Barnes Jonathan. Truth, etc

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70 Truth

The function which—if I am right—is performed by the condition ‘it is

opposed to something’, might be performed in various other ways; and if the

crucial thing is to ensure that the equivalences advert both to holding and

to complete sayables, then perhaps the simplest and least misleading way of

expressing them is this:

It is true that so-and-so if and only if it holds that so-and-so.

It is false that so-and-so if and only if it does not hold that so-and-so.

Those two propositions are very close to my two principles of deﬂa-

tion—closer than anything in Aristotle or in Epicurus.

They are not quite the same as the principles. The principle for truth was

It is true that so-and-so if and only if so-and-so.

The corresponding Stoic proposition is

It is true that so-and-so if and only if it holds that so-and-so.

The Stoic proposition has ‘holds that so-and-so’ where the principle has the

simple ‘so-and-so’. The propositions which I ascribed to Aristotle and to

the Epicureans similarly had ‘it is the case that so-and-so’ rather than just

‘so-and-so’. The difference is not a triﬂe, and the presence of the dummy

verbs ‘hold’ and ‘be the case’ is not pleonastic.

For the deﬂationary principles, as I have formulated them, tacitly suppose

that truth and falsity are not timed. What happens to the principles if that

supposition is rejected? One easy suggestion is this: perhaps the time in the

preﬁx ‘It is true that … ’ is simply picked up by the time in whatever sentence

replaces ‘so-and-so’? In that case, a past instance of the ﬁrst principle will be

It was true that polygamy was deemed a sin if and only if polygamy was

deemed a sin.

A future instance:

It will be true that I shall plant nine bean-rows if and only if I shall plant

nine bean-rows.

And so on.

But the principle will then lose its universality, since it will yield nothing

of the forms

It will be true that polygamy was deemed a sin if and only if …

It is true that I shall plant nine bean-rows if and only if …

In general, if the principle supposes that the time in ‘It is true that …’ picks

up the time in ‘so-and-so’, then the principle will not apply to any cases in

which those two times differ.

Two Principles of Deﬂation 71

A second suggestion invites us to ignore any differences of time in ‘It is

true that …’. Let the principle say something like:

When and only when it is true that so-and-so, then so-and-so.

In that case,

It will be true that polygamy was deemed a sin if and only if polygamy was

deemed a sin

and

It is true that I shall plant nine bean-rows if and only if I shall plant nine

bean-rows.

But then on this second suggestion the principles will rule out any possibility

of a change in truth-values. Given that

It was true that so-and-so if and only if so-and-so

and

It will be true that so-and-so if and only if so-and-so,

then it follows that

It was true that so-and-so if and only if it will be true that so-and-so.

That argument is readily generalized to cover the present as well, and it is

readily transferred from ‘It is true that …’ to ‘It is false that …’.

That second suggestion, which outlaws change in truth-value, has some-

times been ascribed to Carneades. According to Cicero—in a passage which

I have already quoted—Carneades asked:

What could the god himself have looked at in order to predict that Marcellus—the

Marcellus who was three times consul—would die at sea? That was indeed true from

all eternity, but it had no active causes.

( fat xiv 32)

Carneades rejects the Chrysippean view that it is true at a given time that

such-and-such if and only if there are, at that time, causal harbingers or causal

traces that such-and-such—eternal truth does not require eternal chains of

causation. So surely he is suggesting that, say,

It was true that Marcellus will die at sea if and only if Marcellus will die

at sea,

It is true that Marcellus will die at sea if and only if Marcellus will die

at sea,

and

72 Truth

It will be true that Marcellus will die at sea if and only if Marcellus will die

at sea.

After all, what else could he have had in mind?

Well, there is something else which he could have had in mind. Instead of

the three equivalences which I have just offered him, he might have proposed:

It was true that Marcellus will die at sea if and only if Marcellus was going

to die at sea,

It is true that Marcellus will die at sea if and only if Marcellus is going to

die at sea,

and

It will be true that Marcellus will die at sea if and only if Marcellus will be

going to die at sea.

So construed, Carneades’ proposal does not exclude change in truth-value.

The same proposal—which amounts to a third suggestion for adapting

the deﬂationary principles to timed truth-values—may be advanced more

conveniently and more perspicuously if we return to the Stoic formulation:

It is true that so-and-so if and only if it holds that so-and-so.

For the dummy verb ‘hold’ carries, trivially, a tense, and the tense may be

taken (non-trivially) to indicate a time. We may then say, simply enough,

that the time indicated by ‘It is true that …’ marches with the time indicated

by ‘it holds that …’: the time indicated by ‘so-and-so’ is irrelevant—and

there is no need to look for subtle modiﬁcations of the tense of the verb in

‘so-and-so’.

And so it may be concluded that the two ancient principles of deﬂation

could be stated as follows:

It is true at a given time that so-and-so if and only if it holds at that time

that so-and-so.

It is false at a given time that so-and-so if and only if it does not hold at

that time that so-and-so.

Those principles were accepted by Plato, by Aristotle, by Epicurus, by the

Stoics; and no doubt by everyone else. Not that they were argued for or

advanced in triumph—rather, they were presuppositions which went without

argument and generally without saying.

Why so? The modern principles of deﬂation, it is true, are generally

taken to be evident: to be sure, the semantic paradoxes require them to be

Two Principles of Deﬂation 73

formulated with more circumspection than I have accorded them; to be sure,

there is a dispute about whether or not the deﬂationary principles serve to

deﬁne truth and falsity. (It is true that so-and-so if and only if so-and-so: is

that really all ye know on earth and all ye need to know?) But such details

apart, who could question the principles? Who could conceivably suggest

that perhaps it is raining and yet not true that it’s raining, or that perhaps it

is true that it is raining and yet it’s not raining?

But suppose that you are dubious about bivalence: then won’t you be

equally dubious about the principles of deﬂation? You will no doubt accept

conditional versions of the principles, namely:

If either it is true that so-and-so or it is false that so-and-so, then it is true

that so-and-so if and only if so-and-so and it is false that so-and-so if and

only if not so-and-so.

But what if it is neither true nor false that so-and-so? Suppose, for example,

you think that certain sorts of vague assertible have no truth-value—that

such items are assessed by criteria different from the canons of truth and

falsity. Then you will deny, say, that

It is true that France is a hexagon

and you will nonetheless happily assert that

France is a hexagon.

You might, if you were audacious enough, assert that

France is a hexagon—but it’s not true that France is a hexagon.

A sceptic about bivalence is not obliged to follow that road; but it seems to

me to be a road which he might naturally think to follow—and it is not an

evident cul-de-sac.

That being so, why did no ancient adversary of bivalence think to reject the

deﬂationary principles? Well, the ancient versions of those principles—or at

any rate, the items which I have just offered as the ancient versions—do seem

to be trivially true, and to be entirely neutral as far as bivalence is concerned.

For if, doubting bivalence, you want to distinguish between

France is a hexagon

and

It is true that France is a hexagon,

then you will also want to distinguish between

France is a hexagon

and

It is the case that France is a hexagon.

74 Truth

And—even more clearly—if you want to distinguish between

I shall plant the beans

and

It is true that I shall plant the beans,

then you will also want to distinguish between

I shall plant the beans

and

It is the case that I shall plant the beans.

In other words, you are likely to treat ‘It is true that …’ and ‘It is the case

that …’ (or ‘It holds that …’) in the same way; so that you will have no reason

to deny the principles of deﬂation.

Or rather, you will have no reason to deny the principle of deﬂation for

truth. As for its partner—

It is false at a given time that so-and-so if and only if it does not hold at

that time that so-and-so

—the same argument does not go through in quite the same way. But I shall

return a little later to the deﬂation of falsity.

AN ARGUMENT FOR BIVALENCE

Chrysippus strained his sinews to defend his thesis that every assertible is

either true or false. How did he do so? It is reasonable to suppose that Cicero is

referring metaphorically to some Chrysippean arguments, and hence reason-

able to suppose that Chrysippus argued, and argued forcefully and in several

fashions, for his thesis. It would be pleasant to know what those arguments

were, and what—if anything—they proved. But Cicero keeps quiet, and no

other ancient text ascribes any pertinent argument to Chrysippus.

No doubt much of Chrysippus’ effort was negative. He thought that

he could show that the truths about human freedom do not conﬂict with

bivalence; he hoped to solve the paradox of the Liar and the paradox of

the Sorites without supposing that certain assertibles are neither true nor

false. Such efforts were certainly sinew-stretching, and they might properly

be regarded as part of a general defence of bivalence. But did Chrysippus also

go on to the attack? Did he produce arguments in favour of bivalence?

It is not easy to ﬁnd a good argument in favour of the thesis—if only

because, as Cicero put it, the thesis is a foundation of dialectic. For example,

Cicero himself argues against the Epicurean rejection of bivalence as follows:

An Argument for Bivalence 75

If some assertible is neither true nor false, then certainly it is not true. But if it is not

true, how can it not be false? And if something is not false, how can it not be true?

( fat xvi 38)⁶⁴

Whatever the pedigree of that little argument, it will win no prizes at Crufts.

There is another ancient argument which seems a little more robust: it

seeks to derive the principle of bivalence from the principles of deﬂation

together with a law of the excluded middle. The origins of the argument have

been sought in a passage in Book Gamma of Aristotle’s Metaphysics:

Again, it is not possible for there to be anything between a contradictory pair—rather,

it is necessary either to afﬁrm or to deny one thing (whatever it may be) of one thing.

That is clear if we ﬁrst determine what is the true and false. For to say that what is is

not or that what is not is is false, and to say that what is is or that what is not is not is

true; so that he who says that it is or is not will speak truly or will speak falsely. But

what is is not said not to be or to be, neither is what is not.

(Met 1011b15–18)⁶⁵

The passage is in parts bafﬂing; but it is at least clear that it contains both a

law of excluded middle and also a principle of bivalence. Moreover, if we may

rely on the inferential particle in ‘so that he who says …’, Aristotle appears to

offer—as it were incidentally—an argument in favour of bivalence. But the

argument is anything but plain; and in any event, the primary concern of the

text is to commend the law of excluded middle, not to argue for bivalence.

In other words, Aristotle argues to, and not from, the law.

However that may be, the ancient argument which I have in mind—what-

ever its ﬁrst origins—appears clearly and distinctly in Simplicius’ commentary

on Aristotle’s Categories. The Aristotelian text under discussion is this:

Items which are opposed as afﬁrmation and negation evidently are opposed in none

of the previously mentioned ways; for in their case alone it is necessary that always

one of them should be true and one false.

(Cat 13a37–b3)⁶⁶

⁶⁴ si enim aliquid in eloquendo nec verum nec falsum est, certe id verum non est. quod autem verum

non est qui potest non falsum esse? aut quod falsum non est qui potest non verum esse?

⁶⁵ ἀλλὰ μὴν οὐδὲ μεταξὺ ἀντιφάσεως ἐνδέχεται εἶναι οὐθέν, ἀλλ᾿ ἀνάγκη ἢ φάναι ἢ

ἀποφάναι ἓν καθ᾿ ἑνὸς ὁτιοῦν. δῆλον δὲ πρῶτον μὲν ὁρισαμένοις τί τὸ ἀληθὲς καὶ ψεῦδος. τὸ

μὲν γὰρ λέγειν τὸ ὂν μὴ εἶναι ἢ τὸ μὴ ὂν εἶναι ψεῦδος, τὸ δὲ τὸ ὂν εἶναι καὶ τὸ μὴ ὂν μὴ εἶναι

ἀληθές, ὥστε καὶ ὁ λέγων εἶναι ἢ μὴ ἀληθεύσει ἢ ψεύσεται· ἀλλ᾿ οὔτε τὸ ὂν λέγεται μὴ εἶναι

ἢ εἶναι οὔτε τὸ μὴ ὄν.

⁶⁶ ὅσα δὲ ὡς κατάφασις καὶ ἀπόφασις ἀντίκειται, φανερὸν ὅτι κατ᾿ οὐδένα τῶν εἰρημένων

τρόπων ἀντίκειται· ἐπὶ μόνων γὰρ τούτων ἀναγκαῖον ἀεὶ τὸ μὲν ἀληθὲς τὸ δὲ ψεῦδος αὐτῶν

εἶναι.

76 Truth

Aristotle distinguishes four sorts of opposites or counterparts. Contradictory

opposition, which holds (in principle) between an afﬁrmation and a corres-

ponding negation has this special characteristic: if two items are contradictory

opposites, then (in an ancient jargon) they ‘divide truth and falsity’—at any

given time, exactly one of them is true and exactly one of them is false.

In his commentary Simplicius reports an objection which had been

advanced against that Aristotelian claim:

Here too Nicostratus ﬁnds fault, saying that it is not a property of contradictory

opposites to divide the true and the false; for it does not hold of them alone, nor of all

of them. Not of them alone since of jurative and abjurative sayings too it holds that

necessarily one of them is the case (e.g. ‘By God, I did it’, ‘By God, I didn’t do it’); and

the same holds for admiratives (‘How beautiful is the Piraeus’) and for reprehensives

(e.g. ‘He is wicked’, ‘He is not wicked’). Hence it does not hold of contradictories

alone. Nor yet of all of them, he says. For propositions with a future inﬂection are,

because of the nature of the contingent, neither true nor false—for neither ‘There

will be a sea-battle’ nor ‘There won’t be’ is true, but whichever happens to turn out.

(in Cat 406.6–16)⁶⁷

Simplicius then replies—or reports a reply—to Nicostratus. The reply

divides into two halves, one half devoted to each of the two criticisms made by

Nicostratus. Although only the second half is strictly pertinent to the present

business, I shall spend a moment on the ﬁrst half, which addresses the claim

that ‘dividing truth and falsity’ is not peculiar to afﬁrmation and negation.

The ﬁrst part of the reply, ascribed to an anonymous ‘they’, begins by

remarking that in the Categories the division of truth and falsity is invoked

only to distinguish the opposition of afﬁrmation and negation from the

other oppositions which Aristotle is there discussing, so that Nicostratus’

appeal to oaths and the like is irrelevant. That is correct. For Aristotle is not

there concerned to distinguish assertions from other types of saying but to

distinguish contradiction from other types of opposition: when he says ‘of

them alone’ he means ‘of contradictories alone among oppositions’.

⁶⁷ ὁ δὲ Νικόστρατος αἰτιᾶται κἀνταῦθα, λέγων μὴ ἴδιον εἶναι τῶν κατὰ ἀντίφασιν

ἀντικειμένων τὸ διαιρεῖν τὸ ἀληθὲς καὶ τὸ ψεῦδος. οὔτε γὰρ μόνοις οὔτε πᾶσιν αὐτοῖς

ὑπάρχει· οὐ μόνοις μέν, ὅτι καὶ τοῖς ὀμοτικοῖς καὶ τοῖς ἀπομοτικοῖς λόγοις ὑπάρχει τὸ ἐξ

ἀνάγκης θάτερον, οἷον νὴ τὴν ᾿Αθηνᾶν ἔπραξα τάδε· οὐ μὰ τὴν ᾿Αθηνᾶν οὐκ ἔπραξα. ἀλλὰ

καὶ τοῖς θαυμαστικοῖς, φησί, τὸ αὐτὸ ὑπάρχει· ὡς καλός γε ὁ Πειραιεύς· καὶ τοῖς ψεκτικοῖς,

οἷον φαῦλός ἐστιν, οὐ φαῦλός ἐστιν. οὐκ ἄρα μόνοις ὑπάρχει τοῖς κατὰ ἀντίφασιν τοῦτο. ἀλλ᾿

οὐδὲ πᾶσιν, φησίν. αἱ γὰρ εἰς τὸν μέλλοντα χρόνον ἐγκεκλιμέναι προτάσεις οὔτε ἀληθεῖς εἰσιν

οὔτε ψευδεῖς διὰ τὴν τοῦ ἐνδεχομένου φύσιν· οὔτε γὰρ τὸ ἔσται ναυμαχία ἀληθὲς οὔτε τὸ οὐκ

ἔσται, ἀλλ᾿ ὁπότερον ἔτυχεν.—It seems likely that a negative admirative has dropped from the

text.

An Argument for Bivalence 77

But although that is enough to deﬂect Nicostratus’ objection, Simplicius’

anonymous respondents nevertheless add a second consideration. The second

consideration goes like this:

Apart from that, they say, the point has been resolved long ago in the commentaries

on the deﬁnition of the assertible which determines an assertible as that which is true

or false. For a jurative cannot be true or false. Rather, it is reasonable to think that

keeping an oath and perjuring yourself are found among oaths and that being true and

being false cannot be found among them—not even if someone swears about what

is true or false. … But let us grant that those resolutions depend on Stoic subtlety.

(in Cat 406.20–28)⁶⁸

Nicostratus’ respondents indulge in Stoic subtleties, so that—in Simplicius’

view—the Stoa comes to the rescue of the Lyceum. Were the respondents

Stoics who determined to defend Aristotle on this point because on this point

Aristotle had anticipated a Stoic thesis? Or were they Aristotelians who were

happy to borrow a good argument from the Stoics?

However that may be, we happen to know something of what the Stoics

said on the matter of oaths.

Cleanthes said that anyone who swears either keeps his oath or perjures himself at

the time at which he swears. For if he swears as one who will fulﬁll what he swore, he

keeps his oath, and if as one who has the intention not to fulﬁll it, he perjures himself.

Chrysippus said that swearing truly differs from keeping an oath and perjuring

yourself differs from swearing falsely. If someone swears, then on the occasion on

which he swears he certainly either swears truly or swears falsely; for what is sworn by

him is either true or false since it is in fact an assertible. But anyone who swears does

not certainly, at the time at which he swears, either keep his oath or perjure him-

self—unless the time to which the oath has reference is present. For just as someone is

said to keep a contract or to break a contract not when he contracts but when the time

speciﬁed in the agreement is present, so you will be said to keep an oath and to perjure

yourself when the occasion arrives at which you agreed that you would fulﬁll your oath.

(Stobaeus, ecl i xxviii 17–18)⁶⁹

⁶⁸ χωρὶς δὲ τούτων, φασίν, πάλαι λέλυται ταῦτα ἐν ταῖς ἐξηγήσεσιν τοῦ ὅρου τοῦ

ἀξιώματος τοῦ ἀφοριζομένου τὸ ἀξίωμα ὅ ἐστιν ἀληθὲς ἢ ψεῦδος. οὐδὲ γὰρ τὸ ὀμοτικὸν οἷόν

τε ἀληθὲς εἶναι ἢ ψεῦδος, ἀλλ᾿ εὐορκεῖν μὲν ἢ ἐπιορκεῖν ἐν τοῖς ὅρκοις εἰκός, ἀληθεύειν δὲ ἢ

ψεύδεσθαι ἐν αὐτοῖς οὐχ οἷόν τε, κἂν περὶ ἀληθῶν ὀμόσῃ τις ἢ ψευδῶν. ... ἀλλ᾿ αὗται μὲν

ἀπὸ τῆς Στωϊκῆς ἀκριβείας ἔστωσαν αἱ λύσεις.

⁶⁹ Κλεάνθης ἔφη τὸν ὀμνύοντα ἤτοι εὐορκεῖν ἢ ἐπιορκεῖν καθ᾿ ὃν ὄμνυσι χρόνον. ἐὰν μὲν

γὰρ οὕτως ὀμνύῃ ὡς ἐπιτελέσων τὰ κατὰ τὸν ὅρκον, εὐορκεῖν· ἐὰν δὲ πρόθεσιν ἔχων μὴ

ἐπιτελεῖν, ἐπιορκεῖν. Χρύσιππος διαφέρειν ἔφη τὸ ἀληθορκεῖν τοῦ εὐορκεῖν καὶ τὸ ἐπιορκεῖν

τοῦ ψευδορκεῖν· τὸν μὲν ὀμνύντα καθ᾿ ὃν ὀμνύει καιρὸν πάντως ἢ ἀληθορκεῖν ἢ ψευδορκεῖν·

78 Truth

Stobaeus is paraphrasing rather than citing; but there is no reason to think

that the paraphrase is inaccurate; and despite the jargon the main point made

by Chrysippus is simple.

The subject is swearing—or rather, promising on oath. (The oaths in

question concern the swearer’s future behaviour—not the past or the present

or any other aspect of the future.) Chrysippus urges that it is one thing to

promise truly or falsely, another to keep or break your promise. That is so

because the two things are chronologically distinct. On Monday I swore by

the nine Gods to be at your wedding on Saturday; and on Saturday, there I

was. I promised truly on Monday. I kept my promise on Saturday.

Cleanthes appears to suppose that whenever you make a promise, either

you keep it or else you break it. In that case, since every promise is either

truly promised or falsely promised, it seems to follow that I swear truly if and

only if I keep my oath and I swear falsely if and only if I perjure myself. But

that consequence is false. If I break a promise, then I promised falsely. But

I may promise falsely without breaking a promise—perhaps I failed to turn

up at the wedding because I had been kidnapped by pirates, or because I had

died of cirrhosis of the liver. Again, if I keep a promise, then I promised truly.

But I may promise truly without keeping my promise—perhaps I turned

up on Saturday because I had been drugged and dragged along, or because I

thought that it was Sunday. As for Chrysippus, there is nothing in the text

which implies that, in his view, you promise truly if and only if you keep

your oath.

In any event, Chrysippus certainly held that whatever I swear is, when

I swear it, either true or false—for what I swear is an assertible. It might

then seem that Chrysippus disagreed with those Stoics or Stoically minded

Peripatetics who urged, against Nicostratus, that juratives are neither true

nor false; after all, if whatever I swear is either true or false, then surely all

juratives are either true or false? But that is not so. A jurative is a complete

sayable by saying which you may swear something. For example, what P

etain

said when he uttered the phrase

Parbleu, ils ne passeront pas

τὸ γὰρ ὀμνύμενον ὑπ᾿ αὐτοῦ ἢ ἀληθὲς εἶναι ἢ ψεῦδος, ἐπειδὴ ἀξίωμα τυγχάνει ὄν· τὸν δὲ

ὀμνύντα μὴ πάντως καθ᾿ ὃν ὀμνύει χρόνον ἢ εὐορκεῖν ἢ ἐπιορκεῖν, ὅτε μὴ πάρεστιν ὁ χρόνος

εἰς ὃν ἡ ἀναφορὰ τῶν ὅρκων ἐγίγνετο. ὃν τρόπον γὰρ λέγεσθαί τινα εὐσυνθετεῖν ἢ ἀσυνθετεῖν

οὐχ ὅτε συντίθεται ἀλλ᾿ ὅτε οἱ χρόνοι ἐνίστανται τῶν κατὰ τὰς ὁμολογίας, οὕτω καὶ εὐορκεῖν

τις καὶ ἐπιορκεῖν ῥηθήσεται ὅταν οἱ καιροὶ παραστῶσι καθ᾿ οὓς ὡμολόγησεν ἐπιτελέσειν τὰ

κατὰ τοὺς ὅρκους.

An Argument for Bivalence 79

was a jurative. And that—the jurative itself—is neither true nor false. But

thejurativeisnotwhatP

etain swore: what he swore was that the Boche

would not break through, and

The Boche will not break through

is an assertible, not a jurative. As an assertible, it had (according to Chrysippus)

a truth-value—and in fact, it was true.

In a similar way, those complete sayables which the Stoics called hypothet-

icals are neither true nor false—even though what you hypothesize by saying

a hypothetical is either true or false. The hypothetical

Suppose that there is a highest prime number

is neither true nor false. The hypothesis which you hypothesize by saying that

hypothetical, namely

There is a highest prime number

is an assertible, and it has a truth-value—it is false. Let it be added that by

saying

Suppose that there is a highest prime number

you do not make a false assertion; for although you say a false assertible, you

do not assert it—or anything else. The same is true of oaths: when P

etain

swore, he asserted nothing—although he said an assertible.

I turn now to the second part of Simplicius’ reply to Nicostratus—the

reply to his claim that not all assertibles are either true or false. It is a curious

piece of text. Simplicius ﬁrst states the opinion of the Stoics, who hold that

all assertibles, including those about the future, are either true or false. So

in the second part of the reply as well as in the ﬁrst, the Stoics ride to the

rescue of the besieged Peripatetics. But next Simplicius gives the view of the

Peripatetics themselves. According to them, he says,

what is stated about the future is not yet either true or false but will be such or such.

(in Cat 407.12–13)⁷⁰

The Peripatetics are evidently invoking a thesis which they found in chapter 9

of the de Interpretatione; but in doing so, they scarcely appear to answer

Nicostratus: on the contrary, they appear to express their agreement with

him, and their disagreement with the Aristotle of the Categories.Nicostratus

attacks Aristotle. The Stoics defend Aristotle. The Peripatetics ﬁght alongside

Nicostratus.

⁷⁰ ὅσα δὲ περὶ τοὓ μέλλοντος ἀποφαίνεται, ἤδη μὲν οὐκ ἔστιν ἢ ἀληθῆ ἢ ψευδῆ, ἔσται δὲ ἢ

τοῖα ἢ τοῖα.