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dŸ™ and ˜Ëp†rceiná e« d•™.
202 Truth and time
denial12 is either true or false (for both will not hold together with regard to
such items).13 For if it is true to say that it is white, or not white, it is necessary
for it to be white, or not white, and if it is white, or not white, it was true
to af¬rm, or to deny; and if it does not hold, he is speaking falsely, and if
he is speaking falsely, it does not hold. Hence it is necessary that either the
af¬rmation or the denial should be true. Hence nothing14 is or comes to be, or
will be or not be, by chance or however it chances, but everything necessarily
and not however it chances (since either he who af¬rms or he who denies
is speaking truly). For things would have come to be just as not have come
to be: for what is however it chances is not, nor will be, more thus than not
thus. (18a 34“18b 9)
This ¬rst deterministic argument has two parts: the ¬rst (18a 34“18b 4) con-
cludes that Bivalence™s holding for future-tense singular assertions entails
that at every time one member of a contradictory pair of future-tense
singular assertions is true,15 the second (18b 5“9) that if at every time one
member of a contradictory pair of future-tense singular assertions is true,
then whatever will happen is already determined.

The ¬rst part of the ¬rst deterministic argument (18 a 34“18 b 4) can be recon-
structed by employing conventional symbolism (I omit reference to time
because it is inessential at this stage). Begin by assuming Bivalence:
[32] (˜a™ is true ∨ ˜a™ is false) & (˜¬a™ is true ∨ ˜¬a™ is false) (cf. 18a 37“8)
(here ˜a™ is a schematic letter to be replaced with singular af¬rmative asser-
toric sentence-types). Then assume the following conditionals:
[33] ˜a™ is true ’ a (cf. 18a 39“18b 1)
[34] ˜¬a™ is true ’ ¬a (cf. 18a 39“18b 1)
[35] a ’ ˜a™ is true (cf. 18b 1“2)
At 18a 38 I read ˜kat†jasiv kaª ˆp»jasiv™ with some witnesses, Bekker, D¨ bner, Cooke, and
12 u
Weidemann. Other witnesses have ˜kat†jasiv™ (printed by Waitz, Minio-Paluello, and Zadro); yet
others have ˜kat†jasiv £ ˆp»jasiv™ (printed by Pacius, Buhle, and Weise).
13 ˜With regard to such items™ means ˜with regard to individuals™, the ˜–p©™+ dative construction (18a 39)
recalling the ˜–p©™+ genitive construction used ¬ve times in T 48 (at 18a 28, 18a 29“30, 18a 31, 18a 31“2,
and 18a 33 “ cf. 18b 27“8; 19a 35“6; 19b 3“4). Our parenthetical remark can then be paraphrased as
follows: ˜It is not the case that what is said by someone using a future-tense singular af¬rmation and
what is said by someone who is denying just that hold together™. This justi¬es the preceding point that
˜it is clearly necessary for one [sc. exactly one] of them to be speaking truly™ (18a 36“7). The intended
contrast is with af¬rmations and denials which are made non-universally about universals, which can
be both true at the same time. Cf. Ammon. in Int. 140, 4“10; Steph. in Int. 37, 7“10; Ackrill (1963),
135; Weidemann (1979), 30“1; D. Frede (1985), 35, 37; Weidemann (1994/2002), 232, 234, 238.
At 18b 4“5 I read ˜ˆlhq¦ e²nai. oÉd•n™: this reading, presupposed by the translations of Boethius and
14
George the Arab, is printed by Minio-Paluello and Zadro. The other witnesses and most editions
have ˜ˆlhq¦ e²nai £ yeud¦. oÉd•n™.
15 Cf. Craig (1988), 29“30; Weidemann (1994/2002), 232, 236.
Truth and Determinism in de Interpretatione 9 203
[36] ¬a ’ ˜¬a™ is true (cf. 18b 1“2)
[37] ¬a ’ ˜a™ is false (cf. 18b 3)
[38] ˜a™ is false ’ ¬a (cf. 18b 3)
Aristotle is consistent only if he does not accept all of [33]“[38]. For Aristotle
endorses Excluded Middle (cf. 19a 27“32 < T 53), so he must accept that
a ∨ ¬a. Then, if Aristotle accepts [35] and [37], he must admit that ˜a™
is true ∨ ˜a™ is false, a form of Bivalence for af¬rmative assertions which
he rejects. So, Aristotle probably does not accept all of [33]“[38], but he
only presents them as theses to which the advocate of Bivalence is com-
mitted.16
Propositions [32]“[38] “ actually, a subset of them “ entail that in every
contradictory pair of singular assertions at least one member is true:
[39] ˜a™ is true ∨ ˜¬a™ is true (cf. 18a 35“7; 18b 4; 18b 7“8).
To derive [39] from [32], [36], and [38], consider that [38] and [36] obviously
entail
[40] ˜a™ is false ’ ˜¬a™ is true.
But now [40] and [32]™s ¬rst conjunct trivially entail [39]. Since
[41] ¬(˜a™ is true & ˜¬a™ is true) (cf. 18a 38“9)
(because singular assertions are involved),
[42] (˜a™ is true ∨ ˜¬a™ is true) & ¬(˜a™ is true & ˜¬a™ is true).17

The second part of the ¬rst deterministic argument (18b 5“9). The ¬rst part
of the argument established that if Bivalence is true, then in every contra-
dictory pair of singular assertions it is always the case that one member is
true. But then the future is already determined. For, on the one hand, if the
af¬rmative member ˜Tomorrow a™ of a contradictory pair of future-tense
singular assertions is true today, then today it is ineluctable that one day
after today, i.e. tomorrow, it will be the case that a; on the other, if the
contradictory pair™s negative member ˜Tomorrow ¬a™ is true today, then
today it is ineluctable that one day after today, i.e. tomorrow, it will be the
case that ¬a. Hence, either today it is ineluctable that tomorrow it will be
the case that a, or today it is ineluctable that tomorrow it will be the case
that ¬a. The argument can be generalised to cover intervals different from
that of one day.18
16 17
Cf. the subsection to which n. 18 of appendix 6 pertains. Cf. n. 13 above.
18 Cf. Weidemann (1994/2002), 240“1.
204 Truth and time
The second deterministic argument (18 b 9“16):
T 50 Moreover, if it is white now, it was true to say earlier that it would be white,
so that of any of the things that have come to be it was always true to say
that it would be. But if it was always true to say that it is, or that it would be,
it was not possible for this not to be, or not to be going to be. But for what
it was not possible not to have come to be, it was impossible not to have
come to be; and for what it was impossible not to have come to be, it was
necessary to have come to be.19 Hence for all that will be it was necessary
that it should have come to be. Hence nothing will be however it chances
or by chance: for if by chance, then not necessarily. (18b 9“16)20
T 50™s deterministic argument is best described in terms of an argument-
schema which can, by appropriate substitutions, generate many distinct
arguments.21 In what follows, the schematic letter ˜a™ can be replaced with
any present-tense assertoric sentence-type without dates. The argument™s
conclusion is that if it is now the case that a, then it has always been
necessary that now it should be the case that a. Suppose it is now the case
that a. Let t0 be any past time, and let ˜i ™ name the exact interval between
t0 and now. Given Bivalence, at t0 an assertion that is an utterance of ˜In
i it will be the case that a™ was either true or false. Since now, i after t0 , it
is the case that a, the assertion was not false at t0 . Hence it was then true.
Therefore the state of affairs of the assertion™s being true obtained at t0 .
Hence (by the necessity of the present and the past) at t0 it was necessary
that the state of affairs of the assertion™s being true should obtain then.
Therefore at t0 it was necessary that at t0 it should be the case that i later it
would be the case that a. Since i after t0 is now, at t0 it was necessary that
now it should be the case that a. Since t0 was arbitrary, we can conclude
that it has always been necessary that now it should be the case that a.
The conclusion of T 50™s deterministic argument is not yet a formulation
of Determinism. One reason why the conclusion of this argument is not
yet a formulation of Determinism is that it is restricted to the present: its
conclusion is (all appropriate instances of ) ˜If it is now the case that a, then
it has always been necessary that now it should be the case that a™. This
fault can be easily amended by modifying the argument in such a way that
it comes to cover all times: the modi¬ed argument™s conclusion will be (all
appropriate instances of ) ˜For every time t, if at t it is the case that a then

19 Cf. Metaph. 4, 1006b 31“3. 20 T 50™s deterministic argument reappears at 18b 33“19a 6.
21 For similar reconstructions of T 50™s deterministic argument see Ockham in Int. i.vi 8, 2“12; C. J. F.
Williams (1978), 285“7; Sorabji (1980), 91; van Eck (1988), 26“7; Weidemann (1994/2002), 247“8;
Sorabji (1998), 7“8. Some commentators (Baylis (1936), 161“2; D. C. Williams (1951), 292; Haack
(1974/96), 74“81) think the second deterministic argument commits a fallacy of modal operator
shift.
Truth and Determinism in de Interpretatione 9 205
at every time t earlier than t it is necessary that at t it should be the case
that a™. Even this is not yet the thesis with which I identi¬ed Determinism
(˜For every state of affairs s and every time t, if s obtains “ or, respectively,
does not obtain “ at t then at every time t earlier than t it is necessary that
s should obtain “ or, respectively, not obtain “ at t™), but is close enough to
it.22
The distinctive trait of T 50™s deterministic argument is to pass from the
past truth of a future-tense assertion to the state of affairs of the assertion™s
being true obtaining at a past time, and to infer that at this past time it was
necessary that this state of affairs should obtain then. This past necessity is
then ˜transferred™ to what the assertion predicts. At 18b 13“14, the inferences
that substitute equivalent modal attributes (˜it was not possible not to have
come to be™, ˜it was impossible not to have come to be™, and ˜it was necessary
to have come to be™) play no important role.
Note that the determinist must claim that whatever is now the case was
always necessary in the past. The indeterminist can grant that something
which is now the case was necessary at some time or other in the past: e.g. he
can grant that when, a fraction of a second ago, the bullet was very close
to its target, it was necessary that it should hit its target.23

The pre-emptive move (18 b 16“25):
T 51 But neither is it possible to say that neither of the two is true, i.e.24 that
neither it will be nor it will not be. For, ¬rst, while the af¬rmation is false
the denial will not be true, and while this is false the af¬rmation turns out
not to be true. Moreover, if it is true to say that it is white and black, it must
be the case25 that they both hold, and if it is true to say that they will hold
tomorrow, it must be the case that they will hold26 tomorrow. But if it will
neither be nor not be tomorrow, there will be no ˜however it chances™, e.g. a
sea-battle:27 for it would be necessary for the sea-battle neither to have come
to be nor not to have come to be. (18b 16“25)

22 The deterministic argument I presented in the introduction (pp. 35“6 above), although based on
T 50™s deterministic argument, departs from it in that it is formulated directly in terms of states of
affairs and has Determinism as its conclusion.
23 Cf. Harris (1977/78), 50“1; Kirwan (1986), 172, 186; Donini (1989), 7; Enders (1999), 380.
24 ˜I.e.™ (˜o³on™) here introduces a consequence of what precedes.
At 18b 21 I read ˜m”lan de± ™, a reading attested by the ancient translations (with the exception of
25
Boethius™) and printed by Minio-Paluello and Zadro. Laur. 72, 15 reads ˜m”lan™, the other main
manuscripts, Boethius™ translation, and Ammonius have ˜m”ga de± ™, the reading adopted by most
editors. For ˜leuk»n™ and ˜m”ga™ cf. APr. 2.4, 57b 4“17.
At 18b 22 I read ˜Ëp†rxei e«v aÎrion, Ëp†rxein™ with Pacius, Buhle, Weise, Waitz, Cooke, Ackrill, and
26
Weidemann. Minio-Paluello and Zadro print ˜Ëp†rxein e«v aÎrion, Ëp†rxei™, Bekker and D¨ bner u
˜Ëp†rxei e«v aÎrion, Ëp†rxei™.
27 At Div. Somn. 1, 463b 1“3 a sea-battle is an example of something in the ful¬lment of which a man
has no initiative.
206 Truth and time
In T 51 the denier of Bivalence forestalls a possible move of an advocate of
Bivalence. The advocate of Bivalence might say that neither ˜a™ nor ˜¬a™ is
true (for the sake of simplicity, let the temporal quali¬cations be dropped),
thereby committing himself to the claim that neither a nor ¬a (because
otherwise, if either a or ¬a, then, by [35] and [36], which the advocate of
Bivalence surely accepts, either ˜a™ or ˜¬a™ would be true). Such a move
would block the ¬rst deterministic argument, whose ¬rst part established
that Bivalence implies that either ˜a™ or ˜¬a™ is true (cf. above).
The denier of Bivalence takes such a defensive move to have two unac-
ceptable consequences (in drawing these consequences the denier of Biva-
lence appeals to Bivalence because he is showing what the advocate of
Bivalence is committed to).28
(i) Given that ˜a™ is not true, then (by Bivalence) ˜a™ is false, whence
(by [38]) ¬a, whence (by [36]) ˜¬a™ is true. But the advocate of Bivalence
is now claiming that ˜¬a™ is not true. Analogously, given that ˜¬a™ is not
true, then (by Bivalence) ˜¬a™ is false, whence (by the counterpart of [38]
for denials) a, whence (by [35]) ˜a™ is true. But the advocate of Bivalence is
now claiming that ˜a™ is not true.
(ii) If ˜a™ and ˜¬a™ both failed to be true now, then (by Bivalence) ˜a™
and ˜¬a™ would both be false now. Then an argument similar to that of the
second part of the ¬rst deterministic argument (18b 5“9) would show that
it is now necessary (ineluctable) that neither a nor ¬a. So, the advocate of
Bivalence would still be landed with a deterministic position (though one
of a very peculiar sort).29
The position attributed to the advocate of Bivalence, i.e. that neither ˜a™
nor ˜¬a™ is true, seems something more than a theoretical possibility. The
claim that neither the af¬rmative nor the negative member of a contra-
dictory pair is true entails (by Bivalence, which the advocate of Bivalence
of course grants) the claim that both members are false. Elsewhere Aristo-
tle associates this last claim with Anaxagoras. For, according to Aristotle,
Anaxagoras™ primordial mixture was neither white nor black nor of any
other colour, and did not have any property whatsoever, so that no pred-
icate could be truly af¬rmed or denied of it (the assumption here might
be that for a predicate to be truly denied of it, the primordial mixture
should have enjoyed some property incompatible with the one signi¬ed by

28 Cf. Judson (1988), 16; Weidemann (1994/2002), 266“8. Some commentators (Anscombe (1956/68),
19; Strang (1960), 452; Hintikka (1964/73a), 167; van Rijen (1989), 105) wrongly claim that in T
51 Aristotle rules out that both members of a contradictory pair of future-tense singular assertions
could be neither true nor false.
29 Cf. Weidemann (1994/2002), 269“70.
Truth and Determinism in de Interpretatione 9 207
that predicate).30 Aristotle™s mention of white and black at 18b 21 might be
due not only to his desire to have the incompatibility between white and
black mirroring the incompatibility between the predicative expressions
of the members of a contradictory pair, but also to his intention to hint
at Anaxagoras (several times when he reports on Anaxagoras™ primordial
mixture Aristotle mentions white and black).31

The absurdity of Determinism (18b 26“19a 22).
T 52 Thus, the absurdities which result are these32 and others of the same sort,
if of every opposed af¬rmation and denial, either with regard to universals
spoken of universally or with regard to individuals, it is necessary for one to
be true and the other false, and33 that among things that come to be nothing
should be however it chances, but everything should be and come to be of
necessity,34 so that there would be no need to deliberate or to take trouble
(as if we do this, this will be, while if we fail to do this, this will not be).
For nothing prevents someone from having af¬rmed ten thousand years ago
that this would be and someone else having denied it, so that whichever
of the two things it was then true to say will be of necessity. But not even
this makes a difference, whether someone uttered the contradictory pair or
nobody did (for, clearly, this is how objects are even if it is not the case that
someone af¬rmed something35 and another denied it: for it is not because
of the af¬rming or denying that it will be or fail to be), nor does it matter
whether it was ten thousand years ago rather than any other time. Hence,
if in the whole of time things were such that one of the two would be true,
it was necessary for this to have come to be, and each of the things which
have come to be was always in such a condition36 as to have come to be of
necessity. For what someone has truly said would be, it is not possible that
it should not have come to be: and what has come to be it was always true
to say that it would be.
But if these consequences are impossible “ for we see that there is a
principle of what will be both from deliberating and from acting, and that
in general the possibility of being and not being is present in those things
that are not always actual: in these both are possible, to be and not to be,

30 Metaph. 7, 1012a 26“8 (cf. A 8, 989b 6“7; Gaskin (1995), 180; Vuillemin (1996), 139“40).
31 Cf. Ph. 1.4, 187b 5; Metaph. A 8, 989b 8“9; 7, 1011b 29“31; Vuillemin (1996), 139“40.
32 Aristotle is recalling the absurd implication which was shown to follow from the defence against
Determinism attempted in T 51: that ˜it would be necessary for the sea-battle neither to have come
to be nor not to have come to be™ (18b 24“5).
33 The ˜d•™ at 18b 30 answers the ˜m•n™ at 18b 26. Thus, the immediately following ˜that among things
that come to be [. . .]™ corresponds to the initial ˜these™ and ˜others of a similar sort™.
34 At 18b 31 I place a comma after ˜ˆn†gkhv™ instead of the full stop printed by most editors.
At 18b 38 I read ˜katajžsh € ti™ with some witnesses and most editors. Minio-Paluello and Zadro
35
omit ˜ti™.
36 At 19a 3 I read ˜e²cen™ with most editors. Minio-Paluello and Zadro print ˜›cein™.
208 Truth and time
and, therefore, to have come to be and not to have come to be. But it is clear
to us that many things are like this, e.g. that for this cloak it is possible to
be cut up and it will not be cut up, but will wear out before. But not being
cut up is equally possible for it: for it would not have been the case that it
wore out before if it had not been possible for it not to be cut up. Hence the
same holds for the other cases of coming to be, all those which are spoken of
according to this type of possibility. It is then37 clear that not all things are
or come to be of necessity, but some are or come to be however it chances,
and in no way is the af¬rmation or the denial more true, whilst with other
things one of the two alternatives is or comes to be more and in most cases,
while it is none the less possible that the other alternative could have come
to be, and the ¬rst one not. (18b 26“19a 22)
The assumption from which T 52 claims Determinism follows is not Biva-
lence, but the principle that in every contradictory pair of singular or
quanti¬ed assertions one member is true and the other false (at any time).
However, with restriction to singular and quanti¬ed assertions, Bivalence
entails the principle assumed at the beginning of T 52: given Bivalence,
exactly one member of a contradictory pair of singular or quanti¬ed asser-
tions is true (as the argument at 18a 34“18b 4 showed for the case of singular
assertions), and the other is false.
T 52™s attack on Determinism raises problems that are not germane to
the study of Aristotle™s views on truth. I shall therefore leave these problems
aside and concentrate on T 52™s comments on chance, which are important
for understanding Aristotle™s views on truth in Int. 9.

Aristotle™s account of diachronic modalities. Several remarks in Int. 9 sug-
gest that Aristotle is operating with a ˜statistical™ conception of modalities,
according to which a state of affairs enjoys a certain modal attribute just
in case it obtains with a certain frequency. Speci¬cally, in Int. 9 Aristotle
seems to be operating with a statistical conception of chance, according to
which a state of affairs is a matter of chance just in case it obtains just about
as often as it does not.38
However, the assumption that Aristotle in Int. 9 is operating with a
statistical conception of modalities faces objections. According to a ¬rst
objection, T 52™s example rules out a statistical conception of possibility:
although this cloak will wear out without being cut up, so that it is never
cut up, it is possible for it to be cut up. A second objection points out
that, according to Int. 9™s interpretation developed so far, Aristotle is here
37 The ˜then™ (˜Šra™) here (19a 18) answers the ˜if ™ (˜e«™) at the beginning of the paragraph (19a 7)
(cf. Weidemann (1994/2002), 277).
38 18b 8“9; 19a 9“10; 19a 18“22; 19a 35“9. For the statistical conception of modalities in Aristotle see n. 54
of ch. 1.
Truth and Determinism in de Interpretatione 9 209
operating with diachronic modalities, i.e. modal attributes with two ˜slots
for dates™, whose key formulations are instances of the schemata ˜At t it
is necessary that a at t ™, ˜At t it is impossible that a at t ™, etc. However,
diachronic modalities have nothing to do with the statistical conception of
modalities.
Can one attribute to Aristotle a coherent conception of modalities which
accommodates his statistical remarks without being defeated by objections
like those raised in the preceding paragraph? Here is one way to do this for
chance:
[43] For every time t and every non-zero interval i, at t it is chance whether
i later it will be the case that a just in case in the in¬nite course
of time up to i before t, just about half of the times when the total
state of the world resembled in relevant respects the total state of
the world at t were followed i later by a time when it was the case
that a.39
Since there is no clinching evidence for claiming that Aristotle in Int. 9 is
operating with an attribute of chance like the one described by [43], the
suggestion that such an attribute should play a central role in Int. 9 remains
speculative. As for the other modalities, [43]™s obvious companion is:
[44] For every time t and every non-zero interval i, at t it is necessary
(impossible, possible) that i later it should be going to be the case that
a just in case in the in¬nite course of time up to i before t, every (no,
some) time when the total state of the world resembled in relevant
respects the total state of the world at t was followed i later by a time
when it was the case that a.40
Note that [43] and [44] cover only diachronic modalities with a non-zero
interval towards the future: they state, for every time t and every non-zero
interval i, necessary and suf¬cient conditions for it to be chance, necessary,
impossible, or possible at t that a i later. Thus, [44] says nothing about the
necessity of the present or the past.

Aristotle™s solution (19a 23“19b 4).
T 53 Now, that what is should be whenever it is, and that what is not should
not be whenever it is not, is necessary, but it is not necessary that

39 Cf. M. J. White (1981), 239; Weidemann (1987), 181“2; (1994/2002), 280; Gaskin (1996), 54; Enders
(1999), 382“3.
40 Propositions [43] and [44] at least show that those commentators (e.g. Ackrill (1963), 136; D. Frede
(1985), 65; Gaskin (1995), 38) are not obviously right who think that Int. 9 cannot accommodate
Aristotle™s statistical remarks about modalities.
210 Truth and time
everything which is should be, nor that what is not should not be: for,
that everything which is should be of necessity when it is is not the same as
that everything which is should unquali¬edly be of necessity, and similarly
with what is not.41 The same account42 applies also to the contradictory pair:
it is necessary that everything should either be or not be, and either be going
to be or not; but it is not necessary43 to divide and call one or the other
necessary. For example, I mean that it is necessary that either there will be
a sea-battle tomorrow or there will not be one, but it is not necessary that
tomorrow a sea-battle should come to be nor that it should not come to be:
however, it is necessary that one should either come to be or not come to
be.44 So, since sentences are true in the same way as the objects, evidently,
in the case of those which are in such a condition as to be or come to be45
however it chances and admit the contrary states,46 the contradictory pair
will necessarily be in the same condition. This happens with those which not
always ˜are™ or not always ˜are not™:47 for it is necessary that one of the two
members of a contradictory pair concerning these [sc. states of affairs which
not always ˜are™ or not always ˜are not™] should be true or false, but it is not
necessary that this one or this one should be true or false, but it is however
it chances, and it is necessary that one of the two should be more true, but
not already true or false.48 Hence, clearly, it is not necessary that of every
af¬rmation and denial that are opposed one should be true and the other
false. For with what is things work out differently than with what is not but
can be as well as not be “ with these it is as we have said. (19a 23“19b 4)
T 53 divides into three parts: 19a 23“7, 19a 27“32, and 19a 32“19b 4. In the
following subsections I shall analyse them in turn.

Two claims about necessity. T 53™s ¬rst part (19a 23“7) makes two claims. The
¬rst is: ˜That what is should be whenever it is, and that what is not should
41 Aristotle™s distinction here is echoed by Theophrastus: see Alex. Aphr. in APr. 36, 25“9 (< Thphr.
F 14 Graeser); 156, 26“157, 2 (= Thphr. T 100B Fortenbaugh et al. < F 14 Graeser); 141, 1“6 (=
Thphr. T 100D Fortenbaugh et al. < F 14 Graeser); [Ammon.] in APr. 37, 2“4.
The Greek words ˜¾ aÉt¼v l»gov™ (19a 27“8), which correspond to the English ˜the same account™,
42
are absent from one of the main manuscripts (n).
43 I understand ˜ˆn†gkh™ from 19a 28 and I regard ˜q†teron™ and ˜ˆnagka±on™ as objects of ˜e«pe±n™.
Other constructions are possible (see Waitz (1844/46), i 342“3; Weidemann (1994/2002), 293“4).
44 The English present ˜to come to be™ translates the Greek aorist ˜gen”sqai™ (19a 31“2). Here Aristotle
uses the aorist of ˜g©gnomai™ merely for its aspectual connotation (cf. Humbert (1945/60), 144“5).
The temporal connotation is so absent that Aristotle employs the aorist despite the fact that one
would expect a future.
45 Here (19a 34) the words ˜be or come to be™ are supplied from 19a 10“11 and 19a 18“19.
At 19a 34 I take ˜t‡ –nant©a™ as the object of ˜–nd”cesqai™: a similar construction occurs at Metaph.
46
10, 1051b 11. Some translators instead regard ˜t‡ –nant©a™ as the subject of ˜–nd”cesqai™ (see e.g.
Weidemann (1994/2002), 15).
Here (19a 36) I read ˜to±v mŸ ˆeª o”sin £ mŸ ˆeª mŸ o”sin™, which is the reading handed down by most
47
witnesses and printed by all the editions I consulted. One of the main manuscripts (A), however,
reads ˜to±v mŸ ˆeª o”sin™, and Laur. 72, 15 has ˜to±v mŸ ˆeª oÉk o”sin™.
Here (19a 39) I read ˜yeud¦. ãste™, which is the reading handed down by most witnesses and printed
48
by all editors. A and Laur. 72, 3 read ˜yeud¦ e²nai. ãste™.
Truth and Determinism in de Interpretatione 9 211
not be whenever it is not, is necessary™ (19a 23“4). The best interpretation is
achieved by understanding the crucial occurrences of ˜to be™ in the veridical
sense and regarding them as predicated of states of affairs. This makes the
¬rst claim of T 53™s ¬rst part equivalent to:
[45] For every state of affairs s and every time t, if s obtains at t then at t it is
necessary that s should obtain at t. For every state of affairs s and every
time t, if s does not obtain at t then at t it is necessary that s should
not obtain at t.
Proposition [45] states the ˜necessity of the present™. The necessity at play is
ineluctability: if Socrates™ being seated obtains at noon on 1 January 399 bc,
then at noon on 1 January 399 bc it is necessary (ineluctable) that Socrates™
being seated should obtain at noon on 1 January 399 bc (for at noon on
1 January 399 bc nothing can be done about its being the case that at noon
on 1 January 399 bc Socrates is seated); similarly, if Socrates™ being seated
does not obtain at noon on 1 January 399 bc, then at noon on 1 January
399 bc it is necessary (ineluctable) that Socrates™ being seated should not
obtain at noon on 1 January 399 bc.49
The second claim of T 53™s ¬rst part is: ˜It is not necessary that everything
which is should be, nor that what is not should not be™ (19a 24“5). This
second claim is obscure. A clue for its interpretation is provided by Aristotle™s
own explanation of how it differs from the ¬rst claim: ˜For, that everything
which is should be of necessity when it is is not the same as that everything
which is should unquali¬edly be of necessity, and similarly with what is not™
(19a 25“7). Since Aristotle sometimes uses ˜unquali¬edly™ (˜‰pl¤v™, 19a 26)
to mean ˜without restriction to any speci¬c time™,50 the second claim of
T 53™s ¬rst part can be plausibly regarded as equivalent to:
[46] It is not the case that for every state of affairs s and every time t, if s
obtains at t then it is always necessary that s should obtain at t. It is
not the case that for every state of affairs s and every time t, if s does
not obtain at t then it is always necessary that s should not obtain
at t.
The necessity at play in [46] is again ineluctability: it is not the case that
if Socrates™ being seated obtains at noon on 1 January 399 bc, then it is
always necessary (ineluctable) that Socrates™ being seated should obtain at
noon on 1 January 399 bc; similarly, it is not the case that if Socrates™ being
49 Cf. Seel (1982a), 244; Waterlow (1982), 89; Weidemann (1994/2002), 254, 284; Gaskin (1995), 47“8;
Enders (1999), 384“8.
50 Cf. Bonitz (1870), 77a 19“21, cf. Hintikka (1964/73a), 158“9; von Wright (1979), 245, 250; Waterlow
(1982), 90; Weidemann (1994/2002), 283“4; Enders (1999), 391“3.
212 Truth and time
seated does not obtain at noon on 1 January 399 bc, then it is always nec-
essary (ineluctable) that Socrates™ being seated should not obtain at noon
on 1 January 399 bc. Thus, the second claim of T 53™s ¬rst part is almost
a repetition of the denial of Determinism defended in the chapter™s pre-
ceding section (18b 26“19a 22 = T 52): to say that not everything is always “
in particular, antecedently “ necessary is to say that not everything is pre-
determined.51
By asserting [45] and [46], Aristotle warns that upholding the necessity
of the present does not commit one to Determinism.52

The validity of Excluded Middle. In T 53™s second part (19a 27“32) Aristotle
makes three claims:
[47] For every state of affairs s and every time t, at t it is necessary that
either s should obtain at t or s should not obtain at t.
[48] For every state of affairs s, every time t, and every non-zero interval i,
at t it is necessary that i later s should either obtain or not obtain.
[49] It is not the case that for every state of affairs s, every time t, and every
non-zero interval i, either at t it is necessary that i later s should obtain
or at t it is necessary that i later s should not obtain.
The necessity at play in [47], [48], and [49] is still ineluctability.53
By asserting [47] and [48] Aristotle endorses Excluded Middle: he does
not want to be regarded as giving Excluded Middle up because he rejects
Bivalence. By asserting [49] Aristotle makes it clear that his defence of
Excluded Middle does not commit him to Determinism. He warns that
one should not make the fallacious inference which we would characterise
as a distribution of the necessity operator over the disjunction: for every
state of affairs and every interval, it is always necessary that after that interval
the state of affairs should either obtain or not obtain; however, it is not the
case that for every state of affairs and every interval it is always the case that
either it is necessary for the state of affairs to obtain after that interval or it
is necessary for it not to obtain after that interval. For instance, it is now
necessary that tomorrow a sea-battle should either take place or not take
51 Cf. Kirwan (1986), 172.
52 Cf. Strang (1960), 458; Waterlow (1982), 16“28, 89“90; van Rijen (1989), 127“8; Weidemann
(1994/2002), 284“5; Gaskin (1995), 94“6; Enders (1999), 391“3. For different interpretations of the
second claim of T 53™s ¬rst part see D. Frede (1970), 65“6; (1972), 153; von Fritz (1972), 248; M. J.
White (1980), 291“3; Seel (1982a), 244“5; von Wright (1984c), 72“3; D. Frede (1985), 72“3; M. J.
White (1985), 64; Craig (1988), 51; van Eck (1988), 24“5; Donini (1989), 8“9; Strobach (1998), 115.
53 Cf. Seel (1982a), 380; Weidemann (1994/2002), 293; Enders (1999), 394.
Truth and Determinism in de Interpretatione 9 213
place, but it is not the case that either it is now necessary that a sea-battle
should take place tomorrow or it is now necessary that a sea-battle should
not take place tomorrow.

The fallacy of division. The fallacious inference from Excluded Middle to
Determinism, an inference which we would characterise as a distribution
of the necessity operator over the disjunction, is described by Aristotle at
19a 29 as involving some sort of ˜dividing™. What he means can be plausibly
reconstructed by considering his remarks in Sophistici Elenchi concerning
sophistical refutations that depend on a division.54 A sophistical refutation
dependent on division occurs whenever in a dialectical debate a sentence is
understood differently by the answerer who grants it and by the questioner
who derives from it the contradictory of the answerer™s original thesis,
and the questioner™s way to understand the sentence can be described as a
division (thus, the appearance of a refutation depends on the questioner™s
dividing).55 Here is the most illuminating passage:
T 54 Dependent upon combination are those like, e.g. ˜to have the possibility to
walk while sitting™ and ˜to write while not writing™. For it does not mean the
same if one divides or combines when one says that it is possible to walk
while sitting.56 And this, ˜to write while not writing™, also behaves in the same
way if one combines it, for it means that one has the following possibility:
to write while not writing. But if one does not combine, it means that while
he is not writing he has the possibility to write. (SE 4, 166a 23“30)57
In T 54 Aristotle uses the verbs ˜to combine™ and ˜to divide™ to describe
different readings of a sentence containing a modal operator. These readings
depend on the scope assigned to the modal operator.58 Consider Aristotle™s
¬rst example: ˜It is possible to walk while sitting™. One ˜combines™ if one
understands ˜It is possible to walk while sitting™ in such a way that the whole
phrase ˜walk while sitting™ falls within the scope of the modal operator ˜it
is possible to™: ˜It is possible to (walk while sitting)™. One instead ˜divides™
if one understands ˜It is possible to walk while sitting™ in such a way that
only a part of the phrase ˜walk while sitting™ falls within the scope of the
modal operator ˜it is possible to™: ˜While sitting it is possible to walk™. So,

54 For the connection of Int. 9, 19a 29 to the discussion in Sophistici Elenchi see Prior (1953), 324; Brandt
(1965), 94“5; Fine (1984a), 31; B¨ck (1992), 141“2.
a
55 For Aristotle™s conception of sophistical refutations see the subsection to which n. 43 of ch. 4 is
appended.
At 166a 26“7 I follow Wallies, Forster, and Ross in omitting the words ˜kaª mŸ gr†jonta gr†jein™,
56
attested by the main manuscripts with several variants. Earlier editors retain them.
57 Cf. Cael. 1.12, 281b 2“14. 58 Cf. Zaslawsky (1986), 242; Schiaparelli (1999a), 161; (1999b), 58“9.
214 Truth and time
by using the verb ˜to combine™ (˜to divide™) Aristotle probably means that
the person to whom it applies takes the whole (a part) of an expression
as falling within the scope of an operator. Since in T 54 Aristotle uses ˜to
combine™ and ˜to divide™ to describe these different readings which (as we
would put it) depend on assigning a large or a narrow scope to a modal
operator, it is plausible to assume that when in T 53 he says that ˜it is not
necessary to divide™, he means that one need not give a narrow scope to the
modal operator.

How are the ¬rst two parts of T 53 related? At the beginning of the second
part of T 53, before asserting [47], [48], and [49], Aristotle says: ˜The same
account applies also to the contradictory pair™ (19a 27“8). He means that the
account he just offered in T 53™s ¬rst part is relevant to the claims he makes
in the second part, in particular to [49]. This is because were one to miss
the points made in T 53™s ¬rst part, one would have some inclination to
erroneously endorse the claim denied by [49]. To see this, suppose one were
to miss the second point made in T 53, i.e. suppose one were to endorse
the claims which [46] denies. By endorsing the claims which [46] denies,
one would be accepting, on the one hand, that for every state of affairs s
and every time t, if s obtains at t then it is always necessary that s should
obtain at t, and, on the other hand, that for every state of affairs s and every
time t, if s does not obtain at t then it is always necessary that s should
not obtain at t. Let s be a state of affairs, let t be a time, and let i be a
non-zero interval. Let t be a time i after t. One should accept that either s
obtains at t or s does not obtain at t (cf. [47]). From this result one can
then infer that either it is always necessary that s should obtain at t or it
is always necessary that s should not obtain at t . It follows that either at t
it is necessary that s should obtain at t or at t it is necessary that s should
not obtain at t . Hence either at t it is necessary that i later s should obtain
or at t it is necessary that i later s should not obtain. By generalising in the
appropriate way (because s, t, and i were arbitrary), one can conclude that
for every state of affairs s, every time t, and every non-zero interval i, either
at t it is necessary that i later s should obtain or at t it is necessary that i
later s should not obtain “ the claim which [49] denies.59

The ˜equimodality™ of the truth of assertions and states of affairs. At the begin-
ning of the third part of T 53 Aristotle says:
59 Different commentators explain differently Aristotle™s remark ˜The same account applies also to the
contradictory pair™ (19a 27“8): see e.g. Rescher (1968), 189; D. Frede (1970), 67“9; Lowe (1980), 57“8;
D. Frede (1985), 74; van Eck (1988), 31“2; Donini (1989), 9“11; Weidemann (1994/2002), 287“93;
Gaskin (1995), 45.
Truth and Determinism in de Interpretatione 9 215
Sentences are true in the same way as the objects. (19a 33 = T 5)
Since elsewhere Aristotle uses ˜object™ to denote states of affairs, of which he
says that they can be true,60 at 19a 33 he can be plausibly taken to be using
again ˜object™ to denote states of affairs.61 Aristotle™s claim at 19a 33 can
therefore be plausibly taken to be that the modality with which a present-
tense af¬rmative assertion is true is the same as the modality with which
the corresponding state of affairs is true, or “ as I often say “ obtains:62
[50] For every time t and every non-zero interval i, at t it is necessary that
(impossible that, chance whether) a present-tense af¬rmative assertion
should be true i later just in case at t it is necessary that (impossible
that, chance whether) the state of affairs corresponding to the assertion
should obtain i later.
Aristotle believes that there are no ˜negative™ states of affairs corresponding to
negative assertions (e.g. he believes that there is no ˜negative™ state of affairs
like the diagonal™s not being incommensurable corresponding to a negative
assertion that is an utterance of ˜The diagonal is not incommensurable™).63
He is therefore likely to believe that there are no ˜future-tense™ states of
affairs corresponding to future-tense assertions (e.g. he is likely to believe
that there is no ˜future-tense™ state of affairs of a sea-battle occurring in
24 hours corresponding to a future-tense assertion that is an utterance of ˜In
24 hours a sea-battle will take place™). If there are no ˜negative™ or ˜future-
tense™ states of affairs, the ˜equimodality™ of the truth of assertions and states
of affairs can hold only for present-tense af¬rmative assertions. It is for this
reason that [50] mentions only present-tense af¬rmative assertions.
Proposition [50] has an obvious counterpart that concerns present-tense
negative assertions:
[51] For every time t and every non-zero interval i, at t it is necessary that
(impossible that, chance whether) a present-tense negative assertion
should be true i later just in case at t it is necessary that (impossible
that, chance whether) the state of affairs corresponding to the assertion
should not obtain i later.

60 See n. 1 of ch. 1.
61 Cf. Talanga (1986), 78; de Rijk (1987), 40; van Eck (1988), 24; Gaskin (1995), 89. Weidemann
(1994/2002), 295“7 argues that since elsewhere in de Interpretatione Aristotle never uses ˜object™ for
items of which he says that they can be true, the Greek sentence at 19a 33 should be so understood
as to avoid committing Aristotle to such a usage. But in other works Aristotle does use ˜object™ for
items of which he says that they can be true, so Weidemann™s worry seems unjusti¬ed.
62 Cf. Kullmann (1994/95), 297“8; Gaskin (1995), 89. D. Frede (1970), 28, criticises this interpretation
of 19a 33, but her grounds are unconvincing.
63 Cf. the subsection to which n. 15 of ch. 1 is appended.
216 Truth and time
Although Aristotle does not explicitly state [51], he can be plausibly taken
to endorse it.
In the speci¬c case of the modality of chance, Aristotle™s claim of
˜equimodality™ allows a simpli¬ed formulation:
[52] For every time t and every non-zero interval i, at t it is chance whether
a present-tense assertion will be true i later just in case at t it is chance
whether the state of affairs corresponding to the assertion will obtain
i later.

The failure of Bivalence. In the ¬nal bit of the third part of T 53 Aristotle
draws his conclusions with regard to Bivalence:
T 55 [a] It is necessary that one of the two members of a contradictory pair
concerning these [sc. states of affairs which not always ˜are™ or not always ˜are
not™] should be true or false, [b] but it is not necessary that64 this one or this
one should be true or false,65 [c] but it is however it chances, and [d] it is
necessary that66 one of the two should be more true, [e] but not already true
or false. [f ] Hence, clearly, it is not necessary that of every af¬rmation and
denial that are opposed one should be true and the other false. [g] For with
what is things work out differently than with what is not but can be as well
as not be “ with these it is as we have said. (19a 36“19b 4 < T 53)
The attributes of necessity and chance at play in T 55 are, as in many other
crucial points of Int. 9, diachronic: they are most accurately expressed by
instances of the schemata ˜At t it is necessary that a at t ™ and ˜At t it is
chance whether a at t ™ (with ˜t™ and ˜t ™ to be replaced with designations
of times, ˜a™ with an assertoric sentence-type without dates).
T 55 is puzzling: clause [a] seems to commit Aristotle to Bivalence, while
Aristotle should be denying Bivalence. At least two interpretations of T 55
are possible which solve this dif¬culty. The best way to expound these two
interpretations is to display how they paraphrase each of the clauses that
constitute T 55.
64 The ˜m•n™ at 19a 36 is answered by the ˜m”ntoi™ at 19a 38. Since the ˜m•n™ at 19a 36 is closely linked to the
˜ˆn†gkh™ at 19a 36, an occurrence of ˜ˆn†gkh™ should be understood between the ˜oÉ™ at 19a 37 and the
immediately following ˜m”ntoi™ at 19a 38. Hence the rendering of the Greek clauses that correspond
to [a] and [b] by (respectively) ˜It is necessary that . . .™ and ˜But it is not necessary that . . .™.
Cf. ˜ˆn†gkh m•n [. . .] oÉ m”ntoi [. . .] ˆnagka±on™ at 19a 30“1.
65 Alternative translation: ˜[a] It is necessary that either member of a contradictory pair concerning
these should be either true or false, [b] but it is not necessary that it should be this [sc. true] or
this [sc. false]™. On this alternative translation see D. Frede (1970), 71; Bosley (1977), 32“3; D. Frede
(1985), 76; van Eck (1988), 24.
66 Since the Greek clause that corresponds to [d] is an accusative with in¬nitive, it is most probably
still governed by the ˜ˆn†gkh™ at 19a 36: hence, in my translation, the words ˜it is necessary that™ at
the beginning of clause [d].
Truth and Determinism in de Interpretatione 9 217
Interpretation A. According to the ¬rst interpretation of T 55 (henceforth
˜interpretation A™), clause [a] says that at time t it is necessary that of
the two members of a given contradictory pair of future-tense singular
assertions concerning a time t later than t, one should be true at t and the
other false at t . In clause [a] the operator ˜it is necessary that . . .™ af¬rms
necessitas consequentis: it indicates (not that something follows necessarily
from previous results, but) that something obtains necessarily. For instance,
let t be noon on 1 January 399 bc, let t be noon on 2 January 399 bc, let u
be an utterance of ˜In 24 hours a sea-battle will take place™ produced at
noon on 1 January 399 bc, and let v be an utterance of ˜In 24 hours no
sea-battle will take place™ also produced at noon on 1 January 399 bc. Then
u and v are members of a contradictory pair and they both concern noon
on 2 January 399 bc. Clause [a] commits Aristotle to the claim that at noon
on 1 January 399 bc it is necessary that either u should be true at noon on
2 January 399 bc and v false then, or u should be false at noon on 2 January
399 bc and v true then. Clause [a] does not commit Aristotle to Bivalence
because it does not say that at t it is necessary that of the two members of
the given contradictory pair of future-tense singular assertions concerning
the later time t , one should be true at t and the other false at t.67
Clause [b] says that despite [a], at t it is not necessary that the af¬rmative
member of the given contradictory pair of future-tense singular assertions
concerning t should be true at t , nor is it at t necessary that the negative
member of that contradictory pair should be true at t . Thus, in clause
[b] the operator ˜it is not necessary that . . .™ denies necessitas consequentis.
Going back to the last paragraph™s example, clause [b] commits Aristotle
to the claim that at noon on 1 January 399 bc it is not necessary that u
should be true at noon on 2 January 399 bc, and, similarly, at noon on 1
January 399 bc it is not necessary that v should be true at noon on 2 January
399 bc.
Clause [c] strengthens [b]™s denial of necessity by saying that for each of
the two members of the given contradictory pair of future-tense singular
assertions concerning the later time t , at t it is chance whether it will be
true at t . Going back to the example of the last two paragraphs, clause
[c] commits Aristotle to the claim that at noon on 1 January 399 bc it is
chance whether u will be true at noon on 2 January 399 bc, and, similarly,
at noon on 1 January 399 bc it is chance whether v will be true at noon on
2 January 399 bc.

67 For this interpretation of clause [a] see Ackrill (1963), 142; Ihrig (1965), 227; Haack (1974/96), 77;
Seel (1982a), 379“80; Weidemann (1994/2002), 297“8; Liske (1995), 354; Kretzmann (1998), 26.
218 Truth and time
Clauses [d] and [e] consider the case where a certain outcome is
antecedently likely to occur. The necessity operator ˜it is necessary that . . .™
at the beginning of clause [d] af¬rms necessitas consequentiae: it indicates
(not that something obtains necessarily, but) that something follows neces-
sarily from previous results. Clause [e] falls within the scope of this necessity
operator. Hence clauses [d] and [e] introduce two necessary consequences
of previous results: the ¬rst necessary consequence, stated in the second
half of clause [d], is that in some cases at t one member of the given con-
tradictory pair of future-tense singular assertions concerning the later time
t is more likely to be true at t than the other; the second necessary con-
sequence, stated in clause [e], is that despite [d], at t neither member of
the given contradictory pair of future-tense singular assertions concerning
the later time t is ˜already™ true or false (˜already™ has its usual temporal
meaning), i.e. at t both members of the contradictory pair are neither true
nor false. For instance, let t be noon on 1 January 399 bc, let t be noon on
2 January 399 bc, and let w and y be utterances of ˜In 24 hours Socrates will
be sober™ and ˜In 24 hours Socrates will not be sober™ produced at noon on
1 January 399 bc. Then w and y are members of a contradictory pair and
they both concern noon on 2 January 399 bc. In accordance with clause
[d], at noon on 1 January 399 bc the likelihood of w being true at noon on
2 January 399 bc is greater than that of y being true at noon on 2 January
399 bc. Clause [e] commits Aristotle to the claim that despite this, at noon
on 1 January 399 bc neither w nor y is ˜already™ true or false.
Clause [f ] states the conclusion Aristotle was aiming for: with some
contradictory pairs of future-tense assertions, sometimes it is not the case
that one member is true and the other false. This is because with some
contradictory pairs of future-tense assertions, sometimes both members
are neither true nor false.
Clause [g] emphasises that the principle requiring that it should always
be the case that one contradictory assertion is true and the other false has
exceptions with regard not to the present (˜what is™) but to what lies in the
future (˜what is not™, i.e. ˜what is not yet™) and is contingent (˜can be as well
as not be™).

A problem for interpretation A. According to interpretation A, Aristotle
concentrates on certain future-tense singular assertions that are tempo-
rally determinate, i.e. speak about speci¬c times, and he claims that they
are neither true nor false at the times when they are uttered but become
either true or false at the times they speak about. On this conception, the
truth-value of one of these future-tense singular assertions, though
Truth and Determinism in de Interpretatione 9 219
dependent on time insofar as it is only at a time that the assertion has
it, is independent of time insofar as it cannot, even in principle, be differ-
ent at different times. For, according to the conception in question, once
the time the assertion speaks about has come, the assertion is either true or
false, and whatever it is then it remains forever afterwards.68
Now, several Aristotelian passages indicate that Aristotle would endorse
the following claim about present-tense singular assertions, truth-values,
and time:
[h] A present-tense singular assertion is temporally indeterminate, i.e. does
not speak about any speci¬c time. It therefore can, at least in principle,
be true at one time and false at another.69
Aristotle™s endorsement of [h] strongly suggests that he would aver the
following similar claim about future-tense singular assertions, truth-values,
and time:

[i] A future-tense singular assertion is temporally indeterminate. It therefore
can, at least in principle, be true at one time and false at another.
Claim[i] con¬‚icts with the theory attributed to Aristotle by interpretation
A.70

Defence of interpretation A. Some advocates of interpretation A assume that
Aristotle is confused about the bearers of truth or falsehood.71 However, I
feel uneasy at saddling Aristotle with a confusion about such a fundamental
issue.
A more promising defence of interpretation A assumes that Aristotle
endorses neither [h] nor [i] because he thinks that there is an important
distinction between kinds of singular assertions: singular assertions which
do not contain utterances of pseudo-dates (like ˜now™ or ˜tomorrow™) comply
with [h] and [i] (they are temporally indeterminate, and can, at least in
principle, be true at one time and false at another), singular assertions
which do contain utterances of pseudo-dates behave differently “ they are
temporally determinate and cannot, even in principle, be true at one time
and false at another. What can be said for this defence?

68 Cf. Jordan (1963), 12; Hintikka (1964/73a), 151; Ihrig (1965), 219; Hintikka/Remes/Knuuttila (1977),
31“2; Weidemann (1994/2002), 300“1.
69 Cf. the subsection to which n. 1 of ch. 6 appended.
70 Cf. Sorabji (1980), 100; (1998), 8; Mignucci (1998), 62.
71 Cf. Weidemann (1994/2002), 300“1, 308, 325.
220 Truth and time
(i) It credits Aristotle with a sound intuition: according to many modern
logicians and linguists, utterances of pseudo-dates behave differently from
verbal tenses and must be treated as temporally rigid designators.72
(ii) In Categories 4 Aristotle says:
T 56 Each of the things said with no interweaving signi¬es either a substance or
a quantity or a quali¬ed item or a relative or where or when or being-in-a-
posture or having or doing or being affected. (1b 25“7)73
Aristotle then offers examples: man and horse are substances, white and
grammatical are quali¬ed items, yesterday and last-year are items in the
category of time. On the plausible assumption that for Aristotle items in
the categorial scheme can be signi¬ed by parts of sentences, Aristotle is
committed to the view that as an utterance of ˜man™ within an assertion sig-
ni¬es a substance (the universal man) and an utterance of ˜white™ signi¬es a
quali¬ed item (the universal white), so utterances of ˜yesterday™ or ˜last year™
within assertions signify items in the category of time. This makes it plau-
sible to assume that an utterance of ˜tomorrow™ within an assertion should
signify the portion of time which is the day after that when the utterance
is produced. Then an assertion containing an utterance of ˜tomorrow™ is
temporally determinate and cannot, even in principle, be true at one time
and false at another.
(iii) In Topics 5.3 (131b 5“18) Aristotle distinguishes what is always peculiar
to something from what is peculiar to it at a certain moment. Suppose that
in a dialectical debate one is requested to indicate a peculiarity of x : if one
answers by mentioning a y that is peculiar to x at that moment but fails to
specify that it is at that moment that y is peculiar to x, then one™s reply is
objectionable; if instead one answers by mentioning a y that is peculiar to
x at that moment and points out that it is at that moment that y is peculiar
to x, then one™s reply is ¬ne.74 For instance, if one indicates what is peculiar
to Socrates by saying
[j] What is peculiar to Socrates is being seated next to Alcibiades
then one™s reply is objectionable; if instead one says
[k] What is now peculiar to Socrates is being seated next to Alcibiades
then one™s reply is ¬ne. What makes a difference is the presence of an
utterance of ˜now™. Aristotle™s analysis presupposes that an utterance of
˜now™ adds something to the mere utterance of a present-tense verb-phrase
to which it is attached. Moreover, what Aristotle has in mind might be that
72 73 Cf. APo. 1.22, 83b 13“15.
Cf. Landman (1991), 134“5; K. Taylor (1998), 269“82.
74 Cf. 1.5, 102a 22“8; 102b 20“6; 5.1, 128b 16“21; 129a 26“30.
Truth and Determinism in de Interpretatione 9 221
the difference here is that while [j] can pass from being true now to being
false later, [k] cannot.75
(iv) At the end of de Interpretatione 1 Aristotle says that ˜goatstag™ is
neither true nor false ˜unless “to be” or “not to be” is added, either simply
or with reference to time™ (16a 17“18). According to some commentators,76
the phrase ˜either simply or with reference to time™ distinguishes assertions
which lack from assertions which contain utterances of pseudo-dates.77
Regrettably, the above considerations do not prove that Aristotle drew
the distinction attributed to him by the defence of interpretation A. The
problem remains that in no passage does Aristotle explicitly draw this dis-
tinction.78

Interpretation B. An alternative interpretation of T 55 is available “ call it
˜interpretation B ™. Before expounding interpretation B ™s clause-by-clause
paraphrase of T 55, let me sketch the philosophical intuition behind it. The
rejection of Bivalence need not assume that future-tense singular assertions
are temporally determinate. Consider an utterance u of ˜In 24 hours a sea-
battle will take place™. Understand u as temporally indeterminate, i.e. as
not speaking about any speci¬c time (there is no more reason for taking u
to be about the time 24 hours after when it is produced than there is for
taking an utterance of ˜A sea-battle is taking place™ to be about the time
when it is produced). One can also assume that for every time t, u is true
(false) at t just in case at t the state of the world is such that a (no) sea-battle
will take place 24 hours later. If one is not a determinist, one will claim that
sometimes the state of the world is neither such that a sea-battle will take
place 24 hours later nor such that no sea-battle will take place 24 hours later.
One will then be led to admit that there are times when u is neither true nor
false. This amounts to a rejection of Bivalence. This rejection of Bivalence,
however, is based on understanding u as temporally indeterminate. Inter-
pretation B assumes that for Aristotle all assertions are temporally indeter-
minate, and can, at least in principle, have different truth-values at different
times.

Clause-by-clause paraphrase. The ¬rst half of T 55 (clauses [a]“[c]) concen-
trates on states of affairs whose obtaining is antecedently a matter of chance.

75 76 Boeth. in Int. Sec. Ed. 51, 30“52, 6; Ammon. in Int. 29, 12“17.
Cf. Remes (1977), 42“3.
77 For the various interpretations of the passage see Boeth. in Int. Sec. Ed. 51, 2“52, 9; Montanari
(1984/88), ii 76“7; Kneepkens (1994), 162“7.
78 It is worthwhile recalling that certain unnamed (but probably Stoic) opponents of Alexander™s in de
Fato (10. 177, 7“9) seem to regard the proposition (ˆx©wma) expressed by an utterance of ˜A sea-battle
will take place tomorrow™ as temporally indeterminate.
222 Truth and time
Consider a state of affairs s (e.g. the state of affairs of a sea-battle taking
place), a non-zero interval i (e.g. the interval of 24 hours), and a time t
such that in the in¬nite course of time up to i before t, just about half of
the times when the universe resembled in relevant respects the universe at
t were followed i later by a time when s obtained. In such a situation, at t
it is chance whether i later s will obtain. Consider also a contradictory pair
of present-tense singular assertions p and q, where p af¬rms, and q denies,
that s is obtaining (e.g. let p and q be utterances of ˜A sea-battle is taking
place™ and ˜No sea-battle is taking place™), and consider the contradictory
pair of future-tense singular assertions u and v, where u asserts that s will
obtain i later and v asserts that i later s will not obtain (e.g. let u and v be
utterances of ˜In 24 hours a sea-battle will take place™ and ˜In 24 hours no
sea-battle will take place™).
In the situation described, at t it is necessary that i later either the present-
tense af¬rmation p will be true and its denial q false, or p will be false and
q true. This is what clause [a] claims: ˜It is necessary that one of the two
members of a contradictory pair concerning these [sc. states of affairs which
not always “are” or not always “are not”] should be true or false.™ Note that
the members of the contradictory pair in question are present-tense singular
assertions: those present-tense singular assertions whose later truth-value
is crucial to the present truth-value of the future-tense singular assertions
which will refute Bivalence. In clause [a] the operator ˜it is necessary that . . .™
af¬rms necessitas consequentis: it indicates (not that something follows neces-
sarily from previous results, but) that something obtains necessarily. Clause
[a] does not commit Aristotle to Bivalence because it speaks about present-
tense assertions, while it is future-tense assertions which in Aristotle™s view
will refute Bivalence.
However, at t it is not necessary that i later the present-tense af¬rmation p
should be true and its denial q false, and, analogously, at t it is not necessary
that i later p should be false and q true. This is what clause [b] claims: ˜But
it is not necessary that this one or this one should be true or false™. Here ˜it
is not necessary that . . .™ denies necessitas consequentis.
In fact, at t it is chance whether i later the present-tense af¬rmation p
will be true and its denial q false, and, analogously, at t it is chance whether
i later p will be false and q true. This is what clause [c] claims: ˜But it is
however it chances™.
Clauses [d] and [e] go on to consider states of affairs that are antecedently
likely to obtain. Consider a state of affairs s (e.g. the state of affairs of
Socrates™ being sober), a non-zero interval i (e.g. the interval of 24 hours),
and a time t such that in the in¬nite course of time up to i before t, most
Truth and Determinism in de Interpretatione 9 223
but not all of the times when the universe resembled in relevant respects
the universe at t were followed i later by a time when s obtained. In
such circumstances, at t it is likely that i later s will obtain. Consider also
a contradictory pair of present-tense singular assertions r and o, where r
af¬rms, and o denies, that s is obtaining (e.g. let r and o be utterances of
˜Socrates is sober™ and ˜Socrates is not sober™), and a contradictory pair of
future-tense singular assertions w and y, where w asserts that s will obtain i
later and y asserts that i later s will not obtain (e.g. let w and y be utterances
of ˜In 24 hours Socrates will be sober™ and ˜In 24 hours Socrates will not be
sober™).
In such a situation, at t it is necessary that at t the case in which i
later the present-tense af¬rmation r is true should be more likely than
that in which i later the present-tense denial o is true. This is what clause
[d] says by asserting that ˜it is necessary that one of the two should be
more true™. Here the necessity operator ˜it is necessary that . . .™ af¬rms
necessitas consequentis and governs only clause [d] (clause [e] falls outside its
scope).
Still, from what is stated by clause [d] it does not follow that at t it is
necessary that i later the present-tense af¬rmation r should be true and the
present-tense denial o false. This is what clause [e] claims: ˜But not already
true or false™. Here ˜already™ has not a temporal, but a logical sense:79 it
means ˜thereby™. After ˜already™ an occurrence of the necessity operator ˜it
is necessary that . . .™ must be understood.80 The necessity denied by ˜But
<it is> not already <necessary that it should be> true or false™ is necessitas
consequentis. ˜True™ here is supposed to apply to whichever member of the
contradictory pair is likely to be true, ˜false™ to the other member. Clause
[e] is therefore to be paraphrased by ˜It does not follow that it is necessary
that the member of the contradictory pair which is likely to be true should
be true and that the member which is likely to be false should be false™.
The claims concerning present-tense assertions made by clauses [d] and [e]
recall those made at the end of T 52 with regard to states of affairs: ˜With
other things one of the two alternatives is or comes to be more and in most


79 Cf. Bonitz (1870), 314a 10“17; Anscombe (1956/68), 25; Ackrill (1963), 141; Bosley (1977), 34; Sorabji
(1980), 95; Fine (1984a), 35, 45; Judson (1988), 17. For ˜¢dh™ (˜already™) used in a logical sense see Int.
1, 16a 8; APo. 1.1, 71a 23; Ph. 1.4, 187a 36; Metaph. 5, 1015b 13; 21, 1022b 19; EN 5.3, 1130a 2; 10, 1136a 2;
6.10, 1142b 14; 10.6, 1177a 6.
80 The particles in the Greek text suggest an understood ˜ˆn†gkh™ after ˜¢dh™ at 19a 39. For the ˜m•n™
at 19a 38 is answered by the ˜oÉ m”ntoi™ at 19a 39, and this recalls the ˜m•n™ at 19a 36 answered by the
˜oÉ m”ntoi™ at 19a 37“8. But the ˜m•n™ at 19a 36 and the ˜oÉ m”ntoi™ at 19a 37“8 introduce the contrast
between what is and what is not ˆn†gkh (cf. n. 64 above).
224 Truth and time
cases, while it is nonetheless possible that the other alternative could have
come to be, and the ¬rst one not™ (19a 20“2).81
The foregoing has a crucial consequence. Consider again u, an assertion
to the effect that the state of affairs s will obtain i later, and p, an assertion
to the effect that s is obtaining. u, which is a future-tense in¬‚ection of the
present-tense af¬rmation p, is neither true nor false at t: since at t it is not
necessary that i later p should be true, u is not true at t; analogously, since
at t it is not necessary that i later p should be false, u is not false at t. This
is because at t the universe as it has evolved until then is such as to require
the truth (or, respectively, falsehood) of u just in case in whatever possible
way it evolves after t, i after t the universe is such as to require the truth (or,
respectively, falsehood) of p:82 if in some possible developments after t the
universe i after t is such as to require the truth of p whereas in other possible
developments after t the universe i after t is such as to require the falsehood
of p, then at t the universe is not such as to require either the truth or the
falsehood of u (in such a case, the universe as it is at t simply leaves the
truth or falsehood of u at t unsettled “ at t the universe neither matches nor
disagrees with u). This is tantamount to saying that u is true (or, respectively,
false) at t just in case at t it is necessary that i later p should be true (or,
respectively, false). Therefore Bivalence fails. Aristotle does not spell out
this crucial consequence. However, clause [f ] states the consequence of this
consequence which is most important in the context of de Interpretatione
as a whole: that with certain contradictory pairs of future-tense assertions
sometimes it is not the case that one member is true and the other false
(at t it is not the case that u is true and v false, nor is it at t the case that u
is false and v true).
Clause [g] emphasises that the principle that in every contradictory pair it
is always the case that one member is true and the other false has exceptions
with regard not to the present but to what lies in the future and is contingent.

A problem for interpretation B. According to interpretation B, in T 55 Aris-
totle reaches the conclusion that certain future-tense assertions are now
neither true nor false by discussing the future truth or falsehood of present-
tense assertions. This procedure seems awkward: why should claims about
the present truth or falsehood of future-tense assertions be based on a
discussion of the future truth or falsehood of present-tense assertions?
81 Cf. Judson (1988), 17“18.
82 In some passages (Int. 9, 18b 9“11; 19a 4“6; GC 2.11, 337b 3“7) Aristotle explicitly links the truth at a
time of a future-tense assertion with the later truth of the present-tense assertion from which it is
in¬‚ected.
Truth and Determinism in de Interpretatione 9 225
Defence of interpretation B. At the beginning of T 55 Aristotle mentions
states of affairs that ˜not always “are” or not always “are not”™ (19a 36), i.e.
states of affairs that ˜are in such a condition as to be or come to be however
it chances and admit the contrary states™ (19a 34). Since the aim of T 55 is to
establish that certain future-tense assertions are now neither true nor false,
Aristotle is probably assuming that some future-tense assertions which now
are neither true nor false concern states of affairs whose obtaining is a matter
of chance. Since in Int. 9 the modality of chance, like the other modalities,
is diachronic, i.e. is a modal attribute with two ˜slots for dates™, it can be
plausibly assumed that for Aristotle certain future-tense assertions which
now are neither true nor false concern states of affairs for which now it is
chance whether they will obtain later.
Shortly before T 55 Aristotle makes a claim about the ˜equimodality™
of the truth of assertions and states of affairs. In a previous subsection83 I
argued that part of this claim is that for every time t and every non-zero
interval i, at t it is chance whether a present-tense assertion will be true i
later just in case at t it is chance whether the state of affairs corresponding to
that assertion will obtain i later (cf. [52] above). This makes it plausible to
assume that Aristotle wants to introduce certain present-tense assertions for
which it is now chance whether they will be true later, and link them with
the future-tense assertions which now are neither true nor false and concern
states of affairs for which it is now chance whether they will obtain later.
The present-tense assertions in question are those to which the states of
affairs correspond which the future-tense assertions which now are neither
true nor false concern. They are the present-tense assertions from which the
future-tense assertions which now are neither true nor false are in¬‚ected.
The reason why Aristotle™s claims about the present truth or falsehood
of future-tense assertions are based on a discussion of the future truth or
falsehood of present-tense assertions is probably that Aristotle thinks that
the future-tense assertions which now are neither true nor false concern
states of affairs for which it is now chance whether they will obtain later,
and he can link this modality of chance for states of affairs with the truth-
values of assertions only by means of the ˜equimodality™ of the truth of
assertions and states of affairs, ˜equimodality™ which, however, concerns
present-tense assertions.

Assessment of T 55™s two interpretations. Interpretation A seems to saddle Aris-
totle with an inconsistent position about assertions, truth, and time. The

83 See the subsection to which n. 60 above is appended.
226 Truth and time
best possible defence of interpretation A fails because it requires attribut-
ing to Aristotle distinctions for which the textual evidence is slim. Inter-
pretation B avoids saddling Aristotle with an inconsistent position about
assertions, truth, and time. Interpretation B faces its own problem, which,
however, can be solved. Hence, interpretation B is more likely than inter-
pretation A.

Aristotle™s rejection of Bivalence. Interpretation A requires that for Aristotle
an utterance produced today of ˜A sea-battle will take place in 24 hours™
should remain without truth-value at most until tomorrow. In general,
according to interpretation A, although Aristotle rejects Bivalence, he is
none the less committed to a thesis which is close (though not identi-
cal) to Bivalence, i.e. that every assertion sooner or later is either true or
false.
By contrast, interpretation B requires that for Aristotle an utterance
produced today of ˜A sea-battle will take place in 24 hours™ could remain
without truth-value for ever: it is not the case that tomorrow this utterance
is bound to become true or false (tomorrow it will be true, or false, only
if the conditions of the universe tomorrow will be such as to necessitate,
or exclude, a sea-battle taking place the day after tomorrow). In general,
according to interpretation B, Aristotle is committed to avoiding endorsing
the previously mentioned thesis which is close to Bivalence, i.e. the thesis
that every assertion sooner or later is either true or false.
Therefore, although interpretation A attributes to Aristotle a rejection of
Bivalence no less than interpretation B, the rejection of Bivalence attributed
to Aristotle by interpretation B is more ˜serious™ than the one attributed to
him by interpretation A.


3 alternative i nt e rpre tati on s
Realism and anti-realism. My interpretation of Int. 9 is a version of what
is sometimes called an anti-realist interpretation. What distinguishes anti-
realist interpretations is crediting Aristotle with a rejection of Bivalence.84

84 Anti-realist interpretations (often called ˜traditional interpretations™ or ˜standard interpretations™)
were avowed by some Peripatetics (see Simp. in Cat. 407, 6“13, a controversial witness on which cf.
Weidemann (1994/2002), 303; Kretzmann (1998), 24“5; Mignucci (1998), 75“6; Gaskin (2000), 230“
1), some Stoics (see Boeth. in Int. Sec. Ed. 208, 1“7; Simp. in Cat. 406, 34“407, 5 “ cf. Mates (1953/61),
28“9; Mignucci (1989), 52; Weidemann (1994/2002), 305“6; Gaskin (1995), 86; Mignucci (1996b),
283; Kretzmann (1998), 24“5), and the middle-Platonist Nicostratus (see Simp. in Cat. 406, 12“16,
cf. Mignucci (1996b), 305; (1998), 75, 85). It is not clear whether Ammonius and Boethius favoured
Truth and Determinism in de Interpretatione 9 227
However, Int. 9 has been interpreted in different ways too. Discussing all
these interpretations is beyond the scope of this study.85 I restrict myself to
examining brie¬‚y realist interpretations, which constitute the most author-
itative alternative to my favoured exegesis.
According to realist interpretations, in Int. 9 Aristotle does not reject
Bivalence. Rather, he distinguishes ways in which tensed assertions have
whatever truth-value they have: all past- and present-tense assertions
have their truth-values necessarily, some future-tense singular assertions
have them contingently. Aristotle then addresses some deterministic argu-
ments which, if sound, would prove Determinism, and therefore demol-
ish his position: future-tense singular assertions also would have their
truth-values necessarily. He then argues that Determinism is absurd
and criticises the deterministic arguments: they are fallacious because
they give modal operators a narrow scope in contexts requiring a wide
scope.

The anti-realist interpretation is more plausible than the realist.
(i) The anti-realist interpretation ¬ts chapter 9 well within de Interpre-
tatione as a whole. For chapters 7 and 8 discuss exceptions to the principle
that in every contradictory pair it is always the case that one member is true
and the other false. Chapter 7™s exception is indeterminate assertions: some-
times both members of a contradictory pair of indeterminate assertions are
true. Chapter 8™s exception is utterances which seem simple assertions but
really are composite assertions. On the anti-realist interpretation, chapter 9
presents another exception to the same principle: sometimes both members
of a contradictory pair of future-tense singular assertions are neither true
nor false, so it is not then the case that one is true and the other false. Real-
ist interpretations lack an equally smooth account of chapter 9™s position
within de Interpretatione.
(ii) Realist interpretations have an unnatural reading of the chap-
ter™s introduction (18a 28“33) and conclusion (19a 39“19b 4): Albrecht
Becker, who favours a realist interpretation, regards both passages as

an anti-realist interpretation (Gaskin (1995), 146“84 and Weidemann (1994/2002), 305“8 af¬rm they
did, Mignucci (1996b), Skarica (1997), 184, and Mignucci (1998) deny it). Epicurus rejected Bivalence
to block an argument for fatalism (see Cic. Fat. 9.18; 10.21; 16.37“8; Ac. ii 30.97; Nat. Deor. i 25.70),
but it is unclear whether he had in mind Int. 9 (cf. D. Frede (1985), 79; Weidemann (1994/2002),
319; Bobzien (1998), 75“86). For anti-realist interpretations in Antiquity see Lukasiewicz (1922), 125;
(1930), 176“8; Sorabji (1980), 93; Weidemann (1994/2002), 303“8, 319; Mignucci (1996b), 305“10;
(1998), 75, 85; Sorabji (1998), 3, 13.
85 For a discussion of the interpretations of Int. 9 see Dickason (1976), 11“19; Celluprica (1977);
Weidemann (1994/2002), 302“28; Gaskin (1995), 12“192; Grossato (1999).
228 Truth and time
spurious.86 Other commentators87 unearth the theses predicted by a realist
interpretation in the chapter™s introduction and conclusion. For instance,
in their view the introduction™s initial remark, ˜With regard to things that
are and things that have come to be, it is [. . .] necessary that either the
af¬rmation or the denial should be true or false™ (18a 28“9), means ˜With
regard to things that are and things that have come to be, every af¬rmation
or denial is either necessarily true or necessarily false™. This seems to be
bending Aristotle™s words to ¬t what one dreams to ¬nd in them.
(iii) Realist interpretations saddle Aristotle with a disappointing anal-
ysis of the deterministic arguments: dismissing them by claiming that
they trade on the scope of modal operators is hardly satisfactory.88 More-
over, realist interpretations credit Aristotle with the view that whenever
a past- or present-tense assertion is true, it is necessarily true. Does
this after all not saddle Aristotle with Determinism? If tomorrow a sea-
battle will take place, then ˜“A sea-battle will take place tomorrow” is
true now™ is true now, and therefore necessarily true now, whence it
is now necessary that a sea-battle should take place tomorrow. The realist
solution of this dif¬culty is to class ˜“A sea-battle will take place tomor-
row” is true now™ with future- rather than present-tense assertions: despite
the present-tense verb ˜is true™, the assertion is ˜about the future™. (I shall
not address here the dif¬cult question of what it is for an assertion to be
˜about the future™.) What embarrasses realist interpretations is that they
take Aristotle to be silent about this issue.89

Evidence that Aristotle endorsed Bivalence. The anti-realist interpretation also
faces a dif¬culty: outside Int. 9 Aristotle seems to endorse Bivalence. Here
is the evidence.
(i) In Categories 4 Aristotle endorses Bivalence for all af¬rmations and
denials:
T 57 Every af¬rmation and denial90 appears to be true or false, but none of the
things said with no interweaving is either true or false, e.g. ˜man™, ˜white™,
˜runs™, ˜wins™. (2a 7“10)


86 See A. Becker (1936), 74.
87 E.g. Rescher (1963b), 44, 49; Spellman (1980), 121“2; Judson (1988), 9, 18“21.
88 Cf. Judson (1988), 32“3.
89 Cf. Ackrill (1963), 139“40; Prior (1967c), 1; Spellman (1980), 122“3; Kirwan (1986), 187; von Kutschera
(1986), 209, 213; Craig (1988), 28“9; B¨ck (1992), 144“5; Gaskin (1994), 91“3.
a
At 2a 8 I read ˜kat†jasiv kaª ˆp»jasiv™: this reading is attested by some of the main manuscripts
90
and printed by Bekker, D¨ bner, and Cooke. Other manuscripts have ˜kat†jasiv £ ˆp»jasiv™
u
(printed by Pacius, Buhle, and Weise). Waitz, Minio-Paluello, and Bod´us follow other witnesses

and print ˜kat†jasiv™.
Truth and Determinism in de Interpretatione 9 229
(ii) According to Categories 10 (13a 37“13b 3 and 13b 27“35), in a contradic-
tory pair it is always the case that one member is true and the other false.
Since for every af¬rmation or denial there is a contradictory opposite (cf.
Int. 6, 17a 31“3), this entails that every af¬rmation or denial is always either
true or false.
(iii) In de Interpretatione 10 (20a 31“6) Aristotle says that inde¬nite names
(e.g. ˜non-man™) and inde¬nite verbs (e.g. ˜does not run™) might seem to be
denials lacking a verb or a name, ˜but they are not, for a denial must always
be true or false, whilst he who says “non-man” “ without adding anything
else “ has no more said something true or false, indeed rather less so, than
he who says “man”™ (20a 33“6). Here Aristotle seems to postulate that every
denial is always either true or false.
(iv) In de Anima 3.6, 430b 26“7 (< T 24) Aristotle endorses Bivalence for
all af¬rmations.91
(v) In Metaphysics Aristotle avers a semantic version of Excluded Middle
according to which ˜it is necessary that either member of the contradictory
pair should be true™ (8, 1012b 10“11).92 Thus, if an af¬rmation is not true at
t, then its contradictory denial is true at t. Then, by the de¬nition of truth,
the object of which the denial claims that it ˜is not™ in the sense of being
false, at t ˜is not™ in the sense of being false. Then the object of which the
original af¬rmation claims that it ˜is™ in the sense of being true, at t ˜is not™
in the sense of being false. Then, by the de¬nition of falsehood, the original
af¬rmation is false at t. Thus, if an af¬rmation is not true at t then it is false
at t. Hence, an af¬rmation is either true or false at t. A parallel argument
goes through for denials. Then Aristotle is committed to Bivalence.

The anti-realist interpretation can be defended in two ways. (i) The ¬rst
defence assumes that wherever Aristotle seems to endorse Bivalence, he
is really only claiming that every present-tense assertion is always either
true or false. Some support for this line comes from the circumstance that
there is a case for attributing to Aristotle the view that only present-tense
assertions are, strictly, ˜assertions™, while past- and future-tense assertions
are ˜assertions™ merely in a secondary sense: for in de Interpretatione 3 (16b 16“
18) Aristotle says that only certain present indicative forms of a verb are
˜verbs™ (˜§žmata™), while a verb™s past and future forms are not ˜verbs™


91 Cf. 3.3, 427b 20“1; 6, 430b 4“5.
92 Cf. APr. 1.13, 32a 27“8; 46, 51b 32“3; APo. 1.1, 71a 14; Top. 6.6, 143b 15“16; Metaph. 7, 1012a 26“7;
1012a 28; 8, 1012a 31“3; 1012b 3“4. Aristotle uses also several other formulations of Excluded Middle.
On these formulations and their mutual relations see D. Frede (1970), 77“8; (1985), 79“80; Cavini
(1998), 5“7.
230 Truth and time
but ˜in¬‚ections of a verb™ (˜ptÛseiv §žmatov™).93 If he believes that only
present-tense assertions are, strictly, ˜assertions™, those remarks that appear
to commit him to Bivalence could in fact commit him only to the weaker
claim that every present-tense assertion is always either true or false.
(ii) The second defence of Int. 9™s anti-realist interpretation assumes that
Aristotle changed his mind about Bivalence. Many commentators94 now
agree that most of de Interpretatione is an early work of Aristotle™s. Chapter 9
could be a late addition to an early draft of de Interpretatione, and the
denial of Bivalence could be a late development of Aristotle™s thought.95
This hypothesis has some independent support.
(ii.i) Chapter 9 could well have been added later to answer a Megar-
ian objection which was not yet around when the rest of the treatise was
originally written.96
(ii.ii) Chapter 9 is isolated within de Interpretatione: no other passage in
the work refers to or presupposes it.
(ii.iii) In de Interpretatione 6 Aristotle claims that ˜for every af¬rmation
there is a denial opposed to it, and for every denial an af¬rmation™ (17a 32“3).
He defends this claim by saying:
T 58 Since it is possible to assert that what holds does not hold, that what does
not hold holds, that what holds holds, and that what does not hold does not
hold, and similarly for times outside the present, whatever one af¬rmed it is
possible to deny, and whatever one denied it is possible to af¬rm. (17a 26“31)
T 58™s consequent claims that it is possible to contradict. T 58™s antecedent
brie¬‚y discusses the truth and the falsehood of af¬rmations and denials:
such a discussion is relevant because a sophistical argument that it is impos-
sible to contradict was based on the assumption that it is impossible to speak
falsely.97 The ¬rst part of T 58™s antecedent focuses on the truth and the
93 Cf. 5, 17a 10. Elsewhere (Int. 10, 19b 13“14; Po. 20, 1457a 14“23) Aristotle seems to contradict this by
claiming or implying that the past and the future forms of a verb count as ˜verbs™.
94 E.g. Bochenski (1951), 23; D¨ ring (1961), 287; Ackrill (1963), 69; D¨ ring (1966), 49; Sainati (1968),
u u
203“4; Blanch´/Dubucs (1970/96), 28“9; Dickason (1976), 11; Sorabji (1980), 106“7; Graham (1987),
e
115; Brakas (1988), 5; Zanatta (1992), 8“10; Weidemann (1994/2002), 47“51; D. Frede (1998), 88. Other
commentators (e.g. Maier (1899), 40“1, 44, 72; A. Mansion (1913/45), 10; Riondato (1957a), 7; Schuhl
(1960), 34; Adorno (1961), 291, 398; von Fritz (1962), 147, 148; Brandt (1965), 5“10; Magris (1977),
114“15, 122“6, 129; Montanari (1984/88), i 18, 142, ii 63) regard de Interpretatione as a late work.
95 Cf. Maier (1899), 28, 34; A. Becker (1936), 74; Blanch´/Dubucs (1970/96), 42; D. Frede (1970), 11,
e
81; von Fritz (1972), 243; Astroh (1981), 335, 337; D. Frede (1985), 81“2; von Kutschera (1986), 214,
216. Sainati (1968), 240“2 thinks that Int. 9 is later than the preceding eight chapters, but still early.
96 Cf. Celluprica (1977), 37“9.
97 Cf. Vollrath (1959), 24“5; Ackrill (1963), 128; Capozzi (1974), 320, 332; Weidemann (1994/2002),
200; Galluzzo (1997/98), 53. According to Aristotle, Antisthenes claimed both that it is impossible to
contradict and that it is impossible to speak falsely (see Top. 1.11, 104b 19“21; Metaph. 29, 1024b 32“4,
cf. Pl. Euthd. 285d7“286b6; Isocr. Hel. 1; Procl. in Cra. 37 12, 18“23).
Truth and Determinism in de Interpretatione 9 231
falsehood of present-tense assertions, while its second part suggests that
past- and future-tense assertions should behave with regard to truth and
falsehood in the same way as present-tense assertions. In general, nothing
in de Interpretatione™s ¬rst eight chapters suggests that there might be some
difference between past-, present-, and future-tense assertions in connec-
tion with truth and falsehood. Thus, when chapter 9 contrasts past- and
present-tense assertions with future-tense assertions, this contrast comes as
a surprise.98
(ii.iv) Although most of de Interpretatione was probably written at a rather
early stage of Aristotle™s life, the treatise at various points mentions works of
Aristotle which are probably later.99 Thus, the treatise probably underwent
some late revision.
(ii.v) Another passage from de Interpretatione is regarded by some com-
mentators100 as a later addition: chapter 13™s discussion of potentiality and
actuality (at 23a 21“6) presupposes ideas which are developed in the Meta-
physics and which commentators are disinclined to attribute to the early
stage of Aristotle™s thought to which the main bulk of de Interpretatione
should belong.
It might be objected that one passage of de Interpretatione itself (10,
a
20 31“6, discussed above) seems to commit Aristotle to Bivalence. How-
ever, even if this passage were to commit Aristotle to Bivalence, the com-
mitment would be nothing more than an implication of an aside: it might
well be the case that when Aristotle added chapter 9 to the main bulk of
de Interpretatione he failed to notice the implication of this aside and its
inconsistency with the additional chapter™s rejection of Bivalence.101

98 Cf. Sainati (1968), 240“1.
99 Chapter 1, 16a 8“9 refers to de Anima. Chapter 5, 17a 14“15 might be understood as referring to
Metaphysics Z and H, which are probably late works (cf. Magris (1977), 124). Chapter 10, 19b 31
refers to the Prior Analytics, whose analysis of sentences is often regarded as more mature than the
one offered in de Interpretatione 1“6. Chapter 11, 20b 26 refers to the Topics, which, however, were
probably written either before or at the same time as de Interpretatione. At 4, 17a 5“6 the study of
certain non-assertoric sentences is dismissed as more appropriate to rhetoric and poetics, or to the
Rhetoric and the Poetics (cf. Brandt (1965), 6). No other work of Aristotle™s refers to de Interpretatione.
100 Ackrill (1963), 153; Magris (1977), 124“5; Graham (1987), 99“100; Wildberg (1989), 195; Weidemann
(1994/2002), 457.
101 Other solutions are less plausible. Sorabji (1980), 95 suggests that according to an anti-realist
interpretation ˜Aristotle does not regard himself as rejecting Bivalence, but only as qualifying it with
a “yet”™. Whatever the merits of this suggestion, it is not viable on the interpretation of Int. 9 I
defended in the last section. Gaskin (1995), 180 thinks that in some of the above ˜contexts “true
or false” can, without undue strain, be read as “true, false, or true-or-false”™ (where ˜true-or-false™
expresses a third truth-value besides the standard truth and falsehood). I feel some ˜undue strain™
in the suggested reading: were Aristotle to recognise a third truth-value, it would be misleading of
him to claim that every assertion has one of these three truth-values by saying something like ˜Every
assertion is true or false™.
232 Truth and time
External evidence supporting anti-realist interpretations. At the beginning of
de Generatione et Corruptione 2.11 Aristotle says:
T 59 Since in the case of things that change continuously [. . .] we encounter that
which is successively and comes to be this after this with no intermission,
we must investigate whether there is anything it will be of necessity, or there
is nothing of this sort, but it may fail to come to be all things. For it is clear
that there are some [sc. things it may fail to come to be], and this is why ˜will
be™ and ˜is about to™102 are different. For what it is true to say that it will be,
this it must at some time be true to say that it is, whilst what it is now true
to say that it is about to be, there is nothing to prevent that it should not
come to be it “ for a man who is about to go for a walk could well not go
for a walk. (337a 34“337b 7)103
In T 59™s ¬rst part Aristotle considers two alternatives: are some of the
states a thing comes to be in necessary, i.e. necessitated by antecedent
circumstances, or are all these states contingent, i.e. not necessitated by
antecedent circumstances? Aristotle then goes on to argue that at least
some of the states a thing comes to be in are contingent. His argument
is of a ˜semantic™ character. It appeals to the difference between the truth
conditions for assertions whose predicative expression is a future-tense verb
and those of assertions whose predicative expression is a phrase consisting
of ˜is about to™ followed by an in¬nitive. The argument relies on two
assumptions. The ¬rst is that if an assertion whose predicative expression is
a future-tense verb is true at t, then at t it is necessary that the corresponding
present-tense assertion should be true later,104 and this in turn obviously
entails that at t it is necessary that the universal signi¬ed by the predicative
expression should later hold of the object signi¬ed by the subject. The
second assumption is that if an assertion whose predicative expression is
a phrase consisting of ˜is about to™ followed by an in¬nitive is true at t,
it does not follow that at t it is necessary that the corresponding present-
tense assertion should be true later, whence it does not follow that at t it is
necessary that the universal signi¬ed by the predicative expression should
later hold of the object signi¬ed by the subject.105 The existence of assertions

102 Here (337b 4) I read ˜m”llei™, a conjecture by Joachim (partly supported by Phlp. in GC 302, 25 and
306, 12). All manuscripts have ˜m”llon™, the reading printed by Bekker, Weise, D¨ bner, Forster, and
u
Mugler.
103 Cf. Div. Somn. 2, 463b 28“31.
104 I regard the relevant occurrences in T 59 of ˜will be™ (˜›stai™ at 337b 4) and ˜is™ (˜–st©n™ at 337b 5) as
place-holders for verbs in the future and in the present tense (Aristotle™s own example, at 337b 7,
does not contain forms of ˜to be™).
Aristotle™s remarks about assertions whose predicative expression is constructed around a ˜m”llei™ +
105
in¬nitive phrase match the ¬ndings of modern studies of Greek grammar: see e.g. Goodwin (1889),
20; Humbert (1945/60), 154, 168“9. In T 59, the relevant occurrences of forms of the English ˜to be
about to™ translate occurrences of forms of the Greek ˜m”llein™.
Truth and Determinism in de Interpretatione 9 233
of the second kind, i.e. assertions whose predicative expression consists of
˜is about to™ followed by an in¬nitive, is due to some of the states a thing
comes to be in being contingent.
What is important, for present purposes, is the ¬rst assumption: that if
an assertion whose predicative expression is a verb in the future tense is true
at t, then at t it is necessary that the corresponding present-tense assertion
should be true later. Anti-realist interpretations ¬nd a similar assumption
in Int. 9.106
106 Cf. Phlp. in GC 302, 34“303, 5; D. Frede (1970), 22“3; Seel (1982a), 243“4; C. J. F. Williams (1982),
197“8; D. Frede (1985), 41“2; Craig (1988), 13“16; Kullmann (1994/95), 300“3.
a p pe n d i x 1

10, 1051 b 1: the text
Metaph.




The evidence. At 1051b 1 the main witnesses present a variety of readings:
Ab and (probably) ps.-Alexander (in Metaph. 598, 1“2) have ˜kuriÛtata
¿n™; the ¬rst hand of E has ˜kuriÛtaton e«™; J and the second hand of
E have ˜kuriÛtata e«™; William of Moerbeke™s translation presupposes
˜kuriÛtata £™.
Brandis, Bekker, Weise, Schwegler, Bonitz, D¨ bner, Christ, and Jaeger
u
print ˜kuriÛtata ¿n™. Ross (followed by Tredennick and various com-
mentators)1 excises ˜kuriÛtata ¿n™ (he also contemplates the possibility
of transposing it after ˜t¼ m•n™ at 1051a 34). Jaeger suspects a lacuna between
˜kuriÛtata ¿n™ and ˜ˆlhq•v £ ye“dov™: he suggests ˜kuriÛtata ¿n <¡
oÉs©a, le©petai d• –piskope±n t¼ ¿n> ˆlhq•v £ ye“dov™.

An inconsistency? Many editors and commentators2 ¬nd the reading ˜kuriÛ-
tata ¿n™ of Ab at 1051b 1 hard to accept because in Metaphysics E 4 (= T 7),
at 1027b 31, Aristotle says that what ˜is™ in the sense of being true ˜is a differ-
ent thing that “is” from the things that “are” in the strict sense [kur©wv]™:
were the reading ˜kuriÛtata ¿n™ genuine, in Metaphysics 10 Aristotle
would be committing himself to the incompatible claim that what ˜is™ in
the sense of being true is what ˜is™ in the strictest sense. The fact that E 4,
at 1027b 28“9, contains a forward reference to 10 makes it particularly
implausible to assume that Aristotle should entertain such incompatible
views about what ˜is™ in the sense of being true. Moreover in de Anima 2.1,
at 412b 8“9, Aristotle says that actuality is what is meant when ˜unity and
being are spoken of in the strict sense [kur©wv]™.3 On the other hand, one
feels uneasy at ironing the inconsistency away by emending the text.

1 E.g. Oehler (1962/85), 179; Bormann (1982), 3.
2 Jaeger (1912), 51; Ross (1924), ii 274“5; Oehler (1962/85), 179; von Fragstein (1967), 145; Berti (1990),
111“13.
3 Cf. Berti (2000), 6.

234
Appendix 1 235
Solution (i). Jaeger4 tries to resolve the alleged inconsistency between E
4 and 10 by taking ˜kuriÛtata™ to mean something like ˜in the most
common or widespread sense™.5 So: in E 4 Aristotle would be saying that
˜being™ in the sense of being true is different from ˜being™ in the strict sense;
in 10 he would be saying that ˜being™ in the sense of being true is ˜being™ in

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