Quine on the Ground of Logical Truths*

Cong Wang Wen-fang Wang

Abstract.It is well known that Quine objected to the linguistic doctrine of logical truths according to which logical truths are true purely by virtue of the language,or true purely by virtue of the meanings of logical words occurring in them.Quine’s reasons for rejecting the linguistic doctrine of logical truths are various and seemingly powerful.However,a closer look at Quine’s arguments shows that,the authors believe,they are at most inconclusive.In this paper,the authors scrutinize several arguments given by Quine in his work and endeavor to point out the weakness of these arguments.The authors conclude that the linguistic doctrine of logical truths,and hence the analytic/synthetic distinction,is not undermined by Quine’s attacks.

It is well known that Quine objected to the linguistic doctrine of logical truths(“LD”henceforth)according to which logical truths are“true purely by virtue of the language”or true purely by virtue of the meanings of logical words occurring in them.1Quine([12],pp.95-96)characterized what we call“LD”here or what he called“the linguistic theory of logical truth”there as the doctrine that logical truths are“true purely by virtue of the language”or”true by virtue purely of its grammatical structure.”Carnap([3],p.916)on the other hand,characterized logical truths in several different ways:sometimes as truths based on“l(fā)inguistic fiat”,sometimes as true by“l(fā)inguistic conventions”,and sometimes as truths“based on meanings”.(He took the last characterization to be better than the previous two in that the previous two are“psychologically unhelpful”.)All these characterizations are,of course,very vague and arguably non-equivalent,and therefore should be avoided if possible.The alternative characterization of LD as the doctrine that logical truths are true purely by virtue of the meanings of logical words occurring in them is due to Hellman ([4],p.190).This characterization is obviously much more precise than the previous ones and has somehow become standard.However,following Hellman and Boghossian,we will further introduce two ways of explicating this alternative characterization in the paragraph next to the next one,and therefore will not take this formulation of LD as final.LD is a doctrine that was developed by the Vienna Circle on the basis of Wittgenstein’s idea and was officially maintained by Carnap for his whole life.Quine’s reasons to reject LD are various and seemingly powerful;however,a closer look at these arguments will show that,we believe,they are at most inconclusive.In what follows,we will scrutinize several arguments given by Quine in his work and try to point out the weakness of these arguments.We will conclude that LD,and hence the analytic/synthetic distinction,is not undermined by Quine’s attacks.Before we start,however,let us make a couple of preliminary remarks.

First,to foster the following discussion,we shall quickly agree with Quine([9],p.110)that logical truths are adequately characterized as“those true sentences which involve only logical wordsessentially”,whereas what count as“l(fā)ogical words”is simply determined by a given list that,let us assume,includes“not”,“or”,“all”,“is identical with”and so on.More explicitly,what this characterization means is that,given a list of logical words,the so-called“l(fā)ogical truths”can be identified as those true sentences such that“any [non-logical]words [occurring in them]… can be varied at will without engendering falsity.”Thus,“John is identical with John”and“John is a man or John is not a man”are examples of logical truths according to this characterization,for,if we replace“John”and/or“is a man”uniformly with any grammatically admissible expressions we like,the results will be sentences that have the same truth-value,i.e.,truth,as these two.Note that what this characterization intends to do is simply to draw the boundary between logical truths and non-logical ones;it says nothing about how logical truths are supposed to be known or about how their truth is grounded.

To be sure,the characterization of LD as the doctrine that logical truths are true purely by virtue of the meanings of the logical words occurring in them is just a long-winded way to say the simpler thing that logical truths are analytical truths.Understood in this way,it is not surprising that Quine objected to LD,given his famous denouncement of the traditional analytic/synthetic distinction in“Tow Dogmas of Empiricism”([11]).As a matter of fact,however,Quine had launched a series of relentless attacks on LD ever since 1936:first in his article“Truth by Convention”([10]),then in the article“Carnap and Logical Truth”([9]),and finally in the bookPhilosophy of Logic([12]).Quine’s attacks on LD in these writings are,however,out of focus,and this is where our second remark is about.As many philosophers(e.g.,Hellman([4])and Boghossian([2]))have pointed out,Quine’s discursive attacks on the analyticity of logical truths can be and should be sorted into two kinds:those against the epistemic claim that logical truths area prioriknowable and those against the metaphysical claim that logical truths are made true by linguistic conventions.2The epistemic claim and the metaphysical claim are,roughly,Hellman’s([4])LD(II)and LD(III).Boghssian ([2])called these claims“epistemic analyticity”and“metaphysical analyticity”separately,but we find this terminology misleading.Carnap ([3],p.916)seemed to have the epistemic claim in mind when he said that understanding logical truths“is a sufficient basis for the determination of their truth.”In other words,LD can be taken either as an epistemic doctrine that mere grasp of the meanings of the logical words contained in a logical truth suffices for one to be justified in holding the sentence true,or as a metaphysical doctrine that logical truths owe their truth completely to the meanings of logical words therein.We should,therefore,be very careful about which doctrine or version of LD is the target of a specific argument of Quine,for a powerful argument against one of these two versions of LD may not be so against the other.3Boghossian([2])thinks that the epistemic version of LD is defensible but the metaphysical version is not,whereas Hellman ([4])thinks that both LD(II)and LD(III)are defensible.We are inclined to agree with Hellman,for we think that Quine’s attacks hurt neither of them.

With these preliminary remarks in mind,let us proceed to scrutinize Quine’s arguments against LD.We will,however,put our focus more on the two arguments of Quine given in hisPhilosophy of Logic,for it seems to us that philosophers have not paid enough attention to them yet.

1 Quine’s Arguments against LD in Philosophy of Logic(PL)

As we see it,there are at least two new arguments against LD in PL that were not even hinted by Quine in his early writings.The first of these ([12],pp.95-96)aims at what appears to be a common presupposition of both versions of LD,namely,the presupposition that a distinction between logical words and non-logical words can somehow be made,and appeals to the notion of an immanent distinction.Here is how Quine put the argument:

… [T]he very distinction between grammar and lexicon is immanent,and admits of alternative adjustments even in the analysis of one and the same language.As this distinction varies,the distinction between logical truth and other truth varies with it.Insofar,the demarcation of logical truth rests on the whim of the descriptive grammarian.Now one would hesitate to let a sentence vacillate between being true purely by virtue of the language and being true partly by virtue of the nature of the world,according as the grammarian chooses to describe our already existing language in one or other of two permissible ways.

The argument contained in this paragraph,we think,can be faithfully reformulated as the following one(call this argument“PLAr1”):

(1)The distinction between logical words and non-logical words4When Quine([12],p.95)wrote“the distinction between grammar and lexicon”he meant the distinction between grammatical particles and lexicon.This is a distinction often made by grammarians.The parallel distinction in logic is,we take it,the distinction between logical words such as“or”and“is identical with”and non-logical words such as“John”and“is a man”.is immanent and admits of alternative adjustments.

(2)If (1)is true,then the distinction between logical truths and other truths will vary in accordance with how the grammarian chooses their logical words.

(3)If (1),(2)and LD are all true,then what counts as true purely by virtue of the language will vary in accordance with how the grammarian chooses their logical words.

(4)It would be absurd to say that what counts as true purely by virtue of the language will vary in accordance with how the grammarian chooses their logical words.

(5)Therefore,LD is not true.

Put in this way,PLAr1 is no doubt a valid argument,but it is also clear that the advocate of LD will not accept all of its premises.Which premise or premises of PLAr1 can be resisted? We suppose that the advocate of LD should yield to(2)and(4)5We think that(4)is obvious:given a fixed language,one should not allow the distinction between logical and non-logical truths and hence the distinction between analytic and synthetic truths to vary in accordance with how the grammarian chooses logical words.To see the plausibility of(2),readers need only think of the sentence“John is a man or John is not a man”as an example.If we take“or”and“not”to be logical words,it will be a logical truth in the Quinean sense,i.e.,it will remain true no matter how the non-logical words in it are substituted for in a uniform way.However,if we decide to take“John”,“is a man”and“not”to be logical words,it will no more remain true when we substitute“and”for“or”,and hence no more be a logical truth.,but we also think that s/he should cast some doubt on(1)and directly reject(3).Let us explain the problem of(1)first.Note that the notion of an immanent distinction(or an immanent notion in general)mentioned in(1)of PLAr1 is the notion of a grammatical distinction(or a grammatical notion in general)that is defined for a particular language([12],p.19).By contrast,a transcendent distinction(or a transcendent notion in general)is a grammatical distinction(or a grammatical notion in general)that is directed to languages generally.Now,not only did Quine believe that the distinctionhemade between logical words and non-logical words by a list was immanent(obviously it is),he also believed that no transcendent distinction between them is defensible.As a matter of fact,this latter belief is what really is required for the conclusion of PLAr1;for,if the distinction at issue can be made successfully in a transcendent way,we can then simply adopt that transcendent definition and thereby reject(1).But why did Quine think that no transcendent distinction at issue is defensible? As far as we can see,Quine considered in PL only one unsuccessful attempt to define the distinction between logical words and non-logical words in a transcendent way;6The transcendent attempt Quine considered in PL classified lexicon into categories and defined the category of an expression to be the set of all the expressions that are interchangeable with it salva congruitate.([12],pp.18-19)after arguing that it was not satisfactory,he then concluded that“we have no defensible transcendent notion of [logical words]or lexicon”([12],p.60).But this conclusion is certainly too hasty.

In order to cast more doubt on (1),we will briefly sketch here a transcendent way of defining the distinction between logical words and non-logical words that appears to us to be more promising than the one considered by Quine in PL.(We will suggest another one,one that appeals to“occur essentially”,later on in this section.)According to many philosophers,what makes logic so unique is that it is not about anything in particular.So,it is natural to think of logical words in any language as those expressions in that language that are“topic-neutral”.However,we need to sharpen the notion of“topic-neutrality”involved here not only to make the demarcation more precise but also to make sure that the notion so defined will finally turn out to be a transcendent one.Both tasks,it seems to many philosophers(e.g.,Mostowski([8]),Scott([13]),McCarthy([6]),Tarski([16]),van Benthem([1]),Sher([14]),and McGee([7])),can be accomplished by defining a logical word as an expression thatremains invariant in extension under arbitrary permutations of any domain.For details of this kind of definitions,readers are referred to [5].7A problem about the permutation invariance criterion is that it applies only to extensional operators and truth-functional connectives but not to operators in various kinds of intensional logics or hyperintensional ones.Though the invariance criterion can be extended in a natural way to intensional operators and thereby shows that some intensional operators,such as modal operators of S5,are logical,it is still not clear how this criterion can be further extended.Besides,it is always debatable whether judgments by applying this criterion to other operators are always correct.We thank an anonymous reviewer to bring up this issue and think that this issue,though important,has no bite to our moderate conclusion.More to the point:the definition we give several paragraphs later is also a transcendent one and it seems to us that it is more inclusive than this permutation invariance criterion.Notice that,defined in this way,the distinction between logical words and non-logical ones in a language is a transcendent one,one that applicable to languages in general.Now,ifthis particular(or any other)transcendent way of distinguishing logical words from non-logical ones in a language is defensible,we can then reject the premise (1)of PLAr1.We do not mean to suggest that this particular way of defining the distinction at issueisespecially satisfactory;our point is simply that one should not rashly accept Quine’s premise(1)of PLAr1 before all attempts to make a transcendent distinction between logical words and non-logical ones are shown to fail their tasks.

(1)of PLAr1 is therefore dubious.Yet,we think that the advocate of LD can even go a step further to directly reject (3)of that argument.(3)of PLAr1 implies that if the distinction between logical words(or logical truths)and non-logical words(or non-logical truths)can only be immanent and admits of alternative adjustments,then what counts as true purely by virtue of the language will become a relative matter if LD is true.This implication seems to us to be completely objectionable.Before we explain why it is so,however,let us pause for a while and think about this question:suppose the advocate of LD agrees that the distinction between logical and non-logical words and hence the distinction between logical and non-logical truths can only be immanent and admits of alternative adjustments,how would s/he formulate LD?Of course it would be foolish for him or her to formulate it as“all logical truths are true purely by virtue of the meanings of the logical words”,because what counts as logical words or truths in this case will vary according to how the grammarian chooses logical words.A more appropriate way to formulate his or her doctrine,given that s/he accepts that the distinction between logical and non-logical words is immanent,would seem to be“for each such choice,logical truthsunder the choiceare true purely by virtue of the meanings of thechosenlogical words”.Formulated in this way,LD is not absurd,and(3)of PLAr1 does not seem to be the right thing to say.

Given the new formulation,we think that the advocate of LD can reject the abovementioned implication of(3)by at least two ways,one of which is quite straightforward,while the other is more roundabout.The straightforward way is to count all those sentences as“true purely by virtue of languagesimpliciter”that come out logically true undersomechoice of logical words.8Quine([12],p.96)actually hinted this way of rejecting(3)of PLAr1,but he then quickly changed the topic and moved to another argument against LD.After all,LD is nothing but the claim that logical truths are analytical truths;so,as long as logical truths are true purely by virtue of the meanings ofsomewords in them,it really does not matter whether these words appear on this or that list of“l(fā)ogical words”.The roundabout way is to try to define in a transcendent way a category of wordsCthat willincludeevery“ordinary”logical word.9It may or may not contain other words,but this is irrelevant to the current issue.Note that,even if Quine is right about the immanency of the logical/non-logical distinction,it is still not excluded that some broader category C that includes ordinary logical words as a part can be defined in a transcendent way.One obvious candidate for such a category is just the category“words”.If the advocate of LD succeeds in doing this,s/he can then claim that logical truths are true purely by virtue of the meanings ofsomewords inC,hence true purely by virtue of the language;10This category C may or may not have the further use of defining the category of logical words,but this further use is irrelevant to the current issue.and this claim would also make PLAr1 totally irrelevant to the sustainability of LD.Can the advocate of LD find such a categoryC?We think s/he can.What we have in mind is what Quine used to call“words that occursessentiallyin a sentence”.In order to explain it,let us follow Quine’s idea(1936,p.80)a bit.Let us say that an expression E occurs vacuously in a sentenceSiff its replacement by any and every other grammatically admissible expression leaves the truth-value of the sentence unchanged.Sentences after such a replacement are called the“vacuous variants”ofS.Let us also say that an expression E occurs essentially in a sentenceSiff it occurs in all the vacuous variants ofS.So far we have been following Quine,but now let us take a step further and say that an expression E is essentialsimpliciteriff it occurs in all vacuous variants ofsome sentence S.The category“words that are essentialsimpliciter”must include all ordinary logical words as a part,for each of the latter occurs essentially in at least one sentence.11But it seems to us that the category will not include words like“John”and“it”.There may or may not be other words that are essentialsimpliciter,but this is not of our concerned.It is arguably that this definition of“words that are essentialsimpliciter”is a transcendent one.If the advocate of LD claims that logical truths are true purely by virtue of the meanings ofsomewords that is essentialsimpliciter,this claim would make PLAr1 and its premises totally irrelevant to the sustainability of LD.We thus see that both(3)of PLAr1 and PLAr1 itself do not bite.

But Quine had another argument against LD in PL,though it seems to aim only at the metaphysical version of LD rather than the common presupposition of both versions of LD.Quine wrote(p.96):

…How,given certain circumstances and a certain true sentence,might we hope to show that the sentence was true by virtue of those circumstances? If we could show that the sentence was logically implied by sentences describing those circumstances,could more be asked? But any sentence logically implies the logical truths.Trivially,then,the logical truths are true by virtue of any circumstances you care to name—language,the world,anything.

We may call the argument contained in this paragraph“PLAr2”and reformulate it more explicitly as follows:

(1)A sentenceSis true by virtue of a circumstanceC12It does not matter whether we use the singular noun“circumstance”or the plural noun“circumstances”here,for our argument below will go through for either version.If one insists to use the plural,however,s/he can replace(1)of this argument by(1′):(1′)A sentence S is true by virtue of circumstances C1,C2,...,Cn iff〈DC1〉∧〈DC2〉∧...∧〈DCn〉logically implies S.Given that we have plural quantifiers at our disposal,we can still argue for the same conclusion for(1′)as we do for(1).iff the description〈DC〉ofClogically implies S.13In what follows,we use“DC”to stand for the sentence that describes C and“〈DC〉”to refer to the name of the sentence that describes C.

(2)The description of whatever circumstance implies every logical truth.

(3)Therefore,by(1)and(2),a logical truth is true by virtue of every circumstance,linguistic or not,and hence LD is false.

Again,we think that PLAr2 has a valid form but one of its premise,i.e.,(1),is objectionable.Note that(2)in PLAr2 is entailed by the trivial truth that every sentence whatsoever logically implies every logical truth,and hence should not be doubted.Notice also that,by“circumstances”,Quine must mean something like facts,partly for the reason that,otherwise,(1)of PLAr2 will be obviously false simply because of the fact that every truth is logically implied by the description of,but is not true by virtue of,a contradictory circumstance,but mainly for the reason that a circumstance is supposed to be something like a truth-maker,i.e.,something that is responsible for the truth of a true sentence.We shall name this plausible assumption“factuality of circumstances”that circumstances are fact-like entities.We shall also assume,which seems to us to be equally plausible,that every true sentence describes some circumstance and we shall name this further assumption“comprehension principle(CP)”.Once we make these two plausible assumptions explicit,however,it becomes apparent that(1)of PLAr2 is objectionable for at least two related reasons.

First of all,(1)of PLAr2 logically implies the following principle(P1):

(P1)IfSis true by virtue of a circumstanceCwhose description is〈DC〉,thenSis also true by virtue of any circumstanceC*whose description〈DC*〉logically implies〈DC〉.14Here is the proof of the obvious claim that (1)of PLAr2 logically implies (P1).Suppose that S is true by virtue of a circumstance C whose description is〈DC〉.Suppose further that the description〈DC*〉of C* logically implies〈DC〉.By the transitivity of logical implication,the description〈DC*〉of C* logically implies S.Then,by(1)of PLAr2,S is true by virtue of C*.

(P1)in turn implies,to give just a few examples,that“Quine is a philosopher”is true by virtue of the circumstance whose description is“China is in Asia and(if China is in Asia then Quine is a philosopher)”and that“Quine is Quine”is true by virtue of the circumstance whose description is“China is in Asia”.To us,these results are so counter-intuitive that they jointly constitute a good reason to reject(1)or PLAr2,but we are also very sure that Quine would not be moved by these consequences.So we will not put too much emphasis on this objection.

Our second objection to (1)in PLAr2 comes from a slingshot-style argument which endeavors to show thatany truthwhatsoever will be true by virtue of“any circumstances you care to name”if(1)of PLAr2 is true.Here is how the argument goes.LetSbe an arbitrary truth that is implied by the description〈DC〉of a certain circumstanceC,so thatSis true by virtue ofCaccording to (1)of PLAr2.Now,letC*be another arbitrarily chosen circumstance and〈DC*〉be its description.The following“proof”shows thatSis also true by virtue ofC*:

In the above proof,“TDD”refers to any reasonable theory of definite descriptions such as Russell’s theory of definite descriptions,and the premise 3 is justified by the factuality assumption that circumstances are fact-like entities.(P1)and(CP)are principles mentioned in the previous paragraph,while(P2)is the following“principle of extensionality”:

(P2)If“t1”and“t2”refer to the same thing,then“φ(t1)”and“φ(t2)”describe the same circumstances.

As one can easily check,each step of the above“proof”is either justified or valid.This then is the“proof”endeavoring to show that any truth whatsoever is true by virtue of any circumstance you care to name if(1)of PLAr1 is true!

Frankly,what this“proof”really shows is that any truth whatsoever is true by virtue of any circumstance if both (1)of PLAr2 and (P2)are true.15(P1)can be ignored,for it is just a logical consequence of(1)of PLAr2.Because of the intuitive plausibility of(CP)and Factuality assumption,we also suggest that we ignore the possibility that one of them is the culprit of the proof.And we take this“proof”to be a proof byreductio ad absurdum.So at least one of these two assumptions must be wrong,but which one is to be blamed? To give up(1)of PLAr2 is to give up the whole argument PLAr2,while to abandon the principle of extensionality is to take circumstances as“intensional entities”.Yet one of the reasons why Quine wanted to deny the existence of intensional entities is that,were they allowed,it would be possible to define the notion of synonym and therefore the notion of analytic truth.16For example,if propositions,which are intensional entities of a sort,were allowed,we could say that two words are synonymous iff one can be substituted for the other without altering the proposition being expressed.Analytic truths can then be defined in the Fregean way:they turn into logical truths when synonyms are replaced with synonyms.We think that,were circumstances qua intensional entities admitted,a similar definition will work by way of circumstances.So to reject(P2)is to risk resuming the analytic/synthetic distinction.Neither choice seems acceptable to Quine.This proof therefore presents a dilemma to Quine,and we see no way that Quine can escape this dilemma.Especially,Quine cannot respond to it by saying that,according to his verification holism,every sentence is indeed“made true”by every circumstance,for this reply would simply beg the question about the ground of logical truths.

We are inclined to think that the above argument constitutes areductionof Quine’s account of“true by virtue of”in(1)of PLAr2.But what is wrong with that account?Indeed,Quine asked the question:“If we could show that the sentence was logically implied by sentences describing those circumstances,could more be asked?”We think,however,that the advocate of LD could ask more,and the following remark indicates what that more is.The advocate of LD can first distinguish within circumstances“l(fā)ogical”ones from“non-logical”ones.Intuitively,logical circumstances are those that are described by logical truths or involve meaning stipulations or meaning conventions about logical words only,while non-logical circumstances are those that are described by non-logical truths and usually involve at least something beyond meaning stipulations.S/he can then point out two parallel truths about truths in general:(a)every truth is true at least partly by virtue of the language;and (b)every truth is logically implied by the description of some circumstance.Noticing the parallel between(a)and(b),s/he can then identify them as one and the same truth and propose:to say of a true sentenceSthat it islogicallyimplied by the description of some circumstanceC,no matter what kind of circumstanceCbelongs to,is just to say that it is true at least partly by virtue of the language.It is obvious that every true sentence is,by this definition,true at least partly by virtue of the language.However,if it turns out thatallcircumstances whose descriptions logically imply a sentencesSare of the non-logical kind,Swill also be said to be true partly by virtue of the world.Otherwise,(i.e.,if at least one circumstance whose description logically impliesSis of the logical kind)Swill be said to be truepurelyby virtue of language.In short,according to the advocate of LD,the right-hand part of(1)of PLAr2 is more adequate as definiens for“Sis true at least partly by virtue of the language”than as that for“Sis true by virtue of the circumstanceC”.To define“Sis true by virtue of the circumstanceC,”the advocate of LD can and should ask more than what Quine had offered!17More precisely,the advocate of LD will give the following definitions.A sentence S is true at least partly by virtue of the language iff there is a circumstance C whose description 〈DC〉 logically implies S.A sentence is true only partly by virtue of the language iff(i)it is true at least partly by virtue of the language,and (ii)every sentence that both describes some circumstance and logically implyes S describes some non-logical circumstance.A sentence is true purely by virtue of the language iff(i)it is true at least partly by virtue of the language,and (ii)it is not true only partly by virtue of the language.Given the plausible assumption that a logical truth S describes a circumstance C iff C is a logical circumstance,s/he can go on to show that all and only logical truths are true purely by virtue of the language.If s/he further wants to define the relation“S is true by virtue of C”,s/he can say that a sentence S is true by virtue of a circumstance C iff(i)the description〈DC〉of C logically implies S,and(ii)either〈DC〉describes some logical circumstance or every sentence that both describes some circumstance and logically implies S describes some non-logical circumstance.With the same assumption that a logical truth S describes a circumstance C iff C is a logical circumstance,s/he can show by this last definition both(a)that non-logical truths are true only by virtue of non-logical circumstances and(b)that logical truths are true only by virtue of logical circumstances.

We can imagine how Quine would respond to our remarks in the previous paragraph:“The distinction you make between logical and non-logical circumstances not only begs the question of the analytic/synthetic distinction but also is empty in the sense that it is indistinguishable from the non-objectionable distinction between the broadest traits of reality and local traits of reality.So,in the end,you have not shown me that there are sentences that are truepurelyby virtue of language.”But our remarks do not beg the question of the analytic/synthetic distinction,for the logical/non-logical distinction between circumstances is not the same as the analytic/synthetic distinction,nor does the former implies the latter.The logical/non-logical distinction between circumstances appeals to the notion of logical words and/or the notion of logical truths that are both legitimate even to Quine.So Quine is not in a position to complain on this distinction at all.As to Quine’s complaint that our distinction is empty,we will deal with it in next section.

2 Quine’s Arguments against LD in His Early Writings

Quine gave several criticisms and arguments against LD in his early writings.Some of these comments and arguments are directed toward the epistemic version of LD,while others toward the metaphysical one.The most often discussed argument of Quine against the epistemic version of LD is the vicious regress or the infinite regress argument according to which logical truths cannot be justified by meaningconventions18By“conventions”,Quine ([9],pp.117-118)meant legislative convention rather than discursive convention.The former make“deliberate choices and[set]them forth unaccompanied by any attempt at justification other than in terms of elegance and convenience.These adoptions,called postulates,and their logical consequences(via elementary logic),are true until further notice.”The latter“is mere selection,from a pre-existing body of truths,of certain ones for us as a basis from which to derive others,initially known or unknown.”To give us examples of legislative convention,Quine went on to say(p.120)that postulates of deviant logics are legislative postulates.As examples of discursive convention,readers can think of axioms of,say,Peano’s arithmetic system.,since

…the logical truths,being infinite in number,must be given by general conventions rather than singly;and logic is needed then in the metatheory,in order to apply the general conventions to individual cases.([9],p.115)19A relevant but not so obviously the same argument as the vicious regress argument by Quine is the argument that,once we try to formulate those general conventions,we inevitably use the very same logical constants that we try to define implicitly by these conventions.Thus,general conventions circumscribing the meaning of logical constants presuppose meaningfulness of those logical constants that are supposed to be meaningless before we give the conventions.Even though it is not so clear that this argument is the same one as the vicious regress argument,this“self-presupposition problem”is avoided in the same way in Boghossian’s proposal.

We will,however,put this vicious regress argument completely aside in what follows,not because we think that it is unanswerable,but because,on the contrary,we think that its power has been greatly diminished to the minimum by the responses of several philosophers,especially that given by Boghossian ([2]).Boghossian’s response to Quine’s vicious regress argument can be summarized as follows.Logical words(such as“and”and“not”)mean what they mean by virtue of figuring in certain inferential rules involving them (such as the rule of“and”-introduction and the rule of“not”-introduction).The mere“grasp”of these inferential rules suffices for us to be justified in holding true infinitely many logical truths by simply deducing them from these inferential rules alone.The vicious regress problem is avoided because our“grasp”of these inferential rules does not reside in our explicitly writing these rules down in propositional forms but in our beingdisposedto conform to them in our employment of these logical words.So it is not true that,when deducing a logical truth,we need logic again to apply the general conventions to individual cases,says Boghossian.Here,we totally agree with Boghossian and think that the vicious regress problem is no more a threat to the advocate of LD.

What we want to focus on in the rest of this section is another criticism on LD given by Quine in several places,namely the criticism that LD is empty.However,there are,we think,at least three different senses of the criticism“LD is empty”when Quine said it.The first sense is that LD,when interpreted in a certain way,is true of almost every truth.As Quine said:“If in describing logic…as true by convention what is meant is that the primitivescanbe conventionally circumscribed in such a fashion as to generate all and only the accepted truths of logic…,the characterization is empty;… the same might be said of any other body of doctrine as well.”([10],p.102)20Quine([9],p.121)re-asserted the same point in this way:“What seemed to smack of convention…was‘deliberate choice,set forth unaccompanied by any attempt at justification other than in terms of elegance and convenience’;and to what theoretical hypothesis of natural science might not this same character be attributed?”The second sense is that LD amounts to the non-objectionable but empty claim that logical truths are obvious truths.As Quine said:“… if we try to warp the linguistic doctrine of logical truth around into something like an experimental thesis,21Namely,the thesis that deductively irresoluble disagreement as to a logical truth is evidence of deviation in usage(or meanings)of words.([12],p.112)…[it]seems to imply nothing that is not already by the fact the elementary logic is obvious or can be resolved into obvious steps.”([9],p.112)Indeed,Quine even claimed“… logic is obvious;potentially obvious.Logical truths are tied to translation in no deeper sense … than other obvious truths,e.g.,utterances of ‘It is raining’ in the rain.”([12],pp.96-97)The third sense Quine attached to the term“empty”when he said that LD was empty is that saying that a logical truth,such as“(x)(x=x)”,is true purely by virtue of the meanings of logical words occurring in it is indistinguishable from saying that it is true by virtue of an obvious trait of everything.([9],p.113)We will comment on each of these three senses of“empty”in turn in what follows.

If LD is interpreted,Quine said,as the doctrine that the meanings of logical wordscanbe circumscribed through conventional assignment of truth to various axioms(or axiom schemata)and rules in such a way as to generatealland only logical truths,then this“axiomatizational style”of characterization can also be carried beyond logic into mathematics and all empirical sciences.However,if one notices the italic word“all”used here,it is clear that primitives in mathematics cannot be22Due to Godel’s incompleteness theorem.,and it is dubious that primitives in other sciences can be,characterized in the same way that logical words of first-order language are characterized.However,people who are sympathetic with Quine might reply that we should drop the word“all”used here anyway for it excludes too much from the realm of logic23Higher-order logic,for example..We tend to agree with this reply,but then think that Hellman’s reply to Quine*24Quine* is a fictional character in[4].is quite right here even if we drop the word“all”used here.According to Hellman([4],p.190),even though Carnap preferred to use the method of axiomatization to stipulate meanings for logical words inLogical Syntax,this nonetheless must not obscure the fact that the central thesis of LD is simply that logical truths are true solely in virtue of the meanings of the logical words.The meanings of these logical words can be given by any of a given number of ways,e.g.,by truth-tables as in the case of truth-functional connectives,or by direct specification of extensions as in the case of identity,or even by inferential rules as envisioned by Boghossian.Once this is made clear,we think there is no more justification of Quine’s complaint that the same methods of giving meanings to logical words can be applied to any other body of the total science.

What then of the second sense of“empty”? No doubt,logical truths are obvious or,at least,can be reached by obvious steps.But is a logical truth tied to translation in no deeper sense than the obvious truth“it is raining”uttered in the rain? Perhaps so,but this is not the crucial issue here.What is crucial is that we need an account of why logic is obvious.As Hellman([4],p.192)said:“[W]e need an account of why logic is obvious.The sort of account we can give of why‘It is raining’is obvious does not work for logic.Here is a major explanatory role for the linguistic doctrine,essentially its traditional role in logical epistemology.”Hellman did not go on to explain why the sort of account we can give of the obviousness of“it is raining”does not work for logical truths,but we think what he had in mind must be something like the following.When someone utters the obvious truth“it is raining”in the rain,it is obvious whatin the worldmakes that sentence true,namely,the rain.However,if someone utters the equally obvious truth“if it is sunny then it is sunny”also in the rain,it isnotobvious whatin the worldmakes that sentence true.In fact,it seems obvious thatnothing in the worldcould be plausibly said to make the latter sentence true.After all,not only can“if it is sunny then it is sunny”be uttered truly when it is raining,it can also be uttered truly when it is foggy,when it is stormy,when it is at night,when the sun explodes and disappears,or even when there had never been a sun at all in the whole world.So it seems totally inadequate to say that it is made true by any trait of anything in the world at all.Where,then,does the obviousness of its truth come from? LD explains its obviousness in terms of the meanings of the logical word“if…then…”contained in that sentence,and this seems to be an intuitively plausible way to explain the phenomenon.In short,suppose we warp LD around into an experimental thesis,even if doing so will make LD seem to imply nothing that is not already implied by the fact that the elementary logic is obvious or can be resolved into obvious steps,the obviousness of logical truths still needs an explanation that is different from the one given to other obvious non-logical truths.An intuitively suitable explanation is just that logical truths are obvious because of the meanings of the logical words contained in them.

However,this soon leads us to the third sense that LD is empty.What is the difference,asked Quine,between claiming that“(x)(x=x)”depends for its truth on traits of language and claiming that it depends for its truth on an obvious trait,viz.,self-identity,of its subject matter,viz.,everything? And he replied:“[t]he tendency of our present reflections is that there is no difference.”([9],p.113)We must confess that we don’t have the tendency that Quine had.On the contrary,we have a tendency to say that there are quite a few differences between them.We can see at least four differences.First,if one utters the logical truth“if it is raining then it is raining”,Quine will have to say that there is no difference between claiming that it depends for its truth on traits of language and claiming that it depends for its truth on an obvious trait of its subject matter.But what is the subject matter of this sentence? What does“it”refers to here? It is not so clear what the answer is.25“It is raining”is an example of what Strawson called a“feature-placing statement.”Strawson said that feature-placing statements introduce universals“even if they do not by themselves supply an adequate basis for particular-introduction on the required scale.”But,if“it is raining”does not have a subject matter,so is the sentence“if it is raining so it is raining”.For Strawson on feature-placing statements,readers are referred to[15],p.202.So there seems to be a difference between these two ways of claiming things:it is clear what the former claim is about whereas it is not so clear for the latter.Second,if one utters“if Sherlock Holmes exists then Sherlock Holmes exists”,Quine will,again,have to say that there is no difference between claiming that it depends for its truth on traits of language and claiming that it depends for its truth on an obvious trait of its subject matter.But what is the subject matter of this sentence? What does“Sherlock Holmes”refers to here?Nothing! Again,there seems to be a difference between these two ways of claiming things:the former claim is clearly about existents objects,viz.,logical words,while the latter appears not to be about anything at all.Third,claiming that a logical truth depends for its truth on an obvious trait of its subject matter will,while claiming that it depends for its truth on traits of language will not,very likely provoke a doubt in non-philosophers whether therereallyis such a trait asself-identity,orbeing red or not being red,or evenif being red then being blue or not being blue,in its subject matter.Hellman used to call these traits“stipulated universal traits”probably because he,like us,also saw the artificiality of these so-called“universal traits”.Here again,we seem to have a difference between these two ways of claiming things:the former claim is ontologically innocent in a way that the latter is not.Fourth,as Carnap([3],p.920)pointed out,both ways of claiming things are empirically testable,but the responses that will confirm one of them will be quite different from the responses that will confirm the other.The man who believes that“(x)(x=x)”depends for its truth on an obvious trait of everything will,while the man who believes that it depends for its truth on traits of language will not,prepare to retract his judgment in the hypothetical situation of witnessing a counterexample.So here we seem to have a fourth difference between these two ways of claiming things:they have different empirical confirmation conditions.

So far,we have checked 4 different arguments against LD given by Quine.After carefully inspecting each one of them,we find that none of them is compelling.There may be other arguments of Quine aiming at LD that we have overlooked,and there may be other ways of arguing against LD that Quine had not considered.We should not,therefore,conclude that LD is true.Instead,we conclude that Quine’s arguments against LD are at best inconclusive and that LD,and hence the analytic/synthetic distinction,is still a defensible doctrine.