Barnes Jonathan. Truth, etc

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80 Truth

But that is not what the Peripatetics meant to be doing (nor what Simplicius

took them to be doing). Rather, they urged—against Nicostratus—that

future contingent propositions do divide truth and falsity: they do so

inasmuch as, although they may not now be either true or false, they will

at some time be either true or false. In other words, the Peripatetics—these

Peripatetics, whoever they may be—propose a principle of bivalence which

is signiﬁcantly different from the Chrysippean thesis. Whereas Chrysippus

argues that

Whenever it can be asserted that so-and-so, either then it is true that

so-and-so or then it is false that so-and-so,

the Peripatetics in effect suggest that

If it can ever be asserted that so-and-so, then at some time either it is true

that so-and-so or it is false that so-and-so.

Chrysippus’ thesis entails but is not entailed by their thesis. And they

implicitly reject Chrysippus’ thesis inasmuch as, according to them, it does

not hold for all future assertibles. (Perhaps it does not hold for all past

assertibles either?)

That is a highly forced way of interpreting what Aristotle says in the

Categories; but it is an ingenious way of reconciling the Categories with the de

Interpretatione.

In any event, it is the Stoic argument which is the meat of the matter.

Simplicius takes the Stoics to be defending Aristotle against Nicostratus; and

he might be taken to suggest that some Stoics actually said: ‘Nicostratus is

wrong and Aristotle right.’ Perhaps they did; or perhaps, at any rate, some

Stoics, commenting on the Categories, said that Aristotle was right there—and

wrong in the de Interpretatione. But in truth there may be no more behind

Simplicius’ text than the indubitable fact that the Stoics afﬁrmed that every

assertible is either true or false.

Here, then, is the passage of Simplicius’ text which reports the Stoic

view:

As for contradictions bearing on the future time, the Stoics offer the same assessment

as they do for the other cases: as with opposites about present and past items, so too

(they say) with futures—for future opposites and their parts. For either ‘It will be’ is

true or ‘It will not be’, if they must be either true or false (for, according to them,

futures are determined); and if there will be a sea-battle tomorrow, it is true to say

An Argument for Bivalence 81

that there will be; and if there will not be, it is false to say that there will be. But

either there will be or there will not be. Therefore each is either true or false.

(in Cat 406.34–407.5)⁷¹

Simplicius is not citing Chrysippus. He is not citing—and he does not even

purport to be paraphrasing—any Stoic text. Rather, he purports to document

a Stoic opinion and a supporting Stoic argument.

The argument is in parts obscure and puzzling; but the gist of it is presented

in the last few lines of the passage, and it seems to run like this:

Either there will be a sea-battle tomorrow or there will not be a sea-battle

tomorrow.

If there will be a sea-battle tomorrow, then it is true that there will be a

sea-battle tomorrow.

If there will not be a sea-battle tomorrow, then it is false that there will be

a sea-battle tomorrow.

Therefore either it is true that there will be a sea-battle tomorrow or it

is false that there will be a sea-battle tomorrow; and either it is true that

there will not be a sea-battle tomorrow or it is false that there will not be

a sea-battle tomorrow.

Therefore either it is true that there will be a sea-battle tomorrow or it is

true that there will not be a sea-battle tomorrow.

The argument does not turn upon the particular example of the sea-battle, so

that the Stoics may infer a universal conclusion about all future assertibles.

Moreover, the argument does not turn upon the fact that the example is a

future assertible, so that the Stoics may infer—or might have inferred—an

unrestricted conclusion about all assertibles whatsoever. In other words, the

argument promises an entirely general proof of a principle of bivalence.

Simplicius’ presentation of the argument carries some spare ﬂesh—ﬂesh

which is spare in my present context; and its bones may be represented as

follows:

Either so-and-so or not so-and-so

⁷¹ περὶ δὲ τῶν εἰς τὸν μέλλοντα χρόνον ἀντιφάσεων οἱ μὲν Στωϊκοὶ τὰ αὐτὰ δοκιμάζουσιν

ἅπερ καὶ ἐπὶ τῶν ἄλλων. ὡς γὰρ τὰ περὶ τῶν παρόντων καὶ παρεληλυθότων ἀντικείμενα,

οὕτως καὶ τὰ μέλλοντα αὐτά τε, φασίν, καὶ τὰ μόρια αὐτῶν· ἢ γὰρ τὸ ἔσται ἀληθές ἐστιν ἢ

τὸ οὐκ ἔσται, εἰ δεῖ ἤτοι ψευδῆ ἢ ἀληθῆ εἶναι (ὥρισται γὰρ κατ᾿ αὐτοὺς τὰ μέλλοντα). καὶ

εἰ μὲν ἔσται ναυμαχία αὔριον, ἀληθὲς εἰπεῖν ὅτι ἔσται· εἰ δὲ μὴ ἔσται, ψεῦδος τὸ εἰπεῖν ὅτι

ἔσται· ἤτοι δὲ ἔσται ἢ οὐκ ἔσται· ἤτοι ἄρα ἀληθὲς ἢ ψεῦδος θάτερον.

82 Truth

If so-and-so, then it is true that so-and-so

If not so-and-so, then it is false that so-and-so

Hence either it is true that so-and-so or it is false that so-and-so

The argument looks pretty promising. Surely it is valid—cannot its validity

readily be proved in standard modern logic? Its ﬁrst premiss is a law of

excluded middle—and who will deny that law? Its two other premisses are

immediate consequences of the principles of deﬂation—and those principles,

or items very like them, were generally accepted in antiquity.

True, the conclusion of the argument is not, as it stands, the Chrysippean

principle of bivalence: it doesn’t allude to assertibles, and it doesn’t time the

truth and falsity which it introduces. But that is readily dealt with. A simple

modiﬁcation to the argument will replace its ﬁrst premiss by, say,

If it is assertible that so-and-so, then either so-and-so or not so-and-so.

The second and third premisses may be adapted along the lines suggested by

the Stoic deﬂationary propositions. After a little polishing, the argument will

look something like this:

Whenever it is assertible that so-and-so, either it then holds that so-and-so

or it does not then hold that so-and-so.

Whenever it holds that so-and-so, it is then true that so-and-so.

Whenever it does not hold that so-and-so, it is then false that so-and-so.

Therefore whenever it is assertible that so-and-so, either it is then true that

so-and-so or it is then false that so-and-so.

The second and third premisses are no longer the principles of deﬂation—but

they are their ancient counterparts (and so much the better for that). The

ﬁrst premiss is no longer the law of excluded middle—but can hardly seem

less evident than the law of excluded middle.

The argument, I said, looks to be valid; and you might think to establish

its validity along the following lines:

SupposethatattitisassertiblethatP.

Then—by the ﬁrst premiss—there are two possible cases: either at t it

holds that P or at t it doesn’t hold that P.

Take the ﬁrst case: then by the second premiss it’s true at t that P—and

hence, trivially, it’s either true at t that P or false at t that P.

Take the second case: then by the third premiss it’s false at t that P—and

hence, trivially, it’s either true at t that P or false at t that P.

So in any case it’s either true at t that P or false at t that P.

ARetort 83

That argument is impeccable—so long as the ‘either … or …’ in it is taken

to indicate an inclusive disjunction. But Chrysippus’ thesis uses an exclusive

disjunction, and if the ‘either … or …’ is construed exclusively, then the

argument is not valid. I said that ‘it’s true at t that P—and hence, trivially,

it’seithertrueattthatPorfalseattthatP.’Thatisrightif‘either…or…’

is inclusive, wrong if it is exclusive.

If the argument is to conclude to the Chrysippean thesis, in which the

disjunction is exclusive, then it is necessary either to modify the second

and third premisses, or else to add a further premiss or premisses. Now

in fact it is easy enough to make suitable modiﬁcations or additions—and

to do so without introducing any suspect matter into the argument. But

the argument then becomes rather complicated, and the complications

may confuse or disguise the crucial issue. So I shall suppose that the

disjunctions in the argument are to be construed as inclusive. The argument

is then uncontroversially valid. True, its conclusion is not the Chrysippean

thesis itself; but it is one part of the Chrysippean thesis—and the more

controversial part.

The Chrysippean thesis holds both that assertibles must have one truth-

value and also that they can’t have two. The second part of that conjunction

was hardly disputed. True, we happen to know that Chrysippus wrote an

essay Against those who think that items are both true and false (Diogenes

Laertius, vii 196).⁷² The position of this item in the catalogue of Chrysippus’

writings suggests that it was connected to the paradox of the Liar; and the title

suggests that some people had attempted to resolve the paradox by claiming

that some assertibles might be both true and false (at the same time). But we

hear nothing more about that heroic claim, and speculation is pointless. In

any event, it is plain that Chrysippus’ chief adversaries, and his most potent

adversaries, claimed not that assertibles might be both true and false but

that they might be neither true nor false. And against those adversaries an

argument to an inclusive disjunction would have done the trick.

ARETORT

What is the value of the argument? How might, or how should, an Epicurean

have reacted to it? Turn again to the Epicurean texts on bivalence. There are

⁷² Πρὸς τοὺς νομίζοντας καὶ ψευδῆ καὶ ἀληθῆ εἶναι.—Susanne Bobzien drew my attention

to this title.

84 Truth

four items to add to the passage from Cicero’s On Fate which has already

been quoted—but which I shall repeat for convenience:

Chrysippus strains every sinew to persuade us that every assertible is either true or

false. For just as Epicurus feared lest, should he concede this, he would have to

concede that whatever happens happens by fate (for if one or the other is true from

eternity, then it is already ﬁxed; and if it is ﬁxed, then it is necessary—so that he

thinks that both fate and necessity are conﬁrmed in this way) …

( fat x 21)

Oneofthefouritemstobeaddedconﬁrmsthemessageofthattext:

It is just as immutable that <Cato> will come <to the Senate> when it is true that

he will as it is that he came. … And it must be allowed that if this assertible—

Hortensius will come to Tusculum

—is not true, then it follows that it is false. And they want neither of those things.

( fat xii 28)⁷³

It is the Epicureans who ‘want neither of those things’: ﬁrst, they do not want

an immutable future; and secondly, they will not allow that if an assertible

is not true then it is false. It is clear from the context that Cicero means

to ascribe to the Epicureans the thesis which he ascribed to Epicurus in the

earlier passage at x 21.

There is a further pertinent passage from On Fate; but it is better to leave

it to the end. So I take next a passage from the Lucullus:

The Stoics cannot get Epicurus, who despises and ridicules the whole of logic, to

concede that what we express thus—

Either Hermarchus will be alive tomorrow or he will not be alive

—is true, although the logicians establish that everything which is disjoined in the

manner of either Yes or No is not only true but necessary. Notice how cunning is

the man whom they think to be slow. For, he says, if I allow that one or the other is

necessary, then it will be necessary tomorrow either that Hermarchus is alive or that

he is not alive. But there is no such necessity in the nature of things.

(Luc xxx 97)⁷⁴

⁷³ et tamen tam est immutabile venturum cum est verum quam venisse. … etenim erit conﬁteri necesse

si hoc enuntiatum, veniet in Tusculanum Hortensius, verum non est, sequitur ut falsum sit. quorum isti

neutrum volunt.

⁷⁴ etenim cum ab Epicuro qui totam dialecticam et contemnit et irridet non impetrent ut verum esse

concedat quod ita effabimur, aut vivet cras Hermarchus aut non vivet, cum dialectici sic statuant omne

quod ita diiunctum sit quasi aut etiam aut non non modo verum esse sed etiam necessarium, vide quam

sit catus is quem isti tardum putant. si enim, inquit, alterutrum concessero necessarium esse, necesse erit

cras Hermarchum aut vivere aut non vivere. nulla autem est in natura rerum talis necessitas.

ARetort 85

The passage switches disconcertingly from truth to necessity; but if we

disregard that, we may afﬁrm that, according to Cicero, Epicurus denies that

Either so-and-so or not so-and-so

is in all cases true. He does so because he supposes that if it is true that either

so-and-so or not so-and-so, then either it is true that so-and-so or it is true

that not so-and-so. But

Hermarchus will be alive tomorrow

is a future contingent—today, it is neither true nor false. Hence

Hermarchus will not be alive tomorrow

is,today,neithertruenorfalse.Hence

Either Hermarchus will be alive tomorrow or Hermarchus will not be alive

tomorrow

is not true.

A further passage is found in a section of the Nature of the Gods in which

Cicero conducts a rapid discussion of fatalism and similar notions.

Epicurus does the same against the logicians who agree that in all disjunctions in

which either Yes or No is posited one or the other is true. Fearing lest if he conceded

that

Either Epicurus will be alive tomorrow or he will not be alive

was of that sort, then one or the other would be necessary, he denied that the whole

item

Either Yes or No

was necessary.

(nd i xxv 70)⁷⁵

This text too switches from truth to necessity; and in any event it is plain

that Cicero means to ascribe to Epicurus the theses which he ascribes to him

in the Lucullus.

Those two texts add material which is not present in the passage from On

Fate. But the new material is readily appended to the old. There are three

items to consider. First, Epicurus plainly imagines that assertibles which lack

truth-value go in pairs: if a given assertible lacks a truth-value, then so does

its contradictory negation. That is hardly astonishing. After all, if it is not

ﬁxed that there will be a festival at Aix next year, then it is not ﬁxed that

⁷⁵ idem facit contra dialecticos. a quibus cum traditum sit in omnibus diiunctionibus in quibus aut

etiam aut non poneretur alterum utrum esse verum, pertimuit ne si concessum esset huius modi aliquid

aut vivet cras aut non vivet Epicurus alterutrum ﬁeret necessarium, totum hoc aut etiam aut non negavit

esse necessarium.

86 Truth

there will not be a festival at Aix next year. Or rather, what is not ﬁxed is

precisely whether or not there will be a festival. More generally, if it is true

that not so-and-so, then it is false that so-and-so, and if it is false that not

so-and-so, then it is true that so-and-so. Hence if it is neither true nor false

that so-and-so, then it is neither true nor false that not so-and-so.

Secondly, Epicurus maintains that ‘disjunctions in which either Yes or No

is posited’ are not, all of them, true. In other words, he rejects the law of

excluded middle, holding that there are some cases in which

Either so-and-so or not so-and-so

is not true. Doubtless, Epicurus proposes that if it is not true that so-and-so

and not false that so-and-so, then it is not true that either so-and-so or not

so-and-so. If it is not now true that there will be a festival at Aix and not now

false that there will be a festival at Aix, then it is not now true that either

there will be a festival at Aix or there won’t be a festival at Aix.

Does Epicurus think that, in that case, it is now false that either there will

be a festival at Aix or there won’t be a festival at Aix? Or does he rather think

that it is now neither true nor false that either there will be a festival or there

won’t be a festival? The texts do not determine an answer.

Thirdly, Cicero implies that Epicurus’ rejection of the law of excluded

middle took place in a certain argumentative context: he rejected

Either so-and-so or not so-and-so

because he took it to entail

Either it is true that so-and-so or it is true that not so-and-so.

Now it is true that not so-and-so if and only if it is false that so-and-so, so

that Epicurus presumably took

Either so-and-so or not so-and-so

to entail

Either it is true that so-and-so or it is false that so-and-so.

In short, Cicero implies—perhaps correctly—that Epicurus was worried by

an argument which led from a law of excluded middle to a principle of

bivalence.

There is one further item in the Epicurean dossier. It is another passage

from On Fate:

So, pace Epicurus, it is necessary that one is true and one false, so that

Philoctetes will be wounded

was true all eternity ago and

He will not be wounded

false. Unless of course we want to follow the doctrine of the Epicureans when they

ARetort 87

say that such assertibles are neither true nor false—or else, when that shames them,

they say, yet more shamingly, that disjunctions from contraries are true but that

neither of the assertibles in them is true.

( fat xvi 37)⁷⁶

According to this text, the Epicureans say one thing; and then when that

shames them, they say something different—and which in fact is even more

shaming. They adopt one position and then abandon it for another.

The ﬁrst position, as Cicero describes it, seems to be nothing other than

the rejection of bivalence: ‘such assertibles are neither true nor false’. The

second position is this: ‘disjunctions from contraries are true but … neither

of the assertibles in them is true’—that is to say, some disjunctions of the

form ‘Either so-and-so or not so-and-so’ are true even though it is not true

that so-and-so and not true that not so-and-so. If the ﬁrst position was

abandoned in favour of the second, then the story goes something like this:

The Epicureans couldn’t stomach fatalism, so they rejected bivalence. But

they found that rejection too shameful; so they re-admitted bivalence and

claimed instead that there are true disjunctions no disjunct of which is true.

Alas, the second position is even more shaming than the ﬁrst.

That story is intelligible, but I wonder if it is the story which Cicero

really means to tell? If so, then in the second position, the Epicureans accept

bivalence. They also hold that, in some cases, it is true that either so-and-so or

not so-and-so, and not true that so-and-so and not true that not so-and-so. It

follows, trivially, that they hold that in some cases it is not true that so-and-so

and not true that not so-and-so. But if that is so, then they must deny that if

it is false that so-and-so then it is true that not so-and-so. For suppose that

If it is false that so-and-so, then it is true that not so-and-so.

Then

If it is not true that not so-and-so, then it is not false that so-and-so.

Hence if

In some cases it is not true that so-and-so and not true that not so-and-so,

then

In some cases it is not true that so-and-so and it is not false that so-and-so.

That is to say, bivalence does not hold.

⁷⁶ ex iis igitur necesse est invito Epicuro alterum verum esse alterum falsum, et sauciabitur Philocteta

omnibus ante saeculis verum fuit, non sauciabitur falsum. nisi forte volumus Epicureorum opinionem

sequi qui tales enuntiationes nec veras nec falsas esse dicunt aut, cum id pudet, illud tamen dicunt, quod

est impudentius, veras esse ex contrariis diiunctiones sed quae in his enuntiata essent eorum neutrum esse

verum.

88 Truth

Perhaps what makes the second position even more shaming than the ﬁrst

is precisely the fact that it commits the Epicureans to denying that

If it is false that so-and-so, then it is true that not so-and-so?

Cicero does not say so: he does not hint at any difﬁculty with the relationship

between ‘false that so-and-so’ and ‘true that not so-and-so’, and his text

indicates that the greater shame is simply the claim that there may be true

disjunctions in which no disjunct is true. So I incline to think that the

story which I extracted from Cicero’s words is false—and that it is not the

story which Cicero means to tell. Let us say that Cicero has compressed his

account.

The situation is rather this. There are three propositions around which

the Epicureans circle. First, there is the denial of bivalence, which may be

expressed roughly thus:

In some cases it is neither true that so-and-so nor false that so-and-so.

The Epicureans consistently held on to that point—which is indeed the very

centre of the position. Secondly and thirdly, there are these propositions:

(1) In some cases it is not true that either so-and-so or not so-and-so.

(2) In some cases it is true that either so-and-so or not so-and-so but not

true that so-and-so and not true that not so-and-so.

The adjunction of (1) to the central point produces the ﬁrst of the two

positions which Cicero ascribes to the Epicureans. The adjunction of (2) to

the central point produces the second.

The two propositions (1) and (2) are consistent with one another, so that

the Epicureans might have upheld both at once. Cicero implies that they did

not do so: rather, (1) and (2) were embraced as two different ways of getting

round a single obstacle. Cicero says that the Epicureans took the second way

to be less shaming than the ﬁrst; but I guess that that is Cicero’s invention:

I doubt if the Epicureans found either position more shameful than the

other—I doubt if they found either position shameful. I guess, too, that the

two alternative positions were put forward by the Epicureans, in a familiar

Epicurean ploy, as multiple explanations: ‘Maybe it’s (1) and maybe it’s (2).

We can’t tell, and we don’t care: what matters is that there is an explanation,

notwhattheexplanationis.’

However that may be, what was—or might, or should, have been—the

Epicurean response to the argument for the Chrysippean thesis which was

presented in the previous section? The argument went like this:

ARetort 89

Whenever it is assertible that so-and-so, either it then holds that so-and-so

or it does not then hold that so-and-so.

Whenever it holds that so-and-so, it is then true that so-and-so.

Whenever it does not hold that so-and-so, it is then false that so-and-so.

Therefore whenever it is assertible that so-and-so, either it is then true that

so-and-so or it is then false that so-and-so.

According to the ﬁrst of the two Epicurean positions, the ﬁrst premiss of the

argument is false; for there are any number of cases in which an assertible

neither holds nor fails to hold. For example, I can now assert that

I must down to the seas again.

But it neither now holds that I will go down to the sea nor now does not

hold that I will go down to the sea: for the moment my future sea-faring is

in the air.

There could scarcely be a simpler reply to the Stoic argument. Is the

reply not only simple but also reasonable? Well, if the Epicureans simply

deny the law of excluded middle and then shut up, they will not persuade

us that they are serious philosophers. After all, they deny something which

logicians take to be a fundamental principle of logic; and they owe us—and

themselves—some sort of explanation or justiﬁcation for their denial. More

particularly, they need a reply to the following objection: ‘A disjunction—I

mean, an inclusive disjunction or a quasi-disjunction—announces that at

least one of its disjuncts holds, and a negation of an assertible holds if

and only if the assertible does not hold. So consider any Either Yes or No

assertible—say

Either the sedge has withered from the lake or the sedge hasn’t withered

from the lake.

That holds if and only if at least one of its disjuncts holds. Suppose that

the ﬁrst disjunct doesn’t hold—then its negation must hold, and the second

disjunct is its negation. Suppose that the second disjunct doesn’t hold—then

its negation must hold, and the ﬁrst disjunct is its negation. So in any case at

least one of the disjuncts holds—and therefore the disjunction always holds.’

An Epicurean reply might run along the following lines. ‘First, there is

nothing odd about the notion that a sentence may have the form ‘Either so-

and-so or not so-and-so’ and yet fail to be true: suppose that the so-and-so is an

imperative, or an optative, and so on. There is only an oddity when ‘so-and-

so’ is replaced by an assertoric sentence. Now it is true that future contingents

are expressed by assertoric sentences—and that is why our position seems at