PRINCIPLES OF
LOGIC
PART I
THE LOGIC OF THOUGHT
Chapter I.
THE NATURE AND AIM OF LOGIC.
3. The
Place of Logic in Philosophy
§
1. Definition of Logic. Logic may be defined as the
science which directs the operations of the mind in the attainment of truth.
What
do we mean by truth? An assertion is said to be true when it corresponds to the
reality of which the assertion is made. But the verbal statement is merely the
outward expression of the thought within. It is our thoughts which are properly said to be true or erroneous. For present purposes, therefore, we may
define truth as the conformity of the intellect with its object. Thus if I see
a white horse, and judge 'That horse is white', my judgment is said to be true,
because my thought corresponds with the thing about which I am judging.
The
aim of all our mental operations is to attain true judgments. If I endeavour to
establish a geometrical proposition, my object is to arrive in the end at a
judgment, which is in conformity with reality. Now there are certain definite
ways in which, and in which alone, our thinking faculty must proceed if it is
to achieve its task of faithfully representing the real order. Reflection
enables us to observe the operations of the mind; and hence we are able to know
and to catalogue these common types of mental action. In this way we learn the
rules, which we must observe in reasoning, if we are to arrive at a true
result. For, as experience shows us, it is very easy to argue in a way that
will bring us, not to truth, but to error.
It was a boast of the Sophists in ancient Greece that they could make
the worse appear to be the better cause. They managed this end by skilfully
violating the rules which men must observe, if their conclusions are to be
true.
Another definition may be given of Logic, in which the science is
considered in a different
aspect. Logic is the science which treats
of the conceptual representation of
the real order; in other words, which has for its subject-matter things as they are represented in our thought. The difference between this definition and
that which we gave in the first instance, is that this definition expresses the
subject-matter of Logic, while the former expresses its aim. We
shall find as we proceed that the science can scarcely be understood, unless
both these aspects are kept in view.
The work of Logic therefore is not to teach us some
way of discovering new facts. First Francis Bacon, later Descartes, and finally, despite
his admitted genius, John Stuart Mill [N1] failed to recognise this simple fact
and drove logic from the confines of its valid form into the realm of the
physical sciences. The discovery of things belongs to the special sciences,
each in its own sphere. Logic's
purpose, on the other hand, is to assist us in the attainment of truth, because it treats of the way in which the
mind represents things, and thus shows us what are those general conditions of
right thinking, which must be observed whatever subject we are considering.
Where we have a systematic body of securely established
principles and of conclusions legitimately drawn from these principles, there
we have a science.
Thus in the science of Astronomy we start from certain general laws, and have a
body of conclusions derived from these. Mere facts not brought under general
laws do not constitute a science. We are rightly said to have a science of
Logic, for, as we shall see, it consists of a body of principles and legitimate
conclusions, such as we have described.
§
2. Divisions of Logic. The simplest act of the mind in
which it can attain truth is the judgment -- the act by which the mind affirms
or denies something about something else. That which is affirmed (or denied) of
the other is called an attribute: that to which it is said to belong (or
not to belong) is called a subject. Hence we may define a judgment as the act by which the mind affirms or
denies an attribute of a subject.
A
judgment however gives the mind a complex object: for it involves these two
parts -- subject and attribute. We must
therefore take account of a more elementary act of the mind than judgment, viz.:
Simple Apprehension. Simple
apprehension is the act by which the mind without judging, forms a concept of
something. Thus if I should conceive the notion of a triangle, without however
making any judgment about it, I should be said to have formed a simple
apprehension of a triangle. David Hume built much of his system on blatantly
denied this fact. He insisted that immediately the mind conceived of triangle
it had an image of its exact type and size, i.e. scalene or isosceles. Sadly
nobody tried him with a myriagon!
However,
the words true or false cannot be applied to simple apprehensions, just as we
cannot say that the words in a dictionary are true or false. Following Hume,
some philosophers indeed deny that the mind ever forms a simple apprehension;
they hold that in every case some judgment is made. We need not even enter into this question. We
can at least analyse the judgment into simple apprehensions: for every judgment
requires two concepts, one in which the mind expresses the subject, and the
other in which it expresses the attribute. Thus in the example given above, I
must have a concept of horse, and one of whiteness, in order to
say 'The horse is white'. These are the elements which go
to constitute the complex act of judgment, and they can be considered in
isolation from it. Logic therefore must deal with the concept.
There
is a third process of the mind, namely Reasoning or Inference. This is
defined as the act, by which from two
given judgments, the mind passes to a third
judgment distinct from these, but implicitly contained in them. Thus if I say
All roses
wither in the autumn;
This
flower is a rose;
Therefore: This flower wilt wither in the autumn;
or
if I argue
Whatever displays
the harmonious ordering of many parts is due to an intelligent cause;
The world
displays the harmonious ordering of many parts;
Therefore : The world is due to an intelligent cause;
I
am said in each case to infer the third judgment. An inference of the
form which we have employed in these examples, is called a syllogism. The two judgments given are known as the premisses. The judgment derived from
them is the conclusion.
It
is of these three acts of the mind that Logic treats: and the science falls
correspondingly into three main divisions,
-- the Logic (1) of the Concept, (2) of the Judgment, (3) of Inference.
Since
Logic deals with thought, it necessarily takes account to some extent of
language -- the
verbal expression of thought. It does so however from quite a different point
of view to that of Grammar. Grammar is concerned with words as
such. It is the art by which the words employed in significant speech are
combined according to the conventional rules of a language. Hence in it each of the nine parts of
speech is treated independently, and rules are given for their respective use.
On the other hand, the simplest object of which Logic takes account is the
Concept. In its consideration of words, therefore, it does not deal with any of
those parts of speech, which taken by themselves are incapable of giving us an
independent concept. It is conversant not with nine, but with two forms only of
significant utterance, viz.: the Name,
the verbal expression of the Concept, and the Proposition, the verbal expression of the Judgment [N2]. The proposition consists of three parts. These are, (1) the Subject -- that of which the assertion is made: (2) the
Predicate -- that which is
affirmed or denied of the Subject: and (3) the Copula -- the verb is or are which
connects the Subject and the Predicate. The Subject and the Predicate are
called the Terms (from
the Latin terminus -- a
boundary) of the proposition: and the predicate is said to be predicated
of the subject.
§
3. The Place of Logic in Philosophy.
The sciences fall into two broad divisions, viz.: the speculative and
the regulative (or normative) sciences. In the speculative sciences,
philosophic thought deals with those things which we find proposed to our intelligence
in the universe: such sciences have no other immediate end than the
contemplation of the truth. Thus we study Mathematics, not primarily with a
view to commercial success, but that we may know. In the normative sciences, on
the other hand, the philosopher pursues knowledge with a view to the
realization of some practical end. "The object of philosophy," says
St. Thomas of Aquin, "is order. This order may be such as we find already
existing; but it may be such as we seek to bring into being ourselves." [N3]
Thus sciences exist, which have as their object the realization of order in the
acts both of our will and of our intellect. The science which deals with the
due ordering of the acts of the will, is Ethics, that which deals with order in
the acts of the intellect is Logic.
The question has often been raised, whether Logic is science
or an art. The answer to this will depend entirely on the precise meaning which
we give to the word 'art.' The medieval philosophers regarded the notion of an
art as signifying a body of rules by which man directs his actions to the
performance of some work [N4]. Hence they held Logic to be the art
of reasoning, as well as the science of the reasoning process. Perhaps a more
satisfactory terminology is that at present in vogue, according to which the
term 'art,' is reserved to mean a body of precepts for the production of some
external result, and hence is not applicable to the normative sciences.
Aesthetics,
the science which deals with beauty and proportion in the objects of the
external senses, is now reckoned with Ethics and Logic, as a normative science.
By the medieval writers it was treated theoretically rather than practically,
and was reckoned part of Metaphysics.
It
may be well to indicate briefly the distinction between Logic and two other
sciences, to which it bears some affinity.
Logic
and Metaphysics.
The term Metaphysics sometimes
stands for philosophy in general sometimes with a more restricted meaning it
stands for that part of philosophy known as Ontology. In this latter sense Metaphysics deals not with thoughts, as does Logic, but with things,
not with the conceptual order but with the real order. It
investigates the meaning of certain notions which all the special sciences
presuppose, such as Substance, Accident, Cause, Effect, Action. It deals with principles which the special
sciences do not prove, but on which they rest, such as e.g., Every event
must have a cause. Hence it is called the science of Being, since its object is not limited to some
special sphere, but embraces all that is, whether material or
spiritual. Logic on the other hand deals
with the conceptual order, with thoughts. Its conclusions do not relate to
things, but to the way in which the mind represents things.
Logic and Psychology. The object of Psychology is the human soul and all its
activities. It investigates the nature and operations of intellect, will,
imagination, sense. Thus its object is far wider than that of Logic, which is
concerned with the intellect alone. And even in regard to the intellect, the
two sciences consider it under different aspects. Psychology considers thought
merely as an act of the soul. Thus if we take a judgment, such as e.g.,
"The three angles of a triangle are together equal to two right
angles," Psychology considers it, merely in so far as it is a form of
mental activity. Logic on the other hand, examines the way in which this mental
act expresses the objective truth with which it deals; and if necessary, asks
whether it follows legitimately from the grounds on which it is based.
Moreover, Logic, as a regulative science, seeks to prescribe rules as to how we
ought to think. With this Psychology has nothing to do: it only asks, What as a
matter of fact is the nature of the mind's activity?
§
4. The Scope of Logic. Logicians are frequently divided into three
classes, according as they hold that the science is concerned (1) with names
only, (2) with the form of thought alone, (3) with thought as representative of
reality.
(1) The first
of these views - that Logic is concerned with names only - has found but few
defenders. It is however taught by the French philosopher Condillac (1715 -
1780), who held that the process of reasoning consists solely in verbal
transformations. The meaning of the conclusion is, he thought, ever identical
with that of the original proposition.
(2) The theory
that Logic deals only with the forms of thought, irrespective of their relation
to reality, was taught among others by Hamilton (1788 -1856) and Mansel
(1820 -1871). Both of these held that Logic is no way concerned with the truth
of our thoughts, but only with their consistency.
In this sense
Hamilton says: "Logic is conversant with the form of thought, to the
exclusion of the matter" (Lectures. I. p. xi). By these logicians a
distinction is drawn between 'formal truth,' i.e., self-consistency and
'material truth,' i.e., conformity with the object and it is said that Logic
deals with formal truth alone. On this view Mill well observes: "the
notion of the true and false will force its way even into Formal Logic. We may
abstract from actual truth, but the validity of reasoning is always a question
of conditional truth - whether one proposition must be true if the others are
true, or whether one proposition can be true if others are true" (Exam.
of Hamilton, p. 399).
(3) According
to the third theory, Logic deals with thought as the means by which we attain
truth. Mill, whom we have just quoted, may stand as a representative of this
view. "Logic," he says, "is the theory of valid 'thought, not of
thinking, but of correct thinking" (Exam. of Hamilton, p. 388).
To which class
of logicians should Aristotle and his Scholastic followers be assigned? Many
modern writers rank them in the second of these groups, and term them Formal
Logicians. It will soon appear on what a misconception this opinion rests, and
how completely the view taken of Logic by the Scholastics differs from that of
the Formal Logicians. In their eyes, the aim of the science was most assuredly
not to secure self-consistency, but theoretically to know how the mind
represents its object, and practically to arrive at truth.
The
terms Nominalist, Conceptualist, and Realist Logicians are
now frequently employed to denote these three classes. This terminology is
singularly unfortunate: for the names, Nominalist, Conceptualist and Realist,
have for centuries been employed to distinguish three famous schools of
philosophy, divided from each other on a question which has nothing to do with
the scope of Logic. In this class we shall as far as possible avoid using the
terms in their novel meaning.
§ 5. The History of Logic.
It was Aristotle (384 - 322 BC) who laid the foundations of the science
by treating logical questions separately from other parts of philosophy. Six of
his treatises are concerned with the subject: they cover almost the whole
ground.
1.
The Categories -- a treatise on the ten
primary classes into which our concepts of things are divided.
2.
De Interpretatione -- a treatise on terms and
propositions.
3.
Prior Analytics -- a treatise on inference.
4.
Posterior Analytics -- a treatise on the logical
analysis of science.
5.
Topics -- a treatise on the method of
reasoning to be employed in philosophical questions, when demonstrative proof
is not obtainable.
6. Sophistical Refutations
--
an account of
fallacious reasonings.
This group of treatises was afterwards known as the Organon. It should,
however, be noticed that they are separate works. Aristotle himself had no
single word to signify the whole of Logic, and it seems doubtful whether he
viewed it as a single science. The name Logic was introduced by Zeno the Stoic (about 300 BC).
The
successors of Aristotle added but little of permanent value to his great
achievement. Enduring importance however attaches to a small treatise by the
Neo-platonist Porphyry (233 - 304 AD) entitled the Isagogé or Introduction
to the Categories of Aristotle.
In
a certain sense the name of Boethius (B. Severinus Boethius 470 - 525 AD)
constitutes a landmark in the history of Logic: for it was through the medium
of his translation of the Organon, and his commentaries on the Categories
and the Isagogé, that the works of Aristotle and Porphyry were
available for educational purposes in Western Europe from the sixth to the
thirteenth century [N5]. Through this period some knowledge of Logic was widely
possessed, as it was one of the seven liberal arts - Grammar, Dialectic i.e.,
Logic, Rhetoric, Geometry, Arithmetic, Astronomy, and Music - of which higher
education was held to consist.
At
the beginning of the thirteenth century the numerous other treatises of
Aristotle, and the works of his Arabian commentators Avicenna (Ibn Sina 980 -
1037 AD) and Averroes (Ibn Roshd 1126 - 1189 AD) were translated into Latin,
and gave an immense impetus to philosophic study. The mediaeval Scholastics
availed themselves of these works, to build up a thoroughly systematic science
of Logic. It may perhaps be said that
their main advance on Aristotle's treatment lay in the greater accuracy with
which they discriminated the respective spheres of Logic and Metaphysics, and
in their more precise arrangement of the various parts of Logic itself.
The
15th and 16th centuries witnessed the decadence of Scholasticism, and in 1620
an attack was made on the very foundations of the Aristotelian Logic by Francis Bacon in his Novum Organum. Much of his criticism was unfounded, since he
believed that the purpose of Logic was to provide men with a means towards
making discoveries regarding the laws and phenomena of nature. Yet it was of
service in calling fresh attention to the theory of Induction, a part of Logic to which too little attention had been
given by the later Scholastics.
Since
the time of Bacon the whole question of Induction has been very fully discussed
by writers on Logic. The most eminent of these among English thinkers was John
Stuart Mill (1806 - 1873), whose treatment of the subject long held rank as the
classical work on Induction. Many of the points, however, raised by these
writers do not strictly speaking belong to the province of Logic. For,
influenced by Bacon, they have dealt not merely with Induction as a process of
thought, but also with a very different subject, namely the general theory of
scientific investigation. It was indeed
natural that a keen interest should be felt in this question. The
rapid growth and multiplication of the physical sciences during the last three
centuries could not but lead to the codification of their rules and to
reflection on their methods -- in other words to the formation of a philosophy
of evidence. Such a science was
impossible in the middle ages, before the great era of physical investigation
had dawned. At the present day the treatment of this subject forms a part of
every work on Logic. By many writers it is termed Material or Inductive Logic, the
traditional part of the science receiving by way of distinction the name of Formal or Deductive Logic. These names are misleading. The traditional
Logic was, as we have seen not purely formal. And though the treatment of
Induction, properly so called by many of the medieval writers, was inadequate;
yet they all regarded it as falling within their scope. We have therefore preferred to designate the
two portions of this series of lectures The Logic of Thought and
Applied Logic or the Method of
Science respectively. Induction as a process of thought, finds its
place in the first of these two divisions.
NOTE TO CHAPTER ONE
DIFFERENT VIEWS AS TO THE SCOPE OF LOGIC
The difference of opinion as to the true scope of Logic is far
wider than would appear from the triple division which is usually recognized in
logical text-books: and special names are now employed by logicians to indicate
the point of view from which the science is treated. Moreover the threefold
division is, as we have noticed, open to the further objection that it compels
us to group the Scholastic logicians either with the school of Mansel or with
that of Mill, though they have little enough in common with either of these. It
seems, therefore, desirable to enter somewhat more into detail on the
subject. It is therefore important to
give a very brief explanation of the special designations referred to, viz.:
Scholastic Logic, Formal Logic,
Symbolic Logic, Inductive Logic, Transcendental Logic, Logic of the Pure
Idea, Modern Logic. As far as
possible we have availed ourselves of citations from authors representative of
the various views, in order to make clear the meaning of their different terms.
(1) Scholastic Logic. We have
explained above that the Scholastic or
Traditional Logic holds the subject-matter of the
science to be the conceptual representation of the real order. This may be
otherwise expressed by saying that it deals with things, not as they are in
themselves, but as they are in thought. Cardinal Mercier says: "There are
two sciences whose object is in the highest degree abstract, and hence
universal in its applicability. These are Metaphysics and Logic. The object of
Metaphysics is Being considered in abstraction from all individua1
determinations and material properties, in other words the Real as such. . .
. Logic also has Being for its object. "It must not however be
thought that Logic and Metaphysics consider Being from the same point of
view. . . . The object Metaphysics is the thing considered as a
real substance endowed with real attributes. The object of Logic is likewise
the thing, but considered as an object of thought endowed with
attributes of the conceptual order"
(Logique 23 3d ed.)
(2) Formal Logic. The characteristic of this school
is to consider the mental processes in entire abstraction from the relation
which the concept bears to the real order. Logic, says Dean Mansel,
"accepts as valid, all such concepts, judgments and reasonings, as do not
directly or indirectly imply contradictions: pronouncing them thus far to be
legitimate as thoughts, that they do not in ultimate analysis destroy
themselves" (Proleg. Logica, p.
265). Mr. Keynes abstains from deciding whether Formal Logic constitutes the whole
of the science, but says in its regard: "The observance of the laws which
Formal Logic investigates will not do more than secure freedom from
self-contradiction and inconsistency" (Formal Logic, sect; i).
(3) Symbolic
Logic is
a further development of Formal Logic. It is thus defined in Baldwin's Dict.
of Philosophy. "Symbolic logic is that form of logic in which the
combinations and relations of terms and of propositions, are represented by
symbols, in such a way that the rules of a calculus may be substituted for
actively conscious reasoning. Mr. Venn, its ablest exponent in this country,
claims for it the great advantages, that it "generalizes the processes of
the ordinary Logic" showing them as particular cases of wider problems
dealing with relation (Symbolic Logic, Introd. pp. xxi - xxiii.). Though
the subject has engaged the attention of several able men, it has no claim yet
to be considered a science. Almost every investigator has adopted his own
system of symbolic notation. It should further be mentioned, that many thinkers
believe that although it affords scope for much ingenuity, it cannot possibly
contribute in any way whatever to our knowledge of the reasoning process.
(4) Inductive, Empirical,
Material or Applied Logic is a science developed on the basis of the views set
forth in Bacon's Novum Organum. Mill terms it "a general theory
of the sufficiency of Evidence," and "a philosophy of Evidence and of
the Investigation of Nature" (Exam. of Hamilton, p. 402). "Everyone", he says,
"who has obtained any knowledge of the physical sciences from really
scientific study, knows that the questions of evidence presented . . . are such
as to tax the very highest capacities of the human intellect" (ibid.) and
he severely calls to task those who hold "that the problem which Bacon set
before himself, and led the way towards resolving, is an impossible one . . .
that the study of Nature, the search for objective truth, does not admit of any
rules." Granted that there be such a science it must belong, he urges, to
Logic, "for if the consideration of it does not belong to Logic, to what
science does it belong?" (ibid. p. 400). It is manifest that the science Mill here describes, differs
essentially from Logic, as heretofore it had been understood. This
philosophy of evidence deals, not with thought, but with things as they are in
the real order; and its function is to prescribe the due methods of enquiry in
each several science - not merely in the physical sciences as this passage
might suggest. H. Spencer with more consistency than Mill refuses altogether
the name of Logic to the traditional science of that name, and prefers to term
it the Theory of Reasoning (Psychology, pt. vi., c. viii.).
(5) Transcendental Logic is the name
given by Kant to the most fundamental portion of his Critical Philosophy. Kant
started with the assumption that all our knowledge, whether sensitive or
intellectual, is internal to the mind - that we have no immediate knowledge of
the external world. He further assumed that the material of all our knowledge
can be nought but successive pulses of sensation without unity of any kind. If
these purely subjective feelings undergo such a transmutation within us as to
present to our experience an orderly world of matter and motion, this must be
in virtue of an a priori element
- an internal mechanism providing certain 'forms' according to which we
perceive, think and reason. In the Transcendental
Aesthetic - the work
in which he treats of sensible perception - he endeavours to show that space and
time are the 'forms' of our sensitive faculty, while the pulses of sensation
constitute its matter. In the Transcendental
Logiche deals with the 'forms' of intellect (Transcendental Analytic), and of
reasoning (Transcendental Dialectic). The intellectual forms will be noticed later. He gave
them the name of Categories, a
term employed in a very different sense by Aristotle and his followers. They
are "the regular lines imposed by the intellect, on which sensations
settle down with unities, orders, sequences, identities" (Wallace, Kant,
p. 70). The problems raised
in the Transcendental Dialectic fall outside the scope of the present
work.
(6) Logic
of the Pure Idea. This is the name given by Hegel to his system. It will be sufficient for us to advert in the
briefest manner to this philosophy, with which we are only concerned because of
its bearing on Modern Logic. Its
salient feature is the identification of Logic and Metaphysics. Hegel would not
admit the existence of two orders - an order of thought and an order of
reality. Thought, according to him, constitutes reality. Hence the science of
the real - Metaphysics, is to be found in Logic - the science of thought:
"Logic in our sense coincides with Metaphysics" (Wallace, Logic of
Hegel, p. 38). The Universe has its origin in the inner necessity of the
categories of thought. But thought in its fullest development - the thought of
the Whole or the Absolute Idea passes over into
reality. Thought becomes things, and realizes itself as the universe which we
know.
Hegelianism is in fact a form of
Pantheism.
In it things are thoughts, and these thoughts are a Divine Mind evolving itself
in the process of the Universe.
(7) Modern Logic. The treatment of
logical problems known by this name owes its origin to the Hegelian Philosophy. It is plain that
thinkers who deny the distinction between the order of things external to us,
and the order of thought within, were bound to institute a new enquiry into the
nature of those mental acts, which had hitherto been regarded as representative
of the real order. The principal exponents of Modern Logic in England are Mr. Bradley and Mr. Bosanquet: Their
work, however, is very largely based on that of the eminent German logicians Lotze and Sigwart. According to Mr. Bosanquet the only difference between
Logic and Metaphysics lies in the aspect under which they view the same subject
matter. "I make no doubt," he says, "that in content Logic is
one with Metaphysics, and differs if at all simply in mode of treatment - in
tracing the evolution of knowledge in the light of its value and import instead
of attempting to summarise its value and import apart from the details of its
evolution" (Logic, I. 248). The operations of the
mind - judgment and reasoning - are according to this view regarded as vital functions, by which the
totality we call "the real world" is intellectually constituted. The task of Logic is to
analyse the process of constitution (ibid. p3).
Footnotes
[N1] Mill actually
established a magnificent philosophy of evidence by perfecting Aristotle's method of inductive reasoning, which
we will examine later.
[N2] Cf. Boethius, Introduct. ad Syll. Cat. (Migne
P. L. vol. 64, col. y66. A), and De Syll. Cat. lib. 1. (ibid. col.
766. D). Another important difference between Logic and Grammar is to be found
in the fact that Logic is concerned with but one mood -- the Indicative,
Grammar with all the moods equally.
[N3] St. Thomas in Ethic. I.
lect. 1. Sapientis est ordinare. . . . Ordo autem
quadrupliciter ad rationem comparatur. Est enim quidam ordoquem ratio
non facit sed solum considerat, sicut est ordo rerum naturalium. Alius autem
est ordo quem ratio considerando facit in proprio actu, puta cum
ordinat conceptus suos ad invicem et signa conceptuum quae sunt voces
significativae. Tertius autem est ordo quem ratio considerando
facit in operationibus voluntatis. Quartus autem est ordo quem
ratio considerando facit in exterioribus rebus, quarum ipsa est causa, sicut in
arca et domo.
[N4] St. Thomas in An. Post.
I., lect. x.
"Nihil enim aliud ars esse videtur, quam certa ordinatio rationis qua per
determinata media ad debitum finem actus humani perveniunt."
[N5] Two works attributed to St. Augustine were also
recognized authorities at this period. St. Augustine's interest in the science
was not shared by all the fathers, we are told of St. Ambrose, that he used to
exclaim "A Logica Augustini,
libera me Domine".
Copyright © E.D.Buckner 2005.