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170 What is a Connector?

adverb + and + adverb

insofar as, ﬁrst, you recognize that

sentence + (adverb + and + adverb)

is synonymous with

(sentence + adverb) + and + (sentence + adverb),

and, secondly, you understand the latter construction. (Perhaps the shorter

versions are elliptical for or abbreviations of the longer? That is another

question.)

Elucidations of that sort, which explain a non-sentential use of a sentential

connective in terms of its sentential use, are readily available in a vast number

of cases. But there are some truculent items. It may be conceded that

idioms—‘here and there’, ‘to and fro’, ‘heads or tails’, ‘now if ever’, …—are

of no theoretical interest: idioms conform to no rule and are to be learned one

by one. But there are also some non-idiomatic cases in which the elucidation

appears to be blocked.

The arithmetical ‘and’, for example, resists reduction. I have in my hands

a book which I once bought for seven and six; in French I count my age—I

used to count my age—as soixante-et-un; and I think that two and two make

four and neither three nor ﬁve. True, such items are unperplexing; for in

arithmetical examples the word ‘and’ is a synonym for ‘plus’. But that does

not alter the fact that there are numerous cases in which ‘and’ functions as a

connective and is not to be explicated straightforwardly in terms of sentential

connection.

Again, certain verbs block a sentential elucidation: ‘marry’, ‘quarrel’, ‘meet’,

and so on. For

Sampras and Agassi met in the ﬁnal

will not be explained by way of the ungrammatical non-sentence:

Sampras met in the ﬁnal and Agassi met in the ﬁnal.

True, such cases are unperplexing; for

Sampras and Agassi met in the ﬁnal

is synonymous with—and perhaps derives from—

Sampras met Agassi in the ﬁnal.

The verb ‘meet’ is transitive; but some transitive verbs in English allow a

transformation from ‘x verbsy’to‘xandyverb’. In any event,

(name + and + name) + verb

is often synonymous with

name + verb* + name.

Sentential Connectives 171

But that does not eliminate the counterexamples—it conﬁrms them. For

in these cases a nominal connective, ‘and’, is not explicable in terms of the

sentential connective ‘and’.

Again, ordinary verbs will sometimes take an irreducibly complex subject.

Move from men’s singles to mixed doubles:

Graf and Agassi and Seles and Sampras met in the ﬁnal.

That gives way to

Graf and Agassi met Sampras and Seles in the ﬁnal.

But the two ‘and’s in the new sentence cannot be removed in the same

way. Rather, in such cases the connected names are comparable to collective

names—or to plural pronouns or to non-distributive quantiﬁers: ‘The

Opposition voted against the motion’; ‘Ils ne passeront pas’; ‘All the perfumes

of sweet Araby …’. (And I might have thought of the ‘and’ in ‘All the King’s

horses and all the King’s men …’.)

Again, adverbs or adverbial expressions will sometimes foil a sentential

analysis. Thus

Either the President or the Vice-President is always awake

is not equivalent to

Either the President is always awake or the Vice-president is always awake.

And

Bach, Handel, Scarlatti and Berkeley were all born in the same year

is not equivalent to

Bach was born in the same year and Handel was born in the same year

and …

Ofcourse,insuchcases—orinmanyofthem—alogicianwillsniffouta

skulking quantiﬁer. Thus

Bach and Handel were born in the same year

is synonymous with

There is a year such that Bach and Handel were born in it;

and that in turn is synonymous with

There is a year such that Bach was born in it and Handel was born in it

—and there the ‘and’ links a couple of sentences.

But there are some adverbs and adverbial phrases which put up more

resistance. For example,

Hilary and Tensing climbed to the summit together,

The walrus and the carpenter were walking hand-in-hand.

172 What is a Connector?

Those are not synonymous with the ungrammatical

Hilary climbed together to the summit and Tensing climbed together to

the summit,

and

The walrus was walking hand-in-hand and the carpenter was walking

hand-in-hand.

Nor are they easily treated on the model of the men’s singles. To be sure, you

might try:

Hilary climbed with Tensing to the summit,

and

The walrus was walking hand-in-hand with the carpenter.

And there

(name + and + name) + verb

goes over into

name + verb* + name.

But that is not very appealing; for who will think that ‘climb with’ or ‘walk

hand-in-hand with’ are transitive verbs?

Better allow that the ‘and’ in those examples is a genuinely and irreducibly

nominal connective, that it is not to be elucidated by way of the sentential

‘and’. But if that is so for

The walrus and the carpenter were walking hand-in-hand,

surely it must also be so for

The walrus and the carpenter were walking?

After all, how could the addition of an adverb to

The walrus and the carpenter were walking

change ‘and’ from a sentential to a nominal connective?

Those last examples all involve the connective ‘and’. Not only that: in all

of them ‘and’ connects names or nominal expressions. True, there are a few

truculent cases which involve other connectors. For example,

Theirs but to do or die

offers an initial resistance to sentential elucidation.¹ But at least there is a verbal

inﬁnitive there, and inﬁnitives are quasi-sentential. In any event, the nominal

connective ‘and’ is—or so I incline to conjecture—the only English connect-

ive which in the end successfully resists sentential domestication. That is to

say, the preceding remarks—if they are not merely mistaken—say something

not about connectives in general but about nominal conjunction in particular.

¹ The example was brought to my attention by Sabina Lovibond.

Aristotelian Connectors 173

Whatever be made of all that, it seems clear that ‘and’ in English sometimes

functions as a sentential connective and sometimes as a nominal connective,

and that the latter functioning is not explicable—or at least, not always

straightforwardly explicable—in terms of the former functioning. Should we

infer that the word ‘and’ is ambiguous? That seems to me a very dubious

suggestion. True, the sentence

Sampras and Agassi are in the ﬁnal

is ambiguous; but the ambiguity is structural or syntactical—it is not a matter

of the word ‘and’ having two different senses.

Then should we rather infer that the term ‘and’ is not a sentential connective

but a connective tout court —that is to say, an expression which takes a number

of expressions (of speciﬁable sorts) to make an expression (of a speciﬁable sort)?

In that case, how is the sense of a connective tout court to be explained? After all,

those who attempt the sentential domestication of connectives are not moved

by a simple desire for tidiness, nor by an irrational preference for sentences

over other walks of expression: they want their connectives to be sentential

because a sentential connective is relatively easy to deﬁne.

What, for example, does ‘or’ mean? Well, you have mastered the sense

of the sentential connective ‘or’—or rather, you have mastered one of its

senses—once you know that something of the form

sentence + ‘or’ + sentence

is true provided that at least one of the component sentencesistrue.That

sort of thing is at least a promising beginning of an elucidation; and it

can be done for other sentential connectives. If connectives are taken to be

fundamentally nominal, say, or fundamentally neutral, it is far from easy to

see how to begin to explain their senses.

ARISTOTELIAN CONNECTORS

The Greek word closest in sense to ‘connective’ is ‘σύνδεσμος’. As Quintilian

remarked, the best Latin translation of the Greek is ‘convinctio’(i iv 18); but

the word was normally Latinized as ‘coniunctio’, and the normal Latinization

slid into modern languages—so that an English grammarian will normally

speak of conjunctions where an English logician will speak of connectives. I

do not like ‘conjunction’ any more than Quintilian liked ‘coniunctio’; but I

do not want to translate ‘σύνδεσμος’ by ‘connective’ and thereby, without

ado, identify ancient σύνδεσμοι with modern connectives. So I shall use

‘connector’.

174 What is a Connector?

The ancient grammarians had something to say about connectors, and

some of them had rather a lot to say on the topic. But I shall start with a

philosopher.

The word ‘σύνδεσμος’ means ‘link’ or ‘chain’ or ‘bond’. Aristotle frequently

used it of physical linkings (e.g. IA 712a1–2); and he also used it of meta-

phorical bonds—‘Children are thought to be a bind’ (EN 1162a27—but he

was not impressed when others spoke metaphorically of the ‘bond’ between

body and soul: Met 1045b11–16). And he used the word metaphorically, a

dozen times or more, in logico-linguistic contexts.

When Dionysius of Halicarnassus enumerates ‘the parts of sayings, which

some call elements of language’ (and which we now call parts of speech), he

says that

Theodectes and Aristotle and the philosophers of their time brought the number of

the parts up to three, making names and verbs and connectors the primary parts of

language.

(comp verb iv 32;² cf. Dem 48)

Similarly, Quintilian, in his brief history of the parts of speech—a history of

which philosophers rather than grammarians are the protagonists—says that

the ancients, among them Aristotle and Theodectes, spoke only of verbs and names

and connectors—inasmuch as they judged verbs to contain the force of a saying and

names its matter (for what we say is one thing, that about which we say it is another),

while they took connectors to hold names and verbs together—I know that most

people call these items conjunctions, but ‘connector’ seems a better translation of

‘σύνδεσμος’.

(i iv 18)³

Plato uncovered two parts of sayings, the name and the verb. Aristotle found a

third part. The Stoics tracked down a few more. And eventually—according

to the grammatical 1066 and All That —the Greek grammarians reached the

total of eight.

In his surviving works, Aristotle nowhere talks explicitly of the parts

of sayings, and he nowhere explicitly recognizes three such parts. Scholars

² … τῶν τοῦ λόγου μορίων, ἃ δὴ καὶ στοιχεῖά τινες τῆς λέξεως καλοῦσιν. ταῦτα δὲ

Θεοδέκτης μὲν καὶ ᾿Αριστοτέλης καὶ οἱ κατ᾿ ἐκείνους φιλοσοφήσαντες τοὺς χρόνους ἄχρι

τριῶν προήγαγον, ὀνόματα καὶ ῥήματα καὶ συνδέσμους πρῶτα μέρη τῆς λέξεως ποιοῦντες.

³ veteres enim, quorum fuerunt Aristoteles quoque et Theodectes, verba modo et nomina et con-

vinctiones tradiderunt, videlicet quod in verbis vim sermonis, in nominibus materiam (quia alterum

est quod loquimur, alterum de quo loquimur), in convinctionibus autem complexus eorum esse

iudicaverunt. quae coniunctiones a plerisque dici scio, sed haec videtur ex συνδέσμῳ magis propria

translatio.

Aristotelian Connectors 175

suppose that the reports in Dionysius and Quintilian derive from Aristotle’s

lost and mysterious CollectionoftheArtofTheodectes. It may also be recalled

that in the de Interpretatione Aristotle explicitly describes names and verbs, and

also implicitly notices that Greek has connectors. But if the de Interpretatione

uses the term ‘σύνδεσμος’, it offers no analysis or explanation. For that we

must go to the Poetics —and to a part of the Poetics which the source of

Dionysius and Quintilian either did not know or else chose to ignore.

The passage begins with a list of ‘the parts of language as a whole’, namely:

elements, syllables, connectors, names, verbs, articulators, cases, sayings (Poet

1456b20–21).⁴ After the list, there is a sequence of notes on its several

items. The note on connectors, which is immediately followed by a note on

articulators, is textually corrupt; and the corruption infects not merely the

details but the whole thrust of the note—or rather, of the pair of notes. I

may be allowed a brief philological digression.

Our text of the Poetics is based on a couple of Greek manuscripts,

a mediaeval Latin translation, and an Arabic translation (which was itself

founded on an earlier Syriac translation). The note on connectors is differently

transmitted in each of those four witnesses, and the differences are sometimes

marked. Nonetheless, it is possible to establish, with some degree of certainty,

the archetype, or the text which stands behind all our witnesses (and which

in point of fact is virtually identical with the text offered by one of the Greek

manuscripts). It translates thus:

A connector is a non-signiﬁcant expression which neither prevents nor produces a

single signiﬁcant expression from several expressions, being by its nature combined

both at the ends and in the middle, which it is not appropriate to place at the

beginning of a saying in its own right—for example μέν ἤτοι δέ.Or:anon-

signiﬁcant expression which is of such a nature as to produce a single signiﬁcant

expression from more expressions than one.

(Poet 1456b38–1457a5)⁵

There is evidently something awry with that (and in the last sentence I have

been obliged to cheat, since the transmitted Greek makes no sense and will

not translate).

⁴ τῆς δὲ λέξεως ἁπάσης τάδ᾿ ἐστὶ τὰ μέρη· στοιχεῖον συλλαβὴ σύνδεσμος ὄνομα ῥῆμα

ἄρθρον πτῶσις λόγος.

⁵ σύνδεσμος δέ ἐστιν φωνὴ ἄσημος ἣ οὔτε κωλύει οὔτε ποιεῖ φωνὴν μίαν σημαντικὴν ἐκ

πλειόνων φωνῶν πεφυκυῖα συντίθεσθαι καὶ ἐπὶ τῶν ἄκρων καὶ ἐπὶ τοῦ μέσου ἣν μὴ ἁρμόττει

ἐν ἀρχῇ λόγου τιθέναι καθ᾿ αὑτήν, οἷον μέν ἤτοι δέ. ἢ φωνὴ ἄσημος ἡ ἐκ πλειόνων μὲν

φωνῶν μιᾶς σημαντικὸν δὲ ποιεῖν πέφυκεν μίαν σημαντικὴν φωνήν.

176 What is a Connector?

The best modern edition corrects the grammar of the last sentence, so that

it reads:

… to produce a single signiﬁcant expression from more signiﬁcant expressions than

one.⁶

Otherwise it prints the received reading—with a note to say that it is ‘corrupt

and confused’.

The passage consists of two deﬁnitions or explanations. The second, once

its grammar is repaired, is intelligible. The ﬁrst is not—indeed, it is wildly

incoherent. (And the three examples it gives are very peculiar.) How did the

wild incoherence come about? The note on articulators which immediately

follows the note on connectors runs as follows (I translate the text as it is

printed in the best modern edition):

An articulator is a non-signiﬁcant expression which indicates a beginning or an

end or a division of a saying—for example ‘ἀμφί’and‘περί’ and the rest. Or: a

non-signiﬁcant expression which neither prevents nor produces a single signiﬁcant

expression from several expressions, being by its nature placed both at the ends and

in the middle.

(Poet 1457 a6–10)⁷

That text is not completely satisfactory—in particular, the clause ‘for

example … and the rest’ cannot be right. Moreover, Aristotelian articu-

lators are odd birds: the Greek grammarians do not accept them as a part of

sayings—indeed, the Greek grammarians never mention them. (They adopt

the word ‘ἄρθρον’, which I have here translated by ‘articulator’ and for which

‘joint’ might be a better version; but they use it to name the class of ‘articles’.)

However that may be, it is not difﬁcult to see that there has been some

textual interference between the two successive notes, and that a part of the

note on articulators has been wrongly anticipated in the note on connectors.

In that case, the note on connectors must be severely pruned—and the wild

incoherence disappears.

Something must also be done about the illustrative examples; but so far as

I can see, that is a matter of pure speculation.

Although no two scholars agree on anything to do with this text, I cannot

help thinking that Aristotle must have written something like the following

⁶ … ἐκ πλειόνων μὲν φωνῶν μιᾶς σημαντικῶν δὲ ποιεῖν πέφυκεν μίαν σημαντικὴν φωνήν.

I.e. ‘σημαντικόν’ is corrected to ‘σημαντικῶν’.

⁷ ἄρθρον δ᾿ ἐστὶ φωνὴ ἄσημος ἣ λόγου ἀρχὴν ἢ τέλος ἢ διορισμὸν δηλοῖ, οἷον τὸ ἀμφί καὶ

τὸ περί καὶ τὰ ἄλλα. ἢ φωνὴ ἄσημος ἣ οὔτε κωλύει οὔτε ποιεῖ φωνὴν μίαν σημαντικὴν ἐκ

πλειόνων φωνῶν πεφυκυῖα τίθεσθαι καὶ ἐπὶ τῶν ἄκρων καὶ ἐπὶ τοῦ μέσου.

Aristotelian Connectors 177

text. (‘Something like’: I mean, something which has the same sense but does

not necessarily express that sense in the same way.)

A connector is a non-signiﬁcant expression which it is not appropriate to place at

the beginning of a saying in its own right—for example … Or: a non-signiﬁcant

expression which is of such a nature as to make a single signiﬁcant expression from

more signiﬁcant expressions than one.

(Poet 1456b38–1457a5)⁸

There are several oddities in that, to some of which I shall return in another

context. But the second of the two deﬁnitions appears to be intelligible, and

it is the second of the two deﬁnitions which interests me here.

So according to Aristotle, an item is a connector if and only if, itself

non-signiﬁcant, it takes two or more signiﬁcant expressions and produces a

signiﬁcant expression.

Connectors unify expressions. Aristotle will speak of an expression’s

being one ‘by connectors’. When he says that, he uses the singular of

the Greek word, ‘συνδέσμῳ’; but in the contexts of its occurrence, that

cannot mean ‘by a (single) connector’; and although the formula might

just perhaps mean ‘by a connection’, the word ‘σύνδεσμος’takingan

abstract sense, it is far better to suppose that it means ‘by connectors’. In

any event, though connectors may work alone, they also hunt in packs,

and an item may be one single expression on account of a plurality of

connectors.

Connectors are links or bonds; and bonds, in general, are artiﬁcial ways of

producing continuity or unity. That, at least, appears to be the implication

of a passage in which Aristotle speaks of

things which are naturally continuous—not by force (like items which are continuous

by glue or pegs or bonds) but having the cause of their continuity in themselves.

(Met 1052a23–25)⁹

So an expression uniﬁed by a connector will be an accidental unity; and in an

aside in the Parts of Animals in which he is discussing the right way to make

a division, Aristotle warns that

⁸ σύνδεσμος δέ ἐστιν φωνὴ ἄσημος ἣν μὴ ἁρμόττει ἐν ἀρχῇ λόγου τιθέναι καθ᾿ αὑτήν·

οἷον ... ἢ φωνὴ ἄσημος ἣ ἐκ πλειόνων μὲν φωνῶν μιᾶς σημαντικῶν δὲ ποιεῖν πέφυκεν μίαν

σημαντικὴν φωνήν.

⁹ ... εἴ τι φύσει τοιοῦτον καὶ μὴ βίᾳ, ὥσπερ ὅσα κόλλῃ ἢ γόμφῳ ἢ συνδέσμῳ, ἀλλὰ ἔχει

ἐν αὑτῷ τὸ αἴτιον αὐτῷ τοῦ συνεχὲς εἶναι.

178 What is a Connector?

if you do not take the difference of a difference, then necessarily you will make

the division continuous only in the sense in which you make a saying one by

connectors—I mean … accidentally.

(PA 643b17–23)¹⁰

The sort of unity which is secured by connectors is accidental: it contrasts

with an intrinsic or essential unity. In the Poetics Aristotle says that

a saying may be one in either of two ways—by signifying one item or by being

made from several items by connectors (e.g. the Iliad is one saying by connectors,

the deﬁnition of man by signifying one item).

(Poet 1457a28–30)¹¹

He says virtually the same thing in the Posterior Analytics:

A saying may be one in either of two ways—by connectors (like the Iliad )orby

showing one item of one item non-accidentally.

(APst 93b35–37)¹²

Presumably we may generalize from sayings to expressions, so that an item is

non-accidentally one inasmuch as it means or indicates a unitary thing.

That, as in another context I have already hinted, is not very satisfactory.

But the distinction which Aristotle is attempting to draw is not illusory. Take

the expression

It’s light.

Whyisthataunit?Thatistosay:whydoesthatexpressionmakeasingle

saying (rather than several sayings or a sequence of non-sayings)? Well, if that

question has any answer, it must be something like this: it is the meaning of

the expression ‘It’s light’ which guarantees its unity—the semantics and the

syntax of the expression together conspire to determine its unity. Take, on

the other hand,

If it’s day, it’s light.

The unity of that sentence is not determined by its meaning. Rather, it is

determined by the fact that it has the general form

If so-and-so, then such-and-such,

¹⁰ ἐὰν δὲ μὴ διαφορᾶς λαμβάνῃ τὴν διαφοράν, ἀναγκαῖον ὥσπερ συνδέσμῳ τὸν λόγον ἕνα

ποιοῦντας, οὕτω καὶ τὴν διαίρεσιν συνεχῆ ποιεῖν. λέγω δὲ ... κατὰ συμβεβηκός.

¹¹ εἷς δέ ἐστι λόγος διχῶς· ἢ γὰρ ὁ ἓν σημαίνων, ἢ ὁ ἐκ πλειόνων συνδέσμῳ, οἷον ἡ ᾿Ιλιὰς

μὲν συνδέσμῳ εἷς, ὁ δὲ τοῦ ἀνθρώπου τῷ ἓν σημαίνειν.

¹² λόγος δ᾿ εἷς ἐστὶ διχῶς, ὁ μὲν συνδέσμῳ, ὥσπερ ἡ ᾿Ιλιάς, ὁ δὲ τῷ ἓν καθ᾿ ἑνὸς δηλοῦν

μὴ κατὰ συμβεβηκός.

Aristotelian Connectors 179

and any expression of that form, insofar as it has that form, is a unity. In

other words,

If it’s day, it’s light

is not one saying in virtue of anything peculiar to itself: it is one say-

ing in virtue of a feature which it shares with indeﬁnitely many other

expressions.

Perhaps that gives some sense to Aristotle’s dark distinction. But it cannot

be pressed very hard without collapsing; and the distinction itself has no

importance in the later history of grammar. The question of the unity of an

expression will return: the distinction between accidental and essential unity

will not.

In the deﬁnition in the Poetics, Aristotle says that connectors unite sig-

niﬁcant expressions. The term ‘expression’ there will in principle cover any

linguistic item—from a single word to an interminable discourse. In partic-

ular, sayings count as signiﬁcant expressions; and in two or three of the other

passages I have quoted the items which connectors unify are indeed sayings.

In the de Interpretatione Aristotle does not refer to connectors until he has

arrived at a special sort of saying, namely the assertoric saying.

The ﬁrst assertoric saying which is one is afﬁrmation; then negation; and the rest are

one by connectors.

(Int 17a8–9)¹³

And a few lines later the two sorts of unity distinguished in the Poetics are

applied speciﬁcally to assertoric sayings:

An assertoric saying is one either by showing one item or by being one by

connectors: many sayings are those which show many items and not one, or which

are unconnected.

(Int 17a15–17)¹⁴

In those texts, it is natural to think that a saying is a sentence, so that

‘λόγος’ may be translated by ‘sentence’ (or ‘statement’, or the like); and so

Aristotelian connectors—at any rate in his logical writings—may come to

look like sentential connectives.

¹³ ἔστι δὲ εἷς πρῶτος λόγος ἀποφαντικὸς κατάφασις, εἶτα ἀπόφασις· οἱ δὲ ἄλλοι συνδέσμῳ

εἷς.

¹⁴ ἔστι δὲ εἷς λόγος ἀποφαντικὸς ἢ ὁ ἓν δηλῶν ἢ ὁ συνδέσμῳ εἷς, πολλοὶ δὲ οἱ πολλὰ καὶ

μὴ ἓν ἢ οἱ ἀσύνδετοι.