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Transcript of Jaakko Hintikka - Existence and Predication From Aristotle to Frege 2006
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Philosophy and Phenomenologicul Research
V o l . LXXII I , N o. 2, September 2006
Existence and Predication from
Aristotle to FregeRISTO VILKKO
University of Helsinki
JAAKKO HINTIKKA
Boston University
One of the characteristic features of contemporary logic is that it incorporates the
Frege-Russell thesis accord ing to which verbs fo r being are multiply ambiguous. This
thesis was not accep ted before the ninete enth century . In Aristotle existen ce cou ld not
serve alone as a predicate term. However, it could be a part of the force of the predi-
cate term, depe nding on the context. For Kant existence could not even be a part of the
force of the predicate term. Hence, after Kant, existence was left homeless. It found a
home in the algebra of logic in which the operators corresp ond ing to universal and par-
ticular judgments were treated as duals, and universal judgments were taken to be rela-
tive to some universe of discou rse. Because of the du ality, existential qu antifier exp res-sions came to express existence. The orphaned notion of existence thus found a new
home in the existential quantifier.
How did modem logic evolve? One of the many interesting aspects about this
question is that i t has not been asked more often and more emphatically even
though there is no clear answer to it to be found in the literature. Some phi-
losophers might say that what we today call logic was discovered by Frege in
1879 and add that of course genuine discoveries cannot in the last analysis be
explained. If so , we presumably ought to emulate Michael Dummett (1973;199 1) and examine Frege's achievement systematically rather than histori-
cally, among other things looking away from its roots in earlier philosophy
and earlier logic. However, this way of looking at Frege's accomplishments
has been challenged repeatedly, most determinately perhaps by Hans Sluga in
his book Gottlob Frege (1980) and by Gordon Baker and Peter Hacker in
their Logical Excavations (1984). Independently of this particular contro-
versy, one's legitimate curiosity should even after a Dummettian putdown be
tickled by the fact that much of the same logic was discovered independentlyand about the same time by Charles S . Peirce. Is this merely a coincidence?
A good historian should not believe in coincidences any more than a good
detective
EXISTEN CE AND PREDICATION FROM A RISTOT LE TO FRECiE 359
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Others might prefer to try to trivialize the question. Is not logic one and
the same throughout its history? What is supposed to be so novel in Frege
and Peirce? The stock answer seems to be: the theory of quantifiers. Th is
theory is the gist of what Frege and Peirce independently discovered. How-
ever, it may be objected that quantifiers were studied from the very beginning
of Western logic. Already in Aristo tle‘s logic the main ingredients were theideas of universality (‘every A ’ ) and particularity (‘some R ’ ) . If this is the
main part of the story, the genesis of modern logic should be viewed simply
as a continuation of the older traditions in logic which can be traced back
ultimately to A ristotle rather than as a discovery of something radically new.
This po int of view emphasizes that it was Aristotle who laid the foundations
to formal logic, whereas Frege was in position only to develop logic further.
One reason that some philosophers might have for not examining more
closely that background of modern logic is an underestimation of the substan-
tial differences between today’s mathem atically-oriented logic and traditional
philosophically-oriented logic. There nevertheless are differences, some of
them quite striking. For exam ple, the usual way of understanding logic
merely as the doctrine of the laws of correct inference, that is, as the doctrine
of syntax and semantics of exp licit languages, would not have appealed even
to most of 19th century logicians (see Vilkko 2002).
One more specific difference concerns the counterpart or counterparts in a
logical notation to natural language verbs for being, such as the English is,
the German ist, and the ancient Greek estin. With some exceptions, there has
recently been a consensus to the effect that such verbs are multiply ambigu-
ous between the is of predication, the is of existence, the is of identity, and
the is of subsumption. The assumption of such an ambiguity will be called
here the Frege-R ussell ambigu ity thesis, for indeed the currency of this
assumption is due largely to these two logicians. It is built into the very
notations that have been used in logic since their time, in that the allegedly
different meanings are expressed in the usual logical notations differently. The
i s of identity is expressed by the identity sign a =6 , the is of predication byjuxtaposition, or, more accurately speaking, by a singular term ’s filling the
argument slot of a predicative expression P(a) , he is of existence by the exis-
tential quantifier ( 3 ) P ( x ) , and the i s of subsumption by a general conditional
of the form (Vx)(x E S 3 x E P ) . In a introductory logic course students are
not on ly taught to use this no tation but given to understand that the corre-
sponding distinctions are an unavoidable aspect of all valid logic. It is highly
important to understand what the precise import of the Frege-Russell thesis
is. It is often presented as an eternal and immutable logical truth that anylogician at any stage of the history of logic heeded or ought to have heeded.
For example, there are scholars who have criticized Plato for not distinguish-
ing the is of predication from the is of identity. When Michael Frede (1967)
360 RlSTO VOLKKO A N D J A A K K O HINTIKKA
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argued, in his Pradikation und Existenzaussage, that Plato did not, i n the
Sophist, distinguish predicative and existential senses of estin from each
other, at least one reviewer took him to accuse Plato of a major logical blun-
der.
In this essay, we shall concentrate on the predicative and existential senses
of the verb is and largely disregard the development of the other senses. Any
historical discussion of the central questions of logic will have to be con-
ducted agains t the background of Aristotle 's logic , and we shall accordingly
start with a brief analysis of his treatment of verbs for being. This leads
imm ediately into philosophical questions,
Th e attribution of the Frege-Russell thesis to earlier philosophers, includ-
ing ancient Greek ones, has been encouraged by w hat is known among classi-
cists as Herm ann's rule (Herm ann 1801: 84-85). What i t purports to do is to
use the Greek accent system to make some of the Frege-Russell distinctions
in ancient Greek language. In the beginning of the 19th century the German
philologist Gottfried Hermann drew a distinction between the signification
which requires existence as an additional predicate and the signification which
already contains the predicate. According to Charles Kahn, the former was
expressed by means of th e enclitic accent ( ~ T I ) ,hile the latter one was
expressed by the orthotone accent ( ~ ( JT I ) n the first syllable (Kahn 1972:
420). The reason why Hermann's rule favors the Frege-Russell ambiguity
thesis is that on each occasion it allows only one of the alleged Frege-Russell
senses to be present. Hence it is easily taken to imply an ambiguity betweenseparate senses of estin.
It might nevertheless seem easy to dismiss H ermann 's rule as irrelevant. It
is not controversial to maintain that verbs for being have different uses. What
the Frege-Russell ambiguity thesis amounts to is a proposal to explain these
differences in use as being due to the ambiguity of these verbs, that is, to
their having several separate meanings rather than, e .g . , differences due to the
context. Why could we not simply claim that Hermann's rule is a way of
highlighting unproblematic differences in use? A rejection of the Frege-Rus-sell ambiguity thesis allows for the possibility that in some contexts we
cannot distinguish the allegedly different Frege-Russell meanings from each
other and perhaps are forced to say that more than one alleged Frege-Russell
mean ing is present there. Indeed, Jaakko Hintikka (1979; 1983) has argued for
the former possibility in terms of a game-theoretical treatment of the seman-
tics of is. What is more, we will see that the latter situation can be found i n
Aristotle. We shall return to H ermann 's rule later on.
In view of the widespread acceptance of the Frege-Russell ambiguity the-sis it may be surprising to realize, as Hintikka (1979) has pointed out, that
the Frege-Russell thesis is not an unavoidable part of either logic or the
seman tics of natural language. What is true is that natural language verbs for
EXISTENCE AND PREDICATION FROM ARISTOTLE TO FREGE 361
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being are used in several different ways. What the thesis does is to attribute
those differences in use to an ambiguity of a single word, instead of for
instance construing them as being due to differences in the context in which a
verb for being occurs. Hintikka has in fact presented an explicit semantical
treatment of English quantifiers and a number of related notions within the
framew ork of game-theoretical seman tics without assuming the Frege-Russell
thesis. (See Hintikka & Kulas 1985.) He has also pointed out that in some
particular cases the Frege-Russell thesis distinction simply cannot be made,
and also showed that the game-theoretical treatm ent of natura l language quan-
tifiers is closely related to Aristotle's doctrine of catego ries.
What is also striking and what makes these issues relevant to the history
of philosophy and history of logic is the fact that no philosopher before the
nineteenth century embraced the Frege-Russell thesis. Adm ittedly, attempts
have been made to find some of the Frege-Russell distinctions in Plato,
among others by A ckrill (1957) and by van Eck (2000).These attempts have
been persuasively criticized among o thers by Frede (1967) and by Brown (an
unpublished lecture). These discussions have been obscured by the same m-son as the import of Hermann's rule, viz. by a failure to distinguish a words
having different uses from its having different meanings, that is, from its
being ambiguous.
What is more, almost no earlier philosopher even seems to have consid-
ered the Frege-Russell distinction as a possible position. An exception is
Aristotle, who in his Metaphysics does consider the relation of assertions ofpred ication, existence and identity to each other, only to reject any sharp dis-
tinction, writing as follows:
...'one man' and 'man' are the same thing, so are 'existent man' and 'man',and the doubling of the
words in 'one man and one existent man' does not express anything different... and similarly
'one existent man' adds nothing to 'existent man' .. M e t . IV , 1003b26-31.)
Thus Aristotle in effect rejects the Frege-Russell ambiguity thesis. In a full
Aristotelian use of es t in , the first three Frege-Russell senses are present as
components of a single unambiguous force of estin. This leads Aristotle into
difficulties because the different Frege-Russell senses behave differently vis-8-
vis different logical rules. For instance, identity is transitive, while predica-
tion is not always transitive . Part of the way Aristotle tries to cope with
these problems is to admit that on different occasions different Frege-Russe ll
senses m ay be absent from the force of estin. For instance, if I say 'Homer is
a poet' ("Opqpos ~ T T ITO I~T~~S ),t does not imply 'Homer is' ("O~~rpo$
~OTI (V) )
which in the ancient Greek would have been a way of saying 'Homerexists.' (See De int. 11, 21a 20-30.) Here is the existential component of the
former occurrence of estin. Scholars have in fact tried to puzzle out when it is
that Aristotle assumes the existential force to be present. For instance, J. L .
36 2 RISTO V O L KK O A N D J A A K K OH I N T I K K A
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Ackrill (1963) has criticized the Homer example exactly because of its con-
fusing nature with regard to existential import. Scott Carson (2000) has
defended the importance of this example for its context in De interpretatione
and claimed that it lays stress on certain highly important aspects concerning
the nature of the verb ‘to be’ in ancient Greek philosophy. Hintikka and
Halonen (2000), in their turn, have argued that the presence of existentialforce in a potential syllogistic premise may not depend on this premise alone,
but on the stage of the process of constructing an Aristotelian science which
we are considering.
Likewise, in a syllogistic premise like
every B is A
the verb for being can either have existential force or not. Whether or not it
does depends on the term A . In this sense, in any syllogistic science, existen-tial import commitments are carried by the predicate terms of syllogistic
premises. This import can accordingly be proved by means of an ordinary
syllogism as one of its by-products. In other words, Aristotle could argue as
i t were as follows:
every B is an A (and exists)
every C is B
ergo:every C is an A (and exists)
Here B need not be assumed to have existential force. In contrast, the follow-
ing pattern does not represent a valid syllogism according to Aristotle’s
lights:
every B exists and is an A
every C is a B (and exists)
e r go : every C is an A (and exists)
Hence, in a syllogistic science existence need to be assumed only for the wid-
est (generic) term characterizing the purview of that sc ience . For all other
terms in that science, existence can be proved syllogistically. And this is
precisely what Aristotle says in his Analytica posteriora (A 10, 76a 31-37;
B 7, 92b 12-23). Whether or not the predicate term of given syllogisticprem ise of an Aristotelian science can be assumed to have ex istential force
therefore depends on whether the scientist has already proved this force , as
Hintikka and Halonen (2000) have argued.
EXISTENCE AND PREDICATION FROM ARISTOTLE TO FREGE 363
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What this means is that in Aristotelian scientific statements, i . e . syllogis-
tic premises, the existential force was canied by the predicate term. In this
sense, existence was for A ristotle a predicate or, rather, a part of the force of a
predicate. This force depends on the context. Existence could not serve alone
as a predicate term, but this was only because it would have been too broad a
term, not restricted to any one category and hence not an essence of anything.
In so many words: “Existence is not the ousia of anything” (An . post . B 7 ,
92b 13-15).
This statement calls for an explanation. The usual translation of ousia
(ojaia) is essence, and hence the quoted passage might seem to say merely
that mere existence does not distinguish the properties of any class of entities
from those of the others. However, Aristotle’s reasons for his statement are
quite different. For Aristotle, an essential predication is one that specifies the
class of entities to which it applies. Existence cannot be an essence of any-
thing, because a ll existing entities would form a class comprehending entities
from different categories. And such classes are for Aris totle conceptually
impossible, for the categories are precisely the largest classes that we can
coherently consider.
In order to avoid misunders tandings, it m ay be in order to point out that
we are employing the term ‘existen tial force’ in a sense different from its
most comm on use to indicate the nonem ptiness of a term . Here it means the
presence of the existential sense of a verb for being. In a syllogistic context,
i t amounts to the claim that all (possible) instances of a term actually exist.Since predicatively used terms did not always have existential force, the
Aristotelian quantification phrase ‘for some’ did not express actual existence.
If Aristotelian syllogistic was translated into modern logical notation and
interpreted in the same way as this notation, particular quantifier phrases
could only be taken to range over some kind of merely possible objects, not
necessarily over any existing ones.
But it is not the only remarkable fact here that in Aristotle’s syllogistic
logic the predicate term carries some of the existential force of a judgment.An equa lly remarkab le fac t here is that it carries in som e sense and with cer-
tain qualifications all of the ex istential force. One qualification needed in this
statement is that it has to be restricted to actual existence. A ristotelian quanti-
fier phrases like ‘every B’ or ‘some C’ should not in the first place be
thought of as m odern quantifiers ranging over the class of B’s or the class of
C‘s, much less over the class of all actually existing entities of the appropri-
ate category. When Aristotle puts forward a syllogistic premise like ‘every B
is A ,’ he does not mean merely that every actually existing B is A . If we triedto think anachronistically of Aristotle’s syllogistic premises in terms of quan-
tifiers ranging over certain entities, we would have to say that their values are
some sorts of possible individuals. How ever, this is not how Aristotle looked
364 RISTO VOLKKO A N D J A A K K O HI N T I KKA
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upon h is syllogistic premises. For him, they expressed primarily relations of
the forms expressed by the subject and the predicate. A premise like ‘every B
is A ’ says that it is a fact about the form expressed by the term B that it is
always accompanied by the form expressed by A . And since a premise like
‘every B is A’ is thus thought of as dealing in the first place with relations of
forms, the sets of entities instantiating these forms becom e largely irrelevant.
Th e force of such a prem ise certainly is not exhausted by speaking of rela-
tions of inclusion between the se t of entities actually satisfying B and the set
of entities actually satisfying A . Hence the twentieth-century logical nota-
tion, which is based on the idea of quantifiers ranging over a class of values,
can be applied to Aristotle only with considerable care.
It may be true that Aristotle’s logic, like modem logic, dealt with quanti-
fiers, as we have already seen. But what we have seen shows that he dealt
with them in a way radically different from ours, in particular as far as the
relation of quantifiers to the ideas of actual existence and actual universality
are concerned.
This analysis of Aristotle’s logical assumptions puts into perspective one
of the major questions concerning the origins of twentieth-century logic.
Even though the development of modern logic certainly “cannot be seen as a
tree growing from a single seed,” as Volker Peckhaus (2000) has recently
written, it has become commonplace to say that the starting point of modem
logic is the discovery of quantifiers by Frege in 1879 and by Peirce during the
early 1880s. Among other scholars, W. V. Quine (1995) has dated modemlogic from here. According to him, logic became a substantial branch of
mathem atics only with the emergence of general theory of quantification. But
what can be meant by the discovery of quantifiers? Quantifiers are roughly
speaking the logical counterparts to the expressions ‘for every’ and ‘for
som e.’ But the behavior of such expressions were part and parcel of what
Aristotle was trying to study in his syllogistic. Hence we face the question:
What else is new here? Aristotle already studied quantifiers, how could they
be the great novelty of F rege’s and Peirce’s logic?Here a contrastive comparison with Aristotle shows what the so-called
discovery of quan tifiers really amounted to. Earlier i t was seen that according
to him in a premise of a scientific syllogism the existential force (if any) was
carried by and large by the predicate term. The particular quantifier of Aristo-
telian logic was not for him really an existential quantifier. In Frege and his
successors the ex istential force was canied by and large by the ex istential
quantifier. One reason for the second qualification is that in Frege and most of
his imm ediate successors existen tial force was also carried by singular termslike proper names, which were assumed to be nonempty. This unnecessary
assumption was eliminated when logicians began to develop, in the late
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1950s, so-called free logics, beginning with H intikka (1959), and Leblanc and
Hailperin (1959).
The essential novelty of Frege‘s new log ic is therefore not the notion of
quantifier but the location of the existential import in a logical formula. In
the form of a suggestive but oversimplified slogan, one can say that for Aris-
totle existential import was carried by the predicate term while for the mod-
erns it is cam ed by the existential quantifier. This is crucial difference
between Aristotelian logic and modern logic. The profound character of this
difference cannot be exaggerated. There are reasons to be deeply skeptical in
most cases about presumed cases of conceptual incom mensu rability of scien-
tific, mathematical or logical theories. Here we nonetheless have a fairly clear
example where the same words are used so differently in two theories that no
direct comparison of the two theories is possible. Y et there is no insuperable
difficulty about discussing both of them rationally and even relating them to
each other in more complex ways.
Now how did this fundamental change come about? In order to answer this
question, it is helpful to use as a clue the question of the developm ent of an
apparently different aspect of contemporary logic, viz . of the Frege-Russell
thesis of the ambiguity of verbs for being. This thesis is sometimes attrib-
uted to Kant. In his book Kant’s Analyt ic (1966), Jonathan Bennett goes so
far as to speak of the ‘Kant-Frege thesis.’ H e claim s that “the quantified
treatment of existence-statements, formalized by Frege a century later, was
largely pioneered by K ant in the Dialectic” (p. 199). This attribution is inap-propriate i n the literal sense of the thesis. Kant never claimed that verbs for
being like the Germ an ist are ambiguous. Indeed, in addition to the notions of
‘existence’ (‘Dasein,’ ‘Existenz’) ,‘being’ (‘Sein’) ,and ‘is’ (‘ist’) , one finds
from his vocabulary also the unambiguous notion of ‘positing’ (‘setzen’).
Already in 1763 Kan t declared that “the notion of positing is quite simple and
altogether of one kind w ith the notion of being” (K ant 1763: 73), and later,
in the First Critique, he wrote that
‘Being’ s obviously no t a real predicate; that is, it is not a conce pt of something which could be
added to the concept of a thing. It is merely the positing of a thing, or of certain determinations,
as existing in themselves. Logically, it is merely the copula of a judgment. The proposition,
‘Cod s omnipotent‘, conta ins two conc epts, e ach of which has its object-God and om nipo-
tence. The sm all word ‘is’adds no new predicate, but only serves to posit the predicate in its
relation to the subject. ( K rV , B626-627.)
This implies among other things that ‘God is omnipotent’ does not logically
imp ly for Kant that ‘God is.’ What is more, in the title of the f irst paragraph
of the aforementioned precritical essay of 1763 Kant puts i t short and clear:“Existence is by no means a predicate or a determination of any particular
thing” (K ant 1763: 72; cf. Hintikka 1981).
366 RISTO V O L K K O A N D JA A K K O H I N T I KK A
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The distinction between predication and Existenzaussage was for Kant a
difference betw een two uses of the notion of being-a relative and an absolute
one. This is not only different from the distinction of Frege and Russell; it is
incompatible with their distinction.
It is often said that Kant rejected the idea tha t ‘existence is a predicate.’ In
a strictly literal sense, this marks no difference from Aristotle, for whom
existence could not be the essence of anything. But there is a fundamental
difference between the two. Existence could not be a predicate for Aristotle
because it was too general a notion not restricted to any one category, i.e . , to
any one class ofp red icabilia as any decent predicate must. In contrast, if we
examine what Kant meant, we can see that his claim was far stronger than
what the slogan ‘existence is not a predicate’ expresses. He argued that exis-
tence cannot even be a part of the force of a predicate term. As he put it, exis-
tence does not add anything to the concept expressed by the predicate. Hence,
in a judgment of existential, e . g . ‘God exists,’ a subject is taken as i t was
ready made with its essential predicates and merely assert that this particular
complex of predicates is in fact instantiated in reality. As Hintikka has writ-
ten: “Here existence is not one of the configurations of predicates; i t is what
is asserted of the configuration” (Hintikka 1981: 134).
Still other aspects of Kant’s philosophy are relevant here. The history of
the interrelation of the ideas of existence and predication is connected with the
history of the theory of categories . In Aristotle, his theory of categories
encourages strongly the idea that the existential and predicative uses of verbsfor being are parallel. But what precisely is his theory? The answ er is not
obvious, and it is not even obvious what it is that his categories are supposed
to categorize. The distinction between the different categories appears some-
times in Aristotle as a distinction between the largest genera w hose m embers
we can consider together (see, e . g . , Met. IV, 1003b 19-20; An. post . A 2 2 ,
83b, 10-17). If so , different categories mark different uses of existence and
presumably also different uses of identity. These different uses are held
together only by a dependence on one particular type of being, v i z . the beingof substances. But sometimes the distinction appears to separate the different
things that we can predicate of an object (Cut. 4). Categories thus seem to be
the different kinds of predicabilia, and in different categories w e therefore seem
to be dealing with different varieties of predication. At other times Aristotle
correlates the category distinction with a distinction between the different
question words of the ancient Greek, to the extent of using question words
and phrases as labels of the different categories (T op . I, 9). Which one of
these does Aristotle really mean? Scholars have defended strikingly differentlearned opinions on this point. For example, Adolf Trendelenburg (1846)
considered Aristotle’s categories above al l as the most general predicates, ad
Hermann Bonitz (1853) as the largest genera of entities. Jaakko Hintikka
EXI STENC E A N D PR EDI C ATI ON FROM ARISTOTLE TO FREGE 367
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(1986), in his turn, has analyzed the question from the vantage point of the
logic of quantifiers as it is incorporated in natural languages. He has been led
in this way to the answer: all of the above. In the logic of natural language,
at least of such natural languages as English and Greek, the semantics of
quantifier phrases forces these apparently different distinctions to be paralle l.
(Ibid., 96-103.)
This parallelism made it natural for Aristotle to think that the existential
and the predicative senses of einai-if they are different senses in the first
p l a c e d o go together. When they do not, for instance, when the existential
predicative and identificatory senses exhibit different logical behaviour, para-
doxes come about. How Aristotle dealt with them, is a story for another
occasion.
Thus in Aristotle, the category distinctions do not separate the allegedly
different Frege-Russell senses of being from each other. Rather, they separate
the parallel uses of eina i in one category from their u ses in another category.
There is nothing that disallows one and the same use of a verb like einai to
carry both an existential force and a predicative force as long as these two
forces are compatible categorially. Existence is not a predicate for Aristotle,
not because existence and predication are categorially different, but because
existence is used in all the different categories, and hence is not one of the
legitimate category bound predicabilia. The upsho t is an Aristotelian universe
which is split up into different larges t classes of beings. In different classes of
such kind, that is, in different categories, different things can be said of itsmembers, and their members are identified differently.
This overall picture changes radically when we move to Kant’s theory of
categories. Kant says that he is in his theory doing the same thing as Aris-
totle ( K r V , B105), but it is not clear what he means by that statement. It is
perhaps good to keep in mind that evidently Kant‘s knowledge of Ar istotle
was mostly based on such rather inadequate textbooks as Jacob Brucker’s His-
toria critica philosophie (1742-1744). Indeed, ccording to Peter Petersen,
after Melanchthon and before Trendelenburg there was no significant A r i s -
totle-reception (Petersen 1913 : 124-138). One possible answer in any case is
that Kant is, like Aristotle, concerned with the different kinds of questions
that we can raise about the world. But in Kant these differences between dif-
feren t questions do not merely reflect the objective differences between the
different realms of being that we might be talking about. They are differences
between different questions I must ask in order to integrate the messages that
my senses convey to me into a body of my knowledge. In Kant’s phrase, we
are in the category distinctions dealing with distinctions between different“pure concepts of understanding which apply a priori to objects of intuition
in general” (KrV, B105). They correspond to different “logical functions in all
possible judgments” (zbid.). A comparison with Aristotle shows remarkable
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differences. In so far differen t Kantian categories correspond to different kinds
of questions. The answers to questions show up in different aspects of the
logical form of all propositions. They are not questions that can be only
about a certain genus of entities, as Aristotelian categorial questions. They
are questions that arise in connection with any judgment.
The crucial difference between Aristotle and Kant for our present purposes
concerns the status of questions of ex istence and predication in Kant's theory.
The difference is that in Kant questions of existence and questions of inher-
ence and subsistence belong to different categories: the former to the category
of m odality and the latter to the category of relation. Hence, no logical func-
tion can express both. Consequently existence is not only not a predicate, i t
cannot be a part of the force of any predicate .
All this necess itated a radical reinterpretation of the semantics of syllogis-
tic premises. For on e thing, predication and ex istence had to be distinguished
from each other. However, it was not obvious how to conceptualize the rela-
tion of the two. Maybe they were not two meanings of a single word, but
they were not obviously two components of the meaning of a single unam-
biguous word, either. What is crucial, the existential force (i f any) of a syllo-
gistic premise becam e an orphan. It could no longer be im ported to the mean-
ing of the premise by the predicate term. And it was seen that in Aristotelian
logic, the particular quantifier did not necessarily express actual existence,
either.
Kant's influence makes understandable the problem situation in which
thinkers found themselves in the early nineteenth century. They had to keep
apart the existen tial and the predicative uses of verbs for being, whether or
not they were inclined to freeze the distinction into an ambiguity of a single
word or not. This problem situation was not restricted to professional phi-
losophers, either. A case in point is the aforementioned Herm ann's rule. We
are now able to see what there is to be said about it. Around the turn of the
19th century, under the influence of K ant's philosophy, Hermann w as project-
ing the sharp distinction between the different uses of verbs for be ing back tothe Greeks. But the variety of such a projection depends on there actually be-
ing a sharp distinction present in ancient writers, including the major Greek
philosophers. Hence, Hermann's rule cannot be used as evidence for the pres-
ence of the Frege-Russel1 distinction in ancient Greek philosophers. Instead,
the unmistakable absence of any such distinction in writers like Aristotle
should make us wary of the historical accuracy of Hermann's rule. On the
other hand we must acknowledge that Herm ann's rule was already anticipated
by some Byzantine scholars whose motivation was of course not philosophi-cal. Their concern seems to have been at least partly phonetic rather than
semantical, which reduces the interest of their distinction for the purposes of
the history of philosophy.
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If the situation into which Kant had thrust all thinkers was thus felt out-
side philosophy, it is only to be expected that it was perceived independently
and more or less simu ltaneously by several different philosophers. O ne way
of trying to cope with it is to make the Frege-Russell distinction, or some
part of it. Thus it is not at all surprising to find parts of Frege-Russell thesis
put forward by D e Morgan , Peirce, and quite likely still others . Frege’s new
logic was therefore not in all respects a unique discovery that could have been
made by a genius like Frege at any time. His distinctions between allegedly
different senses of being were made very much in a particular historical situa-
tion. As Gordon Baker and Peter Hacker have said, “if Frege had not made the
decisive breakthrough in 1879, others would have made it along the same line
within his lifetime (and nobody had been in a position to do so significantly
earlier)” (Baker&Hacker 1984: 16). It was no accident that Frege‘s philoso-
phical education (such as i t was) was almost exclusively Kantian. Hans Sluga
(1980) has it right: it is important to realize that both Frege’s logical and
philosophical ideas had their ancestry.
These coincidences are not really coincidences. They become even less
surprising when we note that for logicians there existed an obvious way of
finding a home to the orphaned existential force, even in the case of syllogis-
tic premises. This way was to assign it exclusively to the particular quantifier
expression, which was thus turned into our now familiar existential quanti-
fier. This transfer was further encouraged by other facts. For mathematicians
like Augustus De Morgan and George Boole, universality came to mean uni-
versality in some universe of discourse which is the ultimate subject of the
discourse. In virtue of the duality of the universally and particularly quantified
statem ents reflected in their interdefinability, this meant that the particular
statements cam e to express existence in the same universe. Admittedly, Jean
van Heijenoort (1967) has said that Boole’s logic did not have much onto-
logical import. This has to be understood in the right way. The telltale
notion in Boole is the notion of the universe of discourse. By this he did not
mean the actual universe but whatever system of ob jects we choose to speakabout. In his 1847 mathematical analysis of logic Boole understood the uni-
verse as comprehending
every conceivable class of objects whether actually existing or not, it being premised that the
same individual may be found in more than one class, inasmuch as it may possess more than
one quality in comm on w ith other individuals. (Boo le 1847: 15.)
Thus, B oole’s universe is the only class which contains all the individuals
that exist in any class. This is in perfect agreement with De Morgan’s notionof the universe of discourse. In his Formal Logic (1847), which was pub-
lished almost simultaneously with Boole’s Mathematical Analysis of Logic,
De Morgan characterized the universe as a range of ideas which is either
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expressed or understood as containing the whole matter under consideration,
i e . , “merely the whole of w hich we a re considering parts” ( ib id . , 38). In his
greatest work, An Investigation oft h e Laws of Thought (1854), Boole refined
his conception of the universe and wrote that “whatever may be the extent of
the field with in which all the objects of our discourse are found, that field
may properly be termed the universe of discourse” ( ib id . , 42). What is more,
in his late manuscript “Logic and Reasoning,” which was probably a sketch
for an introduction to a nonmathematical exposition of the basic ideas of the
Luws of Thought,Boole says short and clear that the limiting conceptions of
universe and nothing express simply the ideas of exis tence and nonexistence
(Boole 1952 : 218). Rush Rhees has claimed that this was a late change, and
that there may be important reasons for i t (Boole 1952: 30). Indeed, this was
an important change but i t was not as late as Rhees likes to suggest. Boole
did express the is of existence by x = 1 for ‘Something exists’ and respec-
tively x =0 for ‘Something does not exist’ already in his Investigation of the
Laws of Thought (Boole 1854: 189-190). In any case, i t is interesting to
compare this late definition of the universe as expressing simply the idea of
existence to the earlier 1847 definition, where the un iverse covered every class
of objects whether ac tually existing or not.
All in all, what Boole had in mind with his notion of the universe of dis-
course w as that logical truths do not convey any information about th e actual
world, since they are calculated to apply to any old universe of discourse. But
applied to one such dom ain the universal quantifier expresses universality andthe existential quantifier expresses existence with respect to the given
domain.
After Kant and before Frege the most far reaching development in logical
theory was the algebra of logic and theory of re lations that originated around
the mid-19th century with Boole and De Morgan. The following two ideas
came to the forefront. First, the operators corresponding to the syllogistical
standard forms of universal and particular judgments were treated as duals.
Second, universal judgments were taken to be relative to some universe ofdiscourse, and were inevitably taken as the nonexistence of exceptions in that
domain. But because of the duality, existential quantifier expressions came to
express existence. Boole differed from today’s notation of Boolean algebra
only in his use of the unnecessary elective symbol v to denote ‘some’ (thus,
e . g . ,x =vy reads ‘X is some y’ ) . The orphaned notion of existence thus found
a home, no longer in the predicative is but in the existential quantifier. This
helps in explaining the independent discovery of quantifiers by Frege in 1879
and by Peirce in the early 1880s.If De Morgan’s achievem ents seem insignificant from today’s perspective,
i t is because Boole ’s novel and successfu l ideas resulted in logic taking a
totally new direction. What is more, whereas Boole’s notation became widely
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recognized, De M organ’s notation soon fell ou t of date. Undoubtedly Boole
was a more original thinker than De Morgan. In G. C. Smith’s words,
“[Boole] chose interesting and important topics, had new ideas to express
about them, and communicated these incisively. De Morgan, on the other
hand, often wrote at great length without quite reaching the heart of the mat-
ter, although what h e had to say contained interesting-often vividly
expressed-remarks” (Smith 1982: 121).
One historical question concerns the level of B oole’s and De M organ’s
knowledge about the previous achievements in the field of logic. Both of
them became exceptionally well educated by different routes. Their correspon-
dence, for instance, provides good evidence for both of them having been
quite well informed about the previous developments in the field of logic (see
Smith 1982). How ever, Boole did not, for exam ple, know about Leibniz’s
pioneering results in logical calculi. What about Kant, then? Kant’s most
important works were well available in any decent university library and both
De M organ and Boole mastered the German language. Moreover, their contri-
butions contain remarks on what Kant had to say about, e . g . , categories,
hypothetical propositions, or the theory of syllogistic reasoning. However,
the only definite reference (Boole 1854: 239) is made to the so-called Jiische-
Logik (Kant 1800). In other words, the only definite reference is to a secon-
dary source which did not originate from Kant’s hand only , but also from
notes and remarks of his colleagues and students who attended his lectures .
Indeed, Terry Boswe ll(1988) has traced the Jiische-Logik back to four differ-
ent sources: (1) students’ notes, (2) Kant’s own reflections on logic, (3)
Gottlob Benjamin Jasche’s editorial additions, and (4) material from Georg
Meier’s Auszug uus der Vernunftlehre (1752), which Kant used as manual
during his lectures. Although authorized by Kant himself, the Jusche-Logik
is an unreliable source to Kan t’s logic.
De Morgan seems to have been very sensitive with regard to semantical
issues, perhaps even more sensitive than Boole. For example, in a letter to
Boole on February Ist, 1862, De Morgan criticized Sir W illiam Ham ilton’suse of the term ‘some,’ distinguished three different senses of this term, and
claimed that Hamilton had completely confused them (Smith 1982: 87).
How ever, of more importance for our story was his scrutiny of the verb is i n
his Formal Logic (1847).
In the third chapter of his Formal Logic De Morgan discusses first the
general characteristics of the terms of a proposition, as wanted for the abstract
forms of inference, and concentrates thereafter on those of the connecting
copulae is and is not. He sums up the most common uses of the verb is asfollows (ibid.,53):
( 1) Absolute identity, as in ‘The thing he sold you is the one I sold him;’
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(2) Agreement in a certain particular or particulars und erstood , as in ‘He is a Caucasian’ said
of a European in reference to the color of his skin;
(3 ) Possession of a quality, as in ‘The rose is red;’ and
(4) eference of a species to its genus, as in ‘Man is an animal.’
Here we in effect have the Frege-Russell distinction before Frege and Russell.
De Morgan also pointed out that all these uses are independent of the use of
the verb ‘alone,’ i.e.,of the is of existence, as in the expression ‘Man is (i.e.
exists).’ In all these senses, as well as in all such senses which might be
added consistently with the aforementioned conditions, some propositions
sometimes admit of having the sense of is shifted, and some do not. Thus, in
the case of negative propositions it is always possible to reduce the is of
agreement in particulars into that of identity by alteration of the predicate.
For example, if ‘N o A is B in color,’ then absolutely ‘No A is B.’ However,
‘Every A is B in color’ does not give ‘EveryA is B.’ But the first pair might
be connected by a syllogism. (Ibid., 53.)
De Morgan’s idea of a shift in the sense of is is an interesting one, and
deserves more attention than it has received. It is not even clear whether the
shift fails i n universal premises for logical reasons. It may be mentioned that
in the Finnish language there is a construction more generally applicable than
De Morgan’s which can perhaps be thought of as implementing the kind of
shift De Morgan is considering. It is illustrated by the following groups of
synonyms:
Lippu on punainen
Lippu on vj:rilaj:n punainen
Lipun vari on punainen
Han on suomalainen
Hl n on kansalaisuudeltaan suomalainen
H ln on Suomen kansalainen
Hanen nimensj: on Samuel
Han on nime ltlln Samuel
The flag is red
The flag is red in color
The color of the flag is red
He is a Finn o r He is Finnish
He is a Finn by nationality ur
His nationality is Finnish
He is a Finnish national
His name is Samuel
He is Samuel by name
In the last group we are obviously dealing with the identity sense of i s . The
relevant construction can be used also in general statements. More discussion
is nevertheless needed here.
To return to De Morgan, within a few pages of his Formal Logic (49-54)
he manages to write about the different senses, the different meanings, and the
different uses of the verb i s . Even thought he clearly had a sharp sight with
regard to semantical nuances, it seems as if he did not have a clear opinion
about whether the differences in the use of the verb is are due to the multiple
ambiguity of a single word or differences in the context in which it occurs.
EXISTENCE AND PREDICATION FROM ARISTOTLE TO FREGE 373
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The third use of verbs for being, the identity sense, became prominent when
relations and functions were included among the notions studied in logic. In
Aristotelian syllogistic, it did not make much difference whether a phrase like
‘some women are wise’ was in effect parsed as ‘some women are identical
with members of the class of wise people’ or ‘some women have the predi-
cate of wisdom .’ But relational expressions like ‘the teacher of Alexander the
Great’ could not be accommodated in this way. The situation in logic was
correctly perceived to be like the situation in algebra, where identities and
predications had to be distinguished from one another. T his development was
connected with the gradual change of the notion of relation from a relational
predicate (e.g. ‘a brother’) to a genuine entity linking its two terms. (On th is
use of the verb is, see Hintikka, forthcoming.)
The fourth alleged Frege-Russell meaning, the is of subsumption, was
promoted-or necessitated-by the categorical articulation of the reality
described in a logical language into individuals, their properties and relations,
possib ly properties and relations of properties and relations, and so on. A
sharp form of this articulation was Frege’s distinction between saturated enti-
ties (‘objects’) and unsaturated entities (‘functions’). Such articulation was
not peculiar to Frege, bu t foreshadowed in the tradition of the algebra of
logic.
Many philosophers have seen in this categorical articulation the crucial
step in the genesis of modem logic. Be the justification of this claim as it is,
on the level of actual logical rules a related change is more conspicuous. It isthe breakup of what Russell called denoting phrases in th e logical notation.
For instance, when ‘every man is m ortal’ is expressed as ‘(Vn)(x is a man 3
is mortal),’ the phrase ‘every man’ disappears altogether as a whole. ‘Every’
goes into ‘(Vx)’ and ‘man’ becomes the predicate term of the antecedent. This
led to introduction of bound variab les, which do not have any counterpart in
natural languages.
In a historical perspective, this distance between logical and ‘natural’ lan-
guages mean in effect that it was not immediately clear that logical notation,for instance the first-order notation, could actually express the same things as
ordinary discourse. Frege claimed such universality for his Begrzffssschrift,
but did little to demonstrate it or to illustrate it. He did not even emphasize
that quantifiers could serve to define (a la Weierstrass) the basic concepts of
analysis such as continuity and differentiability. A large part of the argumen-
tation needed to persuade philosophers of the expressibility was in fact carried
out by Russell, culminating in his famous essay “On Denoting” of 1905.
Russell even said that the distinction we have associated with his name (andFrege’s) marks “the first real progress in logic since the days of the Greeks.”
He was not right in the sense that the distinction is not an eternal truth about
all possible logics ready to be carved in stone. However, there may be a large
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grain of truth in Russell’s boast. In a deeper sense enhanced awareness of the
different uses of verbs for being and of their differences means genuine pro-
gress in our understanding of logic.’
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