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fact “is” in the sense of being true that it “is” in the sense of being true, or
of a state of affairs which in fact “is not” in the sense of being false that it
“is not” in the sense of being false, is true.™22

17 Cf. Xenakis (1957), 542; B¨rthlein (1972), 22; Wolenski/Simons (1989), 393; Davidson (1996), 267;
a
Knabenschuh de Porta (1997), 192.
18 Cf. Int. 6, 17a 26“30; 14, 23b 7“13; Top. 2.1, 109a 29“30. I know no other Aristotelian passage where ˜to
be™ means ˜to hold of ™ (Bobzien (2002), 372“3 thinks that in Top. 2.4, 111b 17“23 ˜to be™ does mean ˜to
hold of ™, but I ¬nd this unconvincing). However, some commentators (e.g. M. Frede (1967), 94“5)
take a passage of Plato™s Sophist (262e11“263b13) to analyse truth and falsehood by using ˜to be™ to
mean something like ˜to hold of ™.
19 For ˜to be™ and ˜not to be™ used as schematic expressions cf. Metaph. 4, 1005b 35“1006a 1 with
1006b 18“22 and Kirwan (1971/93), 89; C. J. F. Williams (1976), 67.
20 Cf. Int. 9, 18a 39“18b 3; 14, 23a 40“23b 1; 23b 4“6; 23b 7“8; 23b 33“24a 3; SE 5, 168a 9“11; Cael. 1.12, 281b 8“
14; de An. 3.6, 430b 1“3; Metaph. 29, 1024b 22“4; Tugendhat (1966a), 251“2; Prior (1967b), 224;
Sommers (1969/70), 281“2; C. J. F. Williams (1976), 67; Leal Carretero (1983), 45“65, 87; Fox (1987),
199; Ledda (1990), 35“6, 50.
21 Aristotle does use ˜to be™ to mean ˜is true™: see APo. 1.1, 71a 12“14; 2, 71b 25“6 (cf. Mignucci (1975b),
229“30).
22 Cf. Brentano (1889), 24“5, 26“7 (with Srzednicki (1965), 18); Oehler (1962/85), 180“1; Hintikka
(1964/73a), 168; Kahn (1966), 253; Kirwan (1971/93), 117; Kahn (1973a), 336; (1973b), 144; Weingartner
134 ˜Empty™ terms
On interpretation (i) T 28™s de¬nition of truth and falsehood is unac-
ceptably narrow: truth and falsehood would be de¬ned only for existential
assertions.23 The main problem with interpretation (ii) is that there seems
to be no other passage where Aristotle uses ˜to be™ to mean ˜to hold of ™.24
Interpretations (iii) and (iv) also face a dif¬culty: they cannot accommo-
date existential assertions “ in the case of interpretation (iv), this is because
states of affairs are composite items whose ˜being™ in the sense of being true
or ˜not being™ in the sense of being false accounts for the truth or falsehood
only of predicative assertions. To be sure, this defect is less worrying than
interpretation (i)™s incapacity to accommodate predicative assertions. For,
¬rst, a de¬nition of truth and falsehood is much more limited if it cov-
ers only existential assertions than if it covers only predicative assertions.
Second, in T 28 Aristotle is in any case interested mainly in predicative
assertions: immediately before T 28 one of the formulations of Excluded
Middle, which T 28™s de¬nition of truth and falsehood is designed to sup-
port, is ˜It is necessary either to af¬rm or to deny any one thing about one
thing™ (1011b 24). None the less, it would be desirable to ¬nd an interpre-
tation of T 28 that yielded a ˜general™ de¬nition of truth and falsehood
covering all assertions.
Such an interpretation can be obtained by re¬‚ecting on the theory of
truth and falsehood of Metaphysics 10. In this chapter Aristotle dis-
tinguishes two kinds of assertions: those about composite and those about
non-composite items. The classi¬cation generated by this distinction seems
to cover existential as well as predicative assertions: every predicative asser-
tion is about a composite object (a state of affairs composed of universals or
of a universal and an individual); some existential assertion is again about a
composite object (a material substance composed of form and matter); the
remaining existential assertions are about non-composite items (essences
and incorporeal substances). What it is ˜to be™ (˜not to be™) in the sense
of being true (false) differs for items of different sorts. Aristotle is able to
offer a theory of truth which covers all these assertions at one blow: an

(1978), 187“8; K. J. Williams (1978), 68; Simons (1988), 107“8; Wolenski/Simons (1989), 393; Kirkham
(1992), 119“20; Knabenschuh de Porta (1997), 192; Vigo (1997), 8“10; Hafemann (1998), 90“1; Wolff
(1999), 51; Modrak (2001), 54.
23 Cf. Wolenski/Simons (1989), 393. Davidson (1996), 267 claims that interpretation (i) does not make
T 28™s de¬nition of truth and falsehood too narrow because the existential assertions it mentions are
those which ˜in modern terms™ begin with ˜there is an x such that . . .™ or ˜it is not the case that there
is an x such that . . .™ Davidson™s rescue of interpretation (i) takes universal assertions to be reducible
to assertions that begin with ˜it is not the case that there is an x such that . . .™, i.e. to denials of
particular assertions. Aristotle, however, seems to do the opposite: he regards particular assertions
as denials of universal assertions (cf. the subsection to which n. 24 of appendix 3 pertains). Hence,
Davidson™s rescue of interpretation (i) fails.
24 Cf. n. 18 above.
Truth as correspondence 135
af¬rmative assertion is true (false) when and only when the (composite or
non-composite) item it concerns ˜is™ in the sense of being true (˜is not™ in
the sense of being false), a negative assertion is true (false) when and only
when the (composite or non-composite) item it concerns ˜is not™ in the
sense of being false (˜is™ in the sense of being true). I suggest that Aristo-
tle™s de¬nition of truth and falsehood in T 28 expounds this theory. The
de¬nition can then be paraphrased as follows: ˜To say of a (composite or
non-composite) item which in fact “is” in the sense of being true that it “is
not” in the sense of being false, or of a (composite or non-composite) item
which in fact “is not” in the sense of being false that it “is” in the sense of
being true, is false; to say of a (composite or non-composite) item which
in fact “is” in the sense of being true that it “is” in the sense of being true,
or of a (composite or non-composite) item which in fact “is not” in the
sense of being false that it “is not” in the sense of being false, is true.™ On
this interpretation, T 28™s de¬nition of truth and falsehood covers pred-
icative as well as existential assertions. This gives it the edge on the other
interpretations, which make Aristotle™s de¬nition uncomfortably narrow.
Note, however, that even on my preferred interpretation, T 28™s de¬nition
of truth and falsehood is somewhat limited: for Aristotle recognises also
assertions composed of other assertions by means of conjunctions,25 and T
28™s de¬nition is silent about these.
If this reconstruction is correct, Aristotle™s theory of truth can be regarded
as a correspondence theory of truth based on an isomorphism between the
assertion and an object which corresponds to the whole assertion. This
correspondence-as-isomorphism theory of truth for assertions relies on a
simple classi¬cation of assertions. There are just two classes of assertions:
af¬rmations, which assert items ˜to be™ in the sense of being true, and denials,
which assert items ˜not to be™ in the sense of being false. These two classes
of assertions are mapped one-to-one onto precisely two properties that can
hold of the item an assertion is about. This mapping is best explained by
means of the following diagram (where every item in the left-hand side
column mentions a class of assertions, while the item on the same line in
the right-hand side column mentions the corresponding property which
can hold of the item the assertion is about):
1 asserting ˜being™ in the sense of being true ˜being™ in the sense of being true
2 asserting ˜not being™ in the sense of being false ˜not being™ in the sense of being false

An assertion is true just in case either it asserts the relevant item ˜to be™ in
the sense of being true and this item ˜is™ in the sense of being true, or it
25 Int. 5, 17a 8“9; 17a 15“16.
136 ˜Empty™ terms
asserts the relevant item ˜not to be™ in the sense of being false and this item
˜is not™ in the sense of being false.26

(iii.ii) Isomorphism with respect to items corresponding to parts of assertions.
The condition introduced by the correspondence-as-isomorphism concep-
tion is met again by Aristotle™s theory of truth, at a more speci¬c level: in the
de¬nition of truth and falsehood for predicative assertions. A predicative
assertion is about two objects: one is a universal (signi¬ed by the asser-
tion™s predicate), the other is either a universal or an individual (signi¬ed
by the assertion™s subject).27 As in the ¬rst account, the correspondence-
as-isomorphism theory of truth for assertions relies on a classi¬cation
of assertions. The second account™s classi¬cation, however, is more ¬ne-
grained than the ¬rst™s. There are six classes of assertions, and these six
classes are mapped one-to-one onto six two-place relations that can hold
of the universals or individuals an assertion can be about. The classes of
assertions and their mapping onto two-place relations are best explained
by means of a diagram (where, as in the previous one, every item in the
left-hand side column mentions a class of assertions, while the item on
the same line in the right-hand side column mentions the corresponding
two-place relation):
1 asserting the combination of universally being combined in such a way as
holding universally to hold
2 asserting the division of universally being divided in such a way as
failing to hold universally to fail to hold
3 asserting the combination of not being combined in such a way as not
universally failing to hold universally to fail to hold
4 asserting the division of not universally being divided in such a way as not
holding universally to hold
5 asserting the combination of holding being combined in such a way as to hold
6 asserting the division of holding outside being divided in such a way as to hold
outside

(For simplicity™s sake, I rely on a simple classi¬cation that ignores the
distinctions induced by the categories.) An assertion a is true when and only
when either a asserts the universal p signi¬ed by its predicate to be combined
with the universal s signi¬ed by its subject in such a way as universally to
hold of it and p is combined with s in such a way as universally to hold of
it, or a asserts the universal p signi¬ed by its predicate to be divided from
the universal s signi¬ed by its subject in such a way as universally to fail to
26 Cf. Brentano (1889), 24“5, 26“7 (with Srzednicki (1965), 18 and Wolenski/Simons (1989), 393); Oehler
(1962/85), 176“7; Szaif (1998), 520“1.
27 Cf. [17] on pp. 93“4 above.
Truth as correspondence 137
hold of it and p is divided from s in such a way as universally to fail to hold
of it, or . . .28
Note that the two accounts of truth (the one turning on objects corre-
sponding to complete assertions and the one turning on objects signi¬ed by
a predicative assertion™s predicate or subject) are neither incompatible nor
in competition. For the second account can be regarded as a ˜sharpening™ of
the ¬rst: the various types of combinations and divisions between objects
signi¬ed by a predicative assertion™s predicate or subject can be regarded as
ways in which the state of affairs that corresponds to a complete predicative
assertion ˜is™ in the sense of being true or ˜is not™ in the sense of being false “
recall that for a state of affairs ˜to be™ (˜not to be™) in the sense of being true
(false) is to be combined (divided).29

(iv) Mirror-isomorphism. Aristotle™s theory of truth seems to count as a
correspondence theory of truth in a different, stricter sense than the ones
outlined so far. This is because Aristotle™s theory of truth describes each class
of assertions in such a way that each assertion ˜mirrors™ the characteristic
on which the class it belongs to is mapped. Consider the ¬rst class of
assertions in the ¬rst type of correspondence-as-isomorphism theory of
truth: asserting ˜being™ in the sense of being true ˜mirrors™ ˜being™ in the
sense of being true. In general, each class of assertions in Aristotle™s theory
of truth is singled out by the property of asserting that the attribute on
which it is mapped obtains (this can be easily seen in the two diagrams
in the last subsections). This circumstance brings it about that Aristotle™s
theory of truth for assertions counts as a correspondence theory of truth in
that it regards an assertion as true when and only when it ˜asserts its object
to be as it is™.

Aristotle™s formulations of his correspondence theory of truth. Many philoso-
phers regard the Latin formula ˜Veritas est adaequatio rei et intellectus™ (˜Truth
is uniformity of thing and mind™) as a de¬nition of truth as correspon-
dence. This Latin formula originated in the Middle Ages, and is probably
a translation of an Arabic formula created by an unknown medieval Arab
philosopher.30 In Aristotle™s works no Greek sentence occurs that could be
translated by this Latin formula.31
Many philosophers credited with a correspondence theory of truth char-
acterise truth by using some comparative adverb like ˜as™ or ˜in the way™
28 29 Cf. [1] on p. 54 above.
Cf. Joachim (1906), 124“6; Hallett (1988), 8; Crivelli (1996), 158“9.
30 Cf. Muckle (1933); Luther (1966), 206“7, 188; Weingartner (1978), 185; Schulz (1993), 36“7.
31 Cf. Kreiser (1983), 96.
138 ˜Empty™ terms
(e.g. ˜A true assertion asserts things to be as they are™ or ˜. . . in the way they
are™). For instance, in the Euthydemus Plato says:
T 30 There are people who speak of things as they are [Þv ›cei] [. . .], those who
speak the truth. (284c9“284d2)32

Aristotle never characterises truth by employing a comparative adverb, a
fact all the more surprising in view of Plato™s usage.33 But other Aristotelian
formulations suggest a correspondence theory of truth.
(i) In Prior Analytics 2.15, 64b 9“10 Aristotle describes the false conclusion
of a syllogism as ˜contrary to the fact [–nant©ov t¤€ pr†gmati]™.
(ii) In de Anima 3.3, 427a 26“427b 6 Aristotle discusses a position of some
earlier thinkers: thought is perception and ˜like is perceived by like™. He
attacks this position by arguing that it entails the absurd consequence that
all thoughts should be true “ for, obviously, many thoughts are false.34
He seems to assume that the likeness, i.e. similarity, of a perception (or
a thought) to reality entails that the perception (or thought) should be
true.
(iii) Aristotle says that knowledge is ˜measured™ by its object.35 In saying
this he is probably taking issue with Protagoras, who, as Aristotle knew,36
said that a man is the measure of all things. But what does Aristotle mean
by saying that knowledge is ˜measured™ by its object? Since he thinks that
knowledge is true,37 at least part of what he means could be that the
truth of a piece of knowledge consists in its being somehow ˜proportion-
ate™ to its object, which thereby operates as a sort of ˜unit of measure-
ment™.38

32 Cf. Euthd. 284d5; Cra. 385b7“8, if ˜Þv™ at 385b7 and b8 is the comparative ˜as™ rather than the declarative
˜that™; R. v 477b10“11; 478a6; Prm. 161e4“5; Sph. 263b4“5, if ˜Þv™ at 263b4 is comparative rather than
declarative (cf. Crivelli (1990), 92). Alexander (in Metaph. 89, 2“6) mentions a Platonic argument for
Forms which relies on the assumption that ˜what we say truly, this holds™, an assumption that could
be regarded as a characterisation of truth as correspondence (cf. Wilpert (1949), 46“7). Alexander™s
report concerns us because its source could be Aristotle™s de Ideis (it is included in fr. 118, 3 Gigon
382a 24“31). According to Dissoi Logoi 4.2, a sentence is true ˜if things have turned out in the way the
sentence is said™ (cf. Goldin (2002), 236“7).
33 However see Po. 25, 1460b 8“11; 1460b 32“1461a 4; Metaph. 29, 1024b 21“4; [Arist.] Divis. Arist. 31,
50, 8“9. At Int. 9, 19a 33 Aristotle says that ˜sentences are true in the same way as [¾mo©wv . . .
ãsper] the objects™. Some commentators (e.g. Trendelenburg (1846), 14; Bonitz (1848/49), ii 409;
Dickason (1976), 20; Donini (1989), 1; Modrak (2001), 54) regard this remark as a formulation of
a correspondence theory of truth. However, what Aristotle has in mind in this passage seems to be
something narrower than a correspondence theory of truth: see the subsection to which n. 60 of
ch. 7 pertains.
34 Cf. Metaph. 5, 1009b 12“33. 35 Metaph. I 1, 1053a 31“5; 6, 1057a 11“12.
36 a 35“6; K 6, 1062b 12“14 (cf. 1062b 19; 1063a 4). 37 See n. 3 of ch. 1.
Metaph. I 1, 1053
38 Cf. Fiorentino (2001), 278“9, 281“2.
Truth as correspondence 139

2 th e lia r
A version of the Liar. I begin by presenting a version of the Liar that relies on
assumptions Aristotle would probably agree to, and therefore constitutes a
genuine threat to Aristotle™s position.
Let me ¬rst of all formulate some de¬nitions and background assump-
tions “ I trust them to be uncontroversial, at least within an Aristotelian
framework. Let u be an utterance of ˜I am speaking falsely™,39 let k be a time,
let u™s utterer be an individual, and let speaking-truly and speaking-falsely
be universals. Suppose that u is the only assertion produced by u™s utterer
over some period comprising k. Also suppose that u is a singular af¬rma-
tive predicative assertion, that the predicate of u (an utterance of ˜speaking
falsely™) signi¬es the universal speaking-falsely, and that the subject of u (an
utterance of ˜I™) signi¬es the individual who is u™s utterer. Since u is a singular
af¬rmative predicative assertion, by Aristotle™s theory of truth we have that u
is true when and only when speaking-falsely holds of u™s utterer. Since k is a
time, u is true at k just in case speaking-falsely holds of u™s utterer at k.
For the argument to develop, the universals speaking-truly and speaking-
falsely must be de¬ned. To this end, suppose that for every time t and
every individual s, speaking-truly holds of s at t just in case every assertion
produced by s over any period comprising t is true at t ; analogously, suppose
that for every time t and every individual s, speaking-falsely holds of s at t
just in case some assertion produced by s over some period comprising t is
false at t.
The ¬nal supposition is that for every time t and every individual s, either
speaking-truly holds of s at t or speaking-falsely holds of s at t. Note that
if Bivalence holds (i.e. if every assertion is always either true or false), this
¬nal supposition follows from the last paragraph™s de¬nitions.
First, assume that speaking-falsely holds of u™s utterer at k. Then u is
true at k. Since u is the only assertion produced by u™s utterer over some
period comprising k, every assertion produced by u™s utterer over any period
comprising k is true at k. Hence speaking-truly holds of u™s utterer at k.
Thus: if speaking-falsely holds of u™s utterer at k, then speaking-truly holds
of u™s utterer at k. But either speaking-truly or speaking-falsely holds of u™s
utterer at k. Therefore speaking-truly holds of u™s utterer at k.
Second, assume that speaking-truly holds of u™s utterer at k. Then every
assertion produced by u™s utterer over any period comprising k is true

The ancient Liar probably turned on utterances of ˜I am speaking falsely™ (˜–gÜ ye…domai™) (cf. Alex.
39
Aphr. in Top. 188, 19“28; Cavini (1993a), 89, 99), not of ˜This assertion is false™.
140 ˜Empty™ terms
at k. Since u is the only assertion produced by u™s utterer over some
period comprising k, u is true at k. Hence speaking-falsely holds of u™s
utterer at k. Thus: if speaking-truly holds of u™s utterer at k, then speaking-
falsely holds of u™s utterer at k. But either speaking-truly or speaking-falsely
holds of u™s utterer at k. Therefore speaking-falsely holds of u™s utterer
at k.
Hence speaking-truly and speaking-falsely both hold of u™s utterer at k.
Refutations. In Sophistici Elenchi 1 Aristotle says that ˜a refutation is a syl-
logism together with the contradictory of the conclusion™ (165a 2“3).40 He
means that a refutation is a syllogism41 together with the assertion contra-
dicting its conclusion, this assertion being the thesis originally endorsed by
the answerer in a dialectical debate.42
Sophistical refutations. For Aristotle, a sophistical refutation is an apparent
refutation.43 Since a refutation is a syllogism whose conclusion contradicts
the answerer™s original thesis, there are two main ways in which a sophis-
tical refutation may come to be:44 either the argument whose conclusion
is supposed to contradict the answerer™s original thesis appears to be a
syllogism,45 or the conclusion of the argument appears to contradict the
answerer™s original thesis.
The notion of appearance “ as Aristotle understands it with reference to
sophistical refutations “ has two aspects: falsehood (whatever appears so-
and-so is not so-and-so) and delusion (whatever appears so-and-so induces
people to believe it to be so-and-so). Since a sophistical refutation mainly
comes to be either because the argument at its heart appears to be a syl-
logism or because the conclusion of this argument appears to contradict
the answerer™s original thesis, it follows that a sophistical refutation mainly
comes to be either because the argument at its heart is not a syllogism but is
taken to be a syllogism, or because the conclusion of this argument does not
contradict the answerer™s original thesis but is taken to contradict it. Note
that no sophistical refutation is a refutation: ˜sophistical™ in ˜sophistical
refutation™ has a cancelling effect, like ˜fake™ in ˜fake diamond™.
40 Elsewhere Aristotle says that a refutation is ˜a syllogism of the contradictory™: see APr. 2.20, 66b 11;
SE 6, 168a 36“7; 9, 170b 1“2 (cf. 8, 169b 27“8; 10, 171a 1“5).
41 Here, as elsewhere in Sophistici Elenchi, ˜syllogism™ denotes not only those arguments with two
premisses constructed from three terms which are examined in the Prior Analytics, but also other
valid arguments (cf. Gobbo (1997), 330“3).
42 Cf. Cavini (1993b), 68“9; Berti (1996b), 61“2; Gobbo (1997), 333“4; Hitchcock (2000), 209.
43 SE 1, 164a 20“1; 8, 169b 18“23 (cf. 10, 171a 4“5). 44 SE 10, 171a 5“7 (cf. Hitchcock (2000), 209).
45 b 23“5; 101a 1“4; 8.12, 162b 3“5; SE 8, 169b 18“23; 11, 171b 7“11; 171b 18“19; 18, 176b 31“3; Rh.
Top. 1.1, 100
2.24, 1400b 34“5.
Truth as correspondence 141
For Aristotle, what is responsible for the sophistical refutation™s argument
appearing to be a syllogism or for the argument™s conclusion appearing to
contradict the answerer™s original thesis, is either a feature of language or a
move of the questioner™s that does not turn on language. Aristotle normally
refers to sophistical refutations of a given kind by means of a description
that begins with ˜dependent on™ (˜par†™ + accusative): a sophistical refu-
tation is thereby characterised as ˜dependent on™ the feature of language or
the questioner™s non-linguistic move that is responsible for its argument
appearing to be a syllogism or for this argument™s conclusion appearing to
contradict the answerer™s original thesis.46

Expressions used absolutely or with some quali¬cation. Sophistici Elenchi 25
concerns sophistical refutations ˜dependent on something being said strictly
or in some way, place, manner, or relation instead of absolutely™ (180a 23“
4).47 Call them ˜sophistical refutations dependent on the absolute or qual-
i¬ed use of expressions™.48
Sophistici Elenchi 25 contains the only Aristotelian passage that might
be (and has been) taken to discuss the Liar.49 The passage is introduced as
follows:
T 31 ˜Is it possible for the same man at the same time to keep his oath and to break
his oath?™ ˜Is it possible for the same man at the same time to obey the same
man and to disobey him?™ [. . .] Nor if one keeps one™s oath with regard to
this or in this way is it necessary that one should keep one™s oath (for he who
has sworn that he will break his oath, by breaking his oath keeps his oath
with regard to this only, but he does not keep his oath). Nor does he who
disobeys obey, but he obeys in some way.50 (180a 34“180b 2)


I understand the ˜par†™ + accusative (˜dependent on™) construction in Aristotle™s formulae ˜par‡
46
tŸn ¾mwnum©an™ (4, 165b 30), ˜par‡ tŸn ˆmjibol©an™ (4, 166a 6), etc. on the model of ˜par‡ tŸn
l”xin –mpoio“nta tŸn jantas©an™ (4, 165b 25): the ˜par†™ + accusative construction introduces
the factor on which the production (–mpoie±n) of appearance (jantas©a) depends.
47 Cf. SE 4, 166b 22“3.
48 Arguments dependent on the absolute or quali¬ed use of expressions are discussed by Aristotle also in
other passages, both in Sophistici Elenchi (4, 166b 22“3; 5, 166b 37“167a 20; 6, 168b 11“16; 7, 169b 9“12)
and elsewhere (Top. 2.11, 115b 11“35; Rh. 2.24, 1402a 3“29).
49 At EN 7.3, 1146a 21“7 Aristotle perhaps mentions the Liar. However: (i) The text is dubious: most
editors agree with Coraes that the crucial occurrence of ˜yeud»menov™ at 1146a 22 should be expunged
as a dittograph from 1146a 21. (ii) Even if ˜yeud»menov™ were retained, the passage could be speaking
(not of the Liar, but) of the treacherous character of all sophistical arguments (cf. Zell (1820), ii 258“
60). (iii) Even if ˜yeud»menov™ were retained and referred to the Liar, the passage would contribute
nothing signi¬cant to our understanding of Aristotle™s views on the Liar.
50 Some translators (e.g. Maurus (1668), i 624; O. F. Owen (1899/1900), ii 594“5) render ˜ˆpeiq”w™
at 180a 36 and 180b 1 (not by ˜to disobey™, but) by ˜to disbelieve™. However, ˜ˆpeiq”w™ meaning ˜to
disbelieve™ is attested only in late authors.
142 ˜Empty™ terms
T 31 discusses two sophistical refutations dependent on the absolute or
quali¬ed use of expressions. The ¬rst concerns a man swearing that he will
break his oath, the second a man who receives the order ˜Disobey me™. T
31 is followed by the passage that could contain Aristotle™s discussion of the
Liar:
T 32 Similar is the account of the claim that the same man is speaking falsely and
is speaking truly at the same time, but since it is not easy to see which of
the two renderings one should offer, that he is speaking truly or speaking
falsely absolutely, this case appears troublesome. However there is nothing to
prevent him51 from being false absolutely but truthful in some way or with
respect to something,52 and from being truthful with regard to some things
but, none the less, not truthful. (180b 2“7)
T 32™s sophistical refutation concerns a man who ˜is speaking falsely and is
speaking truly at the same time™ (180b 2“3). The argument leading to the
paradoxical conclusion that the same man should be speaking falsely and
truly at the same time is not recorded.

Interpretations of T 32. T 32 prompts various reactions.
(i) Some commentators53 take a sceptical stance: they doubt that the
argument on which T 32™s sophistical refutation turns can be reconstructed.
(ii) Others54 think that T 32™s sophistical refutation has nothing to do
with the Liar: Aristotle is instead describing a pattern of argument which
can be used whenever two contrary properties apply merely to a limited
extent or with some quali¬cation. Imagine the argument developing within
a dialectical debate. The questioner, after drawing the answerer™s attention
to some object which in different parts displays contrary properties to the
same extent, induces him to grant that an assertion where one of those
contrary properties is attributed to the object is both true and false. For
instance, the questioner shows the answerer a sphere which is half-white

At 180b 5 I read ˜kwl…ei d™ aÉt¼n oÉd•n™, the text handed down by the main manuscripts, probably
51
read by Sophonias (anon. in SE 58, 36), and printed by most editors. Michael of Ephesus ([Alex.
Aphr.] in SE 171, 5“6) seems to have read ˜oÉd•n d• kwl…ei t¼n aÉt¼n™, which might also be
presupposed by the Latin translations of Boethius (˜prohibet autem eundem nichil ™) and William of
Moerbeke (˜prohibet autem nichil eundem™). Forster prints ˜kwl…ei d™ t¼n aÉt¼n oÉd•n™, obviously a
misprint for ˜kwl…ei d• t¼n aÉt¼n oÉd•n™. Wallies reads ˜kwl…ei d™ oÉd•n™ and transposes ˜aÉt¼n™
to 180b 7 between ˜d•” and ˜mž™ (Ross strangely has ˜aÉt¼n™ both at 180b 5, between ˜kwl…ei d” and
˜oÉd•n™, and at 180b 7, between ˜d•™ and ˜mž™, and provides no explanation). Some translators (e.g.
Colli (1955), 710; Zanatta (1995), 233) take ˜aÉt¼n™ to refer to a discourse: this is unlikely in view of
the fact that the subject of ˜ye…desqai™ and ˜ˆlhqe…ein™ at 180b 2“3 is not a discourse but a man.
I place the comma after ˜pŸ€ d™ ˆlhq¦ ¢ tinov™ (180b 6): this is the punctuation printed by most
52
editors. Strache/Wallies instead place the comma between ˜pŸ€ d™ ˆlhq¦™ and ˜¢ tinov™. The phrase
˜ˆlhqžv tinov™ is dif¬cult: I take the genitive ˜tinov™ to be an ˜ablative genitive™ introducing an item
with which the person™s sincerity is compared (cf. Humbert (1945/60), 280“1).
53 54 E.g. [Alex. Aphr.] in SE 170, 28“171, 9.
E.g. Kneale/Kneale (1962), 228.
Truth as correspondence 143
and half-black and then gets him to grant that the assertion ˜This sphere is
white™ is both true and false.
(iii) Other commentators55 regard T 32™s sophistical refutation as an
argument that is linked with the ˜real™ Liar but differs from it in a way that
deprives it of its devastating strength (speci¬cally, they take T 32™s sophistical
refutation to lack the self-referential character of the real Liar). According
to these commentators, the questioner focuses the answerer™s attention on
a man who is false (someone who often lies). The answerer is then required
to imagine this man describing himself as false. The answerer is thereby
induced to grant that the man is both false (such he is by hypothesis) and
truthful (because, in describing himself as false, he speaks truly). Aristo-
tle™s solution is to indicate that the answerer did not genuinely contradict
himself. For while one of the two incompatible predicates applies to the
man absolutely, the other applies with some quali¬cation: ˜false™ applies
absolutely (because the man often lies), ˜truthful™ with some quali¬cation
(because the man speaks truly in describing himself as false). The paradox
dissolves in the same way as that of the Indian to whom ˜non-white™ applies
absolutely (because he is black in most of his body), ˜white™ with some
quali¬cation (because he is white in his teeth).56
(iv) Finally, some commentators57 regard T 32™s sophistical refutation as
a version of the real Liar.

Assessment of the various interpretations. (i) However sound a sceptical
approach to the scanty evidence may be, I am disinclined to renounce
the attempt to reconstruct T 32™s sophistical refutation. I therefore dismiss
the sceptical approach.
(ii) The context of T 32™s sophistical refutation tells against its ¬rst recon-
struction. For consider T 31™s ¬rst sophistical refutation. It probably turns
on the following argument. A man swears that he will break his oath. Later
he breaks his oath by not performing certain actions he had sworn he would
perform: e.g. he breaks his oath by not repaying a debt he had sworn he
would repay. But in doing so the man keeps his oath: for he keeps the oath
he had taken by swearing that he would break his oath. He therefore keeps
and breaks his oath at the same time. In his analysis Aristotle points out
that the man keeps one oath: he keeps the oath he had taken by swearing
55 Maurus (1668), i 624; von Kirchmann (1883), 53; Ranulf (1924), 176“9; Spade (1973), 300“6; Zaslawsky
(1982), 77“82; (1986), 244, 246“7; Dorion (1995), 385“6; Fait (1998), 139“40. This interpretation was
favoured by several medieval writers on fallacies (see Spade (1973), 303“6; (1987), 28“9).
56 Cf. SE 5, 167a 7“9.
57 Ockham in SE ii.x 4, 2“12; R¨ stow (1910), 48“53; Bochenski (1951), 101“2; (1962), 152“3; Moline
u
(1969), 398; K. D¨ ring (1972), 108; Montoneri (1984), 98“9; Marrone (1988), 273; Gourinat (2000),
o
199.
144 ˜Empty™ terms
that he would break his oath. But his keeping one oath only warrants that
˜keeps his oath™ should apply to him with some quali¬cation. In order for
˜keeps his oath™ to apply absolutely to him, he must keep all the oaths he
takes. Thus, in the situation envisaged, it is correct to say that the man
breaks his oath, but it is incorrect to say either that he keeps his oath or
that he keeps and breaks his oath at the same time. Again, consider T 31™s
second sophistical refutation. The argument on which it turns probably
goes as follows (I add a few details for clarity). A slave receives from his
master the order ˜Disobey me™. He then disobeys the orders his master sub-
sequently gives him: e.g. his master orders him to repay a certain debt but
he fails to do it. But in doing so the slave obeys the order which his master
had issued by saying ˜Disobey me™. Thus, the slave obeys and disobeys his
master at the same time. In his analysis Aristotle points out that the slave
obeys one of his master™s orders: the order issued by saying ˜Disobey me™.
But his obeying one of his master™s orders only warrants that ˜obeys his
master™ should apply to him with some quali¬cation. In order for ˜obeys
his master™ to apply absolutely to him, he must obey all his master™s orders.
Thus, in the situation envisaged, it is correct to say that the slave disobeys
his master, but it is incorrect to say either that the slave obeys his master or
that he obeys and disobeys his master at the same time.58 Now, the fact that
T 32™s sophistical refutation is presented immediately after those discussed
in T 31, which concern the man who swears that he will break his oath and
the man who is ordered ˜Disobey me™, tells against the ¬rst reconstruction:
if the ¬rst reconstruction of T 32™s sophistical refutation were correct, it
would be awkward to associate T 32™s sophistical refutation with those dis-
cussed in T 31. Moreover, T 31™s ¬rst sophistical refutation strongly suggests
that T 32™s sophistical refutation should turn around an argument closely
connected to the Liar: for one century after Aristotle, Chrysippus seems to
discuss the Liar in connection with the argument of the man who swears
that he will break his oath.59
(iii) This brings us to the second reconstruction of T 32™s sophistical
refutation: can T 32™s sophistical refutation be identi¬ed with the easy-
going argument envisaged by the second reconstruction, the weak strain
of the Liar that lacks self-reference? There is surely a lot going for the
second reconstruction. For T 31™s two sophistical refutations share a curious
characteristic: they are both easygoing arguments, and for each of them
there exists a dif¬cult version involving self-reference which is ignored by
58 Cf. Fait (1998), 140.
59 Chrysipp. Log. Invest., PHerc 307 coll. ix 23“x 6; x 28“31 (cf. R¨ stow (1910), 78“9). I shall return to
u
Chrysippus™ discussion.
Truth as correspondence 145
Aristotle. As for T 31™s ¬rst sophistical refutation, Aristotle does not address
the awkward situation of a man who takes an oath by saying ˜I swear
that I shall break this oath™; as for T 31™s second sophistical refutation,
Aristotle says nothing about the predicament of a man who receives the
order ˜Disobey this order™. Aristotle™s silence on the dif¬cult versions of T 31™s
two sophistical refutations suggests that something similar should be going
on with T 32™s sophistical refutation “ which is precisely what is happening
if T 32™s sophistical refutation is not the real Liar, but an easygoing argument
like the one put forward by the second reconstruction.60
However, several considerations suggest that T 32™s sophistical refutation
should be different from the second reconstruction™s easygoing argument.
(iii.i) Aristotle regards T 32™s sophistical refutation not only as analogous
to those from T 31, but also as harder: it is only about T 32™s sophistical
refutation that Aristotle says that it ˜appears troublesome™ (180b 5). Now,
this is the only passage from Sophistici Elenchi containing the adjective
˜troublesome™ (˜d…skolov™).61 The use of this adjective indicates that T
32™s sophistical refutation is special. If T 32™s sophistical refutation were an
easygoing argument like the one favoured by the second reconstruction,
there would be nothing special about it: it would be in the same league
as those from T 31. This circumstance provides some evidence for assuming
that T 32™s sophistical refutation should be not an easygoing argument like
the one favoured by the second reconstruction, but the real Liar, which is
much harder.62
(iii.ii) A passage from Chrysippus™ Logical Investigations handed down
on a badly damaged papyrus seems to discuss the Liar:
T 3363 Other arguments also tell against the preceding claim [sc. the claim that
the same man will both keep and break his oath]64 and the claim that they
will be speaking falsely and speaking truly at the same time. In all claims of
this sort on one occasion there are things said absolutely, on another with
something further being expressed together in addition. (PHerc 307 col.
x 18“25).65

60 Cf. Fait (1998), 139“40.
61 In the Topics ˜d…skolov™ occurs only once, at 8.1, 156b 34, where it describes not arguments but human
beings: answerers in a dialectical debate who do not play by the game™s rules.
62 Cf. R¨ stow (1910), 50“1.
u
63 My translation is based on the text in Marrone (1997), 93.
64 The claim that the same man will both keep and break his oath seems to have been discussed shortly
before: cf. the letters ˜omn™ at col. x 8, probably a trace of ˜½mn…ein™ (˜to swear™) (cf. col. ix 30).
65 Chrysippus™ attack on those who solve the Liar by claiming that some propositions are both true
and false is echoed by the title of one of his lost works on the Liar: Against those who hold that there
are things both false and true (D.L. 7. 196).
146 ˜Empty™ terms
In this passage Chrysippus seems to have in mind Aristotle™s discussion in
T 32.66 For:
(iii.ii.i) When he mentions the distinction between ˜things said abso-
lutely™ and ˜things said with something further being expressed together in
addition™, Chrysippus seems to be addressing the Aristotelian distinction
between things ˜said absolutely™ and things ˜said in some way, place, manner,
or relation instead of absolutely™ (SE 25, 180a 23“4).67 Chrysippus probably
uses the monster verb ˜to express together in addition™ (˜sunparenja©nein™,
a hapax) to indicate that when a linguistic expression is applied not abso-
lutely but with some quali¬cation, the respect justifying its application is
an additional factor which is part of the meaning but does not surface in
an explicit formulation.
(iii.ii.ii) Chrysippus™ phrase ˜they will be speaking falsely and speaking
truly at the same time [ye…sesqai aÉtoÆv Œma kaª ˆlhqe…sein]™ (col. x
20“1)68 is almost a literal quotation of Aristotle™s phrase ˜the same man is
speaking falsely and is speaking truly at the same time [ye…desqai t¼n
aÉt¼n Œma kaª ˆlhqe…ein]™ (180b 2“3).69
(iii.ii.iii) Chrysippus™ phrase ˜in all claims of this sort [–n pŽsin to±v
toio…toiv, sc. l»goiv]™ (col. x 22“3) echoes the phrase ˜all arguments of this
sort [p†ntev o¬ toio…toi l»goi]™ which Aristotle uses shortly before and
immediately after T 32 (at 180a 32 and 180b 8).70
Chrysippus, who lived one century after Aristotle, surely had more infor-
mation available about Aristotle than we do. If Chrysippus regarded Aris-
totle™s discussion in T 32 as an attempt to solve the real Liar, T 32 probably
was such an attempt.
(iii.iii) Theophrastus wrote a work in three books On the Liar.71 Its
content is unknown, but it is at least clear that Theophrastus was aware
of the importance of the Liar. We do not know whether Theophrastus
addressed the real Liar or some easygoing strain of it. However, in his
list of Chrysippus™ writings Diogenes Laertius (7. 197) mentions a work
(now lost) whose title was Solution according to the Ancients. The context
of Diogenes Laertius™ report suggests that the solution announced by this
title was a solution for the real Liar (for the works which in Diogenes
Laertius™ list come immediately before and immediately after were about
solutions for the real Liar). So Chrysippus, who lived one century after
Aristotle, probably thought that a certain solution for the real Liar had
been formulated so long before as to deserve the label ˜solution according
66 Barnes (1999a), 26“9 shows that Chrysippus could have read Aristotle™s logical writings.
67 Cf. R¨ stow (1910), 80; Ebbesen (1981), i 44; Baldassarri (1985/87), ii 105.
u
68 69 Cf. Marrone (1988), 275. 70 Cf. R¨ stow (1910), 80.
Cf. col. x 12“13; 15“16. u
71 Cf. D.L. 5. 49; R¨ stow (1910), 54; Graeser (1973), 57; Montoneri (1984), 99; Barnes (1999a), 37“8.
u
Truth as correspondence 147
to the ancients™. Later texts often refer to the early Peripatetics as ˜the
ancients™, and it is tempting to think that this later usage originated with
Chrysippus.72 So there is some plausibility in assuming that the solution
for the real Liar which Chrysippus describes as ˜solution according to the
ancients™ was endorsed by the early Peripatetics.73 This provides evidence for
thinking that Theophrastus addressed the real Liar. This, in combination
with Theophrastus™ close association to Aristotle in logic as well as in other
¬elds,74 makes it plausible to assume that Aristotle himself had some views
about the real Liar. But T 32 is the only Aristotelian passage that can be
taken to be about the Liar.
(iv) None of the above considerations is decisive. We cannot con¬dently
claim that T 32™s sophistical refutation turns on the real Liar and not on some
attenuated strain of it (like the one favoured by the second reconstruction),
nor can we rule out that the Liar might have evolved between Aristotle and
Chrysippus, and that Chrysippus, conscious of this development, might be
referring back to the Aristotelian solution of the weak version of the Liar.
Although we cannot con¬dently claim that T 32™s sophistical refutation
turns on the real Liar, it is worthwhile assuming that it does. Thus, hence-
forth I shall assume that T 32™s sophistical refutation turns on some version
of the real Liar, and then ask, ¬rst, what solution Aristotle was offering for
it, and, second, what this solution is worth.

Aristotle™s solution for the Liar: a tentative reconstruction. T 32™s discussion
of its sophistical refutation is compressed, and its interpretation must be
merely conjectural. I begin with the ¬rst half of T 32 (180b 2“5). It is tra-
ditionally interpreted as saying that a man who produced an utterance
of ˜I am speaking falsely™ speaks truly with respect to one content of this
utterance, falsely with respect to another.75 Were this interpretation cor-
rect, Aristotle™s position would be hopeless: what could the two distinct
contents of the utterance of ˜I am speaking falsely™ be?76 It would be better
to avoid saddling Aristotle with so poor a position. Let us then attempt a
new interpretation of Aristotle™s words.
Any plausible interpretation must take into account Aristotle™s claim
that ˜this case appears troublesome™ (180b 5) because ˜it is not easy to see
which of the two renderings one should offer, that he is speaking truly or

72 Cf. Brunschwig (1991), 83“7; Barnes (1999a), 32“3.
73 It is also worthwhile reporting that Chrysippus attacked a solution for the Liar which was based
on some kind of ˜cut™ (tomž) (see D.L. 7. 197). Some commentators (e.g. R¨ stow (1910), 65“6; O.
u
Becker (1957b), 51) think that this solution was the one advocated by Aristotle.
74 75 Cf. Calogero (1927), 359; Mignucci (1999b), 65.
Cf. n. 10 of appendix 4.
76 Cf. R¨ stow (1910), 50; Montoneri (1984), 99; Marrone (1988), 273; Cavini (1993a), 102.
u
148 ˜Empty™ terms
speaking falsely absolutely™ (180b 3“5). Now, when in Sophistici Elenchi 5 he
introduces sophistical refutations dependent on the absolute or quali¬ed
use of expressions, Aristotle does say something pertinent to this claim:
T 34 [Sometimes the distinction between an absolute and a quali¬ed use of a
linguistic expression escapes notice, as] in those cases where it is not easy
to see which of the two should be rendered strictly. Such a situation occurs
when the opposites hold to the same extent, for it seems that one should
grant that the thing is absolutely both or neither: e.g. if one half is white and
the other half black, is it white or black? (167a 15“20)
T 34 is evidently connected with the ¬rst half of T 32: T 34 discusses a
case where the distinction between the absolute and the quali¬ed use of a
linguistic expression is hard to spot, and T 34™s description of this case (˜It
is not easy to see which of the two should be rendered strictly™, 167a 16) is,
from a linguistic point of view, extremely close to that in the ¬rst half of
T 32 (˜It is not easy to see which of the two renderings one should offer,
that he is speaking truly or speaking falsely absolutely™, 180b 3“5). One of
Aristotle™s remarks in T 34 is particularly important for our purpose of
interpreting the ¬rst half of T 32: it is the remark that in the cases in
question ˜the opposites hold to the same extent™ (167a 17). In T 34™s example
the opposites are whiteness and blackness, which hold to the same extent
of (say) a sphere that is half-white and half-black. Since in the ¬rst half
of T 32 the opposites in question are speaking-truly and speaking-falsely,
Aristotle™s position with regard to the Liar is probably that speaking-truly
and speaking-falsely hold to the same extent of a man saying ˜I am speaking
falsely™ (or uttering whatever sentence-type the Liar turns on).77
What does Aristotle mean when he says that in the cases in question ˜the
opposites hold to the same extent™ (167a 17)? One plausible answer is that in
his view the situation where two opposites hold of the same object to the
same extent is that where the strongest consideration available in support of
one opposite holding is counterpoised by an equally strong consideration
in support of the other opposite holding. Consider again the sphere that
is half-white and half-black: whiteness and blackness hold of the sphere to
the same extent because the strongest consideration available in support
of whiteness holding of it (a consideration based on direct observation) is
counterpoised by an equally strong consideration in support of blackness
holding of it (also based on direct observation). A similar account holds
for speaking-truly and speaking-falsely with regard to a man uttering ˜I
am speaking falsely™. The strongest consideration available in support of
speaking-truly holding of this man at k is embodied in one half of the
77 Cf. anon. in SE 58, 31“6; Pacius (1597a), 523.
Truth as correspondence 149
Liar, and is counterpoised by an equally strong consideration in support of
speaking-falsely holding of this man at k, which is embodied in the other
half of the Liar. This is clear in the version of the Liar presented earlier:
the ¬rst half of that version concludes that speaking-truly holds of the man
at k, the second half that speaking-falsely holds of him at k, and the two
halves are equally strong.
In T 34 Aristotle points out that ˜when the opposites hold to the same
extent, [. . .] it seems that one should grant that the thing is absolutely both
or neither™ (167a 17“18). Aristotle does not say how the answerer should
behave in circumstances of the sort described. Of course, the sophist will
entice the answerer to admit that ˜the thing is absolutely both™. But what is
Aristotle™s advice? The most plausible answer is that Aristotle would advise
the answerer to say that ˜the thing is absolutely neither™. Thus, Aristotle™s
position is probably that what one should say with regard to a sphere
which is half-white and half-black is that it is neither absolutely white nor
absolutely black (although it is white in some respect and black in some
respect). Similarly, Aristotle™s position is probably that what one should
say with regard to a man who says ˜I am speaking falsely™ is that at k (a
time within some period over which the utterance is produced) neither
speaking-truly nor speaking-falsely hold absolutely of him (although they
both hold of him in some respect). Aristotle can therefore be plausibly taken
to be committed to the view that an utterance of ˜I am speaking falsely™ is
sometimes neither true nor false.
In his discussion of sophistical refutations dependent on the absolute or
quali¬ed use of expressions, Aristotle acknowledges many ways in which
a linguistic expression may fail to apply absolutely: for he describes these
sophistical refutations as dependent ˜on something being said strictly or
in some way, place, manner, or relation instead of absolutely™ (180a 23“4).
Aristotle does not say in what ˜way, place, manner, or relation™ speaking-
truly and speaking-falsely both hold of a man who says ˜I am speaking
falsely™. He merely argues that they both hold only in a quali¬ed sense
because they hold to the same extent.
The second half of T 32 (180b 5“7) is harder to interpret. It might be (and
has been)78 taken to mean that speaking-falsely holds absolutely of a man
who says ˜I am speaking falsely™ while speaking-truly holds of him merely
with some quali¬cation. The line which this interpretation attributes to
Aristotle seems hopeless: for the assumption that speaking-falsely holds
absolutely of the man whereas speaking-truly holds of him with some
quali¬cation seems no more justi¬ed than the opposite assumption that

78 Anon. in SE 58, 31“6.
150 ˜Empty™ terms
speaking-truly holds absolutely of the man whereas speaking-falsely holds
of him with some quali¬cation. We should therefore ¬nd an alternative
exegesis.
A good starting-point is a feature of the second half of T 32 overlooked
by commentators: Aristotle changes the expressions supposed to have an
absolute as well as a quali¬ed use. For while in the ¬rst half of T 32 the expres-
sions with an absolute and a quali¬ed use are ˜to speak truly™ (˜ˆlhqe…ein™)
and ˜to speak falsely™ (˜ye…desqai™), in the second half they are ˜truthful™
and ˜false™ (˜ˆlhqžv™ and ˜yeudžv™ applied to human beings).79 Why this
change of expression?
Two explanations are possible. First, Aristotle might be comparing the
behaviour of ˜to speak truly™ and ˜to speak falsely™ with that of ˜truthful™ and
˜false™ in order to justify that part of his analysis of the Liar which concerns
˜to speak truly™ and ˜to speak falsely™. More precisely, when he says that
nothing prevents the same man from ˜being false absolutely but truthful
in some respect™ (180b 5“6), Aristotle might be justifying his distinction
between an absolute and a quali¬ed use of ˜to speak truly™ and ˜to speak
falsely™, a justi¬cation which is needed because such a distinction is far from
obvious. The justi¬cation would be that since the distinction between an
absolute and a quali¬ed use is perfectly natural with ˜truthful™ and ˜false™ (it
is easy to see that the same person can be truthful in some respect or with
regard to certain topics while being, properly speaking, not truthful but
false), a parallel distinction between an absolute and a quali¬ed use must
apply also to ˜to speak truly™ and ˜to speak falsely™ (which are obviously
related to ˜truthful™ and ˜false™). Second, Aristotle might be contrasting the
real Liar with a similar but more easygoing paradox. Speci¬cally, note that
the second half of T 32 (180b 5“7) is introduced by an adversative particle
(˜however™, which translates the elided ˜d”™ at 180b 5). Aristotle might thereby
be indicating what differentiates the real Liar, whose formulation involves
˜to speak truly™ and ˜to speak falsely™, from a similar easygoing paradox
formulated by using ˜truthful™ and ˜false™. He might be saying that the
two paradoxes differ because while in the real Liar it is not the case that
one expression applies absolutely and the other with some quali¬cation,
in the easygoing paradox ˜false™ applies absolutely while ˜truthful™ applies
with some quali¬cation. Aristotle would then be alerting his readers to how
different the real Liar is with respect to easygoing arguments like the one
attributed to him by the second reconstruction.80 If this explanation of the
79 29, 1025a 1“13; EE 2.3, 1221a 6; 3.4, 1233b 38;
For this use of ˜ˆlhqžv™ and its cognates cf. Metaph.
1234a 2.
80 See the paragraph to which n. 55 above pertains.
Truth as correspondence 151
change from ˜to speak truly™ and ˜to speak falsely™ to ˜truthful™ and ˜false™
is correct, then Aristotle was aware that the real Liar is much harder than
easygoing arguments like the one envisaged by the second reconstruction,
i.e. that the real Liar is ˜troublesome™.
How satisfactory is Aristotle™s solution? If the interpretation offered in the
preceding subsection is correct, Aristotle can be plausibly taken to be com-
mitted to the view that an utterance of ˜I am speaking falsely™ is sometimes
neither true nor false. Such a position recalls that of de Interpretatione 9,
where Aristotle claims that some future-tense singular assertions are some-
times neither true nor false.
Aristotle™s solution for the Liar is unsatisfactory because it leaves him
exposed to the Strengthened Liar. Consider an utterance v of ˜This assertion
is not true™: v generates a dif¬culty similar to that af¬‚icting an utterance of
˜I am speaking falsely™. On the one hand, if v is not true at a time j within
some period over which v is produced, then at j the universal signi¬ed by
v™s predicate (an utterance of ˜true™) does not hold of the item signi¬ed by
v™s subject (an utterance of ˜this assertion™), so that v is true at j. So, if v is
not true at j it is true at j. Hence v is true at j. On the other hand, if v is true
at j, then at j the universal signi¬ed by v™s predicate does not hold of the
item signi¬ed by v™s subject, so that v is not true at j. So, if v is true at j it is
not true at j. Hence v is not true at j. Therefore at j v is true and not true.
But the escape route that seemed to work with utterances of ˜I am speaking
falsely™ is unavailable in the case of an utterance v of ˜This assertion is not
true™: it does not help to say that at j v is neither true nor false or that at j
v is neither true nor not true. For, in both cases (both in the case in which
at j v is neither true nor false and in the case in which at j v is neither true
nor not true), v is not true at j, and, as we have seen, if v is not true at j it
is true at j.
However, even if Aristotle™s solution for the Liar is unsatisfactory, the
direction Aristotle had begun going is not hopeless. For some modern
coherent and respectable attempts to solve the Liar make moves that resem-
ble Aristotle™s: they treat ˜I am speaking falsely™ as a case where it is inde-
terminate which of the predicates ˜true™ and ˜false™ applies (in analogy to
the well-known cases of vagueness concerning predicates like ˜bald™ and
˜heap™).81 Of course, one cannot say that Aristotle anticipated this modern
solution, especially when one recalls that he never explicitly discussed even
the well-known cases of vagueness.82
81 82
Cf. McGee (1991), 4“7. Cf. Moline (1969), 397“8; Fait (1998), 138, 151.
ch a pt er 5

˜Vacuous™ terms and ˜empty™ terms 1




As we saw in chapter 4, Aristotle™s theory of truth for assertions can
be regarded as a correspondence-as-isomorphism theory of truth: Aris-
totle takes an assertion™s truth to consist in a certain isomorphism
obtaining between the assertion and reality. We also saw that Aristotle™s
correspondence-as-isomorphism theory of truth presents itself in two for-
mats. In the ¬rst, the components of reality with respect to which a true
assertion™s isomorphism holds are objects that correspond to assertions as
wholes (one object corresponding to one complete assertion). In the sec-
ond format, which concerns mainly predicative assertions, the components
of reality with respect to which a true predicative assertion™s isomorphism
holds correspond to parts of the assertion: they are objects, i.e. universals or
individuals, signi¬ed by the assertion™s predicate and subject. A well-known
dif¬culty faced by correspondence-as-isomorphism theories of truth of the
second format is the problem of ˜vacuous™ terms. What happens if either the
subject or the predicate of an assertion is ˜vacuous™, i.e. fails to signify an
item of the appropriate kind?2 A correspondence-as-isomorphism theory
of truth of the second format loses one of its toeholds.3


1 An earlier version of this chapter appeared as Crivelli (2001).
2 I apply ˜(non-)vacuous™ to any expression that fails to signify (signi¬es) an item of the appropriate
kind. I reserve ˜(non-)empty™ for any expression that fails to signify (signi¬es) an existent item of the
appropriate kind.
Every ˜vacuous™ expression is ˜empty™; the converse holds if there are no non-existent items. I believe
that for Aristotle there are no non-existent items, and that therefore for Aristotle an expression is
˜vacuous™ just in case it is ˜empty™. However, the claim that for Aristotle there are no non-existent
items needs to be proved (cf. the subsection to which n. 24 below pertains).
Note that an expression can be ˜vacuous™, and therefore also ˜empty™, while denoting existent
individuals. For instance, if there is no universal walking-white-man (cf. Int. 11, 20a 15“19), ˜walking
white man™ is ˜vacuous™ (because there is no item of the appropriate kind for it to signify), and
therefore ˜empty™, but denotes existent individuals (walking white men).
3 On the problem of ˜vacuous™ terms cf. Trendelenburg (1876), 78; Brentano (1889), 19, 22 (cf. Srzednicki
(1965), 19); Brentano (1915a), 219“20; (1915b), 133“4; (1952), 137“8; Jacobs (1979), 286; Hallett (1988),
8; Fiorentino (2001), 280.

152
˜Vacuous™ terms and ˜empty™ terms 153
Section 1 contains four arguments for the thesis that Aristotle™s reply to
the problem of ˜vacuous™ terms is that in every predicative assertion both the
predicate and the subject are ˜non-vacuous™ in that they signify items of the
appropriate kinds. The ¬rst three arguments appeal to Aristotle™s descrip-
tions of af¬rmative and negative assertions, the fourth to his treatment of
a certain type of anomalou sentence in de Interpretatione 8.
Section 2 argues that Aristotle in fact has a position that is even stronger
than the one attributed to him in section 1: he thinks that in every pred-
icative assertion both the predicate and the subject are ˜non-empty™ in that
they signify existent items of the appropriate kinds.
Section 3 discusses Aristotle™s position on utterances that look like pred-
icative assertions whose predicate or subject is ˜empty™ (e.g. utterances of ˜A
goatstag is white™ or ˜A goat is a goatstag™). These utterances are not genuine
predicative assertions. Rather, they are composite assertions, i.e. utterances
equivalent to utterances constructed from several assertions linked by con-
nective particles. In some cases, what on the surface appears to be a con-
tradictory pair of predicative assertions will really be a pair of composite
assertions which are both false.


1 ˜vac u ou s™ s ub j e c ts or predi cat es
Subjects and predicates are ˜non-vacuous™. Aristotle thinks that in every pred-
icative assertion both the predicate and the subject are ˜non-vacuous™ in
that they signify items of the appropriate kinds. Here are four plausible
arguments for this thesis.

(i) ˜Something asserted about, or away from, something™. Aristotle claims
both that in every af¬rmative predicative assertion something is asserted
about something, and that in every negative predicative assertion some-
thing is asserted away from something.4 Aristotle formulates these claims
with the inde¬nite pronoun ˜something™ in an emphatic position: ˜Some-
thing is asserted about something ™, ˜Something is asserted away from some-
thing ™. Such formulations strongly suggest that for Aristotle in every
af¬rmative or negative predicative assertion both the predicate and the
subject are ˜non-vacuous™ in that they signify items of the appropriate
kinds.5


4 See n. 28 of ch. 2.
5 Cf. Jacobs (1979), 284“6; (1980), 423“5 (contra Simpson (1981), 84“5; Wedin (1990), 136“7).
154 ˜Empty™ terms
(ii) Af¬rmations, denials, joining, and separating. Aristotle thinks that in
every af¬rmative predicative belief one item is joined with one item, and
that in every negative predicative belief one item is separated from one
item.6 He also holds that in every af¬rmative predicative assertion one item
is asserted about one item, and that in every negative predicative assertion
one item is asserted away from one item. He probably regards the operations
of asserting-about and asserting-away-from performed in af¬rmative and
negative predicative assertions as the linguistic counterparts of the mental
operations of joining and separating performed in af¬rmative and nega-
tive predicative beliefs. He therefore probably thinks that the operation of
asserting-about or asserting-away-from performed in a predicative asser-
tion applies to the same items to which the mental operation of joining
or separating applies in the predicative belief expressed by the predicative
assertion.7 But how could something which is not there be joined with, or
separated from, something which is not there?8 Hence Aristotle probably
believes that the operations of asserting-about and asserting-away-from are
performed on items which are there. But now Aristotle is likely to hold that
what is signi¬ed by the predicate of a predicative assertion is asserted about
or away from what is signi¬ed by the subject of that assertion. Hence Aris-
totle is probably committed to the view that in every predicative assertion
both the predicate and the subject signify items that are there.

(iii) Joining and separating performed on inhabitants of the categories. In
the last subsection I pointed out that Aristotle can be plausibly credited
with the view that the operation of asserting-about or asserting-away-from
performed in a predicative assertion applies to the same items to which
the mental operation of joining or separating applies in the predicative
belief expressed by the predicative assertion. In Metaphysics E 4 (1027b 29“
33) Aristotle says that the items joined or separated by an af¬rmative or
negative predicative belief are inhabitants of the categories.9 Hence he is
probably committed to the view that the operations of asserting-about and
asserting-away-from are performed on inhabitants of the categories. But,
as I pointed out in the last subsection, Aristotle probably holds that what
is signi¬ed by the predicate of a predicative assertion is asserted about or
away from what is signi¬ed by the subject of that assertion. Hence Aristotle
is probably committed to the view that in every predicative assertion both
6 Cf. the subsection to which n. 74 of ch. 1 pertains.
7 Cf. the subsection to which n. 35 of ch. 2 pertains.
8 Cf. Miller (1971), 53, 56; Pardey (2000), 17“19.
9 Cf. the subsection to which n. 54 of ch. 2 pertains.
˜Vacuous™ terms and ˜empty™ terms 155
the predicate and the subject signify inhabitants of the categories. Since
he surely believes that the inhabitants of the categories are there, he seems
committed to the view that in every predicative assertion both the predicate
and the subject signify items that are there.

(iv) De Interpretatione 8. In de Interpretatione 8 Aristotle says:
T 35 A single af¬rmation or denial signi¬es a single item about a single item (in
case this last item is a universal, it makes no difference whether the af¬rmation
or the denial signi¬es universally or not). (18a 13“14)
But if a single name is given to two items which do not make up a single
one, there is neither a single af¬rmation nor a single denial.10 For instance,
if somebody were to give the name ˜cloak™ to horse and man, ˜A cloak is
white™ would be neither a single af¬rmation nor a single denial:11 for there
is no difference between saying this and ˜A horse and a man is white™, and
saying this does not differ at all from saying ˜A horse is white and a man is
white™.12 So if these signify many things and are many, clearly the ¬rst also
signi¬es either many things or nothing (for it is not the case that some man
is a horse).13 Hence, in the case of these, too, it is not necessary that one
contradictory should be true and the other false. (18a 18“27)
In T 35 Aristotle speaks of a single name given to ˜two items which do
not make up a single one™ (18a 18). To illustrate, he imagines somebody
giving ˜the name “cloak” to horse and man™ (18a 19“20). Then (18a 20“6) he
considers the expression ˜A cloak is white™, which contains the name ˜cloak™,
and he argues that ˜A cloak is white™ ˜signi¬es either many things or nothing™
(18a 25). Is Aristotle thinking of ambiguity? In other words, when Aristotle
imagines the name ˜cloak™ given to horse and man, is he imagining ˜cloak™ to
be ambiguous? When he says that the expression ˜A cloak is white™ ˜signi¬es
either many things or nothing™ (18a 25), is he claiming that this expression is
either ambiguous or lacking signi¬cation? Some commentators14 answer all

I read ˜oÉ m©a kat†jasiv oÉd• ˆp»jasiv m©a™ (18a 18“19) with some of the main witnesses, Pacius,
10
Buhle, Bekker, Weise, and D¨ bner. Minio-Paluello, Waitz, Cooke, and Zadro, following other wit-
u
nesses, omit ˜oÉd• ˆp»jasiv m©a™.
11 I read ˜oÉ m©a kat†jasiv oÉd• ˆp»jasiv m©a™ (18a 20“1) with all the main witnesses and most editors.
Minio-Paluello and Zadro delete ˜oÉd• ˆp»jasiv m©a™.
12 Here (18a 23) I agree with those translators (e.g. Gohlke (1951), 94; Ackrill (1963), 49) who take Aristotle
to be mentioning a single conjunctive assertion (˜A horse is white and a man is white™). Others (e.g.
Weidemann (1994/2002), 11, 219) take Aristotle to be mentioning two separate simple assertions (˜A
horse is white™ and ˜A man is white™).
13 Some (e.g. Colli (1955), 65; Riondato (1957a), 137; Zanatta (1992), 93; Weidemann (1994/2002), 11,
221) translate ˜[. . .] (for it is not the case that there is some man-horse)™.
14 Ammon. in Int. 126, 11“14; Boeth. in Int. Pr. Ed. 102, 21“4; 103, 12“13; in Int. Sec. Ed. 178, 17“23; 181,
25“8; 183, 5; Steph. in Int. 33, 19“33; anon. in Int. 51, 3“13; Aquinas in Int. 162“3 Spiazzi; Ockham in
Int. i.vi 5, 8“21; Pacius (1597b), 96; (1597a), 77; Maurus (1668), i 70; Steinthal (1863/90), i 245“6;
156 ˜Empty™ terms
these questions af¬rmatively. However, the following considerations show
that the negative answer is more plausible.15
(iv.i) T 35 does not contain expressions like ˜to be said in many ways™ or
˜homonymy™, which Aristotle normally uses in discussing ambiguity.16
(iv.ii) When, in T 35, he imagines somebody giving ˜the name “cloak” to
horse and man™ (18a 19“20), Aristotle intends to explain what he meant in
speaking of a single name given to ˜two items which do not make up a single
one™ (18a 18). In de Interpretatione 11 (20b 13“19) Aristotle returns to the issue
of a single name given to many items which do not make up a single one.
He produces further examples. Animal, biped, and tame are three items
which do make up a single one. Although the phrase ˜biped tame animal™
does in a way signify animal and tame and biped, one can take it to signify
the single item biped“tame“animal consisting of animal, tame, and biped.17
By contrast, walking, white, and man are three items which do not make
up a single one. Even if there were a syntactically simple expression “
˜whitewalker™, say “ which signi¬es walking, white, and man in the same
way as the phrase ˜walking white man™, ˜whitewalker™ would not signify
a single item walking“white“man consisting of walking, white, and man:
for there is no such single item. Since the phrase ˜walking white man™ and
the imaginary name ˜whitewalker™ which is semantically equivalent to it
are not ambiguous, the phenomenon Aristotle has in mind when he speaks
of a single name given to many items which do not make up a single one
cannot be identi¬ed with ambiguity.
It is therefore likely that it is not ambiguity that Aristotle has in mind
when in T 35 he speaks of a single name given to ˜two items which do not
make up a single one™ (18a 18) and offers as an example the name ˜cloak™
given to horse and man. What he does have in mind is probably a situation
analogous to that arising with plural sentences: as the phrase ˜Coriscus and
Callias™ in the plural sentence ˜Coriscus and Callias are at home™ signi¬es
two items (the individuals Coriscus and Callias) which do not make up a
unity (and ambiguity remains out of the picture), so the expressions ˜cloak™
(understood in the way suggested by T 35) and ˜horse and man™ signify two
items (the universals horse and man) which do not make up a unity (and

Riondato (1957a), 71; Sainati (1968), 223; Celluprica (1987), 182, 184; Zanatta (1992), 27“8. Boethius
(in Int. Sec. Ed. 183, 20“1) says that his account of de Interpretatione 8 agrees with that of Aspasius,
Porphyry, and Alexander.
15 Cf. Ackrill (1963), 126, 131; Irwin (1982), 244; Barnes (1994), 98; Weidemann (1994/2002), 220;
Whitaker (1996), 97, 105; Wheeler (1999), 219.
16 Cf. e.g. Top. 5.2, 129b 31; SE 4, 165b 26.
17 At APo. 2.13, 96b 30“5 ˜biped tame animal™ is a possible de¬niens of man. In the Topics (5.1, 128b 16“18;
2, 130a 27“8; 3, 132a 6“9; 8, 138a 10“12; 9, 139a 18“20) ˜animal by nature tame™ expresses a peculiarity of
man.
˜Vacuous™ terms and ˜empty™ terms 157
ambiguity, again, remains out of the picture).18
Aristotle thinks that the expression ˜A cloak is white™ can be analysed in
two ways. He claims that on its second analysis it ˜signi¬es [. . .] nothing
(for it is not the case that some man is a horse)™ (18a 25“6).19 The argument
on behalf of this claim can be variously interpreted. On the interpretation
which seems to me most plausible (an interpretation I shall not defend
here), Aristotle™s argument is the following:
[a] There is no universal horse-and-man which is the ˜logical product™ of
the universals horse and man.20
[b] If ˜A cloak is white™ (on its second analysis, whereby it is treated as
an indeterminate af¬rmative predicative assertion) signi¬es something,
then there is a universal horse-and-man which is the ˜logical product™
of the universals horse and man.
[c] ˜A cloak is white™ (on its second analysis, whereby it is treated as an
indeterminate af¬rmative predicative assertion) signi¬es nothing.
Propositions [a] and [b] are premisses. The rationale of [a] is the idea that
if there were a universal horse-and-man which was the ˜logical product™
of the universals horse and man, it would always be predicated of at least
one individual which at some time or other exists.21 But, far from being
always so predicated, the universal in question would never be predicated
of any individual which at some time or other exists (because no individual
ever existed or will exist that is both a horse and a man). The rationale
of [b] is the principle of Aristotle™s semantics according to which every
indeterminate af¬rmative predicative assertion asserts non-universally that
the universal signi¬ed by its predicate holds of the universal signi¬ed by
its subject.22 For this principle requires that if ˜A cloak is white™ signi¬es
something when it is regarded as an indeterminate af¬rmative predicative
assertion, then there is a universal signi¬ed by its subject ˜cloak™. But this
universal signi¬ed by ˜cloak™ could only be the universal horse-and-man
which is the ˜logical product™ of the universals horse and man. Conclusion
[c] follows from [a] and [b]. A consequence Aristotle ˜leaves to the reader™
is that on its second analysis, the expression ˜A cloak is white™ even fails to

18 Cf. SE 17, 175b 41“176a 10. 19 I shall discuss Aristotle™s ¬rst analysis later.
20 I am assuming that for Aristotle the compound of horse and man “ if there were any such thing “
would be the universal horse-and-man which is the ˜logical product™ of the universals horse and man.
This is a plausible assumption: for at Int. 11, 20b 15“19, where he offers other examples of compounds
which are analogous to the would-be compound of horse and man, Aristotle seems to consider
˜logical products™ of universals.
21 22 Int. 7, 17b 1“12.
Cf. the last subsection of sect. 1 of ch. 2.
158 ˜Empty™ terms
be an assertoric sentence because ˜a sentence is a spoken sound signi¬cant
by convention™ (Int. 4, 16b 26).23
If this interpretation of Aristotle™s argument on behalf of his claim that
˜A cloak is white™ on its second analysis signi¬es nothing is correct, then
Aristotle is probably committed to the view that in every indeterminate
af¬rmative predicative assertion the subject must be ˜non-vacuous™ in that
it signi¬es some universal: if an utterance looks like an indeterminate af¬r-
mative predicative assertion whose would-be subject is ˜vacuous™ in that
it fails to signify a universal, then this utterance is not an indeterminate
af¬rmative predicative assertion because it fails to signify in the way that is
appropriate to such assertions.
Aristotle is probably also committed to the further view that if an
utterance looks like an indeterminate negative predicative assertion whose
would-be subject is ˜vacuous™, then this utterance is not an indeterminate
negative predicative assertion because it fails to signify in the appropriate
way: for if the subject™s being ˜vacuous™ causes a would-be indeterminate
af¬rmative predicative assertion to signify nothing, it is hard to see how
the subject™s being ˜vacuous™ could fail to cause the corresponding would-
be indeterminate negative predicative assertion to signify nothing. So
Aristotle seems committed to a general view about indeterminate pred-
icative assertions: if an utterance looks like an indeterminate predicative
assertion whose would-be subject is ˜vacuous™, then this utterance is not
an indeterminate predicative assertion because it fails to signify in the way
appropriate to such assertions.
Moreover, Aristotle is unlikely to restrict such a view to indeterminate
predicative assertions. That is, Aristotle would probably grant the following:
in every general predicative assertion the subject must be ˜non-vacuous™,
and if an utterance looks like a general predicative assertion whose would-be
subject is ˜vacuous™, then this utterance is not a general predicative assertion
because it fails to signify in the way appropriate to such assertions.

2 ˜empt y™ s ub j ects or p redi cate s
˜Non-vacuous™ vs ˜non-empty™. The previous section™s considerations make it
plausible to credit Aristotle with the view that in every predicative assertion
both the predicate and the subject are ˜non-vacuous™, i.e. signify items of the
appropriate kinds. Does he also believe that in every predicative assertion

23 Cf. Ackrill (1963), 132; Geach (1963), 17; Irwin (1982), 244“5; Whitaker (1996), 97“8. For the reading
cf. n. 96 of ch. 1.
˜Vacuous™ terms and ˜empty™ terms 159
both the predicate and the subject are (not only ˜non-vacuous™, but also)
˜non-empty™, i.e. signify existent items of the appropriate kinds?
Commentators disagree. In the following subsections I offer four plau-
sible arguments on behalf of the af¬rmative answer.

(i) ˜Everything exists™. Aristotle probably believes that all items are existent
items.24 For:
(i.i) The following passage from Topics 4.6 seems a formulation of this
view:
T 36 Being and one are predicated of absolutely25 everything. (127a 33“4)26
One might object that T 36™s provenance from the Topics reduces its evi-
dential value (after all, in the Topics Aristotle often presents views he does
not endorse). The objection is answered by highlighting that T 36 is echoed
by the following cursory remark in Metaphysics 2:
T 37 Being is common to everything. (1004b 20)27
(i.ii) Aristotle, who has a well worked-out ontology, never states that
some items are non-existent. Since this is a somewhat out-of-the-way view,
if a philosopher with a well worked-out ontology never states it then one
can assume that she or he endorses its contradictory, i.e. that all items are
existent.
Now, as we saw in section 1, Aristotle probably holds that in every
predicative assertion both the predicate and the subject are ˜non-vacuous™ in
that there are items of the appropriate kinds which they signify. As we have
just seen, he also probably holds that all items are existent items. Hence
he is probably committed to the view that in every predicative assertion
both the predicate and the subject signify existent items of the appropriate
kinds, i.e. are ˜non-empty™.

(ii) Items within the categorial scheme. As we saw, Aristotle is probably
committed to the claim that in every predicative assertion both the pred-
icate and the subject signify inhabitants of the categories.28 This made it
24 Cf. Wagner (1961/62), 78; Grice (1988), 178. By contrast, Thom (2002), 298“300 attributes to Aristotle
an ontology parallel to Meinong™s, according to which some items exist and others do not.
25 T 36™s context makes it clear that ˜absolutely™ (˜‰pl¤v™) modi¬es ˜everything™ (˜p†ntwn™), not ˜are
predicated™ (˜kathgore±tai™): Aristotle means (not that being and one are absolutely-predicated of
everything, but) that being and one are predicated of absolutely-everything.
26 Cf. 4.1, 121b 5“7; 6, 127a 27“8.
27 The same point is made or implied elsewhere: see Metaph. B 3, 998b 20“1; 4, 1001a 19“22; Z 4, 1030a 21;
I 2, 1053b 20“1; K 1, 1059b 28“9; 2, 1060b 4“5; L 4, 1070b 7“8.
28 Cf. the subsection to which n. 9 above is appended.
160 ˜Empty™ terms
plausible to credit him with the view that there are items of the appropriate
kinds signi¬ed both by the predicate and by the subject of any predica-
tive assertion. Now, the inhabitants of the categories are existent items.29
Hence, if Aristotle is committed to the claim that both the predicate and
the subject of any predicative assertion signify inhabitants of the categories,
he is committed also to the claim that both the predicate and the subject
of any predicative assertion signify existent items of the appropriate kinds,
i.e. are ˜non-empty™.

(iii) De Interpretatione 8. In T 35 (an excerpt from de Interpretatione 8)
Aristotle considers the case of a single name given to ˜two items which do
not make up a single one™ (18a 18); he illustrates it by imagining somebody
giving ˜the name “cloak” to horse and man™ (18a 19“20); he considers the
expression ˜A cloak is white™ (18a 20), which he regards as analysable in two
ways; and he claims that on its second analysis it ˜signi¬es [. . .] nothing
(for it is not the case that some man is a horse)™ (18a 25“6). I previously30
reconstructed Aristotle™s argument for his claim that ˜A cloak is white™,
on its second analysis, signi¬es nothing. Now, if Aristotle allowed some
indeterminate assertion to have a subject which is ˜empty™ because it signi¬es
a non-existent universal, ˜A cloak is white™ would surely be an example of
this case. Then he would not be in a position to claim that ˜A cloak is white™,
on its second analysis, signi¬es nothing.

(iv) The Square of Opposition. Assume the laws of the Square of Opposition,
and assume that every particular predicative assertion is true only when its
subject denotes at least one individual that at some time or other exists.
Take any quanti¬ed predicative assertion, and suppose that at a time t its
subject denotes no individual that at some time or other exists. Consider a
quartet of ˜coincident™ quanti¬ed predicative assertions: a universal af¬rma-
tive, a universal negative, a particular af¬rmative, and a particular negative
predicative assertion in each of which the subject is a token (an utterance) of
the same type as the subject of the original quanti¬ed predicative assertion,
and, similarly, the predicate is a token (an utterance) of the same type as
the predicate of the original quanti¬ed predicative assertion.31 Then at t the
subjects of the particular predicative assertions denote no individual that at
some time or other exists. Then neither particular predicative assertion is
29 Carson (1996), 21“2, doubts that the items in the categorial scheme should be existent items, but his
reasons are unpersuasive.
30 See the subsection to which n. 10 above is appended.
31 For ˜coincident™ see n. 9 of the introduction.
˜Vacuous™ terms and ˜empty™ terms 161
true at t. Then, by the Law of Contradictories, both universal predicative
assertions are true at t. This clashes with the Law of Contraries.32 Thus,
the laws of the Square of Opposition seem to require that in every quan-
ti¬ed predicative assertion the subject should always denote at least one
individual that at some time or other exists.33
Now, if Aristotle believes that in every predicative assertion both the
predicate and the subject are ˜non-empty™, then his theory probably satis¬es
such a requirement. To see this, assume that for Aristotle in every predicative
assertion both the predicate and the subject are ˜non-empty™, i.e. signify
existent universals. Since Aristotle is probably committed to the view that
every universal always holds of some individual or other that at some time or
other exists,34 he is probably committed to the view that in every quanti¬ed
predicative assertion the subject always denotes some individual or other
that at some time or other exists “ as the laws of the Square of Opposition
seem to require.

Objections. Categories 10, 13b 12“33 commits Aristotle to the claim that if
Socrates does not exist, then ˜Socrates is sick™ is false and ˜Socrates is not
sick™ true. Several passages35 commit him to the claim that certain negative
predicative expressions are true of what does not exist. De Interpretatione
11, 21a 25“8 commits him to the claim that although Homer does not exist,
˜Homer is a poet™ is true.
However, these passages do not commit Aristotle to the claim that some
true predicative assertion has an ˜empty™ subject. They only commit him to
the claim that the subject of some true singular predicative assertion refers
to an object that does not exist at the time with respect to which the assertion


32 For the Law of Contradictories and the Law of Contraries see nn. 15 and 17 of appendix 5 and the
portions of the main text they pertain to.
33 Alternative defences of the laws of the Square of Opposition are available that do not assume that in
every quanti¬ed predicative assertion the subject should always denote at least one individual that at
some time or other exists. These alternative defences, however, face their own dif¬culties. I cannot
address here all the issues raised by the Square of Opposition “ for some discussion see Brentano
(1909), 61; Bird (1964), 71“82; Church (1965), 418“24; Dapunt (1968); Cavini (1985), 42“3; Crivelli
(1989), 79“85; Beaney (1996), 32, 273“5; Mulder (1996), 143“9.
34 Cf. the last subsection of sect. 1 of ch. 2.
35 Int. 3, 16b 12“15 (cf. 2, 16a 30“3; 10, 19b 5“18; 20a 31“40; Metaph. K 9, 1066a 15“16); Xen. 4, 978b 15“33;
Metaph. I 3, 1054b 18“21; de Ideis fr. 118, 3 Gigon 378a 23“378b 1 (= Alex. Aphr. in Metaph. 80, 16“17);
378a 45“378b 45 (the passage of the recensio altera that corresponds to Alex. Aphr. in Metaph. 80, 19“81,
2). APr. 1.46, 51b 5“52a 14 (cf. Int. 10, 19b 19“36) is variously interpreted: on one interpretation (see e.g.
Wedin (1978), 188“93; (1990), 142“3) it commits Aristotle to the claim that a negative predicative
expression is true of what does not exist; on another (see e.g. Ross (1949), 422“3; Soreth (1973), 403,
404) no such commitment obtains.
162 ˜Empty™ terms
is evaluated as true or false.36 The passages are consistent with the following
claim:
[27] In every singular predicative assertion, the subject signi¬es an individ-
ual which at some time or other exists (the time when it exists can be
distant both from that at which the assertion is produced and from
that with respect to which it is evaluated as true or false).37 In every
singular predicative assertion, the predicate signi¬es a universal which
always exists, i.e. a universal always predicated of at least one individ-
ual which at some time or other exists. In every general predicative
assertion, both the predicate and the subject signify universals that
always exist.38
Note how natural this way is of understanding the claim ˜In every predica-
tive assertion both the predicate and the subject signify existent items of
the appropriate kinds™: the claim would be implausibly restrictive if it were
to ban from the realm of predicative assertions an utterance of ˜Socrates is
a philosopher™ on the ground that its subject does not signify something
that exists at the time when the utterance is produced or at the time with
respect to which it is evaluated.39

Seeming predicative assertions with an ˜empty™ predicate or subject. Proposition
[27] implies that if an utterance looks like a predicative assertion but its
36 Cf. Kahn (1976), 325, 326; Pardey (2000), 29“31, 40“1.
37 The question whether reference can be made to what does not yet exist is debated in modern logic
(see e.g. Mayo (1962/68), 282“91), but does not seem to have worried ancient logicians: no dif¬culty
was felt in Apollo™s predicting one thousand years in advance that Cypselus would rule Corinth (see
Cic. Fat. 7.13 with D. Frede (1998), 98).
38 Aristotle™s position might seem inconsistent: what he says about ˜Socrates is sick™ might seem to
require that every af¬rmation should be false when no item signi¬ed by its subject exists, while
his discussion about ˜Homer is a poet™ might seem to require that some af¬rmation should be true
when no item signi¬ed by its subject exists. Some commentators (e.g. Oehler (1984), 274) think
there is a genuine inconsistency here. However, as other commentators (Barnes (1986), 208“9; van
Bennekom (1986), 15; Mignucci (1997a), 61; Thom (2002), 299“300) point out, the inconsistency
is merely apparent. Aristotle™s remarks about ˜Socrates is sick™ do not require every af¬rmation to
be false when no item signi¬ed by its subject exists: af¬rmations with predicates other than ˜sick™
(e.g. ˜poet™) may behave differently. For different explanations of Aristotle™s alleged inconsistency
see Thompson (1953/68), 55“7; Ackrill (1963), 111; Kirwan (1971/93), 118; Mignucci (1975b), 238“43;
Jacobs (1979), 286“95; Wedin (1978), 179“88; Dancy (1986), 66“7; Crivelli (1989), 50“1; Charles
(1994), 54“5; Weidemann (1994/2002), 390“1; Carson (1996), 51“70; Goldin (1996), 65“6; Charles
(2000), 94.
39 Two passages are harder to explain away: at Int. 11, 21a 32“3 Aristotle seems to imply that ˜What does
not exist is an object of belief ™ is true; at APr. 1.38, 49a 12“19 and 49a 22“5 he regards ˜The goatstag
is a non-being; the non-being is known as non-being; hence the goatstag is known as non-being™ as
a syllogism. However, in both passages Aristotle™s examples illustrate points that have nothing to do
with the question whether the subject of a predicative assertion can be ˜empty™: I think that if he
were to address these examples in the light of this question, Aristotle would treat them in accordance
with the theory I am attributing to him.
˜Vacuous™ terms and ˜empty™ terms 163
would-be subject or would-be predicate is ˜empty™, then that utterance is not
a predicative assertion. Can Aristotle™s philosophy of language accommo-
date such an utterance? For instance, the name ˜goatstag™ signi¬es neither
an individual which at some time or other exists nor a universal always
predicated of at least one individual which at some time or other exists.
Proposition [27] then entails that any utterance which looks like a pred-
icative assertion with an utterance of ˜goatstag™ as subject (e.g. ˜A goatstag
is white™) or predicate (e.g. ˜Bucephalus is a goatstag™) is not a predicative
assertion. Aristotle acknowledges that ˜“goatstag” signi¬es something™ (Int.
1, 16a 16“17).40 Can his philosophy of language accommodate utterances
that look like predicative assertions whose would-be subject or would-be
predicate is an utterance of ˜goatstag™?

3 one a s sertion v s ma n y a s se rt i on s
How many assertions does an utterance amount to? Aristotle addresses this
question in de Interpretatione 5 and 6:
T 38 The ¬rst single assertoric sentence is the af¬rmation, next is the denial;41
the others are single by virtue of some conjunction. However every asser-
toric sentence must consist of a verb or an in¬‚exion of a verb: for even the
account of man is not yet an assertoric sentence unless ˜is™ or ˜will be™ or
˜was™ or something of this sort is added.42 But why ˜biped walking animal™
is something one and not many (for it will certainly not be one through
being said all together) “ well, to say this belongs to a different inquiry.43 A
single assertoric sentence is either that which reveals a single thing or that
which is single in virtue of some conjunction, while many are those which
reveal many things and not one or those with no conjunction.44 (Let names
and verbs be merely enunciations because it is impossible to speak like this
and to reveal something in such a way as to make an assertion, whether one
is answering a question or not but speaking spontaneously.) Of these the
one is a simple assertion, i.e. that which asserts something about something
or something away from something, the other is compounded of these, i.e.

40 Cf. APo. 2.7, 92b 5“8; Ph. 4.7, 213b 30“1 (on ˜void™). At APo. 2.7, 92b 29“30 Aristotle says that ˜it is
possible to signify things that do not exist™. For the positions taken by the ancient commentators on
the signi¬cation of ˜goatstag™ and other similar nouns see Ebbesen (1986), 118.
41 On the priority of af¬rmations with respect to denials cf. n. 16 of ch. 1 and the corresponding portion
of the main text.
42 Cf. Po. 20, 1457a 24“7.
43 For the problem of the unity of the de¬niens of a de¬nition cf. Int. 11, 20b 17“19; APo. 2.6, 92a 27“33.
For its solution cf. Metaph. Z 11, 1037a 18“20; 12, 1037b 8“1038a 35; H 3, 1043b 23“1044a 14; 6, 1045a 7“
1045b 24.
44 Cf. Int. 8, 18a 13“27; 11, 20b 13“22; APo. 2.10, 93b 35“7; PA 1.3, 643b 18; Metaph. Z 4, 1030b 7“13; H 6,
1045a 12“14; Rh. 3.12, 1413b 29“1414a 1; Po. 20, 1456b 38“1457a 6; 1457a 28“30; Ammon. in Int. 66, 31“67,
19.
164 ˜Empty™ terms
a sentence which is already composite. A simple assertion is a signi¬cant
spoken sound about whether something holds or does not hold, according
to one of the divisions of time; an af¬rmation is an assertion of something
about something, a denial is an assertion of something away from something.
(17a 8“26)
In T 38 on two occasions (at 17a 9 and 17a 16) Aristotle mentions assertions
that are one ˜by virtue of some conjunction™. On the second of these occa-
sions he contrasts assertions that are one ˜by virtue of some conjunction™
with assertions that are many because they are ˜with no conjunction™.

The meaning of ˜conjunction™. In T 38 the relevant occurrences of ˜conjunc-
tion™ probably denote connective particles (linguistic expressions like ˜and™,
˜or™, etc.).45 For:
(i) In Rhetoric 3.12 Aristotle discusses the styles that are appropriate to
different kinds of rhetoric. He says:
T 39 Expressions with no conjunction and involving frequent repetitions are
rightly criticised in written style but not in debating style. (1413b 19“21)
A similar point [sc. that one must deliver one™s speech in a variegated style]
holds for expressions without conjunction, e.g. ˜I went, I met, I begged™.
For one must act this out and not deliver it with the same tone and charac-
ter, as if saying only one thing. Moreover, expressions with no conjunction
have a peculiarity: they seem to say many things at the same time. For a
conjunction makes the many one, so that if it is taken out it is clear that
the one will contrariwise be many. It therefore provides ampli¬cation: ˜I
went, I spoke, I implored™ (what he said seems to survey many things).46
(1413b 29“1414a 1)
In T 39 ˜conjunction™ seems to mean ˜connective particle™:47 what Aristotle™s
examples (˜I went, I met, I begged™ and ˜I went, I spoke, I implored™) con-
spicuously lack are connective particles,48 and it is with regard to linguistic
particles that it makes sense to consider the result of taking them out.49

45 Cf. Ammon. in Int. 66, 31“67, 19; Textor (1870), 25; von Kirchmann (1876), 64; Bywater (1909), 277;
Gohlke (1951), 89“90; Morpurgo-Tagliabue (1967), 52; Antiseri (1969), 53“7; Larkin (1971), 26; Kahn
(1973b), 151, 156; van Bennekom (1975), 404; Belardi (1977), 263“8; Zadro (1979), 112“13; Thornton
(1986), 173“4; Weidemann (1994/2002), 197; Slomkowski (1997), 126. Aristotle applies ˜conjunction™
to ˜and™ (˜ka©™, see Pr. 19.20, 919a 22“5) and ˜or™ (˜¢toi™, see Po. 20, 1456b 38“1457a 6).
Reading ˜poll‡ doke± Ëperide±n ‚sa e²pen™ (1414a 1) with some of the main manuscripts,
46
Cope/Sandys, and Freese (cf. Trenkner (1952/53), 5).
47 This is the view of most translators and commentators (e.g. Maurus (1668), i 808; Steinthal (1863/90),
i 265; Cope/Sandys (1877), iii 150; Freese (1926), 421; Kennedy (1991), 255“6). Trenkner (1952/53),
4“5 and Blettner (1983), 51 dissent.
48 Cf. 3.19, 1420b 2“3. 49 Cf. Pr. 19.20, 919a 22“5.
˜Vacuous™ terms and ˜empty™ terms 165
An aspect of T 39 which is important for present purposes is that it speaks
of expressions where ˜a conjunction makes the many one™ (1413b 32“3), and
it contrasts such uni¬ed expressions with others which are ˜with no con-
junction™ (1413b 29 and 1413b 31): this obviously recalls what we ¬nd in T 38,
and therefore supports the suggestion that in T 38 also ˜conjunction™ should
denote connective particles.
(ii) In Poetics 20 Aristotle offers two de¬nitions of a conjunction:
T 40 A conjunction is a sound without signi¬cation which50 is not apt to be
placed on its own at the beginning of a sentence, e.g. ˜m”n™, ˜¢toi™, ˜d”™;
or a sound without signi¬cation which is of such a nature as to make one
signi¬cant sound out of sounds that are more than one but signi¬cant.51
(1456b 38“1457a 6)

The ¬rst de¬nition is of a syntactic, the second of a semantic character.
The second de¬nition ¬ts well with the interpretation of T 38 according
to which the relevant occurrences of ˜conjunction™ in that passage denote
connective particles.
One might object that ˜conjunction™ in T 38 means (not ˜connective
particle™, but) ˜connection™.52 Support for this objection might come from
passages where Aristotle offers the Iliad as an example of a linguistic expres-
sion which is ˜single by virtue of some conjunction™:53 the Iliad ™s unity is
not a matter of connective particles linking all the sentences in the poem
(a poem of the size of the Iliad will surely contain many sequences of sen-
tences not linked by connective particles, an obvious fact which Aristotle
could hardly overlook) “ rather, the Iliad ™s unity consists in the fact that the
˜action™ narrated is unitary.54 But this is captured by Aristotle™s description
˜single by virtue of some conjunction™ only if, as the objection assumes,
˜conjunction™ means ˜connection™.


Following Margoliouth, I delete ˜¥ oÎte kwl…ei . . . kaª –pª to“ m”sou™ (1456b 38“1457a 3). For a
50

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