ARISTOTLE O N UNIVERSALITY AN D NECESSITY
M. M. MULHERN
Many contemporary writers on modal logic — Prior being
the obvious exception — treat the necessity functor as if it might
be translated without residue either by the universal quantifier
alone or by the universal quantifier with an assertion sign (1)•
That is to say, they treat it as if being true in every case and being
necessarily true were all the same thing. This tendency is not
always immediately apparent — as when modal functors and
quantifiers appear side by side in a quantified modal logic; but
it sometimes does reveal itself, as in attempts to map over modal
systems onto Boolean algebra. In these mappings, " It is necessary
that p" amounts to " p = V " (where V is the universal element
of the Boolean algebra) (
2 The currency of this view, that modality and quantity may
in
) . some sense be identified, is perhaps due to Professor Carnap,
who, although he holds that the symbol 'N ' (which he uses for
logical necessity) "cannot be defined on the basis of the ordinary
truth-functional connectives a n d quantifiers f o r indiv iduals ",
also holds that " a proposition p is logically necessary i f and
only if a sentence expressing p is logically true" (
2
).( A c c o r d i n g
sity1 Press, 1962), pp. 185-193, wherein Prior finds close parallels between
modality
a n d quantity, but resists t he temptation t o mak e a "s imple
)
identification
o f modalit y and quantity". Prior refers t o t he distinction
C
of "universals of law" f rom "universals of fact" made by W. E. Johnson
f
in his Logic (Part I l l ; Cambridge: Cambridge University Press, 1924),
i.5.. He also mentions more recent discussion of the distinction of necesA f rom merely assertoric universals, whic h had as it s starting point
sary
R. .M. CHisHoLm's article " Th e Contrary-to-Fact Condit ional", Mind, I V
(1946),
N
pp. 289-307.
(.
LANGFORD,
Symbolic Logic ( Ne w York : Dov er Publications, 1959).
2
P
()R
Logic,
x i (1946), p. 34.
2
C
I
)fO
R
.R
.,
C
fF
A
o
R
r
N
e
m
A
xa
P
a
l
,m
L
"p
o
ARI STO TLE O N UNI V E RS A L I TY A N D NE CE S S I TY
2 8 9
to Carnap, a sentence "is usually regarded as logically true or
logically necessary if it is true in every possible case" (
sible'
is lef t unexplained i n his formal definition o f logic al
4
truth,
) • ' Pin owhic
s - h a sentence is said to be logically true ( in his
system) when its range is the universal range of state-descriptions ('). By his own admission, Carnap's notion of logical truth
is based o n Wittgenstein's, whic h takes as its criterion the
universality of the range (B)• O f course, it is well known that,
for Wittgenstein, "the only necessity that exists is logical necessity", which is the necessity of properly logical propositions, or
tautologies, which are those propositions true for all the truthpossibilities o f their elementary propositions (
7
view,
any notion of necessity which departs from universal quantification
the outset.
) • A nis dprecluded
o from
n
t h i s
The influence of this sort of view among interpreters of Aristotle's modal logic appears prominently in the work o f Lukasiewicz and Hintik k a. Lukasiewicz contends that Aristotle's
notion of syllogistic necessity must be conveyed, and is conveyed
adequately, by universal quantifiers. Indeed, he declares in so
many words, c iting Analy tic a Pr ior a 25a20-26 b y w a y o f
authority, that "Aristotle uses the sign of necessity in the consequent o f a true implication in order to emphasize that the
implication is true for all values of variables occurring in the
implication", so that "the Aristotelian sign of syllogistic necessity represents a universal quantifier" (
8
) .( P r o f e s s o r
H 4( i n t i k k a ,
)
sentences
whic h contains f or every atomic sentence either that sentence
5
C
or A)its denial, but not both, and no other sentences (p. 50, D7-4).
R
(C
N
Harvard
University Press, 1942), §§ 18-19. Cf . also L . WITTGENSTEIN,
6
A
A
Tractai
us
Logico-Philosophicus, trans. D. F. PEARS and B. F. McGumEss
P
)R
,
(London:
Routledge
& Kegan Paul, 1961), 4.462, 4.463, 5.5262.
C
p
(N
.A
A
positions"
5
are f o r Wittgenstein "possibilities o f existence and non-exis7
R
0
tence
of states of affairs" (4. 3).
)P
.N
(,
T
A
Modern
Formal Logic ( 2 n d ed. enlarged; Ox f ord: O x f o r d Univ ers it y
p
8
r
P
Press,
1957),
p. 11. Cf. § 41, pp. 143-146. Lukasiewicz does recognise that
).a
,J5
c
p
.1
t
.L
,a
4
D
U
t
7
7
K
u
.A
-s
C
6
S
,
fI.
6
.
290
M
.
M. MULHERN
who does not confine his attention to syllogistic necessity, takes
a slightly different line with Aristotle. Omnitemporality is his
concern: " in passage after passage", Hintikka writes, "[Aristotle]
explicitly or tacitly equates possibility with sometime truth and
necessity with omnitemporal tr uth" (
9 As Lukasiewicz notes, Aristotle did not use for quantifiers a
conventional
notation lik e any o f the current ones, so far as
).
is known ("). O n the other hand, Aristotle did make some remarks on the premisses of demonstration from which one might
gather some information about his views on quantification. These
remarks are to be found at Analytica Posteriora 73a21-74a3 ("),
where Aristotle distinguishes three kinds of predicate assignment
to subjects: (1) assignment xcctt ;tar t*, (2) assignment xistfrouirr6,
and (3) assignment m•1164au. I wish to argue in the remainder of
this paper that these remarks belie the historical accuracy of the
accounts o f Aristotle's treatment o f modality given by Lukasiewicz and Hintikka, and that they open a field for modalities
which Wittgenstein and Carnap would close off.
Aristotle has a not ion o f propositional necessity according t o wh i c h
"propositions whic h ascribe essential properties t o objects are n o t
only factually, but also necessarily t rue". Lukasiewicz himself, however,
believes t his t o be an "erroneous distinction", and asserts i n his o wn
behalf t hat "t here are n o t rue apodeictic propositions, and f r o m t he
standpoint o f logic there is no difference between a mathematical and
an empirical t rut h" (p. 205).
(
Ajatus,
9
x x (1957), pp. 65-90; "Aris t ot le and t he 'Mas t er Argument ' of
Diodorus",
Americ an Philosophical Quart erly , i (1964), pp. 101-104;
)
"The
Once
and Future Sea Fight: Aristotle's Discussion o f Future ConJ
tingents i n De Interpretatione ix ", Philosophical Review, lx x iii (1964),
.
pp. 461-492. Professor Hint ik k a has offered more extensive discussions
of H
t he concept o f t ime among t he Greek s i n "Observations o n t he
I
Greek
Concept of Time", Akin's, x x iv (1962), pp. 39-66; and in "Time,
N and Knowledge i n Anc ient Greek Philosophy", Americ an PhiloTruth
sophical
Quarterly, iv (1967), pp. 1-14.
T
('°)
"Aris
ot le had no clear idea of quantifiers and did not use them in
I
hisKworks; consequently, we cannot introduce them int o his syllogistic".
Lukasiewicz, p. 83.
K
(A") Reference is t o Ross's text. Aristotle's Prior and Posterior Analytic& A revised text wi t h introduction and commentary by W. D. Ros s
,
(Oxford:
Ox f ord University Press, 1965).
"
N
e
c
e
s
s
i
t
AR I ST OT L E O N U N I V E R S A L I T Y A N D N E C E S S I T Y
2
9
1
1. Assignment x ur t Iravr6;: Aristotle characterised this k ind
of assignment negatively: V,CUrdt7tOEVT6:, [tiV a l ! TOTITO Xy w 6 (iv
Liii• j
29).- This k ind of assignment seems to correspond to universal
quantification
as ordinarily understood, since it is assignment of
ti
the1predicate to all instances of the subject and at all times. I t
should
be noted, however, that this reference to omnitemporality
on Aristotle's part is not connected by him to any reference to
11
necessity, even though the distinction drawn among three kinds
,
of predicate assignment is designed to shed light on the nature
6;
of premisses
f o r demonstration; and demonstration does, ac[
cording to Aristotle, proceed va àvuyxui(ov (73a24). Indeed, at
C
74a4-12,
Aristotle states flatly that only assignment x06Xou sufF for demonstrative premisses. This seems to suggest that asfices
I
signment
zurà ACIV1
Aristotle
required f o r demonstrative premisses.
- '
T—
Assignment x a D ' u i
6; 2.
of
(
I i vk ind
u ,this
n
e rofs assignment
a l
1definition:
f t ?i,Qtt
ei rf XEyOvva ia t r(.7.)v &70L(.7.):; 7rtiariltôT)v xtra'airrà
q 2rVu6 : a A nTeX
Oro);
(eoz
ivum'xioyrtv
XXX
)i , chKA a
r
i
s
t
o
t lgTOIL:
e
a tv i i o nn
zed
Li
etv6yxn;
(73b16-18).
This definition says that one
-p—giart
br oi pv o e s e s
assi
g
ns
a
predicate
xOEft'ai,r6
in
virtue
of what a subject is and
F
ti inlèy 0 h0 0 1 3 0e
of
it is of necessity.
.fs swhat
oe w Aristotle goes on to point out that it
I o e l vl
is
formally
not
possible
(oi) N • b l E 1
1
il ' r0I n1 ; aeg l
signed
zaft'aixt6,
or
for
one
-i
o z of any pair of opposite predicates
eI i xvs wnot
a t tok belong
s assigned,
so
(i 1 )A a
f ot r
a n toy its subject. He then derives the
rC
m
1
pof
l
e xetiVaisr6 from premisses given previously
tnecessity
h assignment
p r ae di i rc ar t e
V
a sÔthe lawn of excluded middle: (6ar'Et avely-ml O v al et2.toplvat,
and
a
s
e
T t 1
etvàyxil
unlike
, O the discussion of assignment XCUrex aCtVT6:, clear reference
is
made
to necessity, but no reference is made to quantity or
T
t Xd
quantification;
assignment x ar aim') is distinguished fr om asT et x
signment
xarà
71avT6,-;,
if not contrasted with it.
z uV O
' c Tt i
, (O
purposes
(Cf . Ross, APPA, pp. 519, 521). They are ( 1 ) def init ions o r
r 61T
elements
of
definitions of subjects, and (2) attributes definable by refer2
.
i m
ence
) ( t o t heir subjects.
6 ,
T
9 h77
E e3t
v fa
( i 27
3 r 8b
2 s- 3
t
- t 2
292
M
.
M. MULHERN
3. Assignment xctONLou: I n Analytica Posteriora 73b25-74a3,
Aristotle stipulates a technical sense of xallaou, which led Ross
to note: " T his strict sense o f xa06Xou is , perhaps, found nowhere else" in the Aristotelian corpus (
technical
ab predicate
must be both %cruet auvr6g and zall?
s ) . T sense,
o
e
cti
definition — xia0.6Xou bè 4-yco 8 eiv
a yr6.
s Further,
s i g in
n Aristotle's
e d
T
6
C
.
;
TE
ila6prri
xcti
za§'cLiyrô
zed, a i r r à (73b26-27) — a
i
n
third
condition
is
added.
Ross
takes
Aristotle's 11 cr&r6 to signify
t
h
i
s
that the predicate assigned "Mus t be true o f the subject
precisely as being itself, not as being a species of a certain genus",
if it is to be assigned mcaaou. The fact that one finds in b28
the remark rà
ficulty.
Ross rightly observes that this is to be explained on the
x c r i Vthat
grounds
e Aristotle here was making more precise his previous
remarks
r b r à on predicate assignment RoWain6 (")• This precision of
xterminology
c i should be borne in mind in reading Aristotle's succeeding
chapter, in which the moral is drawn that a demonstrai
tion
may
C
C fail i f predicates are not assigned v.a06kou — that is
to
say, both ware( aavr6; and xotWat!rr6 — in its premisses and
O
in its T
conclusion.
6
Now i t s till might be argued that these distinctions whic h
T a
Aristotle makes d o not damage Lukasiewicz's contention, beicause,
r asT everyone knows, Aristotle's requirements for demon6
1 are
' stricter than his requirements for mere syllogism. I t
stration
i
might
be urged that all Lukasiewicz has claimed here is that for
sAristotle a ll v alid moods o f the syllogism represent necessary
ninferences, which is true. Let's have another look, however, at
othe way Lukasiewicz states his claim.
c "...Aristotle [he writes] uses the sign of necessity in the conasequent o f a true implication i n order to emphasize that the
uimplication is true for all values of variables occurring in the
simplication. We may therefore say 'I f A belongs to some B, it is
necessary that B should belong to some A', because it is true that
e
'For all A and for all B, if A belongs to some B, then B belongs
f
to some A'. But we cannot say 'I f A does not belong to some B,
o
r
(
d (3
i 1)
f 4A
- )P
A
P
P
A
P
,
A
p
,.
a5
ARISTOTLE O N UNI V E RS A L I TY A N D NECESSI TY
2 9 3
it is necessary that B should not belong to some A', because it is
not true that T or all A and for all B, if A does not belong to
some B, then B does not belong to some A'. There exist, as we
have seen, values for A and B that verify the antecedent of the
last implication, but do not verify its consequent. I n modern
formal logic expressions lik e 'for all A' or 'for all B', where A
and B are variables, are called universal quantifiers. The Aristotelian sign of syllogistic necessity represents a universal quantifier and may be omitted, since a universal quantifier may be
omitted when it stands at the head of a true formula" (
1be shown that Lukasiewicz's contention, as stated above, is subs ) . toI atnumber
ject
c aof difficulties.
n
First, there is the difficulty about
what Lukasiewicz means by 'variables' in 'where A and B are
variables'. Capital A, B, C in this passage apparently correspond
to the lower case a, b, c, o f Chapter IV, "Aristotle's System
in Symbolic Form", in which Lukasiewicz avows the purpose of
setting out "the system o f non-modal syllogisms according to
the requirements of modern formal logic, but in close connexion
with the ideas set forth by Aristotle himself" (
ter,
1 he remarks:
s ) "By the initial letters of the alphabet a, b, c, d, I denote
term-variables
term-variables
• I n
t ho f athet Aristotelian
c h alogic
p . These
have as values universal terms, as 'man' or 'animal' (")."
The ordinary propositional variables p, q, r, a l s o appear in
this chapter. They do not belong to Lukasiewicz's account o f
syllogistic, however, since he believes that Aristotle did not use
them (
syllogistic
schemata w ith the schemata o f propositional logic.
");
The
t h term-variables a, b, c, a p p a r e n t ly are themselves not used
as
variables either. Instead, in combination with
e propositional
y
one
another
and
as arguments t o the logical constants o f the
a
system
("),
they
are
used to form what Lukasiewicz calls "pror
e
i
t
o
u
e
o
n
l
y
f
o
r
n
r
d
c
d
Aristotle's Syllogistic, p. 11.
Aristotle's Syllogistic, p. 77.
Aristotle's Syllogistic, p. 77.
Aristotle's Syllogistic, § 16.
Aristotle's Syllogistic, p. 77. tuk as iewicz 's logic al constants are
I, 0 , used, as he says, i n t heir mediaeval sense.
294
M
.
M. M UL HE RN
positional functions". His example of a propositional function is
'Aab', to read 'All a is b' or 'b belongs to all a' (").
Lukasiewicz chooses to employ constants with a quantificational sense instead of the quantifiers of the ordinary predicate
calculus; but what he offers can be mapped over onto the ordinary predicate calculus according to a suggestion of Prior's. I n
his exposition o f Lukasiewicz's axiomatisation o f syllogistic,
Prior instructs the reader to "regard the terms 'a', 'b', etc., as
abbreviations for the predicational functions 'tfx', 'Ipf, etc., ' A'
as an abbreviation f or ' M C ' , and ' I ' as an abbreviation f or
If, following Prior, w e regard Lukasiewicz's term-variables
as abbreviations for predicational functions and his constants as
abbreviations f o r quantifiers i n combination w it h truth-functional operators, then the role of both quantifiers and variables
in Lukasiewicz's account is clarified. Prior gives an example of
his understanding of Lukasiewicz's reconstruction of syllogistic
schemata in the following symbolisation of Datisi:
CK(11xClitx0x)(IxKliinx)(ExKcrxtlx) (").
Here the quantifiers range ov er indiv idual variables. T he
same is true in the symbolisation employed by Anderson and
Johnstone, who give for Darii, for example:
Hx[M(x) P ( x ) J , Ex[S(x) & M(x)]/
*
Assuming
that Lukasiewicz is speaking of universal quantifiers
* over the indiv idual variables whic h are arguments in
ranging
* E x tfunctions,
S ( x ) the question
&
predicational
remains: does he mean to
say that
the
formulae
o
f
syllogistic
schemata are true for all
P ( x ) ]
(
values
2 of3their variables, or does he mean to say that syllogistic
schemata are valid under any interpretation of their variables ?
) •
If Lukasiewicz means to say that the formulae of syllogistic
(
(2
(2
0
22
1
)3 John M. ANDERSON and Henry W. JOHNSTONE, Jr., Nat ural Deduction:
2
)A T h e Logic al Bas is o f A x i o m Systems (Belmont : Wads wort h
Publishing
Company, Inc., 1962), p. 177.
)F
r
F
o
i
o
rs
rm
t
m
a
o
a
lt
lL
l
L
o
e
o
g
'
g
ARI STO TLE O N UNI V E RS A L I TY A N D NECESSI TY
2 9 5
schemata are true for all values of their variables, then, since he
regards Aristotelian syllogisms as implications, he must intend
that a syllogism be represented
(
as it [is sometimes written, or with the quantifier omitted but
understood, as Lukasiewicz proposes w h e r e the firs t t w o
blanks are filled w it h the premisses o f the syllogism and the
third blank is filled with the conclusion. However, in the standard predicate calculus o f firs t order, an entire implication
governed by a universal quantifier implies an implication with
each o f its members governed by a universal quantifier — as
in Church's
*333. H A D , B ( a ) A D (a)B (
24
It can readily be seen, upon inspecting the formulation of Prior
.
or of )Anderson
and Johnstone, that, if this is Lukasiewicz's account of syllogistic, it w ill not do. The premisses of syllogistic
schemata need not all be universally quantified. The valid moods
with particular premisses, e.g. Datisi and Darii, illustrated above
with existential quantifiers, have the same syllogistic necessity
as Barbara and Celarent (
2 If, o n the other hand, Lukasiewicz means t o say that syl').
logistic
schemata are v alid under any interpretation o f their
variables, then his use of the universal quantifier in this connexion is precipitate, since quantifiers come into play only when
some interpretation already has been decided upon. But even
granting his precipitate usage, his reading cannot be allowed,
since Aristotelian syllogistic schemata are not v alid syllogisms
under every interpretation of their variables. A schema yields a
valid syllogism for Aristotle only i f these tw o conditions are
satisfied: ( 1) the conclusion is something different fr om the
(24) A . CHURCH, Introduction t o Mathematical Logic (Princeton: Princeton University Press, 1956), 1, 187.
(
2
5
)
A
n
.
P
r
.
296
M
.
M. M UL HE RN
premisses, and (2) the terms of the conclusion are related by a
middle term occurring in both the premisses. I f the same sentence, for instance, were substituted for all the predicational function variables i n one o f the syllogistic schemata symbolised
above, the result might be a valid inference, but it would not be
an Aristotelian syllogism, because i t would not satisfy either
condition. For example, in the implication
if A is predicated of all A , or (x)(Ax A x )
and A is predicated of all A , or (x)(Ax A x )
then A is predicated of all A , or (x)(Ax D Ax),
there is a valid inference, but the inference is warranted rather
by conjunction elimination or simplification — depending on
what sort of logic one prefers — than by any syllogistic device.
Thus, however Lukasiewicz's statements are construed, neither
are they true o f Aristotle's doctrine o f syllogism nor do they
show that "the Aristotelian sign of syllogistic necessity represents
a universal quantifier".
Hintikka's contention that Aristotle "explicitly or tacitly equates possibility w ith sometime tr uth and necessity w it h omnitemporal truth" appears to call for rejection also, but on different
grounds. In the first place, Hintikka's declaration is inconsistent
with an important feature of Aristotle's doctrine which Hintikka himself takes note of. As Hintikka puts it, this is Aristotle's
distinction "between saying on one hand that something is o f
necessity when it is and on the other hand that it is of necessity
hapli3s" ("). According to Hintikka, Aristotle intends to contrast
necessary statements having temporal qualifications with necessary statements lacking "temporal qualifications that would limit
the scope of a statement to some particular moment or interval
of time" (").
The inconsistency arises on tw o counts: ( I ) since Aristotle
recognises necessary statements which have temporal qualifications that limit their scope to some particular moment or interval of time, then it cannot be the case that he "equates... necessity with omnitemporal truth"; and (2) since Aristotle does re(
(2
2
6
7
)
)"
"S
S
e
e
a
a
F
F
i
ig
ARISTOTLE O N UNI V E RS A L I TY A N D NE CE S S I TY
2 9 7
cognise temporally qualified necessary statements, then these
statements do not differ from merely possible statements if Aristotle "equates possibility with sometime truth".
In the second place, Hintikka's contention that the adverb
617E46); " is often used by Aristotle to indicate the absence o f
temporal qualifications", whic h Hintik k a uses as evidence for
the contention that Aristotle equates necessity w it h omnitemporal truth, appears ill-founded where i t might be pertinent.
Hintikka cites nine places in the corpus in support of his contention ("). O f these, (1) Analytica Priora 34b7-11, while it indeed contrasts varà x6vov with evt47);, contains no mention of
necessity. The same is true of (2) De Interpretatione 16a18. I n
the same work, Hintikka's citation (3) — 23a 16 — contains no
time-expression, although ö i occurs in a14. (4) Analytica Priora
30b3 1-40 is about not periods of time but rather tOirtWV 6 v
(b33),
and appears to be a consideration of reference failure. In
(5)
r a w— Analytica Priora 341)17-18 — there is no more than a
summary o f what 34b7-11, cited above, has t o say about the
premisses o f syllogism.
Hintikka's (6) T o p i c a 102a25-26 c o n t r a s t s 6taX65g not
only with Toni but also with Tre6; it. Part of a discussion of the
difference between mind and desire, (7) De Anima 433b9 contrasts iibi with euat.T.);, but with respect to pleasure, not to necessity. I n (8) — De Partibus Animalium 639b25 - the contrast
of 67t46); is with i a o M a a o ; ; the contrast of toi; etibtolg and
Tor; v yEvaEt mio(v is that between the subjects to which something might belong, respectively, einkCo; or 0, H i n t i k ka's last text, ( 9) Metaphysica 1015b11-14, contains no time
expression, but rather a contrast o f -1
ZaA
- •cog.
citations,
6 Of
1 5Hintikka's
u a o i . i nine
v
w i t then,
h only four contain unambiguous
contrasts
of
ILAVo;
with
some
time-expression; and none
e i a w
;
of
' these
, deals
a w iti h necessity. Further, in the entry in Bonitz
which Hintik k a cites, contrasts of evIA.Co
are
- far outnumbered by contrasts of ertA,Co; with other adverbial
expressions
When
; w i t h (").
t i m
e - all of this is brought to bear on Hintik e x p r e s s i o n s
(
2
8
)
"
S
e
a
F
i
298
M
.
M. M UL HE RN
ka's original assertion, what are the results ? Hintikka declares
that " in contexts comparable to the one we have here [De Interpretatione 19a23-27], haplôs is often used by Aristotle to indicate the absence o f temporal qualifications that would limit
the scope of a statement to some particular moment or interval
of time". But, in the first place, this alleged usage of Aristotle's
cannot, on the evidence of the texts adduced by Hintikka, be used
in support o f the contention that Aristotle equates necessity
with omnitemporal truth, since none of the texts contains both
a contrast of C170,17); with some time-expression and a mention
of necessity. Next, i f it is the case that Aristotle "often" uses
(1.1467); to indicate the absence o f temporal qualifications, i t is
also the case, on the evidence of Bonitz, that he more often uses
(171A.Co:, to indicate the absence of qualifications other than temporal ones. Last, if by "contexts comparable to the one we have
here" Hintik k a means contexts in whic h r X ç is opposed to
some qualification or other, then his contention regarding Aristotle's preoccupation w ith temporality falls once again t o the
argument from Bonitz. And if, on the other hand, a comparable
context is one in which 6.70.(7); is opposed to a time-expression,
then his contention obviously cannot be gainsaid — since i t
amounts to "Where Aristotle contrasts (.7cIA.(7)z with a temporal
qualification, there Aristotle contrasts el;Tkir); w it h a temporal
qualification"; but just as obviously it furnishes no support to
his contention and as little aid to the student o f Aristotle.
These considerations aside, Hintikka's contention s till falls in
light o f Aristotle's distinctions in Analytica Posteriora 73a2174a3. Hintikka says, in a note on what he takes to be Aristotle's
equation o f ("OEI and iiverpol, that " f o r Aristotle a genuinely
universal sentence refers to all the individuals existing at different moments of time (An. Pr. I, 15, 34b6ff). Hence if it is true
once, it is tr ue always, and therefore necessarily true according
to the Aristotelian assumptions" (")• But here Hintikka's "genuinely universal sentence" corresponds exactly to assignment
(
2( ") "Sea Fight ", p. 482, n. 26. Cf. "Necessity, Universality, and Time
in 0
Aristotle", pp. 66-67.
)
"
S
e
a
F
i
g
h
ARISTOTLE ON UNIVERSALITY AND NECESSITY 2 9 9
xatex ac tv
- nv .ç bè jai and ! I T * xor t v ; t o t b è ( 7 3 a 2 8 - 2 9 ) — asjièv
signment
to all instances of the subject and at all times. Asr 6z
signment
w h i c %calk auvrô; is not necessary assignment, whereas assignment
xce8'itirt6 is necessary, and assignment x allaou — the
h ,
only
"genuinely
universal" assignment according to the Postei
t
riora text — is also necessary, because it includes assignment
w i
xaD'airr6, along with assignment z atà 3101VT6;•
l l
The interpretive validity of Hintikka's stand thus may be called
binto question, since Aristotle gives no hint that necessity can be
ereduced to an ordinary quantifier notion — his assignment xutex
rACCV
eT6;. Rather, Aristotle distinguishes fr om assignment XCITEA
m
n u l le* a notion of necessity — assignment xotTai)r6 — which
m
b not only to be independent o f assignment youtet aar r k ,
seems
esincer the two are required for assignment xa06X(yo, but which
eseems
d to be independent of quantificational considerations alto,gether.
i
M .
M. MULHERN
sState University of New York at Buffalo
b
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h
ù
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t
v
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