proved very simply by means of the following proposition: A real
centaur does not exist; a centaur _in idea_, however, certainly
exists, and that as often as I imagine it. Whoever does not clearly
recognize here the distinction of the “ὂν ὡς ἀληθές i.e. in the sense
of existing, from ὂν in the sense of real (wesenhaft) will I fear
hardly be brought to recognize it by the fullest illustrations which
might be furnished by further examples. We may, however, also consider
briefly the following point: According to Sigwart, the knowledge of
the existence of anything consists in the knowledge of the agreement
of something represented in idea with, let us say, χ, since I do
not clearly understand with what. What now is necessary in order to
recognize the agreement of something with something else? Manifestly,
the knowledge of everything which is required in order that this
agreement should really exist. But this requires (1) that the one
element exist, (2) that the other element exist, and (3) that between
them there exist the relation of identity since what does not exist
can be neither like something nor different from it. But the knowledge
of the first element constitutes already in itself a knowledge of
existence. Hence the knowledge of the two remaining elements is no
longer necessary to the recognition of any existence, and Sigwart’s
theory leads to a contradiction. (Cf. with what has been said here,
Sigwart’s polemic against my _Psychology_, book ii. chap. vii. in his
work; _The Impersonalia_, p. 50 seq., and _Logic_, vol. i. second
edition, p. 89 seq. note, as well as Marty’s polemic against Sigwart
in the articles: “Über Subjectlose Sätze” in the _Vierteljahrsschrift
für wissenschaftliche Philosophie_, viii. i. seq.)[A]
[A] I had already written my Critique of Sigwart’s notion of existence
when I became aware of a note in his _Logic_, second ed, p. 390, a
passage which, while it has not made it necessary to alter anything
which I had written, has led me to insert it for the purpose of
comparison. “Das Seiende überhaupt,” Sigwart writes, “kann nicht als
wahrer Gattungsbegriff zu dem einzelnen Seienden betrachtet werden;
es ist, begrifflich betrachtet, nur ein gemeinschaftlicher Name.
Denn, da ‘Sein’ für uns ein Relationsprädikat ist, kann es kein
gemeinschaftliches Merkmal sein, es müsste denn gezeigt werden, dass
dieses Prädikat in einer dem Begriffe alles Seienden gemeinsamen
Bestimmung wurzle.” I fear that the reader will, just as little as
myself, attain by this explanation to clearness concerning Sigwart’s
notion of existence. He will perhaps the better understand why all my
efforts regarding it have proved futile.
s
Sigwart has failed to grasp the nature of judgment in general he
is not, of course, able to understand that of the _negative_ judgment
in particular. He has gone so far in error as to deny to it an equal
right as species along with the positive judgment; no negative
judgment is, he thinks, a direct judgment, its object is rather always
another actual judgment or the attempt to form such a judgment.
In this assertion Sigwart is opposed to some important psychological
views which I have made good in my lecture. It would therefore seem
fitting to resist his attack. For this purpose I shall show: (1)
that Sigwart’s doctrine is badly founded; (2) that it leads to an
irremediable confusion, as in that case Sigwart’s affirmative judgment
is a negative judgment, while his negative judgment if indeed a
judgment at all, and not rather the absence of one, is a positive
judgment, and that moreover his positive judgment really involves a
negative one, along with other similar confusions. (3) Finally I think
it will be possible--thanks to Sigwart’s detailed explanations--to
show the genesis of his error.
1. The first inquiry in the case of an assertion so novel and so
widely diverging from the general view, will be as to its foundation.
With regard to this, he insists above all (p. 150) that the negative
judgment would have no meaning if the thought of the positive
attribution of a predicate had not preceded. But what can this mean?
Either there is here a clear _petitio principii_, or it cannot mean
anything more than that a connection of ideas must have preceded. Now
granting this for a moment (although I have in my _Psychology_ shown
its falsity) this would by no means prove his proposition, since
Sigwart himself recognizes (p. 89 note, and elsewhere) that such a
“subjective connexion of ideas” would still not be a judgment; that
there needs rather to be added to it a certain feeling of constraint.
An argument follows later (p. 151) the logical connexion of which I
understand just as little. It is rightly observed that in and for
itself we have the right to deny of anything an infinite number of
predicates, and it is with equal right added that in spite of this,
we do not really pass all these negative judgments. And now what
conclusion is drawn from these premisses? Perhaps this, that the
fact that a certain negative judgment is warranted is not sufficient
in itself to explain the entrance of the judgment. This we may
without hesitation admit. But Sigwart concludes quite otherwise; he
permits himself to assert, it follows from this that the further
condition which is here lacking is that the corresponding positive
affirmation has not yet been attempted. This is indeed a bold leap,
and one which my logic at least is not able to follow. And why, if
one were to inquire further, are not all the positive judgments here
concerned really attempted? The most probable answer, judging by the
examples given by Sigwart (this stone reads, writes, sings, composes;
justice is blue, green, heptagonal, rotating), is, that this has
not been done because the negative judgment has already been made
with evident certainty; for this would best explain why there is no
“danger of any one attributing these predicates to the stone or to
justice.” If, however, any one prefer to answer that “the narrowness
of consciousness” makes it impossible to attempt at the same time
an infinite number of positive judgments, I am content with this
expedient also, only it must then be asked if this appeal ought not to
have been made directly and earlier, since Sigwart himself calls the
possible negative judgments an “_immeasurable_ quantity.”
It is also a curious error (Marty has already called attention to it),
when Sigwart asserts that in contradistinction to what holds good of
the negative judgment “every subject admits only of a limited number
of predicates being affirmed.” But why? Can we not, for example, say a
whole hour is greater than half an hour, greater than a third, greater
than a fourth and so on _ad infin._?... If then, notwithstanding, I do
not really make all these judgments, there are evidently good reasons
for this; above all that the “narrowness of consciousness” forbids it.
But then this might also be applied most successfully in regard to
negative judgments.
Somewhat later we meet a third argument which, as I have already by
anticipation refuted it in my _Psychology_ (book ii. chap. 7, section
v.), will be treated quite shortly here. If the negative judgment
were a direct one, co-ordinated with the affirmative judgment as
species then, thinks Sigwart (p. 155 seq.), whoever in an affirmative
categorical proposition regards the affirmation of the subject as
involved must, to be consistent, regard the denial of the subject
as involved in the negative proposition, which is not the case. The
latter observation is correct, the former assertion, however, quite
untenable, as it involves in itself a contradiction. For exactly
because the existence of each part in a whole is involved in the
existence of the whole, the whole no longer exists if but one of its
parts is missing.
It only remains now to consider a point of language by which Sigwart
believes himself able to support his view. A testimony for it is,
he thinks, to be found in the fact that the symbol for the negative
judgment is formed in every case by means of a combination with the
symbol of affirmation, the word “not” being added to the copula. In
order to judge what is here actually the fact, we will glance for a
moment at the sphere of feeling. Sigwart agrees, I think, with me and
everybody else that pleasing and displeasing, rejoicing and sorrowing,
loving and hating, etc., are co-ordinate with each other. Yet a
complete series of expressions denoting a disinclination of feeling
are found in dependence upon the expression for the corresponding
inclination. For example, inclination, disinclination; pleasure,
displeasure; ease, disease; Wille, Widerwille; froh, unfroh; happy,
unhappy; beautiful, unbeautiful; pleasant, unpleasant;--even “ungut”
is used. The explanation of this is, I believe, not difficult for the
psychologist, notwithstanding the equally primordial character of
these opposite modes of feeling. Ought then the explanation of the
phenomenon lying before us in the expression of the negative judgment,
closely related as it is to the before mentioned phenomenon, to be
really so very difficult, even assuming the primordial character?
As a matter of fact the case must be very bad when thinkers like
Sigwart in making statements so important in principle, and at the
same time so unusual, have to resort to arguments so weak.
2. The grounds on which Sigwart’s doctrine concerning the negative
judgment rest have, therefore, each and all proved untenable. This
must be so; for how could the truth of any doctrine be shown which
would plunge everything into the greatest confusion?
Sigwart finds himself compelled to distinguish between the positive
and the affirmative judgment, and the affirmative judgment--one hears
and wonders at the new terminology--is according to him, closely
examined, a negative judgment. On page 150 he says literally: “The
primordial judgment can certainly not be termed the affirmative
judgment, but is better described as the positive judgment, for
only in opposition to the negative judgment, and _in so far as it
rejects_ the possibility of a negation, is the simple statement A is
B an affirmation,” and so on. Inasmuch as it “rejects.” What else
can that mean than “so far as it denies”? As a matter of fact only
those negations can, according to this new and extraordinary use of
language, be called affirmations! Yet this would really mean, and
particularly when it is said that the proposition A is B _is_ often
such a negation (cf. the expressions just quoted), that the use
of language would be reduced to a confusion quite unnecessary and
altogether unendurable.
Not only is the affirmation--as set forth--according to Sigwart really
a negation but also, paradoxical as it may seem, the negation, on
close consideration, proves to be a positive judgment. It is true,
Sigwart protests against those who, like Hobbes, would regard all
negatives as affirmative judgments with negative predicates. But,
following Sigwart, if this is not so, then these must be affirmative
judgments with affirmative predicates, since he teaches that the
subject is in every case a judgment, the predicate being the notion of
invalidity. On p. 160 he says in the note the negation does away with
a supposition, denies the validity, and this expression, considered
in itself, might be taken to mean that Sigwart assumes here a special
function of denial (absprechen) the contrary of that of affirmation
(zusprechen). But no; a negative copula (cf. p. 153) according to him
there is not.
Now what in the world is one to understand by “denial” (absprechen)?
Does it mean the simple suppression (Aufhörenlassen) of the positive
judgment upon the given subject matter, that is, according to Sigwart,
the falling away of the feeling of compulsion previously given in
a connexion between ideas? This is impossible, since the removal
of this would bring about a condition in which the connexion of
ideas remains, without being either affirmed or denied. How often
does something of which we were previously certain become uncertain
without our on this account denying it. What then is this denying?
May we perhaps say that according to Sigwart it is a feeling oneself
compelled (sich-genötigt-fühlen) to annul, whereas affirming is a
feeling oneself compelled to posit? We should then have to say that
all the while we are passing a negative judgment, we are in reality
always seeking to pass a positive judgment, but that we experience a
hindrance in so doing. The same consciousness, however, is felt by
one who is clearly aware of the entire absence of a positive ground.
For how can any one succeed in believing anything which he at the
same time holds to be entirely ungrounded? Of no one, especially if
Sigwart’s definition of the judgment be applied as the standard,
is this conceivable; that is to say, every one in such a case will
experience failure in such an attempt. Accordingly there is, as
yet, no negative judgment. If then the rejection does not signify a
negative copula it must manifestly be regarded as an instance of the
affirmation of the predicate “false,” or (to use Sigwart’s term) as
its “identification” with the judgment which in this case should be
the subject. This “false” also cannot simply mean “untrue,” for I
can assert “untrue” of thousands of things with regard to which the
predicate “false,” which appears in certain judgments, would not be
in place. If only judgments are true, then of everything which is not
a judgment the predicate “untrue” must be affirmed, though certainly
not on that account the predicate “false.” “False” must therefore be
regarded as a positive predicate; and so from Sigwart’s point of view
absolutely false in principle, certain as it is that the merely not
being convinced (nicht-überzeugt-sein) is no denial, it is equally
certain that we have actually no choice; we should be compelled to
regard every negative judgment as a positive judgment with a positive
predicate. So we arrive at a second and greater paradox.
But here a third factor enters which completes the confusion. If
we examine Sigwart’s view as to the nature of judgment in general,
it may be shown in the clearest manner possible that the simple
positive judgment itself involves in turn, a negative judgment. That
is to say, following Sigwart, every judgment involves besides a
certain combination of ideas, a consciousness of the necessity of
our “identification” (unseres Einssetzens) and the impossibility of
its contradictory (cf. espec. p. 102), the consciousness, moreover,
of such a necessity and impossibility valid for all thinking beings
(cf. pp. 102 and 107), which, by the way, is of course quite as false
as Sigwart’s whole view of the nature of judgment in general. All
judgments without exception are, on account of this peculiarity,
called by Sigwart apodictic: nor will he admit the validity of any
distinction between the assertorical and apodictic forms of judgment
(cf. p. 229 seq.). I now ask: Have we not here a negative judgment
distinctly involved? Otherwise what meaning can be given to the
statement when we hear Sigwart speak of a “consciousness of the
impossibility of the contradictory.” Further I have already shown in
my _Psychology_ how all universal judgments are negative, since to
be conscious of universality means nothing else than to be convinced
that there exists no exception; if this negative be not added, the
most extensive list of positive assertions will never constitute a
belief in universality. When therefore, a consciousness that every
one must so think is here spoken of, there is in this fact a further
proof of what I have asserted, namely that according to Sigwart’s
doctrine of judgment the simplest positive acts of judgment must
involve a negative act of judgment. And yet we are called upon at the
same time to believe that the negative judgment, as set forth (p. 159
seq.), arose relatively late, and that therefore on this, as well as
on other grounds, it is unworthy of being placed side by side, with
the positive judgment as a species equally primordial! Sigwart would
surely not have expected this of us had he been conscious of all that
I have here set forth in detail, and which is the more clearly seen to
be involved in his exposition, often so difficult to comprehend the
more carefully it is submitted to reflection. Of course expressions
may be found where Sigwart, respecting this or that point of detail,
asserts the contrary of what is here deduced; for what else can be
expected where everything is left in such ambiguity, and where the
attempt to make things clear exhibits the most manifold contradictions?
3. Finally, we have still to show the genesis of the error in which
this able logician has involved himself in a relatively simple
question after having once mistaken the nature of the judgment. The
_proton pseudos_ is to be sought in a delusion which has come down
to us from the older logic that to the essence of the judgment there
belongs the relation of two ideas with one another. Aristotle has
described this relation as combination and separation (σύνθεσις καἰ
διαίρεσις) although he was well aware of the imperfect propriety of
the expressions, adding at the same time that in a certain sense
both relations might be described as a combination (σύνθεσις, cf.
_de Anima_, iii. 6). Scholastic and modern logic held fast to the
expressions “combination” and “separation”; in grammar, however,
both these relations were termed “combination,” and the symbol for
this combination the “copula.” Sigwart now takes seriously the
expressions “combination” and “separation,” and so a negative copula
seems to him a contradiction (cf. p. 153), the positive judgment,
on the other hand, appears to be a presupposition of the negative
judgment, since, before a combination has been set up, it cannot be
separated. And so it appears to him that a negative judgment without
a preceding positive judgment is quite meaningless (cf. p. 150 and
above). Consequently we find this celebrated inquirer in a position
which compels him to put forth the most strenuous efforts all to no
purpose--the negative judgment remains inexplicable.
In a note (p. 159) he gives us, as a result of such attempts, a
remarkable description of the process by which we arrive at the
negative judgment--a result in which he believes himself finally
able to rest satisfied. In this account the false steps which he
successively makes become, each in turn, evident to the attentive
observer. Long before the point is reached where he believes himself
to have come upon the negative judgment, he has as a matter of fact
already anticipated it.
He sets out with the correct observation that the first judgments
which we make are all positive in character. These judgments are
evident and made with full confidence. “Now, however,” he continues,
“our thought goes out beyond the given; by the aid of recollections
and associations, judgments arise which are at first also formed in
the belief that they express reality” (which means, according to
other expressions of Sigwart, that the ideas are combined with the
consciousness of objective validity; for this (xiv. p. 98) belongs
to the essence of the judgment) “as, for example, when we expect to
find something with which we are acquainted in its usual place or
pre-suppose respecting a flower that it smells. Now, however, a part
of what is thus supposed _contradicts_ our immediate knowledge.” (We
leave Sigwart to show here how we are able to recognize anything as
“contradictory” when we are not as yet in possession of negative
judgments and negative notions. The difficulty becomes still more
sharply apparent as he proceeds:) “when we do _not find_ what we
expected, we become conscious of the _difference_ between what exists
_merely_ in idea and what is real.” (What does “not find” mean here?
I had not found it previously; obviously I now find that what was
erroneously supposed to be associated with another object is _without_
it, and this I can only do by recognizing the one and denying the
other, i.e. recognize it as _not_ being with it. Further what is meant
here by “difference”? To recognize difference means to recognize that
of two things the one is _not_ the other. What is meant by existing
“merely in idea”? Manifestly, “what exists in idea which is _not_ at
the same time also real.” It would seem, however, that Sigwart is
still unaware that in what he is describing the negative function
of the judgment is already more than once involved. He continues:)
“That of which we are immediately certain is _another_ than that”
(i.e. it is not the same, it is indeed absolutely incompatible with
that) “which we have judged in anticipation, and now” (i.e. after and
since we have already passed all these negative judgments) “appears
the negation which annuls the supposition and denies of it validity.
_And here a new attitude is involved in so far as the subjective
combination is separated from the consciousness of certainty._ The
subjective combination is compared with one bearing the stamp of
certainty, its distinction therefrom recognized, and out of this
arises the notion of invalidity.” This last would almost seem to be
a carelessness of expression, for if invalid were to mean as much
as “false” and not “uncertain” it could not be derived from the
distinction between a combination with and a combination without
certainty, but only from the opposition existing between combination
which is denied and one which is affirmed. As a matter of fact, the
opposite affirmative judgment is not at all necessary to it. The
opposition, the incompatibility of the qualities in a real, is already
evident on the ground of the combination of ideas representing the
opposite qualities which, as I repeat once more, cannot, according to
Sigwart himself (p. 89 note; and p. 98 seq.), be called an attempt
at positive judgment. Although this may now and again happen in the
case of contradictory ideas, it certainly does not happen always. If,
for example, the question is put to me: Does there exist a regular
chiliagon with 1001 sides? then--assuming that I am not perfectly
clear in my own mind, as will be the case with most men, that there
does exist a regular chiliagon, I certainly do not attempt to form a
judgment (i.e. according to Sigwart, confidently assume) that there
exists a regular chiliagon having 1001 sides before forming the
negative judgment that no such figure exists on the ground of the
opposition between the qualities.
Sigwart himself, as his language frequently betrays (cf. e.g. pp. 152
and 150) recognizes at bottom, as he is bound to recognize, in spite
of his attack upon the negative copula, that negation and denial are
just as much a special function of the judgment as affirmation and
recognition. If this be granted, then the range of their application
is by no means so limited as he erroneously asserts. It is false that
in every case where a denial takes place the predicate denied is the
notion “valid.” Even of a judgment we may deny now its validity, now
its certainty, now its _à priori_ character. And just in the same way
the subject of the judgment can change most frequently. Of a judgment
we may deny certainty, and validity; of a request, modesty; and so
in every case, universally expressed, we may deny B of A. Sigwart
himself, of course, does this just like any one else. Indeed he
sometimes speaks unintentionally far more correctly than his theory
would admit, and witnesses, as it were, instinctively to the truth;
as, e.g. p. 151, where he declares not--as he elsewhere teaches--that
the subject of a negative proposition is always a judgment, and its
predicate the term “valid,” but “that of _every subject_ ... _a
countless_ _number of predicates may be denied_.” This is certainly
true and just on this account the old doctrine holds that affirmation
and denial are equally primordial species.