John Stuart Mill.

A system of logic, ratiocinative and inductive : being a connected view of the principles of evidence and the methods of scientific investigation online

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to-day. They affect, not the predicate, but the applicability of the
predicate to the particular subject. That which w^e affirm to be past,
present, or future, is not what the subject signifies, nor what the pre-
dicate signifies, but specifically and expressly what the predication
signifies ; what is expressed only by the proposition, as such, and not
by either or both of the terms. Therefore the circumstance of time is
properly considered as attaching to the copida, which is the sign of
predication, and not to the predicate. If the same cannot be said of
such modifications as these, Caesar may be dead ; Csesar is perhajJS
dead ; It is j^ossihle that Ca?sar is dead ; it is only because these fall
altogether under another head, being properly assertions not of any-
thing relating to the fact itself, but of the state of our own mind in
regard to it; namely, our absence of disbelief of it. Thus, "Caesar
may be dead " means " I am not sure that Caesar is alive."

§ 3. The next division of propositions is into Simple and Complex.
A simple proposition is that in which one predicate is affirmed or
denied of one subject. A complex proposition is that in which there
is more than one predicate, or more than one subject, or both.

At first sight this decision has the air of an absurdity; a solemn dis-
tinction of things into one and more than one ; as if we were to divide
horses into single horses and teams of horses. And it is true that what
is called a complex proposition is often not a proposition at all, but
several propositions, held together by a conjunction. Such, for exam-
ple, is this, Caesar is dead, and Brutus is alive : or even this, Caesar is
dead, hut Brutus is alive. There are here two distinct assertions ; and
we might as well call a street a complex house, as these two propo-
sitions a complex proposition. It is true that the syncategorematic
words and and but have a meaning, but that meaning is so far from
making the two propositions one^ that it adds a third j)roposition to
them. All particles are abbreviations, and generally abbreviations of
propositions ; a kind of short-hand, whereby that which, to be expressed
fully, would have required a proposition or a series of propositions, is
suggested to the mind at once. Thus the words, Caesar is dead and
Brutus is alive, are equivalent to these: Caisar is dead; Brutus is
alive ; it is my wish that the two preceding propositions should be
thought of together. If the words were, Caesar is dead hut Bi-utus is
alive, the sense would be equivalent to the same three propositions


together with a fourth ; " between the two preceding propositions
there exists a contrast :" viz., either between the two facts themselves,
or between the feehngs with which it is my wish that they should be

In the instances cited<Hhe two propositions are kept visibly distinct,
each subject having its separate predicate, and each predicate its sepa-
rate subject. For brevity, however, and to avoid repetition, the pro-
positions are often blended together : as in this, " Peter and James
preached at Jerusalem and in Galilee," which contains four propo-
sitions : Peter preached at JeiTisalem, Peter preached in Galilee,
James preached at Jerusalem, James preached in Galilee.

We have seen that when the two or more propositions comprising
what is called a complex proposition, are stated absolutely, and not
under any condition or proviso, it is not a proposition at all, but a plu-
rality of pi'opositions ; since what it expresses is not a single assertion,
but several assertions, which, if true when joined, are true also when
separated. But there is a kind of proposition which, although it con-
tains a plurality of subjects and of predicates, and may be said in one
sense of the word to consist of several propositions, contains but one
assertion ; and its truth does not at all imply that of the simple propo-
sitions which compose it. An example of this is, when the simple
propositions are connected by the particle or ; as, either A is B or C
is D ; or by the particle if; as A is B //"C is D. In the former case,
the proposition is called disjmictive, in the latter conditional : the name
liypothctical was originally common to both. As has been well
remarked by Archbishop Whately and others, the disjunctive form is
resolvable into the conditional; every disjunctive proposition being
equivalent to two or more conditional ones. " Either A is B or C is
D," means, " if A is not B, C is D ; and if C is not D, A is B." All
hyjiothetical propositions, therefore, though (disjunctive in fonn, are
conditional in meaning ; and the words hypothetical and conditional
may be, as indeed they generally are, used synonymously. Propo-
sitions in which the assertion is not dependent upon a condition, are
said, in the language of logicians, to be categorical.

An hypothetical proposition is not, hke the pretended complex pro-
positions which we previously considered, a mere aggi'egation of
simple propositions. The simple propositions which form part of the
words in which it is couched, form no part of the assertion which it
conveys. When we say. If the Koran comes fi-om God, Mahomet is
the prophet of God, we do not intend to affirm either that the Koran
does come from God, or that Mahomet is really his prophet. Neither
of these simple propositions may be true, and yet the truth of the
hypothetical proposition may be indisputable. "WHiat is asserted is
not the truth of either of the propositions, but the inferribility of the
one from the other. Wliat, then, is the subject, and what the predi-
cate of the hypothetical proposition % " The Koran " is not the subject
of it, nor is " Mahomet :" for nothing is affirmed or denied either of
the Koran or of Mahomet. The real subject of the predication is the
entire proposition, " Mahomet is the prophet of God;" and the affirm-
ation is, that this is a legitimate inference from the proposition, " The
Koran comes from God." The subject and predicate, therefore, of an
hypothetical proposition are names of propositions. The subject is
some one proposition. The predicate is a general relative name

PR0P0SITI0N3. 57

applicable to propositions ; of this foma — " an inference from so anJ
so." A fresh instance is hero aflordod of the remark, tliat all particles
are abbre\'iations ; since "Z/" A is J3, C is D," is found to be an abbre-
\-iation of the following : " Tlie proposition C is D, is a legitimate
inference from the proposition A is B."

The distinction, therefore, between hypothetical and categorical
propositions is not so great as it at first appears. In the conditional,
as well as in the categorical form, one predicate is affirmed of one sub-
ject, and no more : but a conditional propositicm is a proposition con-
cerning a proposition ; the subject of the assertion is itself an assertion.
Nor is this a property peculiar to hypothetical propositions. There
are other classes of assertions concerning propositions. Like other
things, a proposition has attributes which may be predicated of it.
The attribute predicated of it in an hypothetical propasition, is that
of being an inference from a certain other proposition. But this is
only one of many attributes that might be predicated. We may say,
That the wliole is gi-eater than its part, is an axiom in mathematics :
That the Holy Ghost proceeds from the Father alone, is a tenet of
the Greek Church : The doctrine of the divine right of kings was re-
nounced by Parliament at the Revolution : The infallibility of the Pope
has no countenance from Scripture. In all these cases the subject of
the predication is an entire proposition. That which these difterent
predicates are affiiTned of, is the proposition, " the whole is greater
than its part;" the proposition, "the Holy Ghost proceeds fi'om the
Father alone:" the proposition, " kings have a divine right;" tJie prop-
osition, " the Pope is infallible."

Seeing, then, that there is much less difference between hypotheti-
cal propositions and any others, than one might be led to imagine
fi-om their form, we should be at a loss to account for the conspicuous
position which they have been selected to fill in treatises on Logic, if
we did not remember that what they predicate of a proposition, namely,
its being an inference fi'om something else, is precisely that one of its
attributes with which most of all a logician is concerned.

§ 4. The next of the common divisions of Pi-opositions is into Uni-
versal, Particular, Indefinite, and Singular : a distinction founded
upon the degree of generality in which the name, which is the subject
of the proposition, is to be understood. The following are examples:

All men are mortal — Universal.

So)ne men are moital — Particular.

Man is mortal — Indefinite.

Julius Ccesar is mortal — Singular.

The proposition is Singular, when the subject is an individual name.
The individual name needs not be a proper name. " The Founder of
Christianity was crucifieH," is as much a singular proposition as
" Christ was crucified."

AVTien the name, which is the subject of the proposition, is a general
name, we may intend to affiiTn or deny the predicate, either of all the
things that the subject denotes, or only of some. When the predicate
is affirmed or denied of all and each of the things denoted by the sub-
ject, the proposition is universal; when of some non-assignable portion
of them only, it is particular. Thus, All men are mortal; l^^vcry man
is mortal ; are universal propositions. No man is immortal, is also an


universal proposition, since the predicate, immortal, is denied of each
and every individual denoted by the term man ; the negative propo-
sition being exactly equivalent to the following, Evei-y man is not-im-
mortal. But " some men are wise," " some men are not wise," are
particular propositions ; the predicate wise being in the one case
affirmed and in the other denied not of each and every individual de-
noted by the term man, but only of each and every one of some por-
tion of those individuals, without specifying what portion ; for if this
were specified, the proposition would be changed either into a singu-
lar proposition, or into an universal proposition with a different subject;
as, for instance, " all instructed men are wise." There are other forms
of particular propositions: as, "ikZos^men are incapable of self-govem-
ment :" it being immaterial how large a portion of the subject the
predicate is asserted of, as long as it is left uncertain how that portion
is, to be distinguished from the rest.

When the form of the expression does not clearly show whether the
general name which is the subject of the proposition is meant to stand
for all the individuals denoted by it, or only for some of them, the
proposition is commonly called Indefinite ; but this, as Archbishop
Wliately obsei-ves, is a solecism, of the same nature as that committed
by some gi-ammarians when in their list of genders they enumerate the
doubtful gender. The speaker must mean to assert the proposition
either as an universal or as a particular proposition, though he has
failed to declare which : and it often happens that though the words
do not show which of the two he intends, the context, or the custom
of speech, supplies the deficiency. Thus, when it is affirmed that
" Man is mortal," nobody doubts that the assertion is intended of all
human beings, and the word indicative of universality is commonly
omitted only because the meaning is evident without it.

When a general name stands for each and every individual which it
is a name of, or in other words, which it denotes, it is said by logicians
to be distribzited, or taken distributively. Thus, in the proposition,
All men are mortal, the subject, Man, is distributed, because mortality
is affirmed of each and every man. The predicate Mortal, is not dis-
tributed, because the only mortals who are spoken of in the proposition
are those who happen to be men ; while the word may, for aught that
appears (and in fact does), comprehend under it an indefinite number
of objects besides men. In the proposition, Some men are mortal,
both the predicate and the subject are undistributed. In the following,
No men are perfect, both the predicate and subject are distributed.
Not only is the attribute perfection denied of the entire class Man,
but that class is severed and cast out from the whole of the class Per-
fect, and not merely from some part of that class.

This phraseology, which is of great service in stating and demon-
strating the rules of the syllogism, enables us to express very con-
cisely the definitions of an universal and a particular proposition. An
universal proposition is that of which the subject is distributed ; a par-
ticular proposition is that of which the subject is vmdistributed.

There are many more distinctions among propositions than those we
have here stated, some of them of considerable importance. But, for
explaining and illustrating these, more suitable opportunities will occiir
in the sequel.




§ 1. An inquiry into tlie nature of Propositions must have one of
two objects : to analyze the state of mind called Belief, or to analyze
what is believed. AH language recognizes a difference between a doc-
trine or opinion, and the act of entertaining the opinion ; between as-
sent, and what is assented to.

Logic, according to the conception here formed of it, has no con-
cern with the nature of the act of judging or bcheving; the considera-
tion of that act, as a phenomenon of the mind, belongs to another
science. Philosophers, however, from Descartes downwards, and es-
pecially from the era of Leibnitz and Locke, have by no means ob-
served this distinction ; and would have treated with gi-eat disrespect
any attempt to analyze the import of Propositions, unless founded
upon an analysis of the act of Judgment. A Proposition, they would
have said, is but the expression in words of a Judgment. The thingr
expressed, not the mere verbal expression, is the important matter.
When the mind assents to a proposition, it judges. Let us find out
what the mind does when it judges, and we shall know what proposi-
tions mean, and not otherwise.

Conformably to these views, almost all the writers on Logic in the
last two centuries, whether English, Gennan, or French, have made
their theory of Propositions, from one end to the other, a tlieory ot
Judgments. They considered a Proposition, or a Judgment, for they
used the two words indiscriminately, to consist in affirming or denying^
one idea of another. To judge, was to put two ideas together, or to
bring one idea under another, or to compare tAVO ideas, or to perceive
the agreement or disagi-eement between two ideas : and the whole
doctrine of Propositions, together with the theory of Ileasoning (always
necessarily founded upon the theory of Propositions), was stated as if
Ideas, or Conceptions, or whatever other term the ^vriter preferred as
a name for mental representations generally, constituted essentially the
subject matter and substance of those operations.

It is, of course, true, that in any case of judgment, as for instance
when wo judge that gold is yellow, a process takes place in our minds
of which some one or other of these theories is a partially coiTect ac-
count. We must have the idea of gold and the idea of yellow, and
these two ideas must be brought together in our mind. But in the
first place, it is evident that this is only a part of what takes place ; for
we may put two ideas together without any act of belief ; as when we
merely imagine something, such as a golden mountain ; or when we
actually disbelieve : for in order even to disbelieve that Mahomet was
an apostle of God, we must put the idea of Mahomet and that of an
apostle of God together. To determine what it is that happens in the
case of assent or dissent besides putting two ideas together, is one of
the most intricate of metaphysical problems. But whatever the solu-
tion may be, we may venture to assert that it can have nothing what
ever to do with the import of propositions ; for this reason, that propo-
sitions (except where the mind itself is the subject treated of) are not
assertions respecting our ideas of things, but assertions respecting the


things tliemselves. In order to believe that gold is yellow, I must,
indeed, have the idea of gold and the idea of yellow^, and something
having reference to those ideas must take place in my mind ; but my
belief has not reference to the ideas, it has reference to the things.
What I believe is a fact relating to the outward thing, gold, and to the
impression made by that outward thing upon the human organs; not
a fact relating to my conception of gold, which would be a fact in my
mental history, not a fact of external nature. It is true, that in order to
believe this fact in external nature, another fact must take place in my
mind, a process must be performed upon my ideas; but so it must in
everything else that I do. I cannot dig the ground unless I have the
idea of the ground, and of a spade, and of all the other things I am
operating upon, and unless I put those ideas together. But it would
be a very ridiculous description of digging the gi'ound to say that it is
putting one idea into another. Digging is an operation which is per-
formed upon the things themselves, although it cannot be performed
unless I have in my mind the ideas of them. And so in like manner,
believing is an act which has for its subject the facts themselves,
although a previous mental conception of the facts is an indispensable
condition. When I say that fire causes heat, do I mean that my idea
of fire causes my idea of heat] No: I mean that the natural pheno-
menon, fire, causes the natural phenomenon, heat. When I mean to
assert anything respecting the ideas, I give them their proper name, I
call them ideas : as when I say, that a child's idea of a battle is unlike
the reality, or that the ideas entertained of the Deity have a great
effect on the characters of mankind.

The notion that what is of primary importance to the logician in a
proposition, is the relation between the two ideas corresponding to
the subject and predicate (instead of the relation between the two
plienomena which they respectively express), seems to me one of the
most fatal errors ever introduced into the philosophy of L ogic ; and
the principal cause why the theory of the science has made such incon-
siderable progress during the last two centuries. The treatises on
Logic, and on the branches of Mental Philosophy coimected with
Logic, which have been produced since the intrusion of this cardinal
error, though sometimes written by men of extraordinary abilities and
attainments, almost always tacitly imply a theory that the investigation
of truth consists in contemplating and handling our ideas, or concep-
tions of things, instead of the things themselves : a process by which,
I will venture to affirm, not a single truth ever was amved at, except
truths of psychology, a science of which Ideas or Conceptions are
avowedly (along with other mental phenomena) the subject-matter.
Meanwhile, inquiries into every kind of natural phenomena were
incessantly establishing gi-eat and fruitful truths on the most important
subjects, by processes upon which these views of the nature of Judg-
ment and Reasoning threw no light, and in which they afforded no
assistance whatever. No wonder that those who knew by practical
experience how truths are come at, should deem a science futile, which
consisted chiefly of such speculations. Wliat has been done for the
advancement of Logic since these doctrines came into vogue, has been
done not by professed logicians, but by discoverers in the other sci-
ences ; in whose methods of investigation many gi-eat principles of
logic, not previously thought of, have successively come forth into light,


but who have generally committed tlie eiTor of supposing lliat notliin'T
whatever was known of the art of philosopliizing by the old logicians,
because their modem interpreters have written to so little purpose
respecting it.

We have to inquire, then, on the present occasion, not into Judg-
ment, but judgments ; not into the act of belic\'ing, but into the thing
believed. What is the immediate object of belief in a Proposition J
"Wliat is the matter of fact signified by it I AVliat is it to whi'ch, when
I assert the proposition, I give my assent, and call u])()n others to give
theirs I Wliat is that which is expressed by the fonn of discourse
called a Proposition, and the conformity of which to fact constitutes
the truth of the jjroposition ?

§ 2. One of the clearest and most consecutive thinkers whom this
country or the world has produced, I mean Hobbes, has given the fol-
lowing answer to this question. In every proposition (says he), what
is signified Ls, the belief of the speaker that the predicate is a name of
the same thing of which the subject is a name ; and if it really is so,
the proposition is true. Thus the proposition. All men are living be-
ings (he would say), is true, because living being is a name of every-
thing of wliich man is a name. All men are six feet high is not true,
because six feet high is not a name of everything (though it is of some
things) of which man is a name.

What is stated by Hobbes as the definition of a true proposition,
must be allowed to be a property which all tiaie propositions possess.
The subject and predicate being both of them names of things, if they
were names of quite different things the one name could not, consist-
ently with its signification, be predicated of the other. If it be true
that some men are copper-colored, it must be true — and the proposi-
tion does really assert — that among the individuals denoted by the
name man, there are some who are also among those denoted by the
name copper-colored. If it be true that all oxen ruminate, it must
be true that all the individuals denoted by the name ox are also among
those denoted by the name ruminating ; and whoever asserts that all
oxen ruminate, undoubtedly does assert that this relation subsists be-
tween the two names.

The assertion, therefore, which, according to Hobbes, is the only
one made in any proposition, really is made in every proposition : and
his analysis has consequently one of the requisites for being the true
one. We may go a step further ; it is the only analysis that is rigor-
ously true of all propositions without exception. Wliat he gives as
the meaning of projjositions, is part of the meaning of all propositions,
and the whole meaning of some. This, however, only shows what an
extremely minute fragment of meaning it is quite possible to include
wthin the logical fonnula of a proposition. It does not show that no
proposition means more. To warrant us in putting together two words
with a copula between them, it is really enough that the thing or things
denoted by one of the names should be capable, without violation of
usage, of being called by the other name also. If then this be all the
meaning necessarily implied in the foi-m of discourse called a Proposi-
tion, why do I object to it as the scientific definition of what a propo-
sition means ? Because, though the mere collocation which makes the
proposition a proposition, conveys no more meaning than Hobbes con-


tends for, that same collocation combined with other circumstances,
that form combined with other matter, does convey more, and much

The only propositions of which Hobbes' principle is a sufficient ac-
count, are that limited and vmimportant class in which both the predi-
cate and the subject are proper names. For, as has akeady been
remarked, proper names have strictly no meaning; they are mere
marks for indi\ddual objects : and when a proper name is predi-
cated of another proper name, all the signification conveyed is, that
both the names are marks for the same object. But this is precisely
what Hobbes produces as a theory of predication in general. His
doctrine is a full explanation of such predications as these : Hyde was
Clarendon, or, Tully is Cicero. It exhausts the meaning of those
propositions. But it is a sadly inadequate theory of any others. That
it should ever have been thought of as such, can be accounted for only
by the fact, that Hobbes, in common with the other Nominalists, be-

Online LibraryJohn Stuart MillA system of logic, ratiocinative and inductive : being a connected view of the principles of evidence and the methods of scientific investigation → online text (page 10 of 87)