The Basics of Logical Identity

Firstly we can say that logical identity is reflexive. In other words, everything (or every thing) is identical to itself. In symbols:

∀x (x = x)

To translate:

For every x (or for every thing), x must equal x (or everything must be identical to itself). That is, everything has the (quasi)-relation of self-identity..

The logic of identity is also symmetrical. In symbols:

If a = b, then b = a

This can also be expressed in quantificational logic:

∀x ∀y ((x = y) ⊃ (y = x))

To translate:

For every x, and for every y, if x equals — or is identical to — y, then it must also be the case that y is identical to x.

Logical identity is transitive:

If a = b, & b = c, then a = c

The above means that something is “passed on” all the way from a to c. That’s why it’s a transitive relation (or expression). Thus if a is identical to b, and b is identical to c, then a must also be identical to c - by what’s called transitivity. After all, all the symbols above simply refer to one and the same object. This too can be expressed by in quantificational terms:

∀x ∀y ∀z ((x = y) ∧ (y = z) ⊃ (x = z))

To translate:

For every x, for every y, and for every z, if x is identical to y, and y is identical to z, then x must also be identical to z.

All these types of identity are satisfied by every equivalence relation (such as “is the same colour as”). Until now we’ve only talked about relations in the abstract, not specific and concrete kinds of relation. In addition, we haven’t assigned values to the symbols x, y, a and b. So with a = b we can say that the David Jones (i.e., a) and the The Thin White Duke (i.e., b) are in the relation of standing for David Bowie.

Or with a = b, and b = c, then a = c, we can say:

If Mary is the same height as John. And John is the same height as Tony. Then Mary is also the same height as Tony (as well as being the same height as John).

Mary (or a) has the relation of being the same height as (in this case) both b and c (or two different people).

Finally, the logic of identity satisfies Leibniz’s law (or the identity of indiscernibles). This law can be expressed in different ways, such as:

If a is identical to b, then everything true of a is also true of b.

In this version, Leibniz’s law is expressed with reference to the semantic property of truth. We can, instead, express it in terms only of the properties of identical objects which were perhaps initially taken to be two different objects. This, then, would be a de re (as opposed to de dicto) take on logical identity.

We can also say that Leibniz’s law entails the symmetrical notion (mentioned earlier) of logical identity, as expressed thus:

If a = b, then b = a

That is:

((a = b) ⊃ (b = a))

All this can be expressed quantificationally:

∀x ∀y (F) ((x = y) ⊃ F ((x) ≡ F (y)))

To translate:

For every x. For every y. And also for every property (i.e., F). If x equals y, then it is the case that property F belongs to both x and y. (In this case, that property is true of.)

The identity of thing x and thing y is established by the truths applicable to x and the truths applicable to y. We can see if the two sets of truths correspond with each other. Therefore we’ve established that object x is in fact identical to object y.

The symbol ≡ can be seen in the quantificational expression above. This is the symbol for the biconditional.

The biconditional symbol is defined truth-functionally (just as with the constants and connectives). The symbol truth-functionally operates on (or is applied to) the symbols (or expressions) which surround it (or to which it applies). That is, the symbol ≡ operates on, for example, F(x) in the example above; as well as on the F(y) which follows it. More precisely, it’s truth-functional because both F(x) and F(y) both have the truth-value of either true or false. Therefore the symbol ≡ operates on their truth or falsehood in order to come out with something with a different (or the same) truth-value.

In addition, we can say that biconditional symbol ≡ is equivalent to:

((p ⊃ q) ∧ (q ⊃ p))

In other words, the biconditional is symmetrical in nature, unlike the simple logical conditional. That is, if we accept that p entails q, then we must also accept that q entails p. This is unlike this simple conditional:

(p ⊃ q) or (q ⊃ p)

This means: If p then q or if q then p. However, the symbols p ⊃ q alone don’t entail their converse: q ⊃ p. The conditional is therefore asymmetrical.

We can also say that in

p ≡ q or A ≡ B

the q (i.e., a proposition) and B (a state of affairs or an object) above offer us both the necessary and sufficient conditions for p’s and A’s truth.

Now to cite a philosophical example:

m ≡ b

This is a logical expression of mental supervenience in that for every mental change (m) there must be a physical change in the brain (b). However, clearly m and b aren’t identical otherwise we’d have m = b, not m ≡ b. This conditional is also bi because it works in two directions. Alternatively put, when anything happens in the case of m, something must also happen when it comes to b, even though m and b aren’t identical.

The conditional (i.e., not the biconditional) is a different case. That is, in m ⊃ b it’s not the case that every mental change must entail a parallel (though not identical) change in the brain. Thus:

(m ⊃ b) ¬(m ≡ b)

In terms of propositions alone (i.e., not of mental and physical changes), another way of explaining the symbol ≡ is by stating the following:

p ≡ q is true if and only if both p and q are true; otherwise it is false.

In the above, p and q stand for propositions which can be taken as being either true or false. If p is true, then q is also true; even though they aren’t identical propositions. (Similarly, if p is false.) However, if p is true and q is false (or vice versa), then the overall biconditional itself (i.e., p ≡ q) would also be false. Its falsehood would be entailed by the asymmetrical truth-values of both p and q.

Eliminative Materialism

Historically, or I should say in the fairly recent past, there have been many arguments offered against materialism in the mind and matter debate. Philosophers have posited mental phenomena that were supposed to be irreducible to matter (or the brain). Churchland himself offers us four examples: emotions, qualia, raw feels and now - Churchland was writing in 1980 - propositional attitudes. Such things were/are proposed to be both ineliminable and irreducible. Churchland was saying that the goal posts kept on shifting to make way for an irreducible or ineliminable mind (or aspects thereof).

Churchland said that the resistance eliminative materialism encounters surprises him. “After all,” he said, “common sense has yielded up many theories.” Here the reader can fill in his own examples rather than relying on the many that Churchland offers.

Propositional Attitudes

Why are we so absolutely certain that our minds contain propositional attitudes (e.g., beliefs and desires)? Could we possibly make a mistake about the workings of our own minds? Churchland thinks that we can. Many people think that although we can make mistakes, sometimes big ones, about the external world, the same is not true about the internal world (the mind). But the reasons for making mistakes about the external world are pretty similar to those that can be applied to the mind or the mental. An “introspective judgment” is a “conceptual response to one’s internal states”. So just as we rely on contingent and possibly false concepts to acquire a picture of the external world, similar conceptual schemes are brought to bear on our introspective judgments. The mind is not transparent (as Descartes and others have thought). So the judgments we make about the workings of our own minds are “always contingent on the integrity of the acquired conceptual framework (theory) in which the response is framed”. We look through, as it were, contingent and possibly false concepts when we introspect. But what has all this to do with the existence or non-existence of propositional attitudes (which is Churchland’s primary concern)? The answer to this is simple: we may be wrong about our minds being the “seat of beliefs and desires”. That is, beliefs and desires as we know them may not exist. Indeed, a belief in beliefs and desires may be as misplaced, according to Churchland, as the ancient belief that the “star-flecked sphere of the heavens turns daily”.

But let’s be clear about the folk psychologist’s position is on the reality of propositional attitudes. The things we believe and desire, or, more correctly, the propositional content of our beliefs and desires, are effectively quantified over by the folk psychologist. Not only that, but he sees that the relations (e.g., entailment, equivalence and mutual inconsistency) between beliefs and desires and other beliefs and desires are “lawlike”. So all this sounds very much like a scientific theory, despite the fact that we are talking about the mental. And that’s why folk psychology is a theory. Churchland goes into more detail about the theoretical status of folk psychology.

If folk psychology is a theory, it wasn’t thought to be one until the second half of the twentieth century. Churchland thinks that it’s a mystery why the theoretical nature of folk psychology was never recognised, especially bearing in mind that he thinks that it is “so obviously a theory”. Churchland then goes onto compare folk psychology with the theories of mathematical physics. He finds very interesting parallels. But whereas mathematical physics has a domain of numbers to quantify over, folk psychology quantifies over the domain of propositional attitudes.

There are many options on reduction and ineliminativity to be taken in the philosophy of mind. Apart from his own, Churchland cites three alternatives: the identity theory, dualism and functionalism. He summarises them thus:

The Identity Theory

Identity theorists believe that folk psychology “will be smoothly reduced by completed neuroscience, and its ontology preserved by dint of transtheoretic identities”.

Dualism

The dualist “expects that [the mind] will prove irreducible to completed neuroscience”.

Functionalism

The functionalist also “expects that [the mind] will prove irreducible… [because] the internal economy characterised by folk psychology is not…a law-governed economy of natural states, but an abstract organisation of functional states, an organisation instantiable in a variety of quite different material substrates”.

Churchland happily concedes that FP enjoys a “substantial amount of explanatory and predictive success”. And then concludes: “And what better grounds than this for confidence in the integrity of its categories?” Of course, Churchland is being rhetorical here. He doesn’t believe that its explanatory and predictive successes are in fact, after 2,000 years of its hegemony, that great. He then gives a list of its notable failures. He says:

“…consider the nature and dynamics of mental illness, the faculty of creative imagination…Consider our utter ignorance of the nature and psychological functions of sleep….Or consider the miracle of memory, with its lightning capacity for relevant retrieval.”

Folk psychology offers virtually no insights on all the above. It is explanatorily and predictively more or less useless. And the main reason for this, as Churchland perceives it, is how the folk psychologist explains the mechanisms of thought. The folk psychologist sees learning “as the manipulation and storage of propositional attitudes”. That is, within the mind-brain there are sentences or propositions of some kind, or possible analogues of sentences or propositions. It is a thoroughly sentential or propositional approach to learning and thought. But, Churchland argues, something must have predated the storage and manipulation of propositional attitudes. Propositional attitudes couldn’t have shown us how to manipulate propositional attitudes before such they were on the scene. So certain non-propositional mechanisms must have predated the storage and manipulation of propositional attitudes. He says that it “is only one among many acquired cognitive skills” and therefore FP faces “special difficulties”.

Beyond Folk Psychology

So what precisely is Churchland alternative to FP? What does he believe are the mechanism of thought, learning, etc? For a start, his descriptions could be called “scientistic” (I am using that term in a non-judgemental way). He relies heavily on the findings of neuroscience and rejects any a priori philosophising. So I will describe in full his very non-linguistic and non-logical (possibly non-philosophical!) account of mind-brain activity:

“[The neuroscientific theory] ascribes to us, at any given time, a set or configuration of complex states, which are specified…as figurative ‘solids’ within a four- or five-dimensional phase space.”

Clearly there is no mention of logical relations, propositions, beliefs, desires and all the rest. This is essentially the language of neuroscience rather than the language of philosophy. Having said that, these descriptions of brain activity are not necessarily the result, or entirely the result, of research into the nature of the brain. It is a theory after all. So there is as much speculation here as one would find in any philosophical theory. The difference being that the landscape described and terms used are those of neuroscience and not of philosophy. The brain, according to this theory, has read the book of science, and not the book of language and logic.

The mental states that FP postulates are simply not law-governed. It is this that Churchland has a major problem with. It essentially takes FP outside the realm of science and into Kantian world of noumenol freedom. More precisely, propositional attitudes and their relations are not law-governed. Kinematical states and configurations, on the other hand, are law-governed.

There is an alternative to propositional or sentential language. Just as we are familiar with the language of propositional attitudes and their relations, we could become familiar with kinematical states and their relations and interactions. We could “acquire a vocabulary” that could “characterise our kinematical states”. And, of course, these law-governed relations and interactions would be scientifically bona fide. We could also learn how these kinematical states cause behaviour. We would therefore be able to predict behaviour to a higher degree than we do now. More to the point, if we could literally read the brain, we would have first-person access to other mind-brains!

Churchland clearly thinks that philosophers of mind, and philosophers generally, have over-stressed the importance of language when it comes to mentality (and have also, incidentally, lingui-fied and logi-fied the mind itself). (See quote from dynamics paper.) Churchland claims that natural languages “exploit only a very elementary portion of the available machinery, the bulk of which serves far more complex activities beyond the ken of the propositional conceptions of FP”. It is of course very hard to accept that natural languages have been over-stressed, considering the importance of them in the lives of virtually all human beings. But there are other mental activities that are just or more important, it’s just that philosophers, because of their linguistic or logical bias, haven’t really registered them. These alternatives can even be deemed forms of language, according to Churchland. Though their makeup is very different. Their syntactic and semantic structures could be “decidedly alien”. However, these non-natural languages, as it were, “could also be learned and used by our innate systems”. This new language, or these new languages, would have a “new and more powerful combinatorial grammar over novel elements forming novel combinations with exotic properties”. But because they are not

propositional, or even statemental, they could not be evaluated as true or false. Nor could the relations between these elements be “remotely analogous to the relations of entailment, etc. that hold between sentence”.

In order to demonstrate his position Churchland basically says that such a non-natural language already exists in the brains of human beings. He tells us that the left hemisphere of the brain does communicate with the right hemisphere (and vice versa). And, of course, this communication is non-propositional. So if two parts of the same brain can communicate so effectively without propositional forms, then why can’t two brains? Between the two hemispheres of a single brain is what is called the “commissure”. The commissure carries the messages from one hemisphere to the other. It is a kind of bridge between the two. So in order for two separate brains to communicate non-propositionally with each other, we would need to construct an artificial commissure. But we would need more than an artificial commissure to ensure communication between two brains. This is how it could work out, according to Churchland. We would need to implant a transducer in both brains. This transducer would “convert a symphony of neural activity into (say) microwaves radiated from an aerial in the forehead”. This would run through the artificial commissure and enter the recipient brain. And, alternatively, rather than neural activity being converted into microwaves, we would also need to convert microwaves back into neural activity. That is, the information-receiving brain would require this.

And if two brains can communicate in such a manner, why not three or even more? Such are group of artificially connected people could “learn to exchange information and coordinate their behaviour [like their] own cerebral hemispheres”. One result of this, that is, of brains communicating directly with brains, is that “spoken language of any kind might well disappear completely”. Also, in library books we wouldn’t find words and sentences but “long recordings of exemplary bouts of neural activity”. In essence, we would be reading the neurophysiological goings on of other people’s brains. Of course, we would initially need a translation manual from the brain states to our understanding of the brain states. However, if we don’t need a translation manual to understand our own cerebral activities, perhaps we wouldn’t need one to understand other people’s brain workings.

People will of course ask: “How will such people understand and conceive of other individuals?” And Churchland answers his own question by saying: “In much the same fashion that your right hemisphere ‘understands’ and ‘conceives of’ your left hemisphere – intimately and efficiently, but not propositionally!”

Is Eliminative Materialism Self-Contradictory?

There is a well-known argument offered against elimitivist materialism. It revolves around its self-contradictory or incoherent nature. The argument is this. Because eliminative materialists are not meant to believe in propositional attitudes (like belief, intention and knowledge), then their statements in favour of eliminative materialism are “just a meaningless string of marks or noises”. Why is this so? Because they believe in what they say. And they have an intention to communicate. And they have knowledge “of the grammar of the language” and knowledge of the ‘truths’ of their own findings. But belief, intention and knowledge are deemed to be propositional attitudes, and eliminative materialists don’t believe in these things. Here’s the self-contradictory bit. If the statement of eliminative materialism is true, then it is false. It is false because there are no beliefs or knowledge to express, according to its own doctrine. According to itself, the primary statement of eliminative materialism is a “meaningless string of marks or noises” because it cannot be a belief (true or false) and it can’t be knowledge because these things are propositional attitudes. It therefore can’t be true by its own standards. As Churchland himself says: “Therefore it is not true. Q. E. D.”

Patricia Churchland offered a riposte to these ‘refutations’ of eliminative materialism, which Paul Churchland quotes in full. Firstly he offers a psychological rather than philosophical argument. That is, EM is just so radical, revolutionary and, perhaps, in initially counterintuitive, that it is understandable that people react fiercely to it. Churchland finds an historical parallel with eliminative materialism. It revolves around the reaction against vitalism. It was once held that when a vital spirit inhabited inanimate matter, it would become animate (alive). This belief in vital spirits was shared by just about everyone at certain points in history. It was “integrated with many of our conceptions”. So if anyone were to reject vitalism, which they did, the “magnitude of the revisions any serious alternative conception would require” would have encouraged just about everyone, at first, to fiercely reject anti-vitalism (this in fact happened). So, according to Patricia Churchland, the vitalist could have, and perhaps did, offer arguments the anti-vitalist that would be very much like the arguments the anti-eliminativist offers against the eliminativist. This is how it goes:

“The anti-vitalist [eliminativist] says that there is no such thing as vital spirit [propositional attitudes]. But this claim is self-refuting. The speaker can expect to be taken seriously only if his claim cannot. For if the claim is true, then the speaker does not have vital spirit [propositional attitudes] and must be dead [contradicting himself]. But if he is dead [or lacks propositional attitudes], then his statement is a meaningless string of noises, devoid of reason and truth.”

So the antagonist says that the eliminative materialist can only be saying something true if he agrees with him. This effectively means that the eliminativist can only speak the truth about propositional attitudes if he doesn’t believe what he says is the case.

Quine's 'Two Dogmas of Empiricism'

Quine's First Dogma of Empiricism 

i) Analyticity 

ii) Meaning 

iii) Meaning and Essence 

iv) Definitions 

v) What is Analyticity? 

vi) Semantic Rules

Quine’s First Dogma of Empiricism

Analyticity

The problem of analyticity goes back at least as far as Leibniz. It then become the victim of a series of “sign substitutions” (to use Derrida’s term).

The essential distinction we can make is between synthetic and analytic statements (to opt, essentially, for Immanuel Kant’s terms). David Hume, for one, made the following distinction between

relations of ideas

and

matters of fact

The former is essentially 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”. That is, we don't need to look out of the window (or anywhere else) to determine the truth of that statement.

“Matters of fact” are of course matters of the external world. A statement like “Boris Johnson is the Prime Minister” will fit the bill nicely. I can't determine the truth of this statement simply by analysing the contents of my own mind (unless an experience of Boris Johnson being the Prime Minister is 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 at all possible worlds. Hume’s matters of fact, on the other hand, may be true at 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 the 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: he's known 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 Boris Johnson is a politician.

To use Kant’s terms here: the attribute “is a politician” is already conceptually contained in the subject, “Prime Minister Boris Johnson”. (In contemporary speak, the second phrase “is a politician” would be classed as the “predicate” rather than the “attribute”.) To gloss on the Boris Johnson example, we can say that if the subject is true (that Johnson is Prime Minister), then the attribute must be true (that he's a politician).

To generalise: an analytic statement is true “by virtue of meanings [alone] and independently of fact”. So if the subject-term is true, then the predication must be true. The meaning of “Prime Minister Boris Johnson” makes the meaning of “is a politician” true. That is, it can be deemed true without recourse to experience, providing we accept the truth of the subject-term.

Meaning

Quine then moves away from analyticity itself and has something to say about meaning.

His first point is that extensions, references or denotata can't 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 can't 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 isn't 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; though 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. But, again, the meanings of these two examples are clearly not the same. So extensions alone don't provide us with the meanings of terms. Saying something has a heart is clearly not the same as saying that something has a kidney.

Essence and Meaning

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”.

(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)? Is an irrational man not, well, a man? And if an elephant were rational, would it be a man? And so on.

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

Traditionally, according to Quine, only things had essences. And, of course, only linguistic forms have meanings. But, 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.”

The essence of a thing is passed onto the essential meanings of the word that refers to that thing. We now look for the essence in the meaning of a word. Essence “is divorced from the object” and then it's found again by being “wedded to the word”. But, to stress, the word (or the linguistic expression) isn't the essence: it is the meaning prior to or “behind” the word. Meanings provide us with essences. So 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.). Then we had 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 or abstract 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 don't 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're 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". That is, 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.

Despite what's been said, the above isn't a logical truth: it's 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”. So the above can be turned into this:

No non-gay is gay.

(It could be said, strictly speaking, that non-gay isn't a synonym of heterosexual if a non-gay isn't, 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 aren't 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's indeed true that “bachelor” is defined as “unmarried man”. Though how do we find this out? We could look at a dictionary. But, according to Quine, the lexicographer “is an empirical scientist”. That means that he's 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” isn't the meaning of “bachelor”: it's a synonym of that word. Again, there's no need to advert to entities called “meanings”. So not only does

No bachelor is married.

not depend on meanings for its 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 the relation of synonymy (say, between “bachelor” and “unmarried man”) is stipulated or created “by fiat” - to use Quine’s own 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's been created expressly for the purpose of being synonymous with the definiens”.

This seems to be 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's because both synonymous terms are interchangeable “in all contexts without change of truth value”. That is, 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 can also substitute, in this context, “men without wives” for “bachelors” salva veritate. These stipulative synonyms could be almost 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 cognitive synonymy. That is a “complete identity in psychological associations or poetic quality” between words or statements. This kind of synonymy doesn't concern Quine here. The kind of synonymy he's 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?

Quine still has a problem. And that problem is: What is “analytic”? (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're back with the term “analytic”. That is, we're saying that “bachelor” and “unmarried man” are cognitively synonymous (or analytic). We class that which is synonymous by saying that it's analytic; and that which is analytic by saying that it's that which is synonymous. We're arguing in a circle. Again, what is “analytic”?

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. That is, the two predicates just mentioned can be interchanged salva veritate (i.e., while retaining truth). So the two predicates used within the same statement will guarantee synonymy and therefore analyticity. Though 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 (or 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

All and only bachelors are unmarried men.

is true.

We're back to analyticity, which hasn’t been adequately explained. Though there's a synthetic, rather than an analytic, component to the statement above. There's 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:

“Analyticity…seemed most naturally definable by appeal to a realm of meanings.”

Then:

“On refinement, the appeal to meanings gave way to an appeal to synonymy or definition.”

And finally:

“…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 which are all mutually interdependent and inter-definable.

Quine changes his tune a little by forgetting about bachelors and unmarried men to focus on what is a famous 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 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, then 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; though 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 being true? Where is it and what is it?

Semantic Rules

Rudolf Carnap offered another take on analyticity. He said that analyticity is a question of meanings; though he also said that the analyticity is generated by semantic rules. Quine goes into detail about Carnap’s alternative; though he rejects this too.

Carnap said that we firstly formulate an artificial language. Call it Lo. The semantical rules of Lo tell us which statements of the language are analytic.

After this account of Quine’s position on analyticity, we should be able to guess his problem with this approach. I wrote earlier that Lo tells us which statements should be taken as analytic. Yes; but we don’t understand the word “analytic” in the first place. So how do the stipulations of Lo 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”. That is, Lo tells us what statements are analytic; though it doesn't tell us what “analytic” means. So we're back to analyticity again. Quine thinks that Carnap would have been forced back to uninterpreted analyticity thus:

“A statement S is analytic for language Lo, if and only if…” (it's analytic)

More to the point, by “saying what statements are analytic for Lo, we explain ‘analytic-for-L’ but not ‘analytic’” but analytic for…

So instead of explaining the word “analytic”, we can explain “semantical rule” instead. Now Quine makes a holist point about this and the other explications of analyticity. (Quine was 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 semantic rules:

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

It's a member of the set. So why not fill in the blanks here? What is an analytic statement? Relative to a given set of analytic statements, it's easy to say what an analytic statement is: it's a member of the set. But, you guessed it, we're told which statements are analytic, but not what analyticity is!

To get back to semantic rules.

Quine said that semantic 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”

was what Quine was arguing against. This is, in fact, 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, then that statement will be analytic. But 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 concludes:

“…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”.