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For each point of a tree, there is only one backwards route (towards
the past). However, a point of the tree may have many alternative forward
routes (towards the future). In the case of the tree of time, this crucial
feature represents the idea that while the past is unique and determined,
the future is open, i.e. can take many different courses. With regard to
the openness of the future, it is important to be clear that the multiple
alternative forward routes do not represent mere epistemic alternatives: it
is not the case that the multiplicity of the forward routes represents our
ignorance of what the future will be like. Rather, the multiplicity of the
forward routes represents the fact that various alternative future evolutions
are possible. Another important feature is that none of the many forward
routes is privileged in the sense that it represents the future which will be
realised: all forward routes are on a par. Times are conceived of as intimately
tied to the possible world-states obtaining in them: for this reason we speak
Appendix 6 271
of different future possible times rather than of possible future events or
states at the same time.11
The properties of the tree of time reduce to those of its ordering relation
<. This relation, which obtains only between times, is asymmetric and
transitive (and is therefore a strict partial order), has no ˜beginning™ and no
˜end™, and is connected (for any two times there is a further time preceding
both). The property that characterises the tree-structure is that any two
distinct times that are followed by one and the same time are linked by <.
Here is the full formulation:
[112] ∀t ∀s (t < s ’ Xt & Xs).
[113] ∀t ∀s (t < s ’ ¬s < t).
[114] ∀t ∀s ∀u (t < s & s < u ’ t < u).
[115] ∀t ∀s ∀u (t < u & s < u ’ t < s ∨ t = s ∨ s < t).
[116] ∀t ∀s (Xt & Xs ’ ∃u (u < t & u < s)).

Set theory. The expanded semantic theory to be presented relies on a mini-
mal amount of set theory:
[117] ∀x ∃y (My & ∀z (z ∈ y ” z = x)).
[118] ∀x ∀y (Mx & My ’ ∃z (Mz & ∀u (u ∈ z ” u ∈ x ∨ u ∈ y))).
[119] ∀x (Mx & ∀t (t ∈ x ’ Xt) & ∀t ∀s (t ∈ x & s ∈ x ’ t < s ∨ t = s
∨ s < t) ’ ∃u (Mu & ∀t (t ∈ u ’ Xt) & ∀t ∀s (t ∈ u & s ∈ u ’
t < s ∨ t = s ∨ s < t) & ∀y (My & ∀t (t ∈ y ’ Xt) & ∀t ∀s (t ∈ y &
s ∈ y ’ t < s ∨ t = s ∨ s < t) & ∀t (t ∈ u ’ t ∈ y) ’ u = y) & ∀t
(t ∈ x ’ t ∈ u))).
Proposition [117] assumes that for every object there is its singleton, i.e. the
set whose only element is that object. Proposition [118] assumes that for any
two sets there is their union, i.e. the set whose elements are precisely the
elements of those two sets. Proposition [119] makes instead a rather strong
assumption: that every linearly ordered set of times can be extended to a
maximal linearly ordered set of times. This assumption can be regarded as

11 For the representation of time as a tree cf. McCall (1966), 280“1; Prior (1967a), 126“7; Rescher (1968),
209“15; Thomason (1970), 265; Boudot (1973), 454“8; von Wright (1974), 162“6; Code (1976), 184;
McArthur (1976), 37“41; M. J. White (1980), 288; Thomason (1984), 141“2; Yourgrau (1985), 549“50;
Lucas (1989), 99“102, 135“9; Landman (1991), 101“3; Weidemann (1994/2002), 251“4, 285; Le´ n o
(1996), 385“6, 388“9; Mignucci (1996b), 291“2; Strobach (1998), 106“8.
272 The failure of Bivalence
an instance of the Maximal Chain Principle, which is equivalent to Zorn™s
Lemma.12

Branches through the tree of time. A branch is a maximal linearly ordered set
of times:
[120] ∀x (Bx ” Mx & ∀t (t ∈ x ’ Xt) & ∀t ∀s (t ∈ x & s ∈ x ’ t < s ∨
t = s ∨ s < t) & ∀y (My & ∀t (t ∈ y ’ Xt) & ∀t ∀s (t ∈ y & s ∈ y ’
t < s ∨ t = s ∨ s < t) & ∀t (t ∈ x ’ t ∈ y) ’ x = y)).
Every element of a branch is a time:
[121] ∀x ∀t (Bx & t ∈ x ’ Xt).
The proof is trivial.
Whatever precedes an element of a branch is also an element of that branch:
[122] ∀x ∀t ∀s (Bx & t ∈ x & s < t ’ s ∈ x).
This is a well-known result of the theory of trees, and I restrict myself to
sketching the proof. Let a, b, and c be such that a is a branch, b is an element
of it, and c precedes b. Let d be the union of a with the singleton of c. d
can be shown to be a linearly ordered set of times. Since a is a subset of d
and (being a branch) is a maximal linearly ordered set of times, a must be
identical to d. Since c is an element of d, it is also an element of a.
Every time lies on some branch or other:
[123] ∀t (Xt ’ ∃x (Bx & t ∈ x)).
I again restrict myself to sketching the (trivial) proof. Let a be a time. Let
b be the singleton of a. Obviously, b is a linearly ordered set of times. By
[119], b can be extended to a maximal linearly ordered set of times c. Then
c is a branch and a is an element of it.
The day after. One straightforward assumption is that every time that lies
within the day after a given time is preceded by that given time:
[124] ∀t ∀s (Wts ’ t < s).
Another assumption is that on every branch every time is followed by a time
within the day that follows its day “ in short, no branch has a ˜last day™:
[125] ∀x ∀t (Bx & t ∈ x ’ ∃s (s ∈ x & Wts)).

12 Cf. Landman (1991), 115“17.
Appendix 6 273
Correctness is relative to times as well as to their possible futures. Consider a
time t with several ˜forward routes™ stemming from it, i.e. several alternative
possible futures. How can a future-tense assertion (i.e. an utterance of an
instance of ˜It will be the case that a™ or ˜Tomorrow it will be the case
that a™) be evaluated at t? One might lack adequate grounds for such an
evaluation: it might be the case that at t the assertion is correct on one of
its several possible futures but not on another. The best one can then do is
to evaluate the assertion as correct, or not correct, at t relatively to one of its
several possible futures. For such a reason the notion of correctness is here
regarded as relative not only to a time t, but also to a possible future of t,
i.e. as relative to t as well as to a branch of which t is an element (a possible
future of t determines a complete branch because t™s past is unique).13

Correctness at a time on a branch. Present-tense predicative assertions are
correct at a time on a branch just in case they are ˜true™ at that time according
to appendix 5™s de¬nition of truth:
[126] ∀x (Sn x ’ ∀s ∀t (Bs & t ∈ s ’ (Cxts ” Txt))).
A past-tense (future-tense) predicative assertion is correct at a time on a
branch just in case the present-tense predicative assertion of which it is a
past (future) in¬‚ection is correct at some earlier (later) time on the same
branch.14 Analogously, a ˜tomorrow™-assertion is correct at a time t on a
branch just in case the present-tense predicative assertion of which it is a
˜tomorrow™-in¬‚ection is correct on the same branch at some time that lies
within the day after the day in which t lies.
[127] ∀x ∀y (Sn y & Ib xy ’ ∀s ∀t (Bs & t ∈ s ’ (Cxts ” ∃u (u ∈ s &
u < t & Cyus)))).
[128] ∀x ∀y (Sn y & If xy ’ ∀s ∀t (Bs & t ∈ s ’ (Cxts ” ∃u (u ∈ s &
t < u & Cyus)))).
[129] ∀x ∀y (Sn y & It xy ’ ∀s ∀t (Bs & t ∈ s ’ (Cxts ” ∃u (u ∈ s & Wtu
& Cyus)))).
A negative (disjunctive) assertion is correct at a time on a branch just in
case the assertion of which it is the negation is not correct (at least one of
its disjuncts is correct) at that time on that branch:
[130] ∀x ∀y ((Sn y ∨ Sb y ∨ Sf y ∨ St y) & Ic xy ’ ∀s ∀t (Bs & t ∈ s ’
(Cxts ” ¬Cyts))).
13 Cf. Prior (1967a), 122“7; Thomason (1970), 268“70; (1984), 133“4; Weidemann (1994/2002), 256.
14 Cf. n. 82 of ch. 7.
274 The failure of Bivalence
[131] ∀x ∀y ∀z ((Sn y ∨ Sb y ∨ Sf y ∨ St y ∨ Sc y) & (Sn z ∨ Sb z ∨ Sf z ∨ St z ∨
Sc z) & Iv xyz ’ ∀s ∀t (Bs & t ∈ s ’ (Cxts ” Cyts ∨ Czts))).

Tokens of the same type are either both or neither correct at the same time on the
same branch. The ¬rst result in this area concerns present-tense predicative
assertions:
[132] ∀x ∀y (Sn x & Sn y & Oxy ’ ∀s ∀t (Bs & t ∈ s ’ (Cxts ” Cyts))).
Let a and b be such that Sn a & Sn b & Oab. Since Sn b, Vb (by [57]). Then
Sn a & Vb & Oab, so that (by [106]) ((Sa a & Sa b) ∨ (Se a & Se b) ∨ (Si a &
Si b) ∨ (So a & So b) ∨ (Sy a & Sy b) ∨ (Sd a & Sd b)) & Ck ab & Ch ab. Since
Sn a & Sn b & Ck ab, ∃z (Kza & Kzb) (by [64]): let then c be such that Kca
& Kcb. Similarly, since Sn a & Sn b & Ch ab, ∃z (Hza & Hzb) (by [63]): let
then d be such that Hda & Hdb. Let e and f be such that Be & f ∈ e. Then
Xf (by [121]). Since (Sa a & Sa b) ∨ (Se a & Se b) ∨ (Si a & Si b) ∨ (So a & So b)
∨ (Sy a & Sy b) ∨ (Sd a & Sd b), distinguish six cases corresponding to these
six disjuncts.
(1) Sa a & Sa b. Since Sn a, ∃y (Kya & ∀z (Kza ’ z = y) & Uy) (by [60]):
let then g be such that Kga & ∀z (Kza ’ z = g) & Ug. Since Sa a, ∃y (Hya
& ∀z (Hza ’ z = y) & Uy) (by [61]): let then h be such that Hha & ∀z
(Hza ’ z = h) & Uh. Analogously, since Sn b, ∃y (Kyb & ∀z (Kzb ’ z = y)
& Uy) (by [60]): let then i be such that Kib & ∀z (Kzb ’ z = i) & Ui.
Since Sa b, ∃y (Hyb & ∀z (Hzb ’ z = y) & Uy) (by [61]): let then j be such
that Hjb & ∀z (Hzb ’ z = j) & Uj. Since Sn a, ∀s ∀t (Bs & t ∈ s ’ (Cats
” Tat)) (by [126]), so that Cafe ” Taf. Similarly, since Sn b, ∀s ∀t (Bs &
t ∈ s ’ (Cbts ” Tbt)) (again by [126]), so that Cbfe ” Tbf. Since Sa a,
∀t (Xt ’ (Tat ” ∃y ∃z (Kya & Hza & Cu yzt))) (by [66]). Since Xf, Taf
” ∃y ∃z (Kya & Hza & Cu yzf ). Analogously, since Sa b, ∀t (Xt ’ (Tbt
” ∃y ∃z (Kyb & Hzb & Cu yzt))) (again by [66]). Since Xf, Tbf ” ∃y ∃z
(Kyb & Hzb & Cu yzf ). Suppose Cafe. Then Taf. Then ∃y ∃z (Kya & Hza
& Cu yzf ). Let then k and l be such that Kka & Hla & Cu klf. Since Kka &
Kca & ∀z (Kza ’ z = g), k = g & c = g, so that k = c; since Hla & Hda
& ∀z (Hza ’ z = h), l = h & d = h, so that l = d. Since Cu klf & k = c
& l = d, Cu cdf. Then Kcb & Hdb & Cu cdf, so that ∃y ∃z (Kyb & Hzb &
Cu yzf ). Then Tbf, so that Cbfe. Thus: Cafe ’ Cbfe. Vice versa, suppose
Cbfe. Then Tbf. Then ∃y ∃z (Kyb & Hzb & Cu yzf ). Let then m and n be
such that Kmb & Hnb & Cu mnf. Since Kmb & Kcb & ∀z (Kzb ’ z = i),
m = i & c = i, so that m = c; since Hnb & Hdb & ∀z (Hzb ’ z = j),
n = j & d = j, so that n = d. Since Cu mnf & m = c & n = d, Cu cdf. Then
Kca & Hda & Cu cdf, so that ∃y ∃z (Kya & Hza & Cu yzf ). Then Taf, so
that Cafe. Thus: Cbfe ’ Cafe. Hence Cafe ” Cbfe.
Appendix 6 275
The remaining cases (2)“(6) are treated similarly: in each of them we
have Cafe ” Cbfe. Thus, in all cases, Cafe ” Cbfe. But e and f were
arbitrary. Then ∀s ∀t (Bs & t ∈ s ’ (Cats ” Cbts)). But a and b were
arbitrary. Then ∀x ∀y (Sn x & Sn y & Oxy ’ ∀s ∀t (Bs & t ∈ s ’ (Cxts ”
Cyts))).
More results of the same type can be proved on the basis of [132]:
[133] ∀x ∀y (Sb x & Sb y & Oxy ’ ∀s ∀t (Bs & t ∈ s ’ (Cxts ” Cyts))).
[134] ∀x ∀y (Sf x & Sf y & Oxy ’ ∀s ∀t (Bs & t ∈ s ’ (Cxts ” Cyts))).
[135] ∀x ∀y (St x & St y & Oxy ’ ∀s ∀t (Bs & t ∈ s ’ (Cxts ” Cyts))).
[136] ∀x ∀y (Sc x & Sc y & Oxy ’ ∀s ∀t (Bs & t ∈ s ’ (Cxts ” Cyts))).
[137] ∀x ∀y (Sv x & Sv y & Oxy ’ ∀s ∀t (Bs & t ∈ s ’ (Cxts ” Cyts))).

Truth-value gaps: (i) quasi-formal considerations:
(1) We want to think of the truth of an assertion as being determined
exclusively by a time. We shall thereby speak of an assertion a as being true
at a time t. Analogously, we want to think of the falsehood of an assertion
as being determined exclusively by a time. We shall thereby speak of a as
being false at t.
(2) In a preceding subsection it was made clear that t is not in general
enough to evaluate a future-tense assertion as true or false: a possible future
of t (i.e. one of the possibly many ˜forward routes™ stemming from t) may
need to be taken into account. Say that a valuation of a based on t is a
valuation of a carried out with reference to t and, moreover, one possible
future of t.
(3) We want to think that whether a is true at t depends on the valuations
of a which are based on t (i.e. those valuations of a each of which is carried
out with reference to t and, moreover, one possible future of t). Analogously,
we want to think that whether a is false at t depends on the valuations of a
which are based on t.
(4) As far as the valuations of a based on t are concerned, what is deter-
mined exclusively by t is only what is common to all valuations of a based
on t. Hence, as far as the valuations of a based on t are concerned, what
is determined exclusively by t can only be either that a is correct at t on
every possible future of t, or else that a is correct at t on no possible future
of t.
These points suggest (i) that a should be true at t if a is correct at t on
every possible future of t; (ii) that a should be false at t if a is correct at t on no
276 The failure of Bivalence
possible future of t; and (iii) that a should be neither true nor false, i.e., indet-
erminate, at t if a is correct at t on some but not all possible futures of t.15

Truth-value gaps: (ii) intuitive considerations. It is worthwhile re¬‚ecting
on the intuitions behind the last subsection™s quasi-formal considerations.
Think of t as the present moment, and think of the forward routes stemming
from t as the possible futures of t: the past of t is unique, but its future
branches out into several alternatives “ this is how the world now really is.
By requiring that the truth or falsehood of an assertion a should be
determined exclusively by t,16 we are requiring that the truth or falsehood
of a should be determined by how the world is at present. At present the
world is such as to be unique in the direction of the past, but branching
out into alternative possible futures. Up to now the world has been, and
is, going in precisely one way, but from now onwards it could go in several
ways. If a is a future-tense assertion, then how the world is at present
can determine a as true (false) only if a is correct on every (no) possible
future development. Otherwise (i.e. if a is correct on some possible future
developments but not on others), how the world is at present is unable
to determine a as true, and is also unable to determine a as false. In such
circumstances, at present a is neither true nor false, i.e. is indeterminate.17

Truth-value gaps: (iii) truth does not enjoy the disquotational property. Clearly,
the indeterminacy of truth-value of a at the present moment (whose past
is unique whereas its future branches out into several possible evolutions)
is compatible with a™s turning out to be correct ˜on the actual evolution
(whatever that may be) of the present™. Hence, a™s truth now is not entailed
by a™s turning out to be correct ˜on the actual evolution (whatever that
may be) of the present™. The converse entailment holds trivially: if a is true
now, it is correct on every possible evolution of the present, and is therefore
correct ˜on the actual evolution (whatever that may be) of the present™. In
this sense, asserting that a is true now is something stronger than asserting
a: it might be the case that by asserting a, one commits oneself (merely)
to a™s turning out to be correct ˜on the actual evolution (whatever that
15 Cf. van Fraassen (1966), 487, 494; Prior (1967a), 136; Thomason (1970), 272“3; Seeskin (1971), 770“3;
Haack (1974/96), 85“6, 90; M. J. White (1980), 288“91; Thomason (1984), 144“6; Bencivenga et al.
(1986/91), 40“5; Sayward (1989), 129; Gaskin (1994), 85; Weidemann (1994/2002), 320; Williamson
(1994), 144, 156“7; Vuillemin (1996), 160“1; Hafemann (1999), 129.
16 Cf. point (1) of the preceding subsection.
17 Cf. Hildebrand (1884), vi; Prior (1953), 322“3; Lenz (1957), 773“4; Ackrill (1963), 140“1; Hintikka
(1964/73a), 172“3; McCall (1966), 275“6; Patzig (1973), 923; von Wright (1974), 166“7; Dickason
(1976), 20“2; Wolf (1979), 114, 417; Weidemann (1980), 420; M. J. White (1981), 236, 240; Seel
(1982a), 241; M. J. White (1985), 66“7; Craig (1988), 23, 58; D. Frede (1990), 202; Weidemann
(1994/2002), 257“8; Inciarte (1999), 146“7.
Appendix 6 277
may be) of the present™, but does not commit oneself to a™s being true
now (because “ the speaker thinks “ the present branches out into several
possible evolutions, and a is correct on some but not all of these possible
evolutions). Thus, the direction ˜from fact to truth™ of the equivalence that
constitutes the disquotational property of truth can fail.18

Truth-value gaps: (iv) objections and answers. One might object: ˜If the claims
made in the preceding subsections are correct, truth lacks the disquotational
property; but truth enjoys the disquotational property;19 hence some of the
claims made in the preceding subsections are not correct.™ The objection
could be rubbed in: consider a man who one day makes a prediction by
uttering the sentence ˜A sea-battle will take place tomorrow™. The day after,
a sea-battle actually takes place. If the preceding subsections™ claims are
correct, this man cannot say ˜The remark I made yesterday was true™.
This objection can be answered by assuming that there are several notions
of truth, and that the claims made in the preceding subsections concern only
one of these notions of truth “ a ˜loaded™ notion of truth. In particular,
the last subsection™s claim about the lack of the disquotational property
concerns only this ˜loaded™ notion of truth. Obviously, this claim about the
˜loaded™ notion of truth is consistent with the claim that other notions of
truth enjoy the disquotational property. The idea here is that apart from
the ˜loaded™ notion of truth, there is also a ˜plain™ notion of truth: while
the ˜loaded™ notion of truth lacks the disquotational property, the ˜plain™
notion enjoys it.20
But what guarantees that the ˜loaded™ notion of truth should be a notion
of truth at all? Does not its lack of the disquotational property show that it
is not a notion of truth? This development of the objection can be answered
by means of two arguments.
(iv.i) One of our most deeply entrenched (albeit hazy) intuitions about
truth is that for an assertion or a belief to be true is to ˜match™ or ˜correspond
to™ the world. Now, the notion discussed in the preceding subsections is
that of an assertion corresponding to as much of the world as there is at a
given time. Hence, the notion discussed in the preceding subsections is a
notion of truth.
(iv.ii) The notion discussed in the preceding subsections matches certain
tensed uses of the phrase ˜. . . is true™. If at time t it is not yet certain whether

18 Cf. McCall (1966), 274“5; Gaskin (1994), 87; (1995), 85.
19 Cf. Tarski (1933), 187“8; Williamson (1994), 162; K. Taylor (1998), 116.
20 Cf. Peter de Rivo apud Baudry (1950), 94“5, 97“9, 221“3; Albritton (1957), 30, 33; McCall (1966),
270“3, 274“7; von Wright (1974), 174“7; (1984b), 5“10; Weidemann (1994/2002), 255“61; Mignucci
(1996b), 295“6.
278 The failure of Bivalence
at the later time t it will be the case that a, at t one can react to a statement
to the effect that at t it will be the case that a by saying ˜That is not yet
true™. Situations of this kind arise when one reacts to the worry that an as
yet uncertain future calamity could come about: e.g. Jim is on the verge
of bankruptcy and asserts that he is going to lose all his money, but Fred,
who optimistically thinks that matters might be mended, answers by saying
˜That is not yet true™.21 Moreover, if at t it is not yet certain whether at the
later time t it will be the case that a but at t , later than t but still earlier
than t , it becomes certain that at t it will be the case that a, at t one
can react to a statement to the effect that at t it will be the case that a
by saying ˜That is now true™ or ˜That has become true™. Situations of this
sort can arise when what one feared might fail to come about becomes
certain to be going to happen: e.g. Jim has been believing for a long time
that he was going to obtain his share of the inheritance, but only after the
legal uncertainties have been sorted out can his lawyer (who had previously
been reacting to Jim™s remarks by expressing doubt) say ˜Your belief is at
last true™. The fact that the notion discussed in the preceding subsections
corresponds to these uses of ˜. . . is true™ suggests that it is a notion of truth.
According to this argument, the ˜loaded™ notion of truth corresponds to
some tensed uses of ˜. . . is true™ while the ˜plain™ notion corresponds to
other (tensed or tenseless) uses of that phrase.22
The ˜loaded™ and the ˜plain™ notions of truth seem to be connected with
two different ways of regarding the world™s history. The ˜loaded™ notion is
connected to a viewpoint ˜inside™ the world™s history, at a certain stage of it
at which the past is uniquely determined while the future branches out in
several possible alternatives: according to the ˜loaded™ notion of truth, an
assertion is true at a certain time just in case it corresponds to the world at
the stage it has reached at that time. The ˜plain™ notion of truth is connected
with a viewpoint ˜outside™ the world™s history, which is ˜given™ in its totality:
according to the ˜plain™ notion, an assertion is true just in case it corresponds
to the whole world™s history.23 Note that the viewpoint corresponding to
the ˜loaded™ notion of truth, i.e. the viewpoint ˜inside™ the world™s history,
is likely to be that of an agent for whom it is important to regard the future
as at least partially ˜open™.
A further possible objection is that the ˜loaded™ notion of truth can be
ignored because the ˜plain™ notion of truth is more important. However,
this objection makes a dubious move: even granting that the ˜plain™ notion
21 Cf. McCall (1966), 273.
22 On the uses of ˜. . . is true™ corresponding to the ˜loaded™ notion of truth see von Wright (1974), 175.
23 Cf. Peter de Rivo apud Baudry (1950), 94“5, 97“9; Burrell (1964), 47“50; Hartshorne (1965), 58;
McCall (1966), 270“3, 274, 279“81; Jeffrey (1979), 253; M. J. White (1981), 232“5.
Appendix 6 279
of truth is more important, it does not follow that the ˜loaded™ notion can
be ignored. In natural language the tensed uses of ˜. . . is true™ that introduce
the ˜loaded™ notion are common: why should one ignore them? Codifying
the rules that govern their behaviour seems a worthwhile enterprise.

Truth-value gaps: (v) formalities. Let me now state rigorously the principles
which in the preceding subsections were only vaguely characterised:
[138] ∀x ∀t (Sx & Xt ’ (T *xt ” ∀s (Bs & t ∈ s ’ Cxts))).
[139] ∀x ∀t (Sx & Xt ’ (F *xt ” ∀s (Bs & t ∈ s ’ ¬Cxts))).

The two properties of truth coincide on present-tense predicative assertions:
[140] ∀x ∀t (Sn x & Xt ’ (Txt ” T *xt)).
Let a and b be such that Sn a & Xb. Since Sn a, ∀s ∀t (Bs & t ∈ s ’
(Cats ” Tat)) (by [126]) and Sa (by [105]). Since Sa & Xb, T *ab ” ∀s
(Bs & b ∈ s ’ Cabs) (by [138]).
Suppose that Tab. Let c be such that Bc & b ∈ c. Since ∀s ∀t (Bs &
t ∈ s ’ (Cats ” Tat)), Cabc ” Tab. Then Cabc. But c was arbitrary. Then
∀s (Bs & b ∈ s ’ Cabs). Hence T *ab. Thus Tab ’ T *ab. Vice versa,
suppose that T *ab. Then ∀s (Bs & b ∈ s ’ Cabs). Since Xb, ∃x (Bx &
b ∈ x) (by [123]). Let then d be such that Bd & b ∈ d. Then Cabd and Cabd
” Tab. Then Tab. Thus T *ab ’ Tab. Hence Tab ” T *ab. But a and b
were arbitrary. Then ∀x ∀t (Sn x & Xt ’ (Txt ” T *xt)), i.e. [140] holds.

Bivalence fails for ˜tomorrow™-assertions. Consider the tree of time partially
illustrated by the following diagram: m


l


n
Part of the information encoded by this diagram is that Xl & Xm & Xn &
Dlm & Dln & Dmn (i.e. l, m, and n are distinct times) & l < m & l < n.
Let j and k be such that Bj & l ∈ j & m ∈ j & Bk & l ∈ k & n ∈ k (i.e. j
is a branch through l and m, and k is a branch through l and n).
Let Wlm (i.e. m lies within the day after the day within which l lies).
Let c and d be such that Pcdm & ∀t (t ∈ k ’ ¬Pcdt) (i.e. c is predicated
of d at m, but at no time on branch k is c predicated of d ).
Let a and b be such that Sy b & It ab & Kcb & Hdb (i.e. a is a ˜tomorrow™-
assertion constructed from the singular af¬rmative present-tense predicative
280 The failure of Bivalence
assertion b, c is signi¬ed by the predicate of b, and d is signi¬ed by the subject
of b). Since Sy b, Sn b (by [58]). Then Sn b & It ab, so that ∃y (Sn y & It ay).
Then (by [101]) St a, so that (by [105]) Sa.
Since Sy b, ∃y (Hyb & ∀z (Hzb ’ z = y) & Iy) (by [62]). Let then e be
such that Heb & ∀z (Hzb ’ z = e) & Ie. Since Sn b, ∃y (Kyb & ∀z (Kzb
’ z = y) & Uy) (by [60]). Let then f be such that Kfb & ∀z (Kzb ’
z = f ) & Uf.
Suppose T *al. Since Sa & Xl, T *al ” ∀s (Bs & l ∈ s ’ Cals) (by [138]).
Then ∀s (Bs & l ∈ s ’ Cals). Since Bk & l ∈ k, Calk. Since Sn b & It ab, ∀s
∀t (Bs & t ∈ s ’ (Cats ” ∃u (u ∈ s & Wtu & Cbus))) (by [129]). Since
Bk & l ∈ k, Calk ” ∃u (u ∈ k & Wlu & Cbuk). Then ∃u (u ∈ k & Wlu
& Cbuk). Let then g be such that g ∈ k & Wlg & Cbgk. Since Sn b, ∀s ∀t
(Bs & t ∈ s ’ (Cbts ” Tbt)) (by [126]). Since Bk & g ∈ k, Cbgk ” Tbg.
Hence Tbg. Since Bk & g ∈ k, Xg (by [121]). Since Sy b and Xg, Tbg ” ∃y
∃z (Kyb & Hzb & Cs yzg) (by [70]). Hence ∃y ∃z (Kyb & Hzb & Cs yzg).
Let then h and i be such that Khb & Hib & Cs hig. Since Khb & Kcb & ∀z
(Kzb ’ z = f ), h = f & c = f, so that h = c; similarly, since Hib & Hdb
& ∀z (Hzb ’ z = e), i = e & d = e, so that i = d. Since Cs hig & h = c
& i = d, Cs cdg. Then (by [76]) Pcdg. Since g ∈ k & ∀t (t ∈ k ’ ¬Pcdt),
¬Pcdg, which yields a contradiction. Hence ¬T *al.
Suppose F *al. Since Sa & Xl, F *al ” ∀s (Bs & l ∈ s ’ ¬Cals) (by
[139]). Then ∀s (Bs & l ∈ s ’ ¬Cals). Since Bj & l ∈ j, ¬Calj. Since Pcdm,
Cs cdm (by [76]). Then Kcb & Hdb & Cs cdm, so that ∃y ∃z (Kyb & Hzb &
Cs yzm). Since Sy b and Xm, Tbm ” ∃y ∃z (Kyb & Hzb & Cs yzm) (by [70]).
Hence Tbm. Since Sn b, ∀s ∀t (Bs & t ∈ s ’ (Cbts ” Tbt)) (by [126]).
Since Bj & m ∈ j, Cbmj ” Tbm. Hence Cbmj. Since m ∈ j & Wlm &
Cbmj, ∃u (u ∈ j & Wlu & Cbuj). Since Sn b & It ab, ∀s ∀t (Bs & t ∈ s ’
(Cats ” ∃u (u ∈ s & Wtu & Cbus))) (by [129]). Since Bj & l ∈ j, Calj ” ∃u
(u ∈ j & Wlu & Cbuj). Then Calj, which contradicts a previous result.
Hence ¬F *al.
Thus: St a & Xl & ¬T *al & ¬F *al. In other words, Bivalence fails for
some ˜tomorrow™-assertion.
A similar argument, based on the same diagram, establishes that Biva-
lence fails for some future-tense predicative assertion: take a and b to be
such that Sy b & If ab & Kcb & Hdb, and establish that Sf a & Xl & ¬T *al
& ¬F *al.

Excluded Middle is valid: (i) general considerations. In what sense does Int. 9
endorse Excluded Middle? Surely not in the sense of claiming that every dis-
junctive assertion with contradictory disjuncts is always true, or necessarily
Appendix 6 281
true. Again, not in the sense of claiming, with regard to certain disjunctive
assertions with contradictory disjuncts, that they are always true, or neces-
sarily true “ e.g. Aristotle does not claim that utterances of ˜A sea-battle will
take place tomorrow or a sea-battle will not take place tomorrow™ are always
true, or necessarily true. In general, Int. 9™s endorsement of Excluded Mid-
dle does not involve mentioning disjunctive assertions with contradictory
disjuncts.
Int. 9™s endorsement of Excluded Middle involves using some disjunctive
assertion whose disjuncts are future in¬‚ections of contradictory assertions
to state that something is necessary. Here is what Aristotle says:
It is necessary that everything should either be or not be, and either be going to
be or not [. . .]. 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. (19a 28“32 < T53)
Hence, to establish the coherence of Int. 9, it is not necessary to show
that every disjunctive assertion with contradictory disjuncts is always true,
or that every disjunctive assertion whose disjuncts are future in¬‚ections
of contradictory assertions is always true.24 However, showing that every
disjunctive assertion of the kinds described is always true suf¬ces to establish
the coherence of Int. 9. For, if every such disjunctive assertion is always true,
then in particular it is true before any given time. Then, on the basis of the
deterministic argument whose validity he accepts, Aristotle is justi¬ed in
using the disjunctive assertion to state antecedent necessity (ineluctability).
For instance, if an utterance of ˜Tomorrow a sea-battle will take place or
tomorrow a sea-battle will not take place™ is true now, Aristotle is justi¬ed
in saying that it is now necessary that either tomorrow a sea-battle will take
place or tomorrow a sea-battle will not take place. The present semantic
theory can show that every disjunctive assertion of the kinds described is
always true.

Excluded Middle is valid: (ii) formulation with ˜internal negation™. Aristotle
does not recognise ˜external negation™, i.e. an operator ˜it is not the case
that . . .™ whose utterances attach to complete sentences.25 Hence, although
the present semantic theory does have ˜external negation™, appealing to it
would hardly count as a vindication of Aristotle. However, in the present

24 Cf. Linsky (1954), 250“1; D. Frede (1970), 75“6; Sorabji (1980), 94; D. Frede (1985), 77; Weidemann
(1994/2002), 319.
25 However he does sometimes use ˜external negation™: see Int. 11, 20b 35“6.
282 The failure of Bivalence
semantic theory it can be shown that every disjunction whose disjuncts
are ˜tomorrow™-assertions in¬‚ected from contradictory present-tense pred-
icative assertions is always true (this includes utterances of ˜Tomorrow a
sea-battle will take place or tomorrow a sea-battle will not take place™). Here
are the precise formulation and the proof:
[141] ∀x ∀y ∀z ∀u ∀v (Iv xyz & It yu & It zv & ((Sa u & So v) ∨ (Se u & Si v) ∨
(Si u & Se v) ∨ (So u & Sa v) ∨ (Sy u & Sd v) ∨ (Sd u & Sy v)) & Ck uv &
Ch uv ’ ∀t (Xt ’ T *xt)).
Let a, b, c, d, and e be such that Iv abc & It bd & It ce & ((Sa d & So e) ∨ (Se d
& Si e) ∨ (Si d & Se e) ∨ (So d & Sa e) ∨ (Sy d & Sd e) ∨ (Sd d & Sy e)) & Ck de &
Ch de. Since (Sa d & So e) ∨ (Se d & Si e) ∨ (Si d & Se e) ∨ (So d & Sa e) ∨ (Sy d &
Sd e) ∨ (Sd d & Sy e), it follows that (Sa d ∨ Se d ∨ Si d ∨ So d ∨ Sy d ∨ Sd d ) &
(Sa e ∨ Se e ∨ Si e ∨ So e ∨ Sy e ∨ Sd e). Then Sn d & Sn e (by [58]). Then Sn d
& It bd, so that ∃y (Sn y & It by), whence St b (by [101]). Similarly, we have
Sn e & It ce, so that ∃y (Sn y & It cy), whence St c (again by [101]). Then (Sn b
∨ Sb b ∨ Sf b ∨ St b ∨ Sc b) & (Sn c ∨ Sb c ∨ Sf c ∨ St c ∨ Sc c) & Iv abc, so that
∃y ∃z ((Sn y ∨ Sb y ∨ Sf y ∨ St y ∨ Sc y) & (Sn z ∨ Sb z ∨ Sf z ∨ St z ∨ Sc z) &
Iv ayz). Then (by [103]) Sv a. Then (by [105]) Sa. Since Sn d & Sn e & Ck de &
Ch de, Ck ed & Ch ed (by [83]).
Let Xf. Let g be such that Bg & f ∈ g. Then ∃s (s ∈ g & Wfs) (by [125]).
Let then h be such that h ∈ g & Wf h. Since Bg & h ∈ g, Xh (by [121]).
Distinguish two cases.
(1) Suppose that Cehg. Then h ∈ g & Wf h & Cehg, so that ∃u (u ∈ g &
Wfu & Ceug). Since Sn e & It ce, ∀s ∀t (Bs & t ∈ s ’ (Ccts ” ∃u (u ∈ s &
Wtu & Ceus))) (by [129]). Since Bg & f ∈ g, Ccfg ” ∃u (u ∈ g & Wfu &
Ceug). Hence Ccfg, so that Cbfg ∨ Ccfg.
(2) Suppose that ¬Cehg. Since Sn e, ∀s ∀t (Bs & t ∈ s ’ (Cets ” Tet))
(by [126]). Since Bg & h ∈ g, Cehg ” Teh. Hence ¬Teh. Since (Sa d & So e)
∨ (Se d & Si e) ∨ (Si d & Se e) ∨ (So d & Sa e) ∨ (Sy d & Sd e) ∨ (Sd d & Sy e),
distinguish four subordinate cases. (2.1) If (Sa d & So e) ∨ (Se d & Si e), then
((Sa d & So e) ∨ (Se d & Si e)) & Ck de & Ch de. Then (by [90]) ∀t (Xt ’
(Tdt ” ¬Tet)). Since Xh, Tdh ” ¬Teh. Hence Tdh. (2.2) If (Si d
& Se e) ∨ (So d & Sa e), then ((Sa e & So d ) ∨ (Se e & Si d )) &
Ck ed & Ch ed. Then (again by [90]) ∀t (Xt ’ (Tet ” ¬Tdt)).
Since Xh, Teh ” ¬Tdh. Then ¬¬Tdh, whence Tdh. (2.3) If Sy d
& Sd e, then Sy d & Sd e & Ck de & Ch de. Then (by [95]) ∀t
(Xt ’ (Tdt ” ¬Tet)). Since Xh, Tdh ” ¬Teh. Hence Tdh. (2.4) If Sd d &
Sy e, then Sy e & Sd d & Ck ed & Ch ed. Then (again by [95]) ∀t (Xt ’ (Tet
” ¬Tdt)). Since Xh, Teh ” ¬Tdh. Then ¬¬Tdh, whence Tdh. Thus, in
Appendix 6 283
each of the four subordinate cases, Tdh. Since Sn d, ∀s ∀t (Bs & t ∈ s ’
(Cdts ” Tdt)) (by [126]). Since Bg & h ∈ g, Cdhg ” Tdh. Hence Cdhg.
Then h ∈ g & Wf h & Cdhg, so that ∃u (u ∈ g & Wfu & Cdug). Since Sn d
& It bd, ∀s ∀t (Bs & t ∈ s ’ (Cbts ” ∃u (u ∈ s & Wtu & Cdus))) (by [129]).
Since Bg & f ∈ g, Cbfg ” ∃u (u ∈ g & Wfu & Cdug). Hence Cbfg, so that
Cbfg ∨ Ccfg.
Thus, in all cases, Cbfg ∨ Ccfg. Since (Sn b ∨ Sb b ∨ Sf b ∨ St b ∨ Sc b) &
(Sn c ∨ Sb c ∨ Sf c ∨ St c ∨ Sc c) & Iv abc, it follows (by [131]) that ∀s ∀t (Bs
& t ∈ s ’ (Cats ” Cbts ∨ Ccts)). Since Bg & f ∈ g, Cafg ” Cbfg ∨ Ccfg.
Hence Cafg. But g was arbitrary. Then ∀s (Bs & f ∈ s ’ Cafs). Since Sa
& Xf, T *af ” ∀s (Bs & f ∈ s ’ Cafs) (by [138]). Then T *af. But f was
arbitrary. Then ∀t (Xt ’ T *at). But a, b, c, d, and e were arbitrary. Then
∀x ∀y ∀z ∀u ∀v (Iv xyz & It yu & It zv & ((Sa u & So v) ∨ (Se u & Si v) ∨ (Si u
& Se v) ∨ (So u & Sa v) ∨ (Sy u & Sd v) ∨ (Sd u & Sy v)) & Ck uv & Ch uv ’
∀t (Xt ’ T *xt)), i.e. [141] holds.
Similarly, every disjunction whose disjuncts are future-tense predicative
assertions in¬‚ected from contradictory present-tense predicative assertions
is always true:
[142] ∀x ∀y ∀z ∀u ∀v (Iv xyz & If yu & If zv & ((Sa u & So v) ∨ (Se u & Si v)
∨ (Si u & Se v) ∨ (So u & Sa v) ∨ (Sy u & Sd v) ∨ (Sd u & Sy v)) & Ck uv
& Ch uv ’ ∀t (Xt ’ T *xt)).
The proof of [142] resembles that of [141].

Excluded Middle is valid: (iii) formulation with ˜external negation™. Since
Aristotle does not recognise ˜external negation™, proving the validity of
Excluded Middle for assertions formulated with ˜external negation™ goes
beyond the range of tasks which Aristotle can be taken to set for himself.
It is, none the less, worthwhile stating such a result:
[143] ∀x ∀y ∀z ∀u ((Sn y ∨ Sb y ∨ Sf y ∨ St y) & (Sn u ∨ Sb u ∨ Sf u ∨ St u) &
Oyu & Ic zu & Iv xyz ’ ∀t (Xt ’ T *xt)).
The proof, which is straightforward, is omitted.
References




AA. VV. 1936, Actes du Congr`s International de Philosophie Scienti¬que (Sorbonne,
e
Paris, 1935), vi, Paris.
AA. VV. 1953, Actes du XI`me Congr`s International de Philosophie, Bruxelles, 20“26
e e
Aoˆ t 1953, Amsterdam and Louvain.
u
AA. VV. 1960, Atti del XII Congresso Internazionale di Filoso¬a (Venezia, 12“18
Settembre 1958), xi, Florence.
AA. VV. 1975, Scritti in onore di † Carlo Diano, Bologna.
AA. VV. 1985, Sapienza antica. Studi in onore di Domenico Pesce, Milan.
AA. VV. 1986, Philosophie du langage et grammaire dans l™antiquit´, Brussels.
e
AA. VV. 1988, Proceedings of the XVIII International Congress of Papyrology, i, Athens.
Abbagnano, N. 1971, Dizionario di Filoso¬a, 2nd edn, Turin.
Abrusci, V. M., Casari, E., and Mugnai, M. (eds.) 1983, Atti del Convegno Inter-
nazionale di Storia della Logica, San Gimignano, 4“8 dicembre 1982, Bologna.
Ackrill, J. L. 1972, ˜Aristotle on “Good” and the Categories™ = Ackrill (1997),
201“11.
” 1997, Essays on Plato and Aristotle, Oxford.
Ackrill, J. L. (trans. and comm.) 1963, Aristotle, Categories and De Interpretatione,
Oxford.
ACPA = Proceedings of the American Catholic Philosophical Association.
Adorno, F. 1961, La ¬loso¬a antica, i, Milan.
AGPh = Archiv f¨ r Geschichte der Philosophie.
u
Alberti, A. (ed.) 1990, Logica, mente e persona. Studi sulla ¬loso¬a antica, Florence.
” (ed.) 1994, Realt` e ragione. Studi di ¬loso¬a antica, Florence.
a
Albritton, R. A. 1957, ˜Present Truth and Future Contingency™, PR 66: 29“46.
Algra, K. A. A., Barnes, J., Mansfeld, J., and Scho¬eld, M. (eds.) 1999, The Cam-
bridge History of Hellenistic Philosophy, Cambridge.
Algra, K. A. A., van der Horst, P. W., and Runia, D. T. (eds.) 1996, Polyhistor:
Studies . . . Presented to Jaap Mansfeld . . . , Leiden, New York, and Cologne.
Angelelli, I. and Cerezo, M. (eds.) 1996, Studies on the History of Logic: Proceedings
of the III Symposium on the History of Logic, Berlin and New York.
Anscombe, G. E. M. 1956/68, ˜Aristotle and the Sea Battle: De Interpretatione,
Chapter IX™ = Moravcsik (1968), 15“33.
Anscombe, G. E. M. and Geach, P. T. 1961, Three Philosophers, Oxford.


284
References 285
Antiseri, D. (trans. and comm.) 1969, Aristotele, De Interpretatione, Bergamo.
Anton, J. P. 1992, ˜On the Meaning of Kategoria in Aristotle™s Categories™ =
Preus/Anton (1992), 1“18.
AP = Ancient Philosophy.
Apelt, O. 1891a, Beitr¨ ge zur Geschichte der griechischen Philosophie, Leipzig.
a
” 1891b, ˜Die Kategorieenlehre des Aristoteles™ = Apelt (1891a), 101“216.
Apostle, H. G. (trans. and comm.) 1966, Aristotle, Metaphysics, Bloomington, Ind.
and London.
” (trans. and comm.) 1980, Aristotle, Categories and Propositions (De Interpreta-
tione), Grinnell, Ia.
” (trans. and comm.) 1981, Aristotle, On the Soul, Grinnell, Ia.
Arens, H. 1984, Aristotle™s Theory of Language and its Tradition: Texts from 500 to
1750, Amsterdam and Philadelphia.
Astroh, M. 1981, ˜Apophansis und Kontingenz. Zum neunten Kapitel der Schrift
Peri Hermeneias™, Tijdschrift voor Filoso¬e 43: 328“62.
Aubenque, P. 1962/83, Le probl`me de l™ˆtre chez Aristote. Essai sur la probl´matique
e e e
aristot´licienne, 5th edn, Paris.
e
” 1979a, ˜La pens´e du simple dans la M´taphysique (Z 17 et Q 10)™ = Aubenque
e e
(1979b), 69“80.
Aubenque, P. (ed.) 1979b, Etudes sur la M´taphysique d™Aristote “ Actes du VIe
e
Symposium Aristotelicum, Paris.
” (ed.) 1980, Concepts et cat´gories dans la pens´e antique, Paris.
e e
Austin, J. L. 1950, ˜Truth™ = Blackburn/Simmons (1999), 149“61.
Avgelis, N. and Peonidis, F. (eds.) 1998, Aristotle on Logic, Language and Science,
Thessaloniki.
BACAP = Proceedings of the Boston Area Colloquium in Ancient Philosophy.
B¨ck, A. T. 1992, ˜Sailing through the Sea Battle™, AP 12: 133“51.
a
” 2000, Aristotle™s Theory of Predication, Leiden, Boston, and Cologne.
Badawi, A. 1971, Commentaires sur Aristote perdus en Grec, Beirut.
” 1987, La transmission de la philosophie grecque au monde arabe, 2nd edn, Paris.
Baldassarri, M. (ed., trans., and comm.) 1985/87, La logica stoica. Testimonianze e
frammenti, Como.
Bambrough, R. (ed.) 1965, New Essays on Plato and Aristotle, London and New
York.
Bar-Hillel, Y. (ed.) 1965, Logic, Methodology and Philosophy of Science: Proceedings
of the 1964 International Congress, Amsterdam.
Barnes, J. 1986, ˜Peripatetic Negations™, OSAP 4: 201“14.
” 1993, ˜Meaning, Saying and Thinking™ = D¨ ring/Ebert (1993), 47“61.
o
” 1995a, ˜Metaphysics™ = Barnes (1995b), 66“108.
” 1996, ˜Grammar on Aristotle™s Terms™ = Frede/Striker (1996), 175“202.
” 1999a, ˜Aristotle and Stoic Logic™ = Ierodiakonou (1999), 23“53.
” 1999b, ˜Logic: i The Peripatetics™ = Algra/Barnes/Mansfeld/Scho¬eld (1999),
77“83.
Barnes, J. (ed.) 1995b, The Cambridge Companion to Aristotle, Cambridge.
Barnes, J. (trans. and comm.) 1994, Aristotle, Posterior Analytics, 2nd edn, Oxford.
286 References
B¨rthlein, K. 1972, Die Transzendentalienlehre der alten Ontologie, i, Berlin and
a
New York.
Battegazzore, A. M. (ed.) 1993, Dimostrazione, argomentazione dialettica e argo-
mentazione retorica nel pensiero antico. Atti del Convegno di Filoso¬a (Bocca di
Magra, 18“22 marzo 1990), Genoa.
Baudry, L. 1950, La querelle des futurs contingents (Louvain 1465“1475). Textes in´dits,
e
Paris.
Baylis, C. A. 1936, ˜Are Some Propositions neither True nor False?™, Philosophy of
Science 3: 156“66.
Beaney, M. 1996, Frege: Making Sense, London.
Becker, A. 1936, ˜Bestreitet Aristoteles die G¨ ltigkeit des “Tertium non datur”
u
f¨ r Zukunftsaussagen? (Zum 9. Kapitel der Aristotelischen Hermeneutik)™ =
u
AA. VV. (1936), 69“74.
Becker, O. 1957a, Zwei Untersuchungen zur antiken Logik, Wiesbaden.
” 1957b, ˜Chrysippos uber den “L¨ gner”™ = O. Becker (1957a), 50“2.
u
¨
Bekker, I. and Gigon, O. (eds.) 1960/87, Aristotelis Opera, 2nd ed., Berlin.
Belardi, W. 1977, ˜Semantica di s…ndesmov e di ˆs…ndetov in Aristotele™, Rivista
di ¬lologia e di istruzione classica 105: 257“73.
Bencivenga, E., Lambert, K., and van Fraassen, B. C. 1986/91, Logic, Bivalence,
and Denotation, 2nd edn, Atascadero, Calif.
Benson, H. H. 1988, ˜Universals as Sortals in the Categories™, Paci¬c Philosophical
Quarterly 69: 282“306.
Ben-Zeev, A. 1984, ˜Aristotle on Perceptual Truth and Falsity™, Apeiron 18: 118“25.
Berti, E. 1978, ˜The Intellection of “Indivisibles” according to Aristotle, de Anima
III 6™ = Lloyd/Owen (1978), 141“63.
” 1983a, ˜La fonction de M´taph. Alpha Elatton dans la philosophie d™Aristote™
e
= Moraux/Wiesner (1983), 260“94.
” 1983b, ˜Quelques remarques sur la conception aristot´licienne du non-ˆtre™,
e e
RPA 1: 115“42.
” 1990, ˜Heidegger e il concetto aristotelico di verit`™ = Brague/Courtine (1990),
a
97“120.
” 1992, Aristotele nel Novecento, Rome and Bari.
” 1993, ˜Intellezione e dialettica in Aristotele, Metaph. IX 10™ = Battegazzore
(1993), 21“36.
” 1994, ˜Encore sur l™intellection des “indivisibles” selon Aristote, De anima III
6™ = Alberti (1994), 123“36.
” 1996a, ˜Encore sur l™intellection des “indivisibles” selon Aristote, De anima III
6™ = Romeyer Dherbey/Viano (1996), 391“404.
” 1996b, ˜La logica dell™argomentazione ¬loso¬ca tra Aristotele e Ryle™ =
Guetti/Pujia (1996), 59“68.
” 2000, ˜I luoghi della verit` secondo Aristotele. Un confronto con Heidegger™
a
= Melchiorre (2000), 3“27.
Berti, E. (ed.) 1981, Aristotle on Science: The ˜Posterior Analytics™ “ Proceedings of the
Eighth Symposium Aristotelicum Held in Padua from September 7 to 15, 1978,
Padua.
References 287
” (ed.) 1997, Guida ad Aristotele, Rome and Bari.
Besoli, S. 1985, ˜Percezione, verit` e giudizio: luoghi dell™intuizionismo aristotelico™
a
= Besoli (2002), 9“54.
” 2002, Esistenza, verit` e giudizio. Percorsi di critica e fenomenologia della
a
conoscenza, Macerata.
BICS = Bulletin of the Institute of Classical Studies.
Bird, O. 1964, Syllogistic and Its Extensions, Englewood Cliffs, NJ.
Birondo, N. 2001, ˜Aristotle on Illusory Perception: Phantasia without Phantas-
mata™, AP 21: 57“71.
Blackburn, S. and Simmons, K. (eds.) 1999, Truth, Oxford.
Blanch´, R. and Dubucs, J. 1970/96, La logique et son histoire, Paris.
e
Blank, D. (trans. and comm.) 1996, Ammonius, On Aristotle On Interpretation 1“8,
London.
Blank, D. and Kretzmann, N. (eds., trans., and comm.) 1998, On Determinism:
Ammonius On Aristotle On Interpretation 9 with Boethius On Aristotle On
Interpretation 9 First and Second Commentaries, London.
Blettner, E. 1983, ˜One Made Many and Many Made One: The Role of Asyndeton
in Aristotle™s Rhetoric™, Philosophy and Rhetoric 16: 49“54.
Block, I. 1961, ˜Truth and Error in Aristotle™s Theory of Sense Perception™, PQ
11: 1“9.
Bobzien, S. 1998, Determinism and Freedom in Stoic Philosophy, Oxford.
” 2000, ˜Wholly Hypothetical Syllogisms™, Phronesis 45: 87“137.
” 2002, ˜The Development of Modus Ponens in Antiquity: From Aristotle to the
2nd Century ad™, Phronesis 47: 359“94.
Bochenski, I. M. 1947, La logique de Th´ophraste, Fribourg en Suisse.
e
” 1951, Ancient Formal Logic, Amsterdam.
” 1962, Formale Logik, 2nd edn, Freiburg and Munich.
Bod´us, R. (trans. and comm.) 1993, Aristote, De l™ˆ me, Paris.
e¨ a
Bod´us, R. (ed. and comm.) 2001, Aristote, [Cat´gories], Paris.
e¨ e
Boehner, P., Moody, E. A., G´l, G., Gambatese, A., and Brown, S. (eds.) 1978,
a
William of Ockham, Expositionis in Libros Artis Logicae Prooemium, Expo-
sitio in Librum Porphyrii de Predicabilibus, Expositio in Librum Praedica-
mentorum Aristotelis, Expositio in Librum Perihermeneias Aristotelis, Tractatus
de Praedestinatione et de Praescientia Dei respectu Futurorum Contingentium,
St Bonaventure, NY.
Bolton, R. 1976, ˜Essentialism and Semantic Theory in Aristotle: Posterior Analytics,
II, 7“10™, PR 85: 514“44.
Bonitz, H. 1842, Observationes criticae in Aristotelis libros metaphysicos,
Berlin.
” 1862/67, Aristotelische Studien, repr., Hildesheim 1969.
” 1870, Index Aristotelicus, repr., Graz 1955.
Bonitz, H. (ed. and comm.) 1848/49, Aristotelis Metaphysica, Bonn.
Bonitz, H. (trans.) 1890, Aristoteles, Metaphysik, repr., Munich 1966.
Bonomi, A. and Zucchi, A. 2001, Tempo e linguaggio. Introduzione alla semantica
del tempo e dell™aspetto verbale, Milan.
288 References
Bormann, K. 1982, ˜Wahrheitsbegriff und no“v-Lehre bei Aristoteles und einigen
seiner Kommentatoren™, Miscellanea Mediaevalia 12: 1“24.
Bosley, R. 1977, ˜In Support of an Interpretation of On Int. 9™, Ajatus 37: 29“40.
Bostock, D. (trans. and comm.) 1994, Aristotle, Metaphysics: Books Z and H,
Oxford.
Bottani, A., Carrara, M., and Giaretta, P. (eds.) 2002, Individuals, Essence and
Identity: Themes of Analytic Metaphysics, Dordrecht, Boston, and London.
´
Boudot, M. 1973, ˜Temps, n´cessit´ et pr´d´termination™, Les Etudes Philosophiques
e e ee
n.n.: 435“73.
Bradley, R. D. 1959/68, ˜Must the Future Be What It Is Going to Be?™ = Gale
(1968), 232“51.
Brague, R. and Courtine, F. (eds.) 1990, Herm´neutique et ontologie. M´langes en
e e
`
hommage a Pierre Aubenque, Paris.
Brakas, G. 1988, Aristotle™s Concept of the Universal, Hildesheim, Zurich, and New
York.
Brandis, C. A. 1835/66, Handbuch der Geschichte der griechisch-r¨mischen Philoso-
o
phie, Berlin.
” 1862/64, Geschichte der Entwicklungen der griechischen Philosophie und ihrer
Nachwirkungen im r¨mischen Reiche, repr., Hildesheim and New York 1981.
o
Brandis, C. A. (ed.) 1823, Aristotelis et Theophrasti Metaphysica, Berlin.
Brandt, R. 1965, Die Aristotelische Urteilslehre. Untersuchungen zur ˜Hermeneutik™,
Marburg.
Brentano, F. 1862, Von der mannigfachen Bedeutung des Seienden nach Aristoteles,
repr., Darmstadt 1960.
” 1874/1925, Psychologie vom empirischen Standpunkt, ed. by O. Kraus, repr., Ham-
burg 1955 and 1959.
¨
” 1889, ˜Uber den Begriff der Wahrheit™ = Brentano (1930), 3“29.
” 1909, ˜De Interpretatione™ = Brentano (1986), 59“65.
¨
” 1914a, ˜Uber die Entstehung der irrigen Lehre von den entia irrealia™ = Brentano
(1930), 162“4.
” 1914b, ˜Zur Frage der Existenz der Inhalte und von der adaequatio rei et intel-
lectus™ = Brentano (1930), 121“30.
” 1915a, Letter to O. Kraus dated 9 January, 1915, partly quoted in Brentano (1930),
219“20.
¨
” 1915b, ˜Uber den Sinn des Satzes: veritas est adaequatio rei et intellectus™ =
Brentano (1930), 131“6.
” 1930, Wahrheit und Evidenz, ed. by O. Kraus, repr., Hamburg 1974.
” 1952, Grundlegung und Aufbau der Ethik, ed. by F. Mayer-Hillebrand, Bern.
¨
” 1986, Uber Aristoteles, ed. by R. George, Hamburg.
” n.d., ˜Aristoteles™ Lehre von der mannigfachen Bedeutung des Seienden™ =
Brentano (1986), 190“7.
Brown, L. 1994, ˜The Verb “To Be” in Greek Philosophy: Some Remarks™ = Everson
(1994), 212“36.
Brunschwig, J. 1969, ˜La proposition particuli`re et les preuves de non-concluance
e
chez Aristote™, Cahiers pour l™Analyse 10: 3“26.
References 289
” 1979, ˜La forme, pr´dicat de la mati`re?™ = Aubenque (1979b), 131“66.
e e
” 1991, ˜On a Book-Title by Chrysipppus: “On the Fact that the Ancients Admit-
ted Dialectic along with Demonstrations”™, OSAP suppl. vol.: 81“95.
” 1999, ˜Homonymie et contradiction dans la dialectique aristot´licienne™ =e
B¨ ttgen/Diebler/Rashed (1999), 81“101.
u
Brunschwig, J. (ed., trans., and comm.) 1967, Aristote, Topiques, i, Paris.
Buhle, I. T. (ed., trans., and comm.) 1792/1800, Aristotelis Opera Omnia Graece . . . ,
Biponti.
Bullinger, A. 1882, Aristoteles™ Nus-Lehre (De an. III, c. 4“8 incl.), Dillingen.
Burnyeat, M. 2002, ˜De Anima II 5™, Phronesis 47: 28“90.
Burnyeat, M. et al. 1984, Notes on Eta and Theta of Aristotle™s Metaphysics, Oxford.
Burrell, D. 1964, ˜Aristotle and “Future Contingencies”™, Philosophical Studies
(Ireland) 13: 37“52.
Bussemaker, C., D¨ bner, F., and Heitz, A. (eds. and trans.) 1848/74, Aristotelis
u
Opera Omnia Graece et Latine, Paris.
Butler, R. J. 1955, ˜Aristotle™s Sea Fight and Three-Valued Logic™, PR 64: 264“74.
Butterworth, C. E. (trans. and comm.) 1983, Averroes, Middle Commentaries on
Aristotle™s Categories and De Interpretatione, Princeton.
B¨ ttgen, P., Diebler, S., and Rashed, M. (eds.) 1999, Th´ories de la phrase et de la
u e
`
proposition de Platon a Averro`s, Paris.
e
Bywater, I. 1913, ˜Aristotelia V™, The Journal of Philology 32: 107“22.
Bywater, I. (ed. and comm.) 1909, Aristotle, On the Art of Poetry, Oxford.
Cahn, S. M. 1967, Fate, Logic, and Time, New Haven and London.
Calogero, G. 1927, ˜Una nuova concezione della logica prearistotelica™ = Calogero
(1984), 349“62.
” 1927/68, I fondamenti della logica aristotelica, 2nd edn, Florence.
” 1984, Scritti minori di ¬loso¬a antica, Naples.
Capozzi, G. 1974, Giudizio, prova e verit` . I principi della scienza nell™analitica di
a
Aristotele, Naples.
Carson, D. S. 1996, Being and Truth: Elements of Aristotle™s Philosophy of Language,
diss. (Duke University).
Casari, E. 1984, ˜Note sulla logica aristotelica della comparazione™, Sileno 10: 131“46.
Cashdollar, S. 1973, ˜Aristotle™s Account of Incidental Perception™, Phronesis 18:
156“75.
Cassin, B. 1996, ˜Enquˆte sur le logos dans le De anima™ = Romeyer Dherbey/Viano
e
(1996), 257“93.
Cassirer, H. 1932, Aristoteles™ Schrift ˜Von der Seele™ und ihre Stellung innerhalb der
aristotelischen Philosophie, T¨ bingen.
u
Caston, V. 1996, ˜Why Aristotle Needs Imagination™, Phronesis 41: 20“55.
” 1998a, ˜Aristotle and the Problem of Intentionality™, Philosophy and Phenomeno-
logical Research 58: 249“98.
” 1998b, ˜Commentary on Kurt Pritzl: Aristotle on the Conditions of Thought™,
BACAP 14: 202“12.
Caston, V. and Graham, D. W. (eds.) 2002, Presocratic Philosophy: Essays in Honour
of Alexander Mourelatos, Aldershot.
290 References
Cathala, M.-R. and Spiazzi, R. M. (eds.) 1950, S. Thomae Aquinatis in Duodecim
Libros Metaphysicorum Aristotelis Expositio, Turin and Rome.
Cavini, W. 1985, ˜La negazione di frase nella logica greca™ = Cavini/Donnini
Macci` /Funghi/Manetti (1985), 7“126.
o
” 1993a, ˜Chrysippus on Speaking Truly and the Liar™ = D¨ ring/Ebert (1993),
o
85“109.
” 1993b, ˜Aristotele e i modi del paradosso™ = Battegazzore (1993), 61“81.
” 1998, ˜Arguing from a De¬nition: Aristotle on Truth and the Excluded Middle™
= Avgelis/Peonidis (1998), 5“15.
Cavini, W., Donnini Macci` , M. C., Funghi, M. S., and Manetti, D. 1985, Studi
o
su papiri greci di logica e medicina, Florence.
Celluprica, V. 1977, Il capitolo 9 del ˜De interpretatione™ di Aristotele. Rassegna di
studi: 1930“1973, Bologna.
” 1987, ˜Logica e semantica nella teoria aristotelica della predicazione™, Phronesis
32: 166“87.
Charles, D. 1994, ˜Aristotle on Names and Their Signi¬cation™ = Everson (1994),
37“73.
” 1997, ˜Method and Argument in the Study of Aristotle: A Critical Notice of
The Cambridge Companion to Aristotle™, OSAP 15: 231“57.
” 2000, Aristotle on Meaning and Essence, Oxford.
” 2002, ˜Some Comments on Prof. Enrico Berti™s “Being and Essence in Con-
temporary Interpretations of Aristotle”™ = Bottani/Carrara/Giaretta (2002),
109“26.
Chisholm, R. M. 1966, Theory of Knowledge, Englewood Cliffs, NJ.
Chisholm, R. M. and Haller, R. (eds.) 1978, Die Philosophie Franz Brentanos:
Beitr¨ ge zur Brentano-Konferenz (Graz, 4.“8. September 1977), Amsterdam.
a
Christ, W. (ed.) 1906, Aristotelis Metaphysica, 2nd edn, Leipzig.
Church, A. 1965, ˜The History of the Question of Existential Import of Categorical
Propositions™ = Bar-Hillel (1965), 417“24.
Cleary, J. J. 1988, Aristotle on the Many Senses of Priority, Carbondale and
Edwardsville.
Code, A. 1976, ˜Aristotle™s Response to Quine™s Objections to Modal Logic™, Journal
of Philosophical Logic 5: 159“86.
Colli, G. (trans. and comm.) 1955, Aristotele, Organon, Turin.
Conybeare, F. C. 1892, Anecdota Oxoniensia: A Collation with the Ancient
Armenian Versions of the Greek Text of Aristotle™s Categories, de Interpre-
tatione, de Mundo, de Virtutibus et Vitiis, and of Porphyry™s Introduction,
Oxford.
Cooke, H. P. and Tredennick, H. (eds. and trans.) 1938, Aristotle, The Categories,
On Interpretation, Prior Analytics, Cambridge, Mass. and London.
Cope, E. M. and Sandys, J. E. (eds. and comm.) 1877, The Rhetoric of Aristotle,
Cambridge.
Corsi, G., Mangione, C., and Mugnai, M. (eds.) 1989, Atti del Convegno Inter-
nazionale di Storia della Logica. Le teorie delle modalit` (San Gimignano, 5“8
a
dicembre 1987), Bologna.
References 291
Cosenza, P. 1983, ˜Procedimenti di trasformazione nella sillogistica di Aristotele™ =
Abrusci/Casari/Mugnai (1983), 223“8.
” 1987, Logica formale e antiformalismo (da Aristotele a Descartes), Naples.
Craig, W. L. 1988, The Problem of Divine Foreknowledge and Future Contingency
from Aristotle to Suarez, Leiden, New York, Copenhagen, and Cologne.
Cresswell, M. J. 1971, ˜Essence and Existence in Plato and Aristotle™, Theoria
37: 91“113.
Crivelli, P. 1989, ˜Presupposti esistenziali della negazione in Aristotele™, Annali del
Dipartimento di Filoso¬a “ Universit` di Firenze 5: 45“90.
a
” 1990, ˜Il “So¬sta” di Platone. Non essere, negazione e falsit`™, Atti e memorie
a
dell™Accademia Toscana di Scienze e Lettere ˜La Colombaria™ 55: 9“104.
” 1996, ˜Notes on Aristotle™s Conception of Truth™ = Funghi (1996), 147“59.
” 1999, ˜Aristotle on the Truth of Utterances™, OSAP 17: 37“56.
” 2001, ˜Empty Terms in Aristotle™s Logic™, BACAP 17: 237“69, 282“4.
” 2002, ˜Sameness in Aristotle™s Topics™ = Bottani/Carrara/Giaretta (2002),
239“45.
Damschen, G. 2001, ˜Aristoteles, “Analytica Posteriora” A 2, 72a8“9: “Der eine
Teil einer Aussage”™, Hermes 129: 125“8.
Dancy, R. M. 1986, ˜Aristotle and Existence™ = Knuuttila/Hintikka (1986), 49“80.
Dapunt, I. 1968, ˜Zwei Typen von Systemen der traditionellen Logik™, AGPh 50:
275“81.
David, M. 1994, Correspondence and Disquotation: An Essay on the Nature of Truth,
New York and Oxford.
Davidson, D. 1996, ˜The Folly of Trying to De¬ne Truth™, JP 93: 263“78.
D´carie, V. 1961, L™objet de la m´taphysique selon Aristote, Montreal and Paris.
e e
De Corte, M. 1934, La doctrine de l™intelligence chez Aristote, Paris.
de Koninck, T. 1990, ˜La noˆsis et l™indivisible selon Aristote™ = Matt´i (1990),
e e
215“28.
del Punta, F. (ed.) 1979, William of Ockham, Expositio super Libros Elenchorum, St
Bonaventure, NY.
Demoss, D. and Devereux, D. T. 1988, ˜Essence, Existence, and Nominal De¬ni-
tion in Aristotle™s Posterior Analytics II 8“10™, Phronesis 33: 133“54.
Deninger, J. G. 1961, ˜Wahres Sein™ in der Philosophie des Aristoteles, Meisenheim
am Glan.
Denyer, N. 1991, Language, Thought and Falsehood in Ancient Greek Philosophy,
London and New York.
de Rijk, L. M. 1952, The Place of the Categories of Being in Aristotle™s Philosophy,
Assen.
” 1987, ˜The Anatomy of the Proposition: Logos and Pragma in Plato and Aris-
totle™ = de Rijk/Braakhuis (1987), 27“61.
” 1996, ˜On Aristotle™s Semantics in de Interpretatione 1“4™ = Algra et al. (1996),
115“34.
” 2002, Aristotle: Semantics and Ontology, Leiden, Boston, and Cologne.
de Rijk, L. M. and Braakhuis, H. A. G. (eds.) 1987, Logos and Pragma: Essays on the
Philosophy of Language in Honour of Professor Gabriel Nuchelmans, Nijmegen.
292 References
Detel, W. 1998, ˜Aristotle™s Posterior Analytics and the Path to the Principles™ =
Avgelis/Peonidis (1998), 155“81.
Devereux, D. T. 1992, ˜Inherence and Primary Substance in Aristotle™s Categories™,
AP 12: 113“31.
Diamond, C. and Teichmann, J. (eds.) 1979, Intention and Intentionality: Essays in
Honour of G. E. M. Anscombe, Ithaca.
Dickason, A. 1976, ˜Aristotle, the Sea Fight, and the Cloud™, JHP 14: 11“22.
Dilthey, W. 1883, Einleitung in die Geisteswissenschaften. Versuch einer Grundlegung
f¨ r das Studium der Gesellschaft und der Geschichte, i, 7th edn, Stuttgart and
u
G¨ ttingen 1959.
o
Dod, B. G. (ed.) 1975, Aristoteles, de Sophisticis Elenchis, trans. by Boethius, James
of Venice, and William of Moerbeke, Leiden and Brussels.
Donini, P. L. 1989, Ethos. Aristotele e il determinismo, Alessandria.
D¨ ring, A. 1890, ˜Die aristotelischen De¬nitionen von s…ndesmov und Šrqron,
o
Poetik c. 20™, AGPh 3: 363“9.
D¨ ring, K. 1972, Die Megariker. Kommentierte Sammlung der Testimonien,
o
Amsterdam.
D¨ ring, K. and Ebert, T. (eds.) 1993, Dialektiker und Stoiker: Zur Logik der Stoa
o
und ihrer Vorl¨ ufer, Stuttgart.
a
Dorion, L.-A. (trans. and comm.) 1995, Aristote, Les r´futations sophistiques, Paris.
e
DuLac, H. 1949, ˜The Peri Hermeneias: Its Place in Logic and Its Order™, Laval
th´ologique et philosophique 5: 161“9.
e
Duminil, M.-P. and Jaulin, A. (trans. and comm.) 1991, Aristote, Metaphysiques.
Livre Delta, Toulouse.
D¨ ring, I. 1961, Aristotle™s Protrepticus: An Attempt at Reconstruction, Stockholm,
u
G¨ teborg, and Uppsala.
o
” 1966, Aristoteles. Darstellung und Interpretation seines Denkens, Heidelberg.
D¨ ring, I. and Owen, G. E. L. (eds.) 1960, Aristotle and Plato in the Mid-Fourth
u
Century: Papers of the Symposium Aristotelicum Held at Oxford in August 1957,
G¨ teborg.
o
Du Val, G. (ed. and comm.) 1629, Aristotelis Opera Omnia Quae Exstant Graece
et Latine . . . , Paris.
Ebbesen, S. 1981, Commentators and Commentaries on Aristotle™s Sophistici Elenchi,
Leiden.
” 1986, ˜The Chimera™s Diary™ = Knuuttila/Hintikka (1986), 115“42.
Edel, A. 1982, Aristotle and His Philosophy, Chapel Hill, NC.
Edwards, P. (ed.) 1967, The Encyclopedia of Philosophy, New York and London.
Enders, M. 1999, Wahrheit und Notwendigkeit. Die Theorie der Wahrheit bei Anselm
von Canterbury im Gesamtzusammenhang seines Denkens und unter beson-
derer Ber¨ cksichtigung seiner antiken Quellen (Aristoteles, Cicero, Augustinus,
u
Boethius), Leiden, Boston, and Cologne.
Engel, P. 2002, Truth, Chesham.
Engelhardt, P. M. 1953, Die Wahrheit in der Einheit und Entzweiung, diss. (Univ.
of Freiburg i. Br.).
Engmann, J. 1976, ˜Imagination and Truth in Aristotle™, JHP 14: 259“65.
References 293
Evans, G. 1979, ˜Does Tense Logic Rest upon a Mistake?™ = Evans (1985), 343“63.
” 1985, Collected Papers, Oxford.
Everson, S. (ed.) 1994, Language, Cambridge.
” 1995, ˜Proper Sensibles and Kaq¬ AËt† Causes™, Phronesis 40: 265“92.
” 1997, Aristotle on Perception, Oxford.
Fait, P. 1996, ˜Il linguaggio e l™abaco (Aristotele, Soph. El. 1, 165a6“17)™ = Funghi
(1996), 181“90.
” 1998, ˜L™´ristique mise en formules™, Dialogue 37: 131“54.
e
Fattal, M. 1996, ˜L™intellection des indivisibles dans le De anima (iii, 6) d™Aristote.
Lectures arabes et modernes™ = Romeyer Dherbey/Viano (1996), 423“40.
Faust, A. 1931/32, Der M¨glichkeitsgedanke. Systemgeschichtliche Untersuchungen,
o
repr., New York and London 1987.
Field, H. 1972, ˜Tarski™s Theory of Truth™, JP 69: 347“75.
Fine, G. 1980, ˜The One over Many™, PR 89: 197“240.
” 1984a, ˜Truth and Necessity in De Interpretatione 9™, History of Philosophy
Quarterly 1: 23“47.
” 1984b, ˜Separation™, OSAP 2: 31“87.
” 1985, ˜Separation: A Reply to Morrison™, OSAP 3: 159“65.
” 1993, On Ideas: Aristotle™s Criticism of Plato™s Theory of Forms, Oxford.
Fiorentino, F. 2001, ˜Il problema della verit` in Aristotele™, Sapienza 54: 257“302.
a
Fleischer, M. 1984, Wahrheit und Wahrheitsgrund: Zum Wahrheitsproblem und zu
seiner Geschichte, Berlin and New York.
Fonseca, P. 1577/89, Commentarii in Metaphysicorum Aristotelis Stagiritae Libros,
rev. edn, Cologne 1615/24, repr., Hildesheim 1964.
F¨ rster, A. (ed.) 1912, Aristotelis de Anima Libri iii, Budapest.
o
Forster, E. S. and Furley, D. J. (eds. and trans.) 1955, Aristotle, On Sophistical
Refutations, On Coming-To-Be and Passing-Away, On the Cosmos, Cambridge,
Mass. and London.
Fortenbaugh, W. W., Huby, P. M., Sharples, R. W., and Gutas, D. (eds. and trans.)
1993, Theophrastus of Eresus, Sources for His Life, Writings, Thought and
In¬‚uence, Leiden, New York, and Cologne.
Fox, J. F. 1987, ˜Truthmaker™, Australasian Journal of Philosophy 65: 189“207.
Fraser, K. 2002, ˜Demonstrative Science and the Science of Being qua Being™,
OSAP 22: 43“82.
Frede, D. 1970, Aristoteles und die ˜Seeschlacht™. Das Problem der Contingentia Futura
in De Interpretatione 9, G¨ ttingen.
o
” 1972, ˜Omne quod est quando est necesse est esse™, AGPh 54: 153“67.
” 1985, ˜The Sea-Battle Reconsidered: A Defence of the Traditional Interpreta-
tion™, OSAP 3: 31“87.
” 1990, ˜Fatalism and Future Truth™, BACAP 6: 195“227.
” 1998, ˜Logik, Sprache und die Offenheit der Zukunft in der Antike: Bemerk-
ungen zu zwei neuen Forschungsbeitr¨gen™, ZPhF 52: 84“104.
a
Frede, M. 1967, Pr¨ dikation und Existenzaussage: Platons Gebrauch von ˜. . . ist . . .™
a
und ˜. . . ist nicht . . .™ im Sophistes, G¨ ttingen.
o
” 1978, ˜Individuals in Aristotle™ = M. Frede (1987), 49“71, 367.
294 References
” 1981, ˜Categories in Aristotle™ = M. Frede (1987), 29“48, 367.
” 1987, Essays in Ancient Philosophy, Oxford.
¨
Frede, M. and Patzig, G. 1988, Aristoteles ˜Metaphysik Z™: Text, Ubersetzung und
Kommentar, Munich.
Frede, M. and Striker, G. (eds.) 1996, Rationality in Greek Thought, Oxford.
Freese, J. H. (ed. and trans.) 1926, Aristotle, The ˜Art™ of Rhetoric, London and New
York.
Freeland, C. 1992, ˜Aristotle on the Sense of Touch™ = Nussbaum/Oksenberg Rorty
(1992/95), 227“48.
Frege, G. 1918/19, ˜Die Verneinung™, Beitr¨ ge zur Philosophie des deutschen Idealismus
a
1: 143“57.
Funghi, M. S. (ed.) 1996, ODOI DIZHSIOS“Le vie della ricerca. Studi in onore di
Francesco Adorno, Florence.
Gabbay, D. and Guenthner, F. (eds.) 1983/89, Handbook of Philosophical Logic,
Dordrecht, Boston, and Lancaster.
Gagnebin, C. (ed.) 1981, M´taphysique, histoire de la philosophie. Recueil d™´tudes
e e
`
offert a F. Brunner, Neuchˆtel.
a
Gale, R. M. 1961, ˜Endorsing Predictions™, PR 70: 376“85.
Gale, R. M. (ed.) 1968, The Philosophy of Time: A Collection of Essays, London and
Melbourne.
Gallavotti, C. (ed., trans., and comm.) 1974, Aristotele, Dell™arte poetica, n.p.
Galluzzo, G. 1997/98, Il concetto di verit` nei primi scritti di S. Agostino, diss.
a
(University of Pisa).
” 2000, ˜Il tema della verit` dell™Expositio Libri Peryermenias di Tommaso
a
d™Aquino™, Documenti e studi sulla tradizione ¬loso¬ca medievale 11: 217“57.
Gaskin, R. 1994, ˜Fatalism, Foreknowledge and the Reality of the Future™, The
Modern Schoolman 81: 83“113.
” 1995, The Sea Battle and the Master Argument: Aristotle and Diodorus Cronus on
the Metaphysics of the Future, Berlin and New York.
” 1996, ˜Sea Battles, Worn-out Cloaks, and Other Matters of Interpretation:
Weidemann on Aristotle™s Peri Hermeneias™, AGPh 78: 48“59.
” 1998, ˜Simplicius on the Meaning of Sentences: A Commentary on In Cat. 396,
30“397, 28™, Phronesis 43: 42“62.
Gaskin, R. (trans. and comm.) 2000, Simplicius, On Aristotle Categories 9“15,
London.
Geach, P. T. 1963, ˜Aristotle on Conjunctive Propositions™ = Geach (1972), 13“27.
” 1968, ˜History of the Corruptions of Logic™ = Geach (1972), 44“61.
” 1972, Logic Matters, repr., Berkeley and Los Angeles 1980.
Geyser, G. J. A. M. 1917, Die Erkenntnistheorie des Aristoteles, repr., Aalen 1980.
Gigon, O. and Fischer, M. W. (eds.) 1988, Antike Rechts- und Sozialphilosophie,
Frankfurt a. M., Bern, New York, and Paris.
Gobbo, E. 1997, ˜La concezione “diretta” dell™ ›legcov negli Analitici primi e nelle
Confutazioni so¬stiche™, Elenchos 18: 311“57.
Gohlke, P. (trans. and comm.) 1951, Aristoteles, Kategorien und Hermeneutik, Pader-
born.
References 295
” (trans. and comm.) 1961, Aristoteles, Metaphysik, 2nd edn, Paderborn.
Goldin, O. 1996, Explaining an Eclipse: Aristotle™s Posterior Analytics 2.1“10, Ann
Arbor.
” 2002, ˜To Tell the Truth: Dissoi Logoi 4 and Aristotle™s Responses™ = Cas-
ton/Graham (2002), 233“49.
G´ mez-Lobo, A. 1980, ˜The So-Called Question of Existence in Aristotle, An.
o
Post. 2. 1“2™, RM 34: 71“89.
Goodwin, W. W. 1889, Syntax of the Moods and Tenses of the Greek Verb, repr.,
Bristol 1998.
Gourinat, J.-B. 2000, La dialectique des sto¨ciens, Paris.
±
Graeser, A. 1977, ˜On Language, Thought, and Reality in Ancient Greek Philoso-
phy™, Dialectica 31: 359“88.
” 1978, ˜Sprache und Ontologie bei Aristoteles™, Freiburger Zeitschrift f¨ r Philoso-
u
phie und Theologie 25: 443“55.
” 1981, ˜Aristotle and Aquinas on Being as Being True™ = Gagnebin (1981), 85“97.
” 1983a, ˜Aspekte der Ontologie in der Kategorienschrift™ = Moraux/Wiesner
(1983), 30“56.
” 1983b, Die Philosophie der Antike 2: Sophistik und Sokratik, Plato und Aristoteles,
Munich.
Graeser, A. (ed. and comm.) 1973, Die logischen Fragmente des Theophrast, Berlin
and New York.
Graham, D. W. 1987, Aristotle™s Two Systems, Oxford.
Grant, C. K. 1957, ˜Certainty, Necessity and Aristotle™s Sea Battle™, Mind 66: 522“31.
Grayeff, F. 1974, Aristotle and His School: An Inquiry into the History of the Peripatos
with a Commentary on Metaphysics Z, H, L and Q, London.
Grice, P. 1988, ˜Aristotle on the Multiplicity of Being™, Paci¬c Philosophical Quarterly
69: 175“200.
Grossato, A. 1999, ˜La critica del capitolo 9 del De interpretatione di Aristotele
mediante la logica formale moderna™ = Zadro (1999), 397“443.
Grote, G. 1880, Aristotle, ed. by A. Bain and G. C. Robertson, 2nd edn, London.
Gudeman, A. (ed. and comm.) 1934, Aristoteles, PERI POIHTIKHS, Berlin.
Guetti, C. and Pujia, R. (eds.) 1996, Atti del convegno ˜Momenti di Storia della
Logica e di Storia della Filoso¬a™, Roma, 9“11 novembre 1994, Rome.
G¨ nther, H.-C. and Rengakos, A. (eds.) 1997, Beitr¨ ge zur antiken Philosophie.
u a
Festschrift f¨ r Wolfgang Kullman, Stuttgart.
u
Haack, S. 1974/96, Deviant Logic, Fuzzy Logic: Beyond the Formalism, 2nd edn,
Chicago and London.
Hadot, P. 1980, ˜Sur divers sens du mot pragma dans la tradition philosophique
grecque™ = Aubenque (1980), 309“19.
Hafemann, B. 1998, Aristoteles™ Transzendentaler Realismus. Inhalt und Umfang erster
Prinzipien in der ˜Metaphysik™, Berlin and New York.
” 1999, ˜Inde¬nite Aussagen und das kontingent Zuk¨ nftige: Akzidenzien allge-
u
meiner Gegenst¨nde und graduelle Wahrheit in Aristoteles™ De Interpretatione
a
7 und 9™, Philosophiegeschichte und logische Analyse 2: 109“37.
Hallett, G. L. 1988, Language and Truth, New Haven and London.
296 References
Halper, E. C. 1989, One and Many in Aristotle™s Metaphysics: The Central Books,
Columbus, Ohio.
Hamblin, C. L. 1970, Fallacies, London.
Hamlyn, D. W. 1962, ˜The Correspondence Theory of Truth™, PQ 12: 193“205.
Hamlyn, D. W. (trans. and comm.) 1968/93, Aristotle, De Anima: Books II and
III (with Passages from Book I), 2nd edn (with contributions by C. Shields),
Oxford.
Harris, L. D. 1977/78, ˜Solving the “Naval Battle”™, PAS n.s., 78: 45“61.
Hartshorne, C. 1965, ˜The Meaning of “Is Going to Be”™, Mind 74: 46“58.
Harvey, P. J. 1975, Aristotle on Truth with Respect to Incomposites, diss. (University
of Michigan).
” 1978, ˜Aristotle on Truth and Falsity in De Anima 3. 6™, JHP 16: 219“20.
Heidegger, M. 1924/25, Platon. Sophistes, ed. by I. Sch¨ ssler, Frankfurt a. M. 1992.
u
” 1925/26, Logik: Die Frage nach der Wahrheit, ed. by W. Biemel, 2nd edn, Frank-
furt a. M. 1995.
” 1926, Die Grundbegriffe der antiken Philosophie, ed. by F.-K. Bust, Frankfurt a.
M. 1993.
” 1927, Sein und Zeit, 10th edn, T¨ bingen 1963.
u
” 1930, Vom Wesen der menschlichen Freiheit. Einleitung in die Philosophie, ed. by
H. Tietjen, Frankfurt a. M. 1982.
” 1930/31, ˜Platons Lehre von der Wahrheit™ = Heidegger (1967), 109“44.
” 1946, ˜Brief uber den “Humanismus”™ = Heidegger (1967), 145“94.
¨
” 1967, Wegmarken, Frankfurt a. M.
Heinaman, R. 1981, ˜Non-substantial Individuals in the Categories™, Phronesis 26:
295“307.
Henle, P., Kallen, H. M., and Langer, S. K. (eds.) 1951, Structure, Method, and
Meaning: Essays in Honor of Henry M. Sheffer, New York.
Hennigfeld, J. 1994, Geschichte der Sprachphilosophie. Antike und Mittelalter, Berlin
and New York.
Herbertz, R. 1913, Das Wahrheitsproblem in der griechischen Philosophie, Berlin.
Hicks, R. D. (ed., trans., and comm.) 1907, Aristotle, De Anima, Cambridge.
Hildebrand, H. 1884, Aristoteles™ Stellung zum Determinismus und Indeterminismus,
diss. (University of Leipzig).
Hintikka, J. 1957, ˜Necessity, Universality and Time in Aristotle™, Ajatus 20: 65“90.
” 1964/73a, ˜The Once and Future Sea Fight: Aristotle™s Discussion of Future
Contingents in De Interpretatione IX™ = Hintikka (1973), 147“78.
” 1964/73b, ˜Aristotle and the “Master Argument” of Diodorus™ = Hintikka
(1973), 179“213.
” 1967/73, ˜Time, Truth, and Knowledge in Aristotle and Other Greek Philoso-
phers™ = Hintikka (1973), 62“92.
” 1973, Time and Necessity: Studies in Aristotle™s Theory of Modality, Oxford.
” 1986, ˜The Varieties of Being in Aristotle™ = Knuuttila/Hintikka (1986), 81“114.
” 1999, ˜On Aristotle™s Notion of Existence™, RM 52: 779“805.
Hintikka, J., Remes, U., and Knuuttila, S. 1977, Aristotle on Modality and Deter-
minism, Amsterdam.
References 297
Hitchcock, D. 2000, ˜Fallacies and Formal Logic in Aristotle™, HPL 21: 207“21.
Hiz, H. (ed.) 1978, Questions, Dordrecht.
Hope, R. (trans.) 1952, Aristotle, Metaphysics, repr., Ann Arbor, Mich. 1994.
Horn, H.-J. 1994, Studien zum dritten Buch der aristotelischen Schrift De anima,
G¨ ttingen.
o
HPL = History and Philosophy of Logic.
Hughes, R. I. G. (ed.) 1993, A Philosophical Companion to First-Order Logic, Indi-
anapolis, Ind. and Cambridge, Mass.
Humbert, J. 1945/60, Syntaxe grecque, 3rd edn, Paris.
Ierodiakonou, K. (ed.) 1999, Topics in Stoic Philosophy, Oxford.
Ihrig, A. H. 1965, ˜Remarks on Logical Necessity and Future Contingencies™, Mind
74: 215“28.
Inciarte, F. 1999, ˜Aristotle and Aquinas: The Principle of Excluded Middle™, Philoso-
phiegeschichte und logische Analyse 2: 139“48.
Irmscher, J. and M¨ ller, R. (eds.) 1983, Aristoteles als Wissenschaftstheoretiker, Berlin.
u
Irwin, T. H. 1977, Plato™s Moral Theory: The Early and Middle Dialogues, Oxford.
” 1982, ˜Aristotle™s Concept of Signi¬cation™ = Scho¬eld/Craven Nussbaum
(1982), 241“66.
” 1988, Aristotle™s First Principles, Oxford.
Isnardi Parente, M. (ed., trans., and comm.) 1980, Speusippo, Frammenti, Naples.
Jacobs, W. 1979, ˜Aristotle and Non-Referring Subjects™, Phronesis 24: 282“300.
” 1980, ˜The Existential Presuppositions of Aristotle™s Logic™, Philosophical Studies
37: 419“28.
Jaeger, W. W. 1911, ˜Emendationum aristotelearum specimen™ = Jaeger (1960),
1“38.
” 1912, Studien zur Entstehungsgeschichte der Metaphysik des Aristoteles, Berlin.
” 1923, Aristoteles: Grundlegung einer Geschichte seiner Entwicklung, Berlin.
” 1960, Scripta minora, i, Rome.
Jaeger, W. W. (ed.) 1957, Aristotelis Metaphysica, Oxford.
Jeffrey, R. C. 1979, ˜Coming True™ = Diamond/Teichmann (1979), 251“60.
JHP = Journal of the History of Philosophy.
Joachim, H. H. 1906, The Nature of Truth, Oxford.
” 1948, Logical Studies, Oxford.
Joachim, H. H. (ed. and comm.) 1926, Aristotle, On Coming-to-Be & Passing-Away,
Oxford.
Jordan, Z. 1963, ˜Logical Determinism™, NDJFL 4: 1“38.
JP = The Journal of Philosophy.
JSL = The Journal of Symbolic Logic.
Judson, L. 1988, ˜La bataille navale d™aujourd™hui: De Interpretatione 9™, RPA
6: 5“37.
Kahn, C. H. 1966, ˜The Greek Verb “To Be” and the Concept of Being™, Foundations
of Language 2: 245“65.
” 1973a, The Verb ˜Be™ in Ancient Greek, Dordrecht and Boston.
” 1973b, ˜On the Terminology for Copula and Existence™ = Stern/Hourani/Brown
(1973), 141“58.
298 References
” 1973c, ˜On the Theory of the Verb “To Be”™ = Munitz (1973), 1“20.
” 1976, ˜Why Existence does not Emerge as a Distinct Concept in Greek Philos-
ophy™, AGPh 58: 323“34.
” 1978, ˜Questions and Categories: Aristotle™s Doctrine of Categories in the Light
of Modern Research™ = Hiz (1978), 227“78.
” 1985, ˜On the Intended Interpretation of Aristotle™s Metaphysics™ = Wiesner
(1985), 311“38.
Kal, V. 1988, On Intuition and Discursive Reasoning in Aristotle, Leiden, New York,
Copenhagen, and Cologne.
Kapp, E. 1942, Greek Foundations of Traditional Logic, New York.
Keeler, L. 1932, ˜Aristotle on the Problem of Error™, Gregorianum 13: 241“60.
Kennedy, G. A. (trans. and comm.) 1991, Aristotle, On Rhetoric: A Theory of Civic
Discourse, New York and Oxford.
Kenny, A. 1967, ˜The Argument from Illusion in Aristotle™s Metaphysics (G, 1009“
10)™, Mind 76: 184“97.
Kessler, M. 1976, Aristoteles™ Lehre von der Einheit der De¬nition, Munich.
Ketchum, R. J. 1998, ˜Being and Existence in Greek Ontology™, AGPh 80: 321“32.
King-Farlow, J. 1958/59, ˜Sea-Fights without Tears™, Analysis 19: 36“42.
Kirkham, R. L. 1992, Theories of Truth: A Critical Introduction, Cambridge, Mass.
and London.
Kirwan, C. 1986, ˜Aristotle on the Necessity of the Present™, OSAP 4: 167“87.
Kirwan, C. (trans. and comm.) 1971/93, Aristotle, Metaphysics: Books G, D, and E,
2nd edn, Oxford.
¨
Knabenschuh de Porta, S. 1997, ˜Uber die Contingentia Futura und ihre episte-
¨
mologischen Implikationen™ = Offenberger/Vigo (1997), 189“240.
Kneale, M. 1974, rev. of Hintikka (1973), PQ 24: 369“70.
Kneale, W. C. and Kneale, M. 1962, The Development of Logic, Oxford.
Kneepkens, C. H. 1994, ˜From Eternal to Perpetual Truths: A Note on the Mediae-
val History of Aristotle, De interpretatione, Ch. 1, 16a18™, Vivarium 32: 161“85.
Knuuttila, S. 1993, Modalities in Medieval Philosophy, London and New York.
Knuuttila, S. and Hintikka, J. (eds.) 1986, The Logic of Being: Historical Studies,
Dordrecht.
Kraus, O. 1930, introduction and notes to Brentano (1930).
Kreiser, L. 1983, ˜Aristotelischer und Nicht-Aristotelischer Wahrheitsbegriff ™ =
Irmscher/M¨ ller (1983), 96“9.
u
Krell, D. F. 1975, ˜On the Manifold Meaning of Aletheia: Brentano, Aristotle,
Heidegger™, Research in Phenomenology 5: 77“94.
Kretzmann, N. 1998, ˜Boethius and the Truth about Tomorrow™s Sea Battle™ =
Blank/Kretzmann (1998), 24“52.
Kretzmann, N., Kenny, A., and Pinborg, J. (eds.) 1982, The Cambridge History of
Later Medieval Philosophy, Cambridge.
Kullmann, W. 1994/95, ˜Einige Gedanken zur Entwicklung deterministischer
Lehren bei den Griechen und zu Aristoteles, De interpretatione 9™, Wiener
Studien 107/108: 291“306.
Landman, F. 1991, Structures for Semantics, Dordrecht, Boston, and London.
References 299
Lang, P. 1911, De Speusippi Academici scriptis, repr., Hildesheim 1965.
Larkin, M. T. 1971, Language in the Philosophy of Aristotle, The Hague and Paris.
Lask, E. 1912, Die Lehre vom Urteil = Lask (1923), 283“463.
” 1923, Gesammelte Schriften, ed. by E. Herrigel, ii, T¨ bingen.
u
Leal Carretero, F. M. 1983, Der aristotelische Wahrheitsbegriff und die Aufgabe der
Semantik, diss. (University of Cologne).
Ledda, G. 1990, ˜Verit` e poesia nella Poetica di Aristotele™, Annali del Dipartimento
a
di Filoso¬a “ Universit` di Firenze 6: 3“57.
a
Lemmon, E. J. 1956, rev. of Anscombe (1956/68), JSL 21: 388“9.
Lenz, J. W. 1957, ˜Looking Back at the “Sea Fight Tomorrow”™, JP 54: 773“4.
Le´ n, J. C. 1996, ˜Indeterminism and Future Contingency in Non-Classical Logics™
o
= Angelelli/Cerezo (1996), 383“95.
Leszl, W. 1970, Logic and Metaphysics in Aristotle: Aristotle™s Treatment of Types of
Equivocity and Its Relevance to His Metaphysical Theories, Padua.
” 1971, ˜Metodi di analisi nella ¬loso¬a di Aristotele™, Rivista di ¬loso¬a 62: 325“53.
” 1975, Aristotle™s Conception of Ontology, Padua.
Lewinsohn, W. 1911, ˜Zur Lehre von Urteil und Verneinung bei Aristoteles™, AGPh
24: 197“217.
Lewis, F. A. 1991, Substance and Predication in Aristotle, Cambridge.
Linke, P. F. 1924, ˜Die Existentialtheorie der Wahrheit und der Psychologismus der
Geltungslogik™, Kant-Studien 29: 395“415.
” 1965, ˜Die Unhaltbarkeit des aristotelischen Wahrheitsbegriffs “ und die Folgen™,
ZPhF 19: 306“19.
Linsky, L. 1954, ˜Professor Donald Williams on Aristotle™, PR 63: 250“2.
Liske, M.-T. 1985, Aristoteles und der aristotelische Essentialismus: Individuum, Art,
Gattung, Freiburg and Munich.
” 1988, ˜Das veritative “ist” und der logische Atomismus in Platons Theaitetos™,
AGPh 70: 147“66.
” 1995, ˜In welcher Weise h¨ngen Modalbegriffe und Zeitbegriffe bei Aristoteles
a
zusammen?™, ZPhF 49: 351“77.
Lloyd, A. C. 1981, Form and Universal in Aristotle, Liverpool.
Lloyd, G. E. R. and Owen, G. E. L. (eds.) 1978, Aristotle on Mind and the Senses:
Proceedings of the Seventh Symposium Aristotelicum, Cambridge.
Long, A. A. 1981, ˜Aristotle and the History of Greek Scepticism™ = O™Meara (1981),
79“106.
Loux, M. J. 1991, Primary Ousia: An Essay on Aristotle™s Metaphysics Z and H,
Ithaca and London.
Lowe, M. F. 1980, ˜Aristotle on the Sea-Battle: A Clari¬cation™, Analysis 40:
55“9.
LSJ = Liddell, H. G., Scott, R., and Jones, H. S., A Greek-English Lexicon, 9th
edn with a revised supplement, Oxford 1996.
Lucas, J. R. 1989, The Future: An Essay on God, Temporality, and Truth, Oxford.
Lugarini, L. 1955, ˜Il problema delle categorie in Aristotele™, Acme 8: 3“107.
¨
Lukasiewicz, J. 1910a, Uber den Satz des Widerspruchs bei Aristoteles, trans. by
J. Barski, Hildesheim, Z¨ rich, and New York 1993.
u
300 References
¨
” 1910b, ˜Uber den Satz des Widerspruchs bei Aristoteles™, Bulletin interna-
tional de l™Acad´mie des Sciences de Cracovie, Classe de Philosophie et d™Histoire
e
n.n.: 15“38.
” 1918, ˜On Three-Valued Logic™ = Lukasiewicz (1970), 87“8.
” 1922, ˜On Determinism™ = Lukasiewicz (1970), 110“28.
” 1930, ˜Philosophical Remarks on Many-Valued Systems of Propositional Logic™
= Lukasiewicz (1970), 153“78.
” 1957, Aristotle™s Syllogistic from the Standpoint of Modern Formal Logic, 2nd edn,
Oxford.
” 1970, Selected Works, ed. by L. Borkowski, Amsterdam, London, and Warsaw.
Luther, W. 1966, ˜Wahrheit, Licht und Erkenntnis in der griechischen Philosophie
bis Demokrit. Ein Beitrag zur Erforschung des Zusammenhangs von Sprache
und philosophischem Denken™, Archiv f¨ r Begriffsgeschichte 10: 1“240.
u
Magris, A. 1977, ˜Aristotele e i Megarici. Contributo alla storia del determinismo
antico™, Atti dell™Accademia delle Scienze di Torino 111: 113“33.
Maier, H. 1896/1936, Die Syllogistik des Aristoteles, 2nd edn, repr., Hildesheim 1969.
” 1899, ˜Die Echtheit der Aristotelischen Hermeneutik™, AGPh 13: 23“72.
Manetti, G. (ed.) 1996, Knowledge through Signs: Ancient Semiotic Theories and
Practices, Brussels.
Mann, J. A. 1958, Existential Import and the Aristotelian Syllogistic, Washington,
D.C.
`
Mansion, A. 1913/45, Introduction a la physique aristot´licienne, 2nd edn, Louvain.
e
Mansion, S. 1946/76, Le jugement d™existence chez Aristote, 2nd edn, Louvain.
Mansion, S. (ed.) 1961, Aristote et les probl`mes de m´thode. Communications
e e
pr´sent´es au Symposium Aristotelicum tenu a Louvain du 24 aoˆ t au 1er septembre
`

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