Chapter
IV.
THE LAWS OF THOUGHT.
5. Other Views as
to the Source of the Laws of Thought
§
1. The Laws of Thought. In each science there are certain principles
or laws, which are recognized as fundamental within that science. Every
conclusion which it claims to have demonstrated, depends for its validity on
the truth of those principles. Such for instance are the definitions of Euclid
in regard to Geometry (the science of abstract spatial extension), and the laws
of motion in regard to the science of Mechanics. In each case the principles have their own
sphere of application. They are principles of this or that science, and beyond
it they are not operative. There
are, however, certain laws, which are not confined within the limits of any one
of the special sciences, but which apply to all that is, to all that has
a right to the name of Being or
Thing. For instance the law of causality which
lays down that every event must have a cause, is such a principle as
this. It is not a law of one of the special sciences, but is true of all
things. It belongs to that universal science of Metaphysics or Ontology, of
which something has been said in Ch. 1, §3.
Just as there
are laws which apply to the whole realm of Being to the real order in its
full extent so too there are laws which govern the whole of the conceptual
order, and on which depends the validity of every judgment, whatever it may be. These are the Laws of Thought, which form the
subject of this most important lecture. They are three in number: --
(1) The Law
of Contradiction, viz. Contradictory
judgments (e.g. A is B, A is not B) cannot
both be true.
(2) The Law
of Identity, viz. Everything is
what it is.
(3) The Law of Excluded Middle, viz.: Of two contradictory judgments (A is B, A is
not B) the one must be true, the other false.
These three
laws we shall proceed to consider in detail. But first, it will be well to ask
ourselves in what sense they are termed laws. For the word 'law' is used in
various senses. In its primary signification it means an ordinance imposed by a
legitimate superior on the body politic, and carrying with it an obligation of
obedience. But it is also employed to signify a uniform mode of acting observed
by some natural agent. In this sense we use the term 'laws of nature,' e.g. the
law of gravitation, the law that water under a certain pressure freezes at 32o
F., etc. Laws of nature are only
called laws by analogy: there is of course, no question here of the obedience
which one will ought to yield to another. The law is simply our description of
the way in which the agent does in fact act.
It tells us what is, not what ought to be. In yet another
meaning we use it to denote a norm or standard, to which we must conform in
order to achieve some end. Thus we may speak of the laws of perspective. If we
wish our drawing to be accurate, we must observe them. Otherwise, we shall not
attain our object.
It is in this
last sense that we employ the word, when we speak about the laws of thought. It
is certainly the case that we are unable to judge a pair of contradictory
propositions to be true, if we are conscious of the contradiction. But it not infrequently happens that men
unconsciously hold opinions, which are really contradictory the one of the
other, though because they are expressed in different words, or from some
confusion of mind, their mutual opposition is not recognized. Hence the laws of
thought cannot strictly be termed laws in the second of the senses we have
noticed above. But since in all our mental judgments our end and object is to
attain truth, they are rightly termed laws in the last sense mentioned: for if
they are not observed, our judgments are not true but false.
§
2. The Law of Contradiction.
The form in
which we have given the principle of Contradiction, 'Contradictory
judgments cannot both be true,' is that in which, with various slight
modifications it is several times enunciated by Aristotle [N1]. He, moreover, is careful to point out that
where judgments are contradictory to each other, the predicate must be referred
to the subject in the same way in each, and the point of time must be
identical. "A refutation," he says, "occurs when something is
both affirmed and denied of one and the same subject . . . and when it is
denied in the identical respect, relation, manner and time, in which it has
been affirmed." [N2]. It
might be true to say both that the prime minister is capable,' and that 'the
prime minister is not capable,' if the capacity referred to was in the one case
capacity for government, in the other capacity for writing Greek verse: or if
we were speaking of different periods in his life.
Mill adopts a
more cumbrous phraseology. He gives the law as follows: 'The affirmation of an
assertion and the denial of its contradictory are logical equivalents, which it
is allowable and indispensable to make use of as logically convertible" (Exam.
of Hamilton, p. 414).
This law, as
we have said, is a ruling principle of the whole conceptual order. It applies
to all that is thought. But the order of thought of conceptual Being
is essentially a representative order. It manifests the order of things. And
this law of thought is the conceptual expression of a fundamental necessity of
the real order: to the logical principle corresponds a metaphysical principIe.
This metaphysical law may be stated: "The same attribute cannot at one and
the same time both belong and not belong to the same thing "(Arist. Met.
III., c. 3, § 10). Another
form in which it is frequently expressed, is: "It is impossible for the
same thing both to be and not to be, at the same time." [N3]. How closely the logical principle represents
the metaphysical will at once be seen, if we express the former as: "The
same attribute cannot at one and the same time be both affirmed and denied of
the same thing." But the student
should be careful to distinguish the various expressions of the law, and when
dealing with logical questions not to state the principle in a metaphysical
form, nor vice versa.
This law
Aristotle declares to be the first of all axioms, and the most certain of all
principles (Met. X., c. 5, § 1).
* The
question will doubtless suggest itself, on what grounds this is asserted to be the
first of all axioms. A brief examination will show us that the principle of
Contradiction is the first Analytic proposition, which we attain through an
analysis of our most primary notion the notion of 'Being' or 'thing.'
This
notion, which we apply equally to all entities whatever, calls for a brief
consideration.
We
are accustomed to name objects from their various determinations and
perfections. We term one man a 'runner,' because the perfection denoted by the
word 'to run,' characterizes him, and we call another a 'painter' for a similar
reason. Further, we apply these denominatives to them, even though the
perfection is not at the moment in a state of actualization. The man is called a 'runner' or a 'painter,'
not because he is actually running or painting, but because he has the capacity
to do so: the capacity or potency remains even when he is not eliciting the
act. 'Being' is a denominative of this
type. It is applied to objects in virtue of that primary perfection signified
by the verb 'to be,' namely 'to exist.' The notion which expresses this primary
characteristic of 'Being' or 'actuality,' is clear to us from the dawn of our
intelligence. It is absolutely simple. We cannot explain it by any that is simpler for
its simplicity is ultimate. Indeed were there not primary notions of this kind,
it would be impossible to explain anything. The mind would be lost in an
infinite regress, as it endeavoured to find some idea which did not itself need
elucidation.
What
then is the Analytic proposition which unfolds the intension of this term,
which is the first principle to emerge from the consideration of our primary
concept? Its very simplicity prohibits
our explaining it otherwise than by declaring its difference from its opposite,
viz, that it is essentially opposed to non-existence [N4]. Yet we cannot state the principle as 'A
Being is that which is not non-existent,' for as we have noticed, 'Being'
is applied not merely to that which does at present exist, but to such objects
of thought as we see can exist. A chiliagon may be termed a
'thing' or a 'Being.' Our proposition must be expressed, 'A Being which is,
cannot at the same time not be'; or as otherwise phrased, 'It is
impossible for the same thing both to be and not to be at the same time.' Here
then we have the principle of Contradiction, as the first of principles derived
by analysis from the primary notion.
In
regard of each Being, however, we must consider not merely its existence, but
its nature: that which makes it what
it is. The principle may be enunciated not merely in reference to
the former, but to the latter: for the nature of an entity determines the mode
of its existence. As thus expressed, we get the form 'The same attribute cannot
at the same time both belong and not belong to the same thing.' The logical
expression, as we have seen, is identical with this, save that it refers to the
mental act by which we judge about the thing: 'The same attribute cannot at the
same time be both affirmed and denied of the same thing.'
§
3. The Law of Identity. This
principle is often stated in the form A = A. This,
however, is manifestly a formula, and not the enunciation of a philosophic
principle. Locke (Essay, Bk. 4, c. 7) enunciates it as 'Whatever is,
is,' and this form appears to be philosophically correct. Like the principle of
Contradiction, this law is an Analytic proposition explicative of the concept
of Being. Its connection with that
principle will appear plainly if we express it as 'A Being which is, is.' In this form we see that the only difference between the two is
that in the one case we affirm that things which exist, exist : in the other,
that things which exist, cannot not exist.
Like the
principle of Contradiction also, it may be enunciated in reference to the
nature, which determines the existence.
Leibniz has given expression to the law in this form. He words it
'Everything is what it is.' Leibniz's form will serve us also for the logical
order, if it be understood as signifying that every subject of predication is
what it is, i.e. that whatever attribute is affirmed of any subject, is in fact
an attribute of that subject.
Mill somewhat
unnecessarily introduces the question of verbal expression. He enunciates the
law as: "Whatever is true in one form of words, is true in every other
form of words, which conveys the same meaning" (Exam. of Hamilton, p.
409).
It is the
universal practice at present to treat the principle of Identity separately
from the principle of Contradiction.
Scholastic authors, however, do not admit its claim to rank as a really
independent principle. At most they admit that it is a rudimentary form of the
principle of Contradiction [N7]. They urge that the predicate of an Analytic
proposition must in some way explicate the notion of the subject. This
principle does not do so. The predicate and the subject are the same concept.
It is mere tautology.
There is, it
may be owned, some force in this objection. The principle tells us nothing. Yet
we must remember that Being is a concept which does not admit of
analysis properly so called. Hence perhaps justification may be found for a
tautologous principle here, which could not be adduced in any other case. The
form is permissible, because it is indicative of the fact, that we have arrived
at the limits of all explanation. But in order for the principle to convey any
information, and to be of any service, it must be developed into the law of
Contradiction.
The
separate treatment of the two principles first became usual after the time of
Leibniz. It is true that Parmenides the Eleatic (circa BC. 490) had enunciated the principle Being is (eon emmenai) as the
foundation of his philosophy. But Aristotle emphatically affirms that the law
of Contradiction is the first of all principles: and his decision for long went
undisputed. Among medieval authors the Spanish Scotist Antonius Andrew (ob.
1320) argues that the first
place should belong to the principle 'Every Being is a Being' (Omme Ens est Ens, Qq. in Met. IV.,
Q. 4). But the authority both of St. Thomas (Met. IV., lect. 6) and of Scotus (Quaest. sup. Met. IV., Q. 3) was against him: and he is expressly
refuted by Suarez (Disp. Met. III., § 3). Leibniz however makes the principle of Identity,
which he gives as 'Everything is what it is,' the first of the primitive truths
of reason which are affirmative, and the principle of Contradiction, 'A
proposition is either true or false' the first of the negative truths (Nouv. Ess. IV., 2, § i). He further says, "the statement that a thing is what it
is, is prior to the statement that it is not another thing" (Nouv. Ess.
IV.. 7, § 9).
Here as it would seem, is the real ground for the introduction of
the principle of Identity as distinct from that of Contradiction. It appeared
impossible that the primary analytic principle should be negative. If however,
the view taken in the last section is accurate, the negative form is the
necessary consequence of the primary character of the principle. We can only
explain the perfectly simple by distinguishing it from that which it is not.
§
4. The Law of Excluded Middle. Aristotle
enunciates this principle in the form given above, "Of two
contradictory judgments, the one must be true and the other false" (Met.
III., c. 8, sects 3, 4). He says also, "Between the two members of
a contradiction, there is no middle term" (Met. III., c. 7, § i)
[N5].
As a
metaphysical principle, it is stated, 'A thing must either be or not be.' The truth
of this is evident from the immediacy of the opposition between being and
not- being. The truth of the logical principle is capable of
demonstration as follows. Where we have two contradictories, we have
affirmation and negation, is and is not. If the member which constitutes the
mental judgment corresponds with the reality, whether it be in affirmation or
negation, then the mind has attained truth. Should it, however, not be in
conformity with its object, the judgment is false. That is to say, the mind has
either judged that what is, is not, or that what is not, is.
Wherever,
therefore, the judgment is false, the contradictory judgment, whether it be the
affirmative is, or the negative is not, will be true. Hence of
two contradictories, the one must be true, the other false [N6].
The close
connection between the logical principle and the metaphysical at once appears,
when we reflect, that in affirmation, we are attributing a certain conceptual
being to the subject; in negation, we assert that it does not possess this
being (Ch. 3, § 2). All contradictories therefore present the alternative
between being and not being.
The way in
which the principle is expressed by certain logicians, "Of any two
contradictory predicates, one must belong to every subject," is
unsatisfactory. It supposes that the predicates, and not the propositions,
are contradictory to each other, and is represented by the formula, 'A is
either B or not-B.' But, as we have seen, the primary form of negation is the
negative judgment, not an affirmative judgment with a negative predicate; and
in the expression of a fundamental law, it is the primary form that we
need. Mill employs the following formula
- "It is allowable to substitute for the denial of either of two
contradictory propositions, the assertion of the other" (Exam. of
Hamilton, p. 416).
It should be
carefully noted that the law of Excluded Middle is in no way concerned with
Contrary terms [N8]. We have explained Contrary terms as those which
express the widest possible difference among classes belonging to the same
genus, e.g. 'white, black,' 'convex, concave,' 'love, hatred.' There is, of
course, a mean between terms such as these. Objects possessed of any other
variety of colour are neither white nor black; a plane surface is neither
concave nor convex; and indifference is neither love nor hatred. It is
manifest, however, that an object must be either white or not white, convex or
not convex; and that in regard to any particular individual, it is either true
that we do or that we do not feel love towards him.
The
principle has not passed unchallenged. Mill, in the interests of the empiricist
philosophy, declared the law to be a mere generalization from experience. We
have no grounds, he thought, for regarding it as necessary. Indeed he goes
further, and maintains that "it is not even true except with a large
'qualification. . . . 'Abracadabra is a second intention,' is
neither 'true nor false. Between the true and false there is a third
possibility, the Unmeaning." Such an argument can scarcely be treated as
serious. An unmeaning proposition is not a judgment at all. Of more moment
perhaps is the Hegelian objection. The very basis of the Hegelian philosophy is
the reconciliation of opposites. Becoming is supposed to owe its origin to the
union of Being and Not-Being, and the whole of Nature is regarded as
constituted by this dialectic development. Hegel himself argues against the
principle of Excluded Middle by pointing out that between + A and -A lies A. As
against this view, it is urged that in Hegel's system the opposites are in fact
contraries not contradictories, and that the individual does not owe its origin
to them, but that they are obtained by abstraction from the individual. Thus if it be urged that at dawn we can say
with equal truth 'It is day' and 'It is not day,' and that the state of dawn is
constituted by these opposites, it is answered that the two moments are not, as
alleged, contradictory opposites, but the contraries 'dark' and 'light': and
that dawn is not in any sense constituted by a dialectic development out of
darkness and light, though we can mentally abstract these concepts from the
state of dawn.
§ 5. Other Views
as to the Source of the Laws of
Thought. In other schools of
philosophy, very various accounts are given as to the nature and origin of
these laws. It seems well to notice here three theories differing widely from
that set forth in the preceding sections. These views respectively regard the
laws of thought (1) as
subjective laws of the understanding, of
whose objective, validity, however, we can have no rational guarantee, (2) as principles determining the
growth of that 'ex perience,' which men erroneously distinguish into thought on
the one hand, and things on the other hand, (3) as mere generalizations from
experience.
The
first view is that of Kant. Among English logicians it is explicitly taught by
Mansel. He tells us that the principles of thought are "laws under which
the mind is compelled to think, and which it cannot transgress, otherwise than
negatively by ceasing to think at all."
"It may be," he adds, "that the conditions of possible
thought correspond to conditions of possible being, that what is to us
inconceivable is in itself non-existent. But of this, from the nature of the
case, it is impossible to have any evidence" (Proleg. Logica, 7r, 72).
It is needless to point out that
such a view as this leads directly to philosophic scepticism. The second view
is represented by Mr. Bosanquet. We have already called attention to the theory
held by the neo-Hegelian school of logicians, according to which the operations
of the mind are vital functions by which the so-called 'real' world has been
constituted. It is under this aspect Mr.
Bradley regards the laws of thought. He holds that we cannot say that these
principles are merely laws of thought, if by that we mean thought as
distinguished from things: "Since a separation between intelligence and
experience is purely fictitious, there is nothing to be gained by cutting down
the content of these principles to a minimum in the hope of restricting their
reference to thought as opposed to things." They are "the animating principles of
growth" which govern the development of experience: and if we recognize
them as "postulates of know ledge," this is because "on analysis
of experience, they are found to be active factors in it from the first" (Logic, II. 205- 207).
Mill
(Logic, I., p. 308. Exam. of Hamilton, p. 417) explicitly repudiates the view
that these principles are subjective laws of the thinking faculty. He holds
that they are conclusions derived from a constant experience of their truth. We
have never as a matter of fact known any case where two contradictories have
been simultaneously true. Hence we
rightly lay down a general but empirically discovered principle to that effect.
As for the law of Excluded Middle, we have already seen that he holds that it
needs qualification before it can be admitted as universally true. It must, he admits, be owned that "we
cannot now conceive the opposite of these laws to be true. But this
inconceivability is of little value as a criterion of truth to those who know
how artificial, modifiable, the creatures of circumstances and alterable by
circumstances, most of the supposed necessities of thought are." Constant experience of one character is, in
his view, sufficient to lead us to regard its opposite as inconceivable.
Footnotes
[N1] Met.
III., c.6, § 10.
[N2] Soph. Elenchi.c.5 § 5.
[N3] It is to be observed that the principle of
contradiction is a modal proposition de
impossibili, and the principle of Excluded Middle a modal de necessario (ch. 3. 9).
[N4] On Being
and Not-being as the primary concepts of the understanding, see St.
Thomas, Opusc. 44, Summa
Totius Logicae, Tract 3, c. 1, Ad videndum. cf. Summa Theol. I..
Q. 11 Art. a. ad 4
[N5]
[N6] Arist. Met. III., 7, §1; St. Thomas, in Met. Iv., lect. 16.
[N7] Pesch.
Instit. Logicae, vol. 3,
§ 1230. Ad usum principii
identitatis quod attinet, illud a Peripateticis nunquam in sua propria forma
adhibitum videmus. Est enim vagum et indeterminatum, et principiorum potius
radicem continet et germen imperfectum.
[N8] Mr.
Bosanquet's views as to negation lead him into this error. He holds that
negation qud negation is
void of all significance, and that the true value of a negative judgment is to
be sought in its positive content. Hence he concludes that the principle of
Excluded Middle relates to contraries (Logic, II. 2101. A full treatment of the import
of the negative judgment and of the relation between contradictory and contrary
propositions, will be found in St. Thomas, Opusc. De Quatuor Oppositis, cc. I, 2.
Copyright © E.D.Buckner 2005.