And therefore it will be a quasi-analytic statement. It’s a strange statement that requires you to take the subject-phrase as true. A synthetic statement can be made true, as it were, if it is required that you take either the subject phrase or the predicate as true. Providing we take the subject-term as true then it will indeed be analytic.

Conclusion

Quine denied the distinction between analytic and contingent synthetic statements. Rosenberg puts it this way:

If these two proposals are coherent, then the experimental evidence that tests quantum mechanics can lead us to surrender, for factual reasons, principles of logic and mathematics we supposed to be necessarily true. (29)

Alternatively there is the pre-Quinian claim that analytic or necessary statements are without empirical content. Some – or all – of them in fact are. Quine rejects the

metaphysical theses Positivists supposed to be without empirical significance (29).

Above and beyond all this, Quine does not even think that strict synonymy

is a clear enough notion for us to be able to say with confidence that it is or is not preserved.

Quine argued elsewhere that the notion of synonymy was not even itself a clear term. That was because synonymy relies on the notion of statemental analyticity. And, of course, the notion of statemental analyticity in turn relies on the notion of synonymy. That is, terms are deemed as being synonymous if they can be put in a statement so as to create a purely analytic statement. This means that they can be used essentially to form a statemental tautology. But we can only say or know that a sentence is genuinely analytic if we can also see that it contains two terms that are generally deemed to be synonymous with one another. So synonymy depends on analyticity, and analyticity depends on synonymy. What is in fact analytic and synonymous can only be determined within this small circle of terms. But if there is no alternative to defining one term in terms of the other, it is not surprising that Quine finds the term ‘strict synonymy’ not a clear notion. The definition of strict synonymy depends on an analytical statement that itself also depends on taking certain terms to be synonymous. The analytical statement does not actually show us what synonymy is. It simply shows use how we can determine synonymy and how we can use two synonymous terms in order to make an analytical statement. However, the analytical statement does not actually tell us what synonymy is. Similarly, if analytical statements depend on the prior acceptance and knowledge of synonyms, then such an analytical statement cannot really tell us what analyticity is, only how analytic statements are created on the prior acceptance of two synonymous terms taking up, in some cases, the subject-term and the predicate-term

To repeat. At first, the statement

Everything green is extended.

does seem analytic because nothing can be green without it also being extended. That is, only extended things can have the property of greenness. Now we can say that the word ‘green’ contains the concept of [extension]. That statement is in essence tautological – it says the same thing twice. And if that is the case, it is true no matter what. Not only that, but it must also be analytic because the predicate, ‘is extended’ is contained in the subject term, ‘everything green’. And because it cannot be shown to be false, it must be analytic rather than synthetic. Quine accepts that the statement is true. Perhaps he also accepts that it is necessarily true. However, his problem is with the word ‘analytic’. What does that term actually mean? As Quine says, people tell us what statements are analytic, but not what analyticity is. This would be like pointing out various people who are holy, without telling us what the term ‘holy’ means or is. Again, what does ‘is analytic’ attribute to the statement ‘Everything green is extended’?  We can now say that Quine is asking a metaphysical or ontological question about analyticity, not a question about the semantic status of ‘Everything green is extended’. He is asking not what ‘analyticity’ means, but what analyticity is.

Quine goes on to argue that perhaps we can have analyticity only within the confines of a theory of an artificial language. Such a language will provide us with a ‘semantic rule’ that will determine which statements within a language are in fact analytic. If a statement has a certain form, then we can call that form ‘analytic’. But now we have a problem with

explaining and justifying the ‘semantic rule’.

Why is there such a ‘semantic rule’ that stipulates analyticity? Again, what is it attributing to the statements that abide by the ‘semantic rule’? The problem has simply been shifted from analyticity itself, to the ‘semantic rule’ that attributes analyticity to certain statements. What does the ‘semantic rule’ attribute to statements that are called ‘analytic’ within that artificial language? Again, the metaphysical question is not answered, but simply sidestepped.

There are possibly no statements that are immune from falsification. Therefore no propositions are necessarily true (i.e., the ones we know a priori). Why is this? According to Rosenberg:

…any proposition can be surrendered as a result of a falsifying experiment.

This is because

in the actual history of science the most central and firmly held of our beliefs have sometimes been surrendered. (30)

Not even logic and mathematics are safe. What about contingent factual propositions? These can assume a quasi-necessary character, according to Rosenberg:

…any proposition, no matter how apparently factual, no matter how apparently vulnerable to falsification, can be preserved in the face of any possible falsifying experiment. (30)

Is there an example of this? Rosenberg writes:

We may in all consistency maintain that the earth is flat, attributing all apparent evidence against this belief to the falsity of one or another of the auxiliary assumptions. (30)

It is not just the case that so-called necessarily true statements can be falsified due to scientific knowledge and experiment; it is also the case that seemingly empirical statement can be treated as if they are necessary truths in that they can be made immune from falsification. How is this done? Well, take the claim that

The earth is flat.

which was believed by many people for many centuries. This claim was sustained and maintained by

attributing all apparent evidence against this belief to the falsity of one or another of the auxiliary assumptions.

We thought that the belief that the earth is flat is false because some of the ‘auxiliary assumptions’ lead to the disbelief in the earth’s flatness were themselves false. Quite simply it was believed that the earth is not flat because of faulty or false assumption. The Marxist, according to Popper, worked in the opposite direction. He essentially made Marx’s many theories un-falsifiable by qualifying each one with a ‘auxiliary hypothesis’. A central Marxist theory was seen to be false by outsiders. However, the theory was saved by the creation of an ‘auxiliary hypothesis’ that effectively qualified and changed the original thesis thus making it un-falsifiable.