On the Notion of Logical Form

YUNQING LIN

Beihang University

INTRODUCTION

The notion of logical form plays a central role in the philosophy of language and in linguistics.This is clearly shown in Burge's remark that“the development of a vastly more sophisticated sense of logical form，as applied to natural language”is a“major，and possibly durable contribution”to philosophy in the last forty years（Burge 1992：49）.In spite of this，the logical form approach to natural language is not universally accepted.In fact，the later Wittgenstein explicitly denies the existence of logical form behind language，and argues that the whole idea is based on a misunderstanding of the workings of language.It is worth noting that this Wittgenstein is the same man who proposed the very idea of logical form earlier in his Tractatus.Since Wittgenstein is a great thinker and philosopher，there must be some truth in his claim.Yet，in spite of the brilliance of and insights in the later Wittgenstein's philosophy of language，the linguistics and philosophy communities have remained largely unaffected.Philosophers and linguists alike have been happy with their pursuit of the logical form of natural language.

The situation is a very intriguing one，and there are two explanations for it，both very plausible.One is that philosophers and linguists believe that there does exist a hidden logical form，and simply think that Wittgenstein is wrong in denying it.Another is that they find Wittgenstein's later philosophy on language plausible，but they feel that it does not seem to be useful for their specific problems.To persuade philosophers and linguists belonging to this latter category to abandon their search for logical form，one must show that what can be done by using it can be done through another means.To do this to the scholars of the former kind one must do more than this：one must also show that their logical form is in fact an illusion.But providing an alternative to logical form is still vitally important，otherwise the scholars may never feel convinced and may never want to give up their search for it.In this paper I shall attempt to achieve both these goals.I shall argue that the notion of“logical form”has no well－defined meaning.I shall also suggest a new way of looking at logical form.

THT USE OF LOGICAL FORM

Let's begin our discussion with the question：What is logical form？It is a simple question，yet it is extremely difficult to answer.There may never be a unique definition for it，as the later Wittgenstein（1953）would say.Here we can do no better than to follow his slogan：“Don't ask for the meaning，ask for the use”.We must see how this notion has been used in philosophy and linguistics.

In Tractatus Wittgenstein（1961）claims that the world is logically constructed，and that language mirrors this logical structure.He says that language on the whole does not do this directly，i.e.，the appearance of our language is generally not the same as the logical structure of reality.But he submits that there are elementary propositions in our language which indeed correspond to the logical nature of the world，and suggests that other propositions can be seen as constructed from such elementary ones through a logical operation comprising conjunction，disjunction，negation，and so on.The analysis of an everyday proposition into a certain combination of elementary propositions thus explicates its logical form.If a proposition can be successfully analysed in this way，then the proposition is true if（i）the elementary propositions correctly depict certain parts of the reality，and（ii）the combination of the former correctly depicts the actual arrangement of the latter，otherwise the proposition is false.However，if a proposition can not be thus analysed，then it is nonsensical.Thus，Wittgenstein remarks that what can be said can be said clearly（through reducing them to elementary propositions and thus explicating their logical form），and what cannot be said we must pass over in silence（because they are nonsensical）.Wittgenstein believes that every proposition in our language can be subjected to his logical analysis so that it can be known to be true or false or nonsense：nothing else will be needed.So he thinks that he has solved all the problems in philosophy.

Though Tractatus is probably the best example of logical atomism，it is Russell who first proposes it.After showing that mathematics can be reconstructed in terms of logic on the basis of some simple categories，e.g.，sets（Whitehead ＆Russell 1927），he goes on to show that our conception of time instants and intervals can be logically constructed from perceived events and their temporal relationships（Russell 1956）.These led him to claim that all our knowledge about the external world is constructed from our sense data，which he takes to be basic entities（Russell 1914）.It is the earlier Wittgenstein who applies logical atomism to natural language and carries it to the extreme，as we have seen in the preceding text.But their attitudes towards natural language are different.While the earlier Wittgenstein believes that ordinary language is in perfect order and seeks justifications for this in Tractatus，Russell thinks that natural language is imprecise and that this is the source of many philosophical problems.Russell believes that it is necessary to explicate the logical form of natural language sentences in order to solve them.For example，compare the following two sentences：

（1）Aristotle is famous.

（2）The present King of France is wise.

Both（1）and（2）have the same grammatical form consisting of a grammatical subject and grammatical predicate.But there is a difference between them.According to Russell（1）first mentions a person，which exists in reality，and then says something about him，but（2）does not mention anything existent.Russell says that（1）has a genuine subject＋predicate form，while the logical form of（2）is actually the conjunction of the following three sentences：

（3）There is a King of France.

（4）There is no more than one King of France.

（5）There is nothing which is both King of France and is not wise.

These three“together may be taken as defining what is meant”by（2）（Russell 1919）.With such analyses Russell hopes to make the meaning of sentences clear，and to solve many philosophical problems.

We have just seen how Russell uses logical form to explicate the difference of meaning between sentences which have a similar surface form.This use is also prominent in linguistics.Take Chomsky's favourite examples：

（6）John is easy to please.

（7）John is eager to please.

The surface form of these two sentences are the same，which is：Noun＋Verb＋Adjective＋Infinitive.But their meanings are rather different.The first says：

（8）（For one）to please John is easy，

whereas the second means that John is eager to please someone.To make this difference clear，it is then said that the logical forms of（6）and（7）reflect the surface forms of（8）and（7）respectively.①

If two sentences have the same surface form，we are apt to interpret them in the same way.In the above example，（6）and（7）look very similar：they are both of the form：Noun＋Verb＋Adjective＋Infinitive.So we tend to give them the same interpretation，and we then make mistakes.Ryle（1932）says that we are“misled”by sentences like（6）because they should have a different logical from，and he then calls them“systematically misleading expressions”.He gives many examples，one of which concerns the following pair of sentences：

（9）John is reprehensible.

（10）Unpunctuality is reprehensible.

Sentence 9means something like：

（11）John should be reproved，he should be ashamed of himself.

But sentence 10does not.We cannot reprove unpunctuality，nor does it make sense to say that unpunctuality should be ashamed of itself.So（9－10）are different，so they must have different logical forms.（9）is fine，its logical form is directly related to its grammatical form.But（10）is‘misleading'；it conceals its real logical form，②which is：

（12）Anyone who is unpunctual is reprehensible.

There are sentences whose logical forms seem to be the same，but still they have different meanings.Consider the following two sentences：

（13）John knew Mary.（14）John kissed Mary.

The logical forms of both sentences seem to be close to their surface form，but there are differences between the two sentences.We can say that John was kissing Mary，but we cannot say that John was knowing Mary.Moreover，knowing seems to be a mental state while kissing aphysical phenomenon.So some scholars，e.g.，Fillmore（1968），Halliday（1994），and Dik（1989），have sought to explicate these differences in terms of different processes and semantic roles.So knowing is generally called a mental process，and kissing a material process；and John is said to be an experiencer in（13）but an agent in（14）.Such information has been incorporated into logical form.

Even if two sentences involve the same process type，they can still have different meanings.Take（15）and（16）for instance：

（15）John slammed Mary.

（16）John kicked Mary.

Both hitting and kicking are said to be material processes，but the two sentences do not mean the same.（15）involves John's hands，while（16）involves John's feet.To reflect this difference，some researchers（e.g.，Lakoff 1971；Schank 1975；Jackendoff 1990）think that they should be of different logic forms，e.g.

（17）John STRIKE Mary with HAND.（18）John STRIKE Mary with FOOT.

These researchers seek to employ semantic primitives and decompose other words into combinations of them.

Davidson（1967a）observes that people frequently use“it”（or“that”）to refer to events（actions）mentioned in previous discourse.Consider his favourite example：

（19）Jones buttered the toast in the bathroom with a knife at midnight.

（20）Please tell me more about it.

As Davidson（ibid.：116）points out，the pronoun“it”in（20）“...doesn't refer to either Jones or the knife，but to what Jones did－or so it seems”.Since“it”is usually used to refer to a“singular term”，there must be，so Davidson suggests，a singular term in（19）which stands for the action performed by Jones.But the problem is that no such singular term is explicit in（19）.To solve this problem，Davidson proposes that sentences like（19）should be assigned an event，and that this event should be made explicit in their logical form.Thus，the logical form of（19）should be this：

（21）There is an event of Jones'buttering the toast，the instrument is a knife，the place is in the bathroom，and the time is at midnight.

One advantage of this ingenious proposal is that the inference from（19）to（22）below，which is not possible in standard predicate logic without invoking ad hoc rules，now comes out immediately in predicate logic：

（22）Jones buttered the toast.

The MOTIVATIONS OF LOGICAL FORM

The survey of different uses of logical form in the preceding section is by no means comprehensive，yet it reveals certain common motivations behind them.There are two types of motivations：metaphysical and practical.The metaphysical element is most evident in Tractatus.There Wittgenstein asserts that the world is logically constructed and language reflects this logical structure.This assertion is metaphysical and there is no way of verifying it.There is also a metaphysical ingredient in other works discussed in the preceding section，which is that natural language must have a logical form and must operate according to a hidden logic.Let us leave the metaphysical motivations of logical form aside，because they do not seem to be able to advance our real understanding of language.The practical motivations are much more important，to which I shall now turn.

From last section's exposition we can see that all the works mentioned link logical form to meaning.They all say that if two sentences have the same surface form but differ in meaning，then they must have different logical forms.Logical form is used to make meaning clear.There are three ways to achieve this，as we can see from the preceding section.Let us discuss them in turn.

（23）It is often felt necessary to alter significantly the surface form of some sentences in order to bring out their real logical form，as in the cases of（6）and（10）.Such sentences are blamed for being misleading，or concealing their true form.

（24）It is often felt that a sentence does not say enough.For example，（14）does not say that John is an agent，and

（15）does not say that John used his hands.Such a sentence is then seen as deficient，and it is suggested that this deficiency is to be made up for in the logical form of the sentence，into which such semantic information is put.（25）It is also often felt that natural language does not allow certain inferences.For example，it is thought that natural language does not provide a mechanism for us to infer（22）from（19）.But if we translate（19）in its logical form（20），then（22）is immediately obtainable through predicate logic.This is therefore claimed to be another advantage of logical form.

The above three ways of doing logical from have largely been taken for granted.But actually none of them stands on absolutely firm ground.There is no reason why we should interpret sentences of the same surface form，e.g.，（6－7）and（9－10），in the same way.Why（6）and（10）are seen as misleading is only because one wants to impose this“same－surface－form－same－interpretation”rule.There is no reason why we should abide by this rule.If we drop it，if we have ways of arriving at appropriate interpretations in such cases，then we shall no longer need（23）.

（24）is even more problematic.What semantic information should be“stuffed”into logical form，and how much？From（15）we know that John slammed Mary，most likely on her face or on her bottom，that John's hand moved very fast，that Mary most likely felt pain，that she probably had angered him，that John was near to Mary enough to reach her，etc.，etc.Why only put STRIKE and HAND in the logical form？Why not all of these（can this be possible）？Now consider semantic roles.What are the so called agents and patients？Are there a priori definitions for them without actually looking at what verbs are used and how they are used in sentences？What cannot be said using ordinary words，e.g.John did the slamming，Mary was slammed，that can only be said by resorting to such contrived concepts？In any case，semantic roles attempt to capture certain semantic information in a sentence.But as we have just said，why should we only consider this bit of information and ignore others？It is not easy to draw such a line.In fact it is not clear at all whether such a line can be drawn.

This conveniently leads us to examine（25）.If it is difficult or impossible to determine what and how much semantic information to put into logical form，then why include such information at all？This is indeed suggested by Davidson（1967b）.He proposes that words in a sentence remain unaltered in the logical form，that is，they need not be further analysed.What about the semantic information mentioned above？Well，we can let logic help us to obtain it.This can be done through implication，etc.，as in the case of（19）and（22），and with the help of semantic postulates，as in the case of（15）and（17）.The latter also accords with Lyons'remark that semantic primitives can be replaced by semantic postulates（Lyons 1995）.The approach suggested by Davidson avoids the problem faced in（24），but it rests on two assumptions：（ⅰ）that predicate logic is problem free，and（ⅱ）that natural language does not provide inference mechanisms.If either assumption is false，then（25）will not stand.Let us now turn to the very topic of predicate logic in the next section.I shall return to inference in natural language in Section 5.

THT NOTIONS OF SUBJECT AND PREDICATE

The notion of predicate has a very long history.It has long been thought that a sentence expresses a complete thought，and that it has the form subject＋predicate.The subject is said to be something to which the predicate applies.There are two major ways of talking about subjects and predicates.One way is that the subject is one part of a sentence and the predicate is the other part.

（26）John loves Mary.

On this interpretation，sentence（26）has the subject“John”and the predicate“loves Mary”.The other major way is that predicates have arguments，and arguments are filled by subjects（cf.Strawson 1974）.③In this terminology，the subjects of（26）are“John”and“Mary”，and the predicate is simply“loves”.And in predicate logic，this is written as：

（27）loves（john，mary）

We shall be talking only about this second usage，although our discussion will also apply to the first usage.It is evident that predicates play a leading role in predicate logic，and most introductions to predicate logic give much more space to predicates than to subjects.I shall therefore concentrate on predicates.

The notion of predicate has been taken for granted in logic，philosophy and formal semantics，and as such has rarely been challenged.It is the basis of predicate logic：without it predicate logic would have to disappear.But what are predicates？There are two ways to answer this question：by giving ageneral definition，and by giving examples.The general definition of a predicate is that a predicate，together with its subjects，forms a complete sentence.In other words，predicates carries“propositionhood”.This definition alone is not of much use when one tries to determine the predicate in a given sentence，because it is too vague and general.Examples are then brought in to help.We are told that，in（27）“loves”is the predicate；that in（28）：

（28）The rose is red，

“red”is the predicate；and that the predicate in（29）is“sings”：

（29）A man sings.

After this all too brief description，we are often left to work out which are the predicates in other sentences by ourselves.Problems and arbitrariness then start to creep in.There are arguments why“is”is not apredicate in（28）（Halliday 1994），and whether“exist”is a predicate or not（Wolfram 1989：chap 6）.In（30）the predicate is said to be“rained”，but the subject is said to be empty；so the logical form looks like（31）.In（32）“seems”is seen as the predicate，but“that John is going to win”is seen as the only subject.Thus the logical form of（32）looks like something like（33）：

（30）It rained.

（31）Rained.

（32）It seems that John is going to win.

（33）That John is going to win seems.

（34）It is kind of you to come to see me，

In（34）：“kind”is said to be the predicate，and“you to come to see me”the only subject.In this case the logical form of（34）is seen effectively as that shown in（35）：

（35）Is kind［you to come to see me］.

It is then said that“you”in（35）lacks“case”and that we have to insert an“of”between“kind”and“you”in order for“you”to receive“case”.This operation，called“of－insertion”，is said to be due to an abstract（and possibly innate）syntactic principle called Case Filter④（Chomsky 1986；see also Haegeman 1994）.But so far（35）has not got a subject，so it is suggested that we must add a dummy subject“it”.And this operation is said to be due to Extended Projection Principle，⑤which is probably also innate（see Haegeman 1994）.

In a sentence like（36）the word“eager”alone is said to be the predicate.To accommodate the other parts of the sentence，it is suggested that“eager”takes two subjects，one is“John”，and the other being“John to please”（or“PRO to please”，where“PRO”is a non－overt pronoun，cf.Chomsky 1986；see also Haegeman 1994）and not just“to please”.So the logical form of（36）turns out to be something like（37）：

（36）John is eager to please.

（37）John is eager［John to please］.

Examples like these are abundant in the literature.Much research has been devoted to unveiling the logical form of sentences.But the discoveries are often baffling.For example，though（31），（33）and（37）look more like sentences than logical forms found in the literature，they nevertheless show what the corresponding logical forms would look like.It is obvious that they look queer，and this queerness disquiets us.We need to understand where this queerness comes from，that is，what causes scholars to advance such strange logical forms.If we ponder over this question hard enough，we shall see that the queerness is rooted deeply in the principle（38）：

（38）Every sentence，or every clause rather，must have the same form：subject＋predicate.

This principle is interwoven with two other principles.One is（39）：

（39）Subjects must refer to things.

So，in the case of（30），because“it”doesn't seem to refer to anything it is then said that the sentence has an“empty”or“zero”subject.Similarly，in（32）“it”is said to be a“dummy”subject，the real one being“that John is going to win”.The other principle is（40）：

（40）If a sentence has two verbs then it must have two clauses（one of them may be subordinate）.

Thus，in the case of（36），“to please”must be a（subordinate）clause.So according to principle（38），this clause must have a subject；and since there is not one in the clause“to please”，another one，which is“John”or“PRO”，is added explicitly.

These three principles have long been established.They have formed a frame through which we view language.But we must pause and ask whether these principles are indeed valid.First，consider（38）.What are the grounds for saying that every sentence must have subjects and a predicate？The arguments in the literature have never been conclusive.Instead of seeking justifications for（38），which are often metaphysical，it's more useful to understand why（38）should have come into existence.The reason is due to the proponents'urge to see uniform structure behind things.Having found that some sentences，e.g.（26）and（28），first mention something and then say something about it，and hence exhibit the pattern subject＋predicate，the proponents then generalise this to all sentences.If certain sentences do not explicitly conform to this pattern，then they are blamed for concealing the true logical form，which does conform to this pattern.But sentences themselves cannot be guilty in whatever sense.It seems to be a mistake in the first place to make all sentences fit into one single pattern when in fact only some sentences do.

Once we liberate ourselves from the restrictions imposed by（38），the very notion of subject and predicate will be under doubt，and（39）will become doubtful too.We shall say more about this in the next section.Let us now examine（40），which concerns the concept of clause.Though this concept is widely used in grammar，exactly what a clause is is far from being clear（Matthews 1981：chapter 8）.The general practice has been to follow principle（40）.The problem with（40）is the same as with（38）：it is an overgeneralisation from some cases，e.g.（41）and（42），which contain genuine clauses，to all cases，including（6），（7）and（34）（repeated here for convenience）：

（41）John said that he saw Mary yesterday.

（42）They rang me before I had finished my breakfast.

（6）John is easy to please.

（7）John is eager to please.

（34）It is kind of you to come to see me.

The reason for this over－generalisation is again the urge to seek a uniform structure behind all sentences.There are no conclusive grounds for holding（40）to be true.And in fact there is good reason to treat sentences like（6），（7）and（34），as simple ones，i.e.as consisting of only one clause，as we shall see in the next section.

WORD USE，SENTENCES，AND PREDICATES

From the preceding section we can see that logical form is tightly related to grammar.For one thing，the concept of predicate is inseparable from that of sentence（and of clause）.As we have already mentioned，predicates are seen as carrying sentencehood：together with subjects they form sentences.Without a proper understanding of sentences，it is unlikely to reach a proper understanding of predicates.But what are sentences？We mentioned that sentences are often defined as expressing complete thoughts.But this definition is not helpful，because the concept of thought is even less clear.To understand what sentences are we must start from things simpler than sentences.What can be simpler in this context than words？！In the rest of this section I shall only present the main ideas，for a detailed argument and presentation see Lin（1999，2002）.

In learning to speak a language，we learn words and how they are used.And as a result we know such things.For example，we know，among many others，the following ways of how to use certain words：

（43）Somebody says something.

（44）You ring somebody.

（45）You do something.

（46）Something happens.

（47）Something happens before something else happens.

These are rules of word use that we must follow in speaking English.We cannot arbitrarily alter the order，e.g.we cannot say“＊Somebody something says”；we cannot simply drop some words，e.g.we do not normally say“＊You ring”.Now，consider sentence（42）again，repeated here for convenience：

（42）They rang me before I had finished my breakfast.

The reason why we know that this sentence is grammatical is，I argue，that we know that words in this sentence are used according to（43－47）.

Apart from（43－47）speakers of English also know the use of other words.Many of these words are used in ways similar to（43－47），but many others do not fall under these patterns.But they fall under other patterns.For example，we have：

（48）It is of somebody to do something，

where“”can be filled by afamily of adjectives，such as“kind”，“generous”，“silly”，“rude”，and the like.One can say that（48）specifies the use of such words.The reason why we know that（34）is a grammatical sentence is precisely because it conforms to（48）.

Don't we also have the following ways to speak about things：

（49）Somebodyis to do something to，and

（50）Somebodyis to do something？

Yes，we do.We also know that the blank space in（49）can be filled by“easy”and“difficult”，while in the blank space in（50）we can put“eager”，“anxious”，“willing”，“reluctant”，“ready”，and so on.That we are able to recognise（6）and（7）as being grammatical and also being different can be satisfactorily explained by saying that they correspond to（49）and（50）respectively.

Next，let us consider weather sentences.We have learned to talk about weather using：

（51）It（rains，snows，etc.）.

（52）It is（windy，foggy，cold，hot，etc.）.

We use these sentences happily every day，and we never seem to bother about whether“it”refers to anything（does one ask questions like What rained？）.Why should we create unnecessary problems for ourselves，e.g.by saying that the logical form of（30）is something like（31）？

Now consider the use of the word“seem”.How is the word used？Several ways of using it come out straight from our heads：

（53）You seem to（be happy，be a student，like the song，etc.）.（54）Something seems to be the case.

（55）It seems that something is the case.⑥It is evident that sentence（32）corresponds to（55），which describes a common use of“seem”.It is indeed queer that we should ignore this fact of language and try to dig out something from behind，say（33），for there is nothing hidden behind（32）or（55）.

We are now in a position to answer the question posed at the beginning of this section：What is a sentence？We see that there is no unique form of all sentences：some sentences exhibit certain patterns while others fall under others.What determines sentence patterns is the way in which words are used.Expressions like（43－55）enumerated above are about word use，and they each specify a form of sentence.Any string of words which corresponds to such an expression is then a sentence.Such expressions therefore carry with them sentencehood.

If the essence of predicates is that they carry sentencehood，then predicates have to be expressions like（43－55）.Let us explore the effect this has on principles（38－40）.We see that（38）can still hold，but it now means that every sentence is formed based on an expression like（43－55）by replacing general words like“you”，“somebody”，and“something”with more concrete words，or filling some blank spaces with words.I shall call expressions such as（43－55）sentence frames.⑦The notion of predicate is drastically changed.A predicate is no longer a single word，it is now a sentence frame like（43－55）.But we must bear in mind that sentences，even though they still have the formsubject＋predicate in this new sense of predicate，do not have a single form，because predicates now have various forms，as shown in（43－55）.In this sense，the original meaning of（38）is lost：（38）in the original sense no longer holds.

What about（39）？Since the word“it”is simply part of the expressions of the use of some words，as in（51）and（55），it does not need to refer to anything.In fact the question of whether“it”in such cases refers to something simply does not occur.What becomes of（40）now？We see that it is not true either.Sentences（34），（6）and（7），correspond to（48－50）respectively，they are straightforward and simple sentences，and they therefore do not need to be analysed into two clauses each.Their predicates，if one insists on having them，are not single words，rather they are（48－50）respectively.With this，it is easy to see that analyses such as（37）are unnecessary.

MEANING AND INFERENCE

In Section 2we analysed the motivations of logical form.We saw that the basic motivation of logical form is to explicate meaning，and that there are basically three ways of doing this：（23），（24），and（25）.I said that if we could give different interpretations to sentences like（6）and（7），then（23）will no longer be necessary.I remarked that（24）is problematic，because it is difficult and probably impossible to decide how much semantic information to put into logical form.We saw that（25）seems to be a more plausible approach than（24），but it relies completely on predicate logic to provide a mechanism for inference.All these hang on the problem of inference.It is natural to ask：With the original concept of predicate replaced by the one given in the last section，what will become of predicate logic？To put this question in a rather different way，it becomes：Without predicate calculus how can inference be performed through ordinary language？

Recall that predicate logic operates on logical form，that is，sentences must be translated into expressions consisting of subjects，predicates，conjunctions，material implications，etc.In this sense predicate logic is called formal logic.It is natural to think that inference in ordinary language also operates on the basis of form.And I suggest that it is indeed the case.Since sentences have various forms，instead of a uniform logical form，we should expect that inference in language also takes many forms.In the rest of this section we shall show that inference in language can be performed through the forms of sentences（i.e.sentence frames），e.g.（43－55）.

First，in most cases we not only know how words are used，we also know what they mean.For example，we know：

（56）If you ring somebody，you call him on the telephone.

（57）If it is kind of somebody to do something，then that he does it is kind.（58）If somebody is easy to do something to，then to do it to him is easy.

（59）If somebody is eager to do something，then he wants to do it very much.

It is readily seen that the if－parts of（56－59）are all about the use of some words，and they are actually（44）and（48－50）.The then－parts of（56－59）are also expressions of word use.If we apply（56－59）to sentences（42），（34）and（6－7），we shall get the corresponding meaning of each of the sentences.⑧

One might say that（56－59）are equivalent to semantic postulates in logic（or formal semantics）.But this is exactly the point.What can be done in terms of semantic postulates，which have the form specified by predicate logic，can be done in ordinary language through the forms of sentences.This shows that language can do without logic in at least one area of inference.

One advantage of Davidson's logical form of action sentences is that it allows certain inference.For example，by translating sentence（19）into his logical form，predicate logic then immediately gives us（22）.It is true that ordinary speakers can easily infer（22）from（19），but Davidson's explanations assume that speakers are equipped with predicate logic，which is unrealistic（Strawson 1992）.Another way of explaining this inference ability is this：we simply know

（60）If you did something at a certain time，in a certain place，in a certain way，or for a certain reason，etc.，then you

did it.

And once we know that（19）corresponds to“you did something at a certain time”（which is a sentence frame），then we instantly deduce from it“you did it”，e.g.“John buttered the toast”.This is another case to show that language has its own means for inference.

Questions like What are the counterparts of propositional calculus and universal instantiation in natural language？remain to be answered.But I have pointed out a vital link between predicate logic and ordinary language.The link is that predicates in predicate logic are the counterpart of sentence frames（expressions of word use）in ordinary language.Both predicate logic and inference in ordinary language operate on the basis of form，the difference being that the latter makes use of sentence frames.We have seen in the preceding section that word use determines sentence forms，and explains the notion of grammar without resorting to uniform and abstract syntax.There is good reason to expect that it can cast light on how the logic of ordinary language works.

ORDINARY LANGUAGE AND ITS LOGIC

At the beginning of the paper we observed that there is an intriguing situation in linguistics and philosophy.On the one hand，the later Wittgenstein explicitly and strongly rejects the idea of logical form，but on the other hand philosophers and linguistics are still in active search for logical form.It's time for us to explain why this situation exists.

One of the major claims in Philosophical Investigations is that language does not have a uniform logical structure（form）.It follows then that language in reality has various forms.But what are the forms of language？Wittgenstein does not say what the various forms are.Language is，however，structured，and must have certain forms，and this is one important concern of linguists and philosophers.Simply pointing out that there is no hidden logical form does not solve the problem，and it cannot convince the linguist/philosopher that their effort is misplaced.

As we have seen in the preceding texts，logical form is used to explicate meaning，and this conveniently utilises the inference mechanism provided by predicate logic.Wittgenstein points out in Philosophical Investigations that the meaning of words/sentences depends on the concrete situations in which they are used，and that it is the explanation given on each of such concrete situations.This observation of meaning is very insightful，and most scholars would agree with it.But Wittgenstein does not say how the ordinary speaker knows the meaning of words/sentences or gives explanations.Inference is inevitably relevant to such an ability，for the ordinary speaker cannot simply memorise the meaning of all sentences（in all possible situations）.Now，if logical form is rejected，so is logic.How is inference then performed？To put it another way，what is the logic of ordinary language？To this Wittgenstein does not provide an answer either.⑨

The present paper has tried to answer the questions raised in the two preceding paragraphs.It places words and their use at the centre of the inquiry.It argues that sentence frames are the basis of grammar and ordinary logic.⑩It advances the idea that grammar and logic are intimately related.This idea is plausible，because when we learn a language we not only master the grammar but also master the logic at more or less the same time.It is helpful to look at language from a wider angle.To achieve a deep understanding of how language really works it is essential to consider simultaneously various aspects of language，e.g.grammar，semantics，logic，convention，and communication，etc.Lin（1999，2002）argues that sentence frames are conventionalised ways of expressing and communicating meaning，that they constitute grammar，and that there is no need to postulate abstract and innate syntactic principles.Lin（1997）and the present paper suggest that sentence frames are also the basis of the logic of ordinary language.In the field of development psychology，researchers have been arguing that people employ a（large）number of concrete reasoning schemas instead of abstract logical rules as in predicate－calculus（Braine 1990，1994；Cheng ＆Holyoak 1985；Cheng et al.1986）.Such schemas are also closely related to sentence frames discussed in this paper.

Predicate logic is a wonderful achievement in formalising inference.Much can be gained from it.But when we apply it to language，we then find it to be too restrictive.In Section 4it was shown that predicates，in the sense of carrying sentencehood，are actually conventionalised ways of using words.Predicates in this new sense are no longer single words，they are now sentence frames.As predicate logic operates on logical form，ordinary logic also operates on form.The new sense of the notion“predicate”gives us a new way of looking at the logic of ordinary language，which I hope will lead us to a better understanding of it.

NOTE

①For a precise formulation of the logical forms of（6）and（7），see Chomsky（1986）and Haegeman（1994）.See also（37）below.

②Ryle later（Rorty 1992：305）admitted that his conception exposed in Ryle（1932）had been heavily influenced by logical atomism，and said that he no longer held that ordinary language is misleading.

③Note that subjects here do not mean grammatical subjects：on this conception subjects includes both grammatical subjects and grammatical objects.

④Case Filter says that every noun phrase must have case.

⑤This principle states that every clause must have a subject.

⑥“Something is the case”can be regarded as a general form of sentences.But this does not mean that all sentences must be decomposed into two parts corresponding to“something”and“is the case”.For example，“There is a tree in the garden”cannot be easily thus decomposed.The point is this：“Something is the case”is a convenient way of referring to any sentences，while any particular sentence is produced on the basis of one or more sentence frames.There are many different sentence frames，they do not have a single，unique form.See discussions below.

⑦Lin（1999，2002）argues that sentence frames are rules of grammar，that they are conventionalised，that they are known to the speaker，and that they are created to facilitate communication，and so on.Lin also argues that there is no need to postulate abstract or innate syntactic principles.This conceptions of grammar rules（e.g.，sentence frames）is consistent with the later Wittgenstein's（1953）idea of rules in the language game.

⑧This is not to advocate a“dictionary”view of meaning，which implies that meaning is fixed.According to Wittgenstein（1953：456），if somebody just said“I rang Mary”and I now simply mimic his voice and also say“I rang Mary”，then I did not really ring Mary（i.e.，call her on the telephone）.But this is due to the meaning of the word“mimic”.It is true that the meaning of words/sentences depends on the situations in which they are used，but we must know the meaning of the words/sentences which describe such situations and perform corresponding inference.

⑨It must be made clear that Wittgenstein's（1953）task is not to explain what the structure and logic of ordinary language are.His concern is to dissolve philosophical problems and point out the kind of confusions we tend to have when we philosophise.But linguists and philosophers are interested in the structure and logic of language，and they want to explain what they are.This is why they postulate logical form or syntactic form.Their motivation is undoubtedly valid.But in postulating logical form（or syntactic form），linguists and philosophers have made some subtle errors.The present paper argues that one such error is in the notions of“subject”and“predicate”.Other errors are discussed in Lin（2002）.

⑩For an idea of“ordinary logic”see also Sommers（1982）and G.H.Harman（1996）.

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