or indirect, is not distinguished from the Generic Judgment, resting
on a connection of content or presumption of causality. “All the [1]
papers have been looked over” should be distinguished from “All
triangles have their three angles equal to two right angles.”
[1] “The” as here used indeed practically = “these,” so
that, by our analysis, such a judgment has no claim to rank
as a universal judgment It is difficult to find a plainly
collective judgment which has not some affinity to judgment with
demonstrative pronoun or proper name. A judgment in which “All
M.P.’s” stands as subject, has affinity with the latter.
(2) The nature of the Universal Judgment is not examined with a view
to the distinction between Categorical and Hypothetical. The common
Logic does not go behind the grammatical form, which on this point is
not decisive.
(iv.) The Hypothetical Judgment [1] is said to consist of two
categorical propositions, or to be “_complex_” But of course it is a
simple judgment, _prima facie_ expressing a relation of reason and
consequent. Its parts are not Judgments, for they are not such as to
stand alone.
[1] Bain, p. 85; Jevons, p. 160.
(v.) The Disjunctive Judgment is often (_e.g._ by Mill and Bain) said
to be equivalent to two Hypothetical Judgments. The strange thing
is that both of these writers take the wrong two. [1] If we allow
conversion of a Hypothetical Judgment two are enough, but of course
they must be the two which cannot be got from each other by conversion,
viz. the two beginning, “If A is B ...” and “If A is not B ...”
respectively. If we do not admit conversion we must have all four.
Let the disjunction be, “This signal light is either red or green.”
In order to know this we must know not {116} only that, “If it is
red it is not green” (with its equivalent, “If it is green it is not
red”), but that, “If it is not red it is green” (with its equivalent,
“If it is not green it is red”). The former by itself leaves open the
possibility that it may be not red or green, but blue or yellow; the
latter by itself the possibility that when it is red it may also at
the same time be green. The former secures that the two terms exclude
each other; the latter, that, taken together, they exclude all other
predicates.
[1] Mill, ch. iv.; Bain, p. 86.
In any case, the disjunctive is more than any combination of
Hypotheticals, and really tends to be Categorical, and ought not to be
claimed as Conditional.
_Which are Categorical?_
2. We will now look at these Judgments in order, consider their real
meaning, and also ascertain the limits of the Categorical Judgment,
viz. that which affirms the existence of its Subject, or in other
words, asserts a fact.
_The Particular Judgment_
(i) The Particular Judgment of common Logic, “Some S. is P.,” has
different meanings according as it is understood naturally, or tied
down to be a result of enumeration.
In any case it is an imperfect, unscientific Judgment, in which the
mind cannot rest, because it has an undefined limitation imposed upon
the Subject.
_Its natural meaning_
(_a_) For the natural meaning, take the example, “Some engines can
drag a train at a mile a minute for a long distance.” [1] This does
not _mean_ a certain number of engines, though of course they _are_ a
certain number. It {117} means certain engines of a particular make,
not specified in the Judgment. The Judgment is Categorical, because
the undefined reservation implies a reference to something unanalysed,
but merely touched or presented in experience. If it was a mere idea
it would have to be clear; and if the full description or definition
were inserted, the Judgment would cease to affirm the existence of
the engines in question. _And the Judgment itself challenges this
completion._
[1] To be accurate, the Judgment would demand the insertion of
precise details about train, distance, and other matters. But
this illustrates the point of the text, because the assignment
of such details would naturally extend to the Subject, and then
the “Some” would be displaced.
_A narrower meaning_
(_b_) A more artificial meaning is to take the Judgment as not formed
by imperfect description, but by imperfect enumeration (understanding
it almost wholly in denotation). “Some Conservatives are in favour
of women’s suffrage.” This means or may mean that we have counted a
certain number, large or small, who are so, and we may or may not know
about the others. _Thus understood, the Judgment challenges complete
enumeration_; it contains of course the elements of a fraction--half,
most, nine-tenths of, and so on.
This again is Categorical; not merely because it implies counting, but
because it implies counting units separately given to experience.
The Particular Judgment does not include our Impersonal and
Demonstrative Judgments; they are not classed in the common text-books.
But as referring to perception they too are categorical and assert
facts, whether they have ideas to help out the perceptive reference or
not. And there is no reason against including them under the Particular
Judgment. The assertion, “This engine can drag a train a mile a
minute,” is much the same kind of Judgment as, “Some engines can, etc.”
Either of these would be false {118} if no such engines existed. _These
Judgments are of the essence of perception_. They have the connection
of content and the undefined complex of presentation struggling
together in them. They assert fact.
_Singular Judgment_
(2) The Singular Judgment of the common Logic is pretty much our
Judgment with a proper name, which I call Individual, and which, as we
saw, is in part rightly called universal--because the Subject extends
beyond perception, and the Predicate follows the Subject. But it is
a concrete or individual Universal, not an abstract Universal, and
therefore asserts the existence of its Subject. The reason why it is
taken to assert the reality of its Subject must be, I suppose, that
it _can_ assert this, its Subject being a name for an existence that
has limited reality within the temporal series, and _cannot_ assert
anything else, not having any general fixed content or connotation
which could imply a _general_ connection of Subject and Predicate. The
general connection of content which is so fatal to the asserting of
fact does not exist in this case. We see this in Mill’s instance. “The
summit of Chimborazo is white,” When the Subject is a unique name with
precise connotation, “The centre of gravity of the material universe
is variable,” then we are passing into the abstract Universal, and I
think we may take such a Judgment perhaps as one of the best examples
of a conjunction of categorical and hypothetical meaning, _i.e._ of
a connection of content ascribed to a Subject affirmed to exist. But
usually one meaning or the other is uppermost.
These Judgments, called Singular or Individual, correspond to the
region of history or narrative. The realities {119} with which they
deal have their definite position in a single system of time and space,
and this is often made emphatic by the use of tenses. But these change
with the date relative to the speaker, so that a Judgment with real
tense must once have been false, or must become false by lapse of
time. Thus the Judgment of fact may be not absolutely true. Nothing is
genuinely true which a change of date can make false. The permanently
true time-relations between Subject and Predicate are determined by
their content, and the copula is not a tense, but a mere sign of
affirmation. The Singular as Categorical is sharply distinguished from
the Abstract Universal, with which common Logic classes it.
_Universal Judgment_
(3) Down to this point the judgment states a _fact_. When we come to
the ordinary universal affirmative, we see at once that it may express
very different meanings. In its natural meaning it strongly _implies_
that its Subject has a particular existence within the series of time
and space, but hardly asserts it.
_Import of Propositions_
Mill, for example, says “the objects are no longer individually
designated, they are pointed out only by their attributes;” “most of
them not known individually at all.” That means that the explicit
Subject is not made of individuals. The natural meaning is disputed; I
incline to think with Venn, that the Subject is naturally taken _more_
in Denotation (not solely, which is unmeaning), and the Predicate
_more_ in connotation. But clearly in literal form the Subject is
simply a significant idea, and its existence in things or events is
not affirmed though it may be strongly implied. Hamilton [1] {120}
says quite calmly--“‘Rainy weather is wet weather’ is a Categorical
Proposition; ‘If it rains it will be wet’ is Hypothetical.” Between
the two I can see no distinction of meaning at all. [2] If indeed we
take the Universal Affirmative in the pure sense of aggregate formed
by enumeration, and therefore finite, it _may_ be said that we assert
the existence of the individuals composing it; but this is a very
unreal view of the meaning of the Judgment (though suggested by its
customary form), and even then it would be hard to prove that we
continue to think of the Subject as individuals. This reference to
a finite aggregate makes the _Collective Judgment_ or _Judgment of
Allness_. It cannot really exist in the case of a class like man, of
unknown extension, and is confined, at its widest, to such cases as
“All present Members of Parliament have to take a line on the Irish
question.” This _might_ be Categorical, but need not be so.
[1] _Lectures_, vol, iii. p. 327.
[2] Contrast Jevons, _Elementary Logic_, p. 163.
Otherwise, the Universal Affirmative of common Logic is literally
Hypothetical, though in some cases it may strongly imply the assertion
of reality. Dr. Venn has discussed this question. [1] He says the
implication of existence is much stronger with a single-word Subject
than with a many-worded Subject; _i.e._ perhaps with a natural than
with an artificial conception. But in any case, the expressed bond with
perception is lost, and in pure form the Subject is a mere abstract
idea, so that the relations of content entirely predominate over the
implication of existence.
[1] _Empirical Logic_, pp. 258-9.
Thus the Universal Affirmative in its full meaning fairly {121}
represents the sciences of classification, combining a subordinate
meaning of Allness or numerical totality with a primary meaning of
connotation of attributes or presumed causality. When we say “All the
Buttercup family have an inferior corolla,” of course we mean that
there is a reason for this. Often we omit the term all, as in “Heat
is a mode of motion.” In doing this we wipe out the last trace of a
reference to individual objects, and we pass to the pure hypothetical
form which absolutely neglects the existence of objects.
_“Hypothetical” Judgment_
(4) The simplest type of this Judgment is, if A is B it is C. This
Judgment corresponds to abstract science, but it is only making
explicit what was implied in the Universal Affirmative. That
expressed a presumption of causality, this expresses a clear Reason
and Consequent or scientific necessity. The point of this form is
(i.) that it drops all reference to individual objects, (ii.) that
it challenges you to explain how the Subject-content is tied to the
Predicate-content. “Water boils at 212°,” is a statement we should
generally pass in so-called Categorical form, because it does not
challenge any great accuracy of connection. But “If water boils, it
is at a temperature of 212°,” puts us upon asking, “Is the condition
adequate?” and we see at once that we must at least say, “If water
boils _under pressure of one atmosphere_, it is at a temperature of
212°,” or else the judgment is untrue. Of course we may apply the form
rightly or wrongly, as you may fill up your census paper rightly or
wrongly. We can only say that it calls upon you to put in an adequate
condition. Therefore I rather object to the form “If A is, B is,”
because it adds very little to the so-called Categorical shape.
{122} We have now to ask how the Hypothetical Judgment connects its
content with reality, _i.e._ how it is a Judgment at all? And the same
explanation must apply to so-called Categorical Judgments, which can be
thrown into this form without change of meaning.
The point from which the explanation starts is taking hypothesis as
supposition. This is much more true, I think, than connecting it with
_doubt_. In Dr. Venn’s _Empirical Logic_ the connection of Hypothetical
Judgment and doubt to my mind disfigures the whole treatment of the
Scientific Judgment. Supposition is distinct from affirmation--that
is true--but just because it is distinct from affirmation, it cannot
indicate doubt. It probably arose out of doubt, but as a method of
science it does not imply doubt, but only the accurate limitation of
attention. What doubt is there when we judge “If equals be added to
equals, the wholes are equal”? We are attending to one particular
thread of the nexus.
Hypothetical Judgment, then, is Judgment that starts from a
supposition. Every supposition is made upon a certain basis of
Reality. Take as an extreme case, “If you ask permission of A.B., he
will refuse it.” This is a supposition and its result, on the basis
of the known character of A.B. And the full judgment is “A.B. is of
such a character, that, supposing you ask him for permission, etc.”
The Hypothetical Judgment may be true, as an assertion about A.B.’s
character, though you may never ask.
Here, then, is the clue to the analysis of _all Abstract Judgments_,
Like Perceptive Judgment, they affirm something of Reality, but they
do this indirectly and not directly. {123} Underlying them there is
the implied Categorical Judgment, “Reality has a character, such
that, supposing so and so, the consequence will be so and so.” And
if this implied assertion is true, then the Hypothetical Judgment is
true, although its terms may be not only unreal, but impossible. “If
a microscopic object-lens with a focal length of 1/100 in. were used,
its magnifying power with an A eye-piece would be so many diameters.”
This is a mere matter of calculation, and is unquestionably true,
depending upon the effects of refraction upon the optical image. But I
do not suppose that such an object-lens could be made, or used. Does
such a Judgment, although true, express a _fact_? No, I should say not,
although common usage varies. I remember a _Pall Mall_ leading article
which said, “It is an absolute fact, that, if Mr. Gladstone had not
done something--the Government would have committed--some iniquity
or other.” Is this what we call a fact? We observe that the content
actually mentioned was never real at all. The implied connection
with reality is “There existed in reality a condition of things
(unspecified) in which _if_ Mr. Gladstone, etc., etc.” Are mathematical
truths facts, and in what sense? Abstract truth need not, and perhaps
cannot express fact, but implies fact indirectly.
_Disjunctive Judgment_
(5) The Disjunctive Judgment “A is either B or C,” is again not
a judgment of doubt but a mode of Knowledge, It may be taken as
numerical; then it gives rise to the statement of Chances. But in its
perfect form it is appropriate to the exposition of a content as a
system, and it may be taken as returning to the Categorical Judgment,
and combining it with the Hypothetical, because its {124} content is
naturally taken as an individual, being necessarily concrete.
The peculiar point of the Disjunctive is that it makes negation
positively significant.
“This signal light shows either red or green.” Here we have the
categorical element, “This signal light shows some colour,” and on the
top of this the two Hypothetical Judgments, “If it shows red it does
not show green,” “If it does not show red it does show green.” You
cannot make it up out of the two Hypothetical Judgments alone; they do
not give you the assertion that “it shows some colour.” [1]
[1] The example in the text, chosen for its simplicity, may
be objected to as involving perceptive concreteness by the
pronoun “this.” You can have a disjunction, it may be said,
dealing with “the triangle” as such; and why should this be
more “Categorical” than the assertion that the triangle has
its angles = three right angles? Still, it might be replied,
the development of a single nature into a number of precise
and necessary alternatives, always gives it an implication of
self-completeness.
Does this state a fact? I think it implies a fact much more distinctly
than the hypothetical does, but of course it is a question whether an
alternative can be called a fact. It seems a precise expression of
some kinds of reality, but it is not a solid single momentary fact.
It is very appropriate to the objects of philosophy as the higher
concrete science, which are conceived as systems of facts bearing
definite relations to each other; _e.g._ “Society is a structure of
individual characters, having positions which are not interchangeable.”
Taken all as a mass, they are conjunctively connected, but taken in
distinguishable relations they are disjunctively related. A human
being as such has some position and no other, and this is ultimately
determined by {125} the nature of the social whole to which he
belongs. He is if this, nothing else, and if nothing else, then this.
A more artificial example, which illustrates the degree in which
actual abstract knowledge and purpose can be embodied by man in
machinery, is the interlocking system of points and signals at a great
railway station. I suppose that the essence of such a system lies in
arrangements for necessarily closing every track to all but one at a
time of any tracks which cross it or converge into it. The track X
receives trains from A, B, C, D; if the entrance for those from A is
open, B, C, and D are _ipso facto_ closed; if A, B, and C are closed,
D is open, and so on. This is a disjunction consciously and purposely
incorporated in material fact, and differs from a Disjunctive Judgment
only in so far as existence necessarily differs from discursive thought.
The disjunction seems to complete the system of judgments, including
all the others in itself, and it is wrong in principle to distinguish,
_e.g._ between a hypothetical and categorical disjunction, or to
consider how a disjunction can be denied. For disjunction in itself
implies a kind of individuality which is beyond mere fact and mere
abstract truth, though allied to both; and all intelligible negation
is under, not of, a disjunction. Negation of a disjunction would
mean throwing aside the whole of some definite group of thoughts as
fallacious, and going back to begin again with a judgment of the
simplest kind. It amounts to saying, “None of your distinctions touch
the point; you must begin afresh.”
{126}
LECTURE VIII NEGATION, AND OPPOSITION OF JUDGMENTS
_Distinction between Contrary and Contradictory opposition_ [1]
1. The only important point in the traditional diagram of opposition
of Judgments is the distinction between contrary and contradictory
opposition, the opposition, that is, between A and E, and the
opposition between A and O, or E and I.
[1] Read Bain, pp. 55-6, on “Negative Names and the Universe
of the Proposition,” also on “Negative Propositions,” p. 83
ff.; Venn, _Empirical Logic_, pp. 214--217; Jevons, _Elementary
Logic_, ix., on “Opposition of Propositions”; Mill, ch. iv. § 2.
In _Contrary_ Opposition the one Judgment not only denies the other,
but goes on to deny or assert something more besides. The mere
grammatical shape “No man is mortal” conceals this, but we easily see
that it says more than is necessary to deny the other, “All men are
mortal.”
In _Contradictory_ Opposition, the one Judgment does absolutely nothing
more than is involved in destroying the other.
The _Contrary_ Negation has the advantage in positive, or at least in
definite import.
The _Contradictory_ or pure Negation has the advantage in the
exhaustive disjunction which it involves.
This is plain if we reflect that Contrary Negation only {127} rests on
the Law of Contradiction, “X is not both A and not A.”
_Ordinary Diagram of Opposition of Judgments_.
[The diagram has diagonal lines, not represented here, from corner A to
corner O, and from corner E to corner I, each labelled “Contradictory
Opposition”. Tr.]
A E
Contrary Opposition.
Sub-contrary Opposition.
I O
A = Universal Affirmative. All men are mortal.
E = Universal Negative. No men are mortal.
I = Particular Affirmative. Some men are mortal.
O = Particular Negative. Some men are not mortal.
Sub-contrary Opposition has no real meaning; the judgments so opposed
are compatible.
It is not _true_ both that “All M.P.’s are wise,” _and_ that “No
M.P.’s are wise,” but both may be false; while Contradictory Negation
implies the Law of Excluded Third or excluded Middle, “X is either
A or not A,” the principle of disjunction, or rather, the simplest
case of it. It is not {128} _false_ both that “All M.P.’s are wise”
and that “Some M.P.’s are not wise.” The point is, then, on the one
hand, that in Contradiction you can go from falsehood to truth, [1]
while in Contrariety you can only go from truth to falsehood; but also
that in Contradiction the Affirmative and Negative are not at all on
a level in meaning, while in Contrariety they are much more nearly
so. Then if we leave out the relations of mere plurality, of All and
Some, which enable you to get contrary negation in pure negative form
in the common Logic, we may say generally that in contrary negation
something is asserted, and in contradictory negation taken quite
literally nothing is asserted, but we have a “bare denial,” a predicate
is merely removed. In actual thought this cannot be quite realised,
because a bare denial is really meaningless, and we always have in our
mind some subject or universe of discourse within which the denial is
construed definitely. But this definite construing is not justified by
the bare form of contradiction, which consists simply in destroying a
predication and not replacing it by another. In as far as you replace
it by another, defined or undefined, you are going forward towards
contrary negation.
[1] _I.e._ Contradictory alternatives are exhaustive.
_Contrary Negation_
2. Thus, Contrary Negation in its essence is affirmation with a
negative intention, and we may take as a type of it in this wider
sense the affirmation of a positive character with the intention of
denying another positive character. _E.g._ when you deny “This is a
right-angled triangle” by asserting “This is an equilateral triangle,”
you have typical contrary negation. It is not really safe to speak of
contraries except with reference to _judgments_, intended to deny each
{129} other; but it is common to speak of species of the same genus as
contraries or opposites, because the same thing cannot be both. [1]
[1] Bain, p. 55 ff.
We must therefore distinguish _contrary_ from _different_. Of course
the same thing or content has many different qualities, and even
combines qualities that we are apt to call contrary or opposite. But
as Plato was fond of pointing out, a thing cannot have different or
opposing qualities in the same relation, that is to say, belonging to
the same subject under the same condition. The same thing may be blue
in one part of it and green in another, and the same part of it may be
blue by daylight and green by candlelight. But the same surface cannot
be blue and green at once by the same light to the same eye looking in
the same direction. _Different_ qualities become _contrary_ when they
claim to stand in the same relation to the same subject. Right-angled
triangles and equilateral triangles do not deny each other if we leave
them in peace side by side. They are then merely different species of
the same genus, or different combinations of the same angular space.
But if you say, “This triangle is right-angled,” and I say “It is
equilateral,” then they deny each other, and become true contraries.