This thirty-page essay on Aristotle's logic was originally published in Kames'
Sketches of the History of Man in 1774, when Reid was 64.
It is useful and interesting in a number of ways.
It is helpful even today as an introduction to Aristotle's logic,
which it summarises in a comprehensive, clear and economical way.
(Despite the fact, as Reid admits, that lack of courage and patience prevented
him from ever reading the whole work).
It provides an insight into views of traditional logic in the eighteenth century,
showing in particular the neglect of the systems of scholastic logic in that period.
Reid is sympathetic to traditional semantics,
and notes that much useful work on the structure of language was done by the scholastic logicians.
Nevertheless, his view of logic is mostly negative.
It is also interesting for Reid's insightful remarks (chapter 6, sec. 1) about the defects of the traditional
system of logic. He says, for example, that it fails to explain propositions without a subject and predicate,
as 'it rains'; that the hypothetical proposition 'whatever is A is not B' is not obviously
affirmative or negative; that it assumes all propositions have two terms,
when many propositions have more than two terms;
that identity propositions cannot be regarded as either universal or particular propositions,
and that Aristotelian logic, being unable to explain arguments such as 'A=B and B=C therefore A=C',
is therefore useless for mathematics. This anticipates difficulties raised much later by logicians such as Frege.
But one idea is especially good, and may still be of interest to students of early modern philosophy.
This is Reid's observation (chapter 2, sec. 1) of an interesting continuity
between the Aristotelian account of the proposition, and the early modern theory of knowledge.
He argues that the (then modern) empiricist theory of knowledge is simply a modification of the ancient
theory of the predicables, a classification of all the possible ways in which the predicate can be related
to the subject, and thus a classification of all possible judgments.
The doctrine of the Five Universals, or Quinque Voces, or Predicables,
was an essential part of the scholastic systems of logic, taken from the Isagoge of Porphyry (c. 1, 5),
based on remarks made by Aristotle in the Categories
(c. 2, 5).
It depends on the assumption that judgment connects two terms, the predicate and the subject,
by affirming or denying the one of the other.
According to the theory, there are five possible relations in which the predicate can stand to the subject.
The first is where the the predicate is the genus of the subject, as in Reid's example proposition
'This is a triangle,' 'Jupiter is a planet.'
The genus is that part of the essence of the subject which it has in common with other kinds of thing.
In the second the predicate is a species of the subject, as in, 'This triangle is right-angled.'
The species of a subject is its essence or definition or quidditas, its 'whatness'.
The third is where the predicate is the specific difference of the subject,
as in 'Every triangle has three sides and three angles.'
The specific difference is that part of the essence which distinguishes the subject from other things of the
same genus or kind.
The fourth is where the predicate is a property of the subject,
as in 'The angles of every triangle are equal to two right angles.'
A property is an attribute that is not part of the essence of the subject,
but somehow results from the essence, and is found in all things that possess it.
The fifth is where the predicate is accidental to the subject, as in 'This triangle is neatly drawn.'
An accident is an attribute that is not part of the essence, nor follows from it as with a property.
The predicables are thus a complete enumeration of all the kinds of things that can be affirmed of any subject.
All that can be said of anything whatsoever, is either the genus of the thing, or its species,
or its specific difference, or some property or accident belonging to it.
Though the rejection of the idea that things have essences or species was fundamental to the ideas
of early modern philosophers such as Locke and Hume,
Reid notices mischievously that the doctrine of of the predicables bears comparison with the theories
they substituted in its place.
Locke, in the Essay on the Human Understanding argues that all our knowledge consists in perceiving certain agreements and disagreements between two ideas.
(See Bk IV c. 5,
where he says that truth is the correct joining of signs, i.e. of words or ideas,
according as the things signified by them agree or disagree with one another, and
Bk IV c. 1,
where he says that knowledge
is the perception of the agreement or disagreement of ideas).
He classifies all such possible agreements,
and hence all judgments, into four types, namely, Identity and Diversity, Relation, Co-existence and Real Existence.
Here are four predicables given as a complete enumeration, says Reid, and yet not one of the ancient predicables is included in the number.
Similarly in A Treatise of Human Nature,
(Bk I Pt I sec 5)
Hume says that all knowledge is a perception of the relations of our ideas,
which may be comprised under seven heads:- 1, Resemblance; 2, Identity; 3, Relations of Space and Time;
4, Relations of Quantity and Number; 5, Degrees of Quality; 6, Contrariety; 7, Causation.
These may be further reduced
(Pt III sec 1) to two main classes,
namely those which are the object of truth and certainty because they depend on the connection of ideas
(1, 4, 5, 6), and those (2, 3, 7) which do not depend on the connection of ideas,
and cannot be the object of truth and certainty. This division is the cornerstone of all Hume's philosophy.
Here, says Reid, are seven predicables given as a complete enumeration, where all the predicables of the ancients,
as well as two of Locke's, are left out.
Reid's point is of course ironic, that (then) modern doctrines are arbitrarily rearranged versions of an
ancient theory.
The whole of the early modern theory of knowledge rests upon on the Aristotelian doctrine that judgment
connects two terms.
This idea would not be challenged until the late nineteenth century:
by the theory of multiple generality, that there can more, or less than two terms in a proposition.
A further irony that Reid would not have known was that in Frege's theory of judgment, there is still a fundamental division of judgments into two kinds:
those that connect concepts (all mammals are land-dwellers) and those which connect an object with a concept (Socrates is is a land-dweller).
For Mill's comments on the Predicables, see the museum page here.
Chapter I
Section I
OF THE AUTHOR
Aristotle had very uncommon advantages: born in Greece in an age when the philosophical
spirit had long flourished, and was in its greatest vigour; brought up in the court of
Macedon, where his father was the king's physician; twenty years a favourite scholar of
Plato; and tutor to Alexander the Great, who both honoured him with his friendship, and supplied
him with everything necessary for the prosecution of his enquiries.
These advantages he improved by indefatigable study, and immense reading.
He was the first we know, says Strabo, who composed a library; and in this the
Egyptian and Pergammenian kings copied his example. As to his genius, it would be disrespectful
to mankind not to allow an uncommon share to a man who governed the opinions of the most enlightened
part of the species near two thousand years.
If his talents had been laid out solely for the discovery of truth and the good of mankind, his laurels
would have remained for ever fresh; but he seems to have had a greater passion for fame than for truth,
and to have wanted rather to be admired as the prince of philosophers than to be useful;
so that it is dubious whether there be in his character most of the philosopher or of the sophist.
The opinion of Lord Bacon is not without probability, That his ambition was as boundless as that of his
royal pupil; the one aspiring at universal monarchy over the bodies and fortunes of men, the other over
their opinions. If this was the case, it cannot be said that the philosopher pursued his aim with
less industry, less ability, or less success than the hero.
His writings carry too evident marks of that philosophical pride, vanity, and envy,
which have often sullied the character of the learned. He determines boldly thngs above all human knowledge;
and enters upon the most difficult questions, as his pupil entered on a battle, with full assurance of success..
He delivers his decisions oracularly, and without any fear of mistake. Rather than confess his ignorance,
he hides it under hard words and ambiguous expressions, of which his interpreters can make what pleases them.
There is even reason to suspect that he wrote often with affected obscurity; either that the air of mystery
might procure greater veneration, or that his books might be understood only by the adepts who
had been initiated in his philosophy.
His conduct towards the writers that went before him has been much censured. After the manner of the
Ottoman princes, says Lord Verulam, he thought his throne could not be secure unless he killed off all
his brethren. Ludovicus Vives charges him with detracting from all philosophers, that he might derive that
glory to himself of which he robbed them. He rarely quotes an author but with a view to censure, and is not very
fair in representing the opinions which he censures.
The faults we have mentioned are such as might be expected in a man who had the daring ambition to be transmitted
to all future ages as the Prince of Philosophers, as one who had carried every branch of human knowledge
to its utmost limit, and who was not very scrupulous about the means he took to obtain his end.
We ought, however, to do him the justice to observe that, although the pride and vanity of the Sophist
appear too much in his writings in abstract philosophy, yet, in natural history, the fidelity of his narrations
seems to be equal to his industry; and he always distinguishes between what he knew and what he had by report.
And, even in abstract philosophy, it would be unfair to impute to Aristotle all the faults, all the obscurities,
and all the contradictions are to be found in his writings. The greatest part, and perhaps the best part,
of his writings are lost. There is reason to doubt whether some of those we ascribe to him be really his;
and whether what are his be not much vitiated and interpolated. These suspicions are justified by the
fate of Aristotle's writings, which is judiciously related, from the best authorities, in Bayle's dictionary,
under the articles Tyrannion, to which I refer.
His books on Logic, which remain, are, 1. One book of the Categories. 2. One of Interpretation. 3.
First Analytics, two books. 4. Last Analytics, two books. 5. Topics, eight books. 6. Of Sophisms, one book.
Diogenes Laertius mentions many others that are lost. Those I have mentioned have commonly been published
together, under the name of Aristotle's Organon, or his Logic; and, for many ages, Porphyry's Introduction to
the Categories has been prefixed to them.
Section II.
OF PORPHRY'S INTRODUCTION.
In this introduction, which is addressed to Chrysaorius, the author observes, That,
in order to understand Aristotle's doctrine concerning the Categories, it is necessary to know what a
Genus is, what a Species, what a Specific Difference, what a Property,
and what an Accident; that the knowledge of these is also very useful in Definition, in Division,
and even in Demonstration; therefore, he proposes, in this little tract, to deliver shortly and simply the
doctrine of the ancients, and chiefly of the Peripatetics, concerning these five Predicables,
avoiding the more intricate questions concerning them; such as, Whether genera and species
do really exist in nature? or, Whether, they are only conceptions of the human mind? If they exist in nature,
Whether they are corporeal or incorporeal? and, Whether they are inherent in the objects of sense,
or disjoined from them? These, he says, are very difficult questions, and require accurate discussion;
but that he is not to meddle with them.
After this preface, he explains very minutely each of the "five words" above mentioned,
divides and subdivides each of them, and then pursues all the agreements and differences between one and
another through sixteen chapters.
Section III.
OF THE CATEGORIES.
The book begins with an explication of what is meant by synonymous or univocal words,
what by homonymous, or equivocal, and what by paronymous, or denominative.
Then it is observed, that what we say is simple, without composition or structure, as man, horse,
fights, runs; or it has composition and structure, as a man fights, the horse runs.
Next comes a distinction between a subject of predication; that is, a subject of which anything is affirmed
or denied, and a subject of inhesion. These things are said to be inherent in a subject, which,
although they are not a part of the subject, cannot possibly exist without it, as figure in the thing figured.
Of things that are, says Aristotle, [1.] some may be predicated of a subject, but are in no subject;
as man may be predicated of James or John, but is not in any subject. [2.] Some again are in a
subject, but can be predicated of no subject. Thus my knowledge in grammar is in me as its subject,
but it can be predicated of no subject; because it is an individual thing. [3.] Some are both in a subject,
and may be predicated of a subject, as science, which is in the mind as its subject, and may be predicated
of geometry. [4.] Lastly, Some things can neither be in a subject nor be predicated of any subject.
Such are all individual substances, which cannot be predicated, because they are individuals; and cannot be
in a subject, because they are substances. After some other subtleties about Predicates and Subjects,
we come to the Categories themselves; the things above mentioned being called by the schoolmen the
antepraedicamenta. It may be observed, however, that, notwithstanding the distinction now explained,
the being in a subject, and the being predicated truly of a subject, are, in the Analytics,
used as synonymous phrases; and this variation of style has led some persons to think that the Categories
were not written by Aristotle.
Things which may be expressed without composition or structure are, says the author, reducible to the
following heads:- They are either Substance, or Quantity, or Quality, or Relatives or
Posture, or Place, or Time, or Having, or Doing, or Suffering. These are
the Predicaments or Categories. The first four are largely treated of in four chapters; the other are lightly
passed over, as sufficiently clear of themselves. As a specimen, I shall give a summary of what he says on the
category of Substance.
Substances are either primary - to wit, individual substances; or, secondary - to wit,
the genera and species of substances. Primary substances neither are in a subject, nor can be predicated
of a subject; but all other things that exist, either are in primary substances, or may be predicated of them.
For whatever can be predicated of that which is in a subject, may also be predicated of the subject itself.
Primary substances are more substances than the secondary; and of the secondary, the species is more a substance
than the genus. If there were no primary, there could be no secondary substances.
The properties of substance are these:- 1. No substance is capable of intention or remission. 2. No substance
can be in any other thing as its subject of inhesion. 3. No substance has a contrary; for one substance cannot
be contrary to another; nor can there be contrariety between a substance and that which is no substance.
4. The most remarkable property of substance is, that one and the same substance may, by some change in itself,
become the subject of things that are contrary. Thus the same body may be at one time hot, at another cold.
Let this serve as a specimen of Aristotle's manner of treating the categories. After them, we have some chapters,
which the schoolmen call the postpredicamenta; wherein, first, the four kinds of opposition of terms
are explained; to with relative, privative, of contrariety, and of contradiction.
This is repeated in all systems of logic. Last of all, we have distinctions of the four Greek words which
answer to the Latin ones - prius, simul, motus, and habere.
Section IV.
OF THE BOOK CONCERNING INTERPRETATION.
We are to consider, says Aristotle, what a Noun is, what a Verb, what Affirmation,
what Negation, what Enunciation, what Speech. Words are the signs of what passeth
in the mind; Writing is the sign of words. The signs both of writing and of words are different in
different nations, but the operations of mind signified by them are the same. There are some operations of
thought which are neither true nor false. These are expressed by nouns or verbs singly, and without composition.
A Noun is a sound, which, by compact, signifies something without respect to time, and of which no part
has signification by itself. The cries of beasts may have a natural signification, but they are not nouns:
we give that name only to sounds which have their signification by compact. The cases of a noun, as the genitive,
dative, are not nouns. Non homo is not a noun, but, for distinction's sake, may be called a
Nomen Infinitum.
A Verb signifies something by compact with relation to time. Thus, valet is a verb; but
valetudo is a noun, because its significance has no relation to time. It is only the present tense of
the indicative that is properly called a verb; the other tenses and moods are variations of the verb.
Non valet may be called a verbum infinitivum.
Speech is sound significant by compact, of which some part is also significant. And it is either
enunciative, or not enunciative. Enunciative speech is that which affirms or denies. As to speech
which is not enunciative, such as a prayer or a wish, the consideration of it belongs to oratory
or poetry. Every enunciative speech must have a verb, or some variation of a verb. Affirmation is the
enunciation of one thing, concerning another. Negation is the enunciation of one thing from another.
Contradiction an affirmation and negation that are opposite. This is a summary of the first six chapters.
The seventh and eighth treat of the various kinds of enunciations or propositions, universal, particular,
indefinite, and singular; and of the various kinds of opposition in propositions, and the
axioms concerning them. These things are repeated in every system of logic. In the ninth chapter,
he endeavours to prove, by a long metaphysical reasoning, that propositions respecting future contingencies
are not, determinately, either true or false; and that, if they were, it would follow that all things happen
necessarily, and could not have been otherwise than as they are. The remaining five chapters contain many
minute observations concerning the aequipollency of propositions both pure and modal.
CHAPTER II.
REMARKS.
Section I.
OF THE FIVE PREDICABLES.
The writers on logic have borrowed their materials almost entirely from Aristotle's Organon, and
Porphyry's Introduction. The Organon, however, was not written by Aristotle as one work. It comprehends
various tracts, written without the view of making them parts of one whole, and afterwards thrown together
by his editors under one name, on account of their affinity. Many of his books that are lost would have
made a part of the Organon, if they had been saved.
The three treatises, of which we have given a brief account, are unconnected with each other, and with those
that follow. And although the first was undoubtedly compiled by Porphyry, and the two last probably by
Aristotle, yet I consider them as the venerable remains of a philosophy more ancient than Aristotle.
Archytas of Tarentum, an eminent mathematician and philosopher of the Pythagorean school, is said to have wrote
upon the ten categories; and the five predicables probably had their origin in the same school. Aristotle, though
abundantly careful to do justice to himself, does not claim the invention of either. And Porphyry, without
ascribing the latter to Aristotle, professes only to deliver the doctrine of the ancients, and chiefly of
the Peripatetics, concerning them.
The writers on logic have divided that science into three parts; the first treating of Simple
Apprehension and of Terms; the second, of Judgment and of Propositions; and the third,
of Reasoning and of Syllogisms. The materials of the first part are taken from Porphyry's
Introduction and the Categories; and those of the second from the book of Interpretation.
A Predicable, according to the grammatical form of the word, might seem to signify whatever
might be predicated, that is, affirmed or denied, of a subject; and in this sense every predicate would be
a predicable. But the logicians give a different meaning to the word. They divide propositions into
certain classes, according to the relation which the predicate of the proposition bears to the subject.
The first class is that wherein the the predicate is the genus of the subject, as when we say,
"This is a triangle," "Jupiter is a planet." In the second class, the predicate is a species of
the subject; as when we say, "This triangle is right-angled." A third class is when the predicate is the
specific difference of the subject; as when we say, "Every triangle has three sides and three angles."
A fourth, when the predicate is a property of the subject; as when we say, "The angles of every
triangle are equal to two right angles." And a fifth class when the predicate is something accidental
to the subject; as when we say, "This triangle is neatly drawn."
Each of these classes comprehends a great variety of propositions, having different subjects and different predicates;
but in each class the relation between the predicate and the subject is the same. Now, it is this relation
that logicians have given the name of a predicable. Hence it is, that, although the number of predicates be
infinite, yet the number of predicables is no greater than that of the different relations which may be
in propositions between the predicate and the subject. And if all propositions belong to one or other of the
five classes above mentioned, there can be but five predicables - to wit - genus, species, differentia,
proprium, and accidens. These might, with more propriety perhaps, have been called the five
classes of predicates; but use has determined them to be called the five predicables.
It may also be observed, that, as some objects of thought are individuals, such as Julius Caesar, the city of
Rome; so others are common to many individuals, as good, great, virtuous, vicious. Of this last kind
are all things that are expressed by adjectives. Things common to many individuals were by the ancients called
universals. All predicates are universals, for they all have the nature of adjectives; and, on the
other hand, all universals may be predicates. On this account, universals may be divided into the same classes
as predicates; and as the five classes of predicates above mentioned have been called the five predicables,
so, by the same kind of phraseology, they have been called the five universals; although they may more
properly be called the five classes of universals.
The doctrine of the Five Universals, or Predicables, makes an essential part of every system of logic, and has
been handed down without any change to this day. The very name of predicables shews, that the author of
this division, whoever he was, intended it as a complete enumeration of all the kinds of things that can be affirmed
of any subject; and so it has always been understood. It is accordingly implied in this division, that all that
can be affirmed of anything whatsoever, is either the genus of the thing, or its species, or its
specific difference, or some property or accident belonging to it.
Burgersdyck, a very acute writer on logic, seems to have been aware that strong objections might be made
to the five predicables, considered as a complete enumeration: But, unwilling to allow any imperfection in this
ancient division, he endeavours to restrain the meaning of the word predicable so as to obviate
objections. Those things only, says he, are to be accounted predicables, which may be affirmed - of
many individuals - truly - properly - naturally - and immediately. The consequence of putting
such limitations upon the word predicable is that, that, in many propositions, perhaps in most,
the predicate is not a predicable. But, admitting all his limitations, the enumeration will still be
very incomplete; for of many things we affirm, truly, properly, and immediately, their existence, their end,
their cause, their effect, and various relations which they bear to other things. These, and perhaps many more,
are predicables in the strict sense of the word, no less than the five which have been so long famous.
Although Porphyry, and all subsequent writers make the predicables to be in number five, yet Aristotle himself,
in the beginning of the topics, reduces them to four, and demonstrates that there can be no more. We shall give
his demonstration when we come to the topics, and shall only here observe, that, as Burgersdyke justifies the
fivefold division, by restraining the meaning of the word predicable, so Aristotle justifies the fourfold
division, by enlarging the meaning of the words property and accident.
After all, I apprehend that this ancient division of predicables, with all its imperfections, will bear
a comparison with those that have been substituted in its stead by the most celebrated modern philosophers.
Locke, in his "Essay on the Human Understanding," having laid it down as a principle, That all our knowledge
consists in perceiving certain agreements and disagreements between our ideas, reduces these agreements and
disagreements to four heads - to wit, 1, Identity and Diversity; 2, Relation; 3,
Co-existence; 4, Real Existence. Here are four predicables given as a complete enumeration, and yet
not one of the ancient predicables is included in the number.
The author of the "Treatise of Human Nature," proceeding upon the same principle, that all our knowledge is
only a perception of the relations of our ideas, observes, "That it may perhaps be esteemed an endless task
to enumerate all those qualities which admit of comparison, and by which the ideas of philosophical relation
are produced; but, if we dilegently consider them, we shall find, that, without difficulty, they may be
comprised under seven heads:- 1, Resemblance; 2, Identity; 3, Relations of Space and Time;
4, Relations of Quantity and Number; 5, Degrees of Quality; 6, Contrariety; 7, Causation."
Here again are seven predicables given as a complete enumeration, wherein all the predicables of the ancients, as well
as two of Locke's, are left out.
The ancients, in their division, attended only to categorical propositions which have one subject and one
predicate; and of these to such only as have a general term for their subject. The moderns, by their definition of
knowledge, have been led to attend only to relative propositions, which express a relation between two subjects,
and these subjects they suppose only to be ideas.
Section II.
OF THE TEN CATEGORIES, AND ON DIVISIONS IN GENERAL.
The intention of the Categories or Predicaments is, to muster every object of human apprehension
under ten heads; for the categories are given as a complete enumeration of everything which can be expressed
without composition and structure - that is, of everything which can be either the subject or the predicate
of a proposition. So that, as every soldier belongs to some company, and every company to some regiment, in
like manner everything that can be the object of human thought has its place in one or other of the categories;
and, by dividing and subdividing properly the several categories, all the notions that enter into the human
mind may be mustered in rank and file, like an army in the day of battle.
The perfection of the division of categories into ten heads has been strenuously defended by the followers
of Aristotle, as well as that of the five predicables. They are, indeed, of kin to each other; they breathe
the same spirit, and probably had the same origin. By the one we are taught to marshal every term that can
enter into a proposition, either as subject or predicate; and, by the other, we are taught all the possible
relations whcih the subject can have to the predicate. Thus the whole furniture of the human mind is presented
to us at one view, and contracted, as it were, into a nutshell. To attempt, in so early a period, a methodical
delineation of the vast region of human knowledge, actual and possible, and to point out the limits of every
district, was indeed magnanimous in a high degree, and deserves our admiration, while we lament that the human
powers are unequal to so bold a flight.
A regular distribution of things under proper classes or heads is, without doubt, a great help both to memory
and judgment. And as the philosopher's province includes all things, human and divine, that can be
objects of inquiry, he is naturally led to attempt some general division like
that of the categories. And the invention of a division of this kind, which the speculative part of mankind
acquiesced in for two thousand years, marks a superiority of genius in this inventor, whoever he was.
Nor does it appear that the general divisions which, since the decline of the Peripatetic philosophy,
have been substituted in place of the ten categories are more perfect.
Locke has reduced all things to three categories - viz., substances, modes,
and relations. In this division, time, space, and number,
three great objects of human thought, are omitted.
The author of the 'Treatise of Human Nature' has reduced all things to two
categories - viz., ideas, and impressions; a division which is very well adapted to his system,
and which puts me in mind of another made by an excellent mathematician in a printed thesis I have seen.
In it the author, after a severe censure of the ten categories of the Peripatetics, maintains that there neither
are nor can be more than two categories of things - viz., data and quaesita.
There are two ends that may be proposed by such divisions. The first is, to methodise or digest in order
what a man actually knows. This is neither unimportant nor impracticable; and, in proportion to the solidity and
accuracy of a man's judgement, his divisions of the things he knows will be elegant and useful.
The same subject may admit, and even require, various divisions, according to the different points
of view from which we contemplate it; nor does it follow, that, because one division is good,
therefore another is naught. To be acquainted with the divisions of the logicians and metaphysicians,
without a superstitious attachment to them, may be of use in dividing the same subjects, or even those of a
different nature. Thus Quintillian borrows from the ten categories his division of the topics of rhetorical
argumentation. Of all methods of arrangement, the model anti-philosophical seems to be the invention of this age;
I mean the arranging the arts and sciences by the letters of the alphabet, in dictionaries and encyclopaedias.
With these authors the categories are, A, B,C, &c.
Another end commonly proposed by such divisions, but very rarely attained, is to exhaust the subject divided,
so that nothing that belongs to it shall be omitted. It is one of the general rules of division, in all systems
of logic, That the division should be adequate to the subject divided: a good rule without doubt,
but very often beyond the reach of human power. To make a perfect division, a man must have a perfect
comprehension of the whole subject at one view. When our knowledge of the subject is imperfect,
any division we can make must be like the first sketch of a painter, to be extended, contracted, or mended,
as the subject shall be found to require. Yet nothing is more common, not only among the ancient, but even
among modern philosophers, than to draw, from their incomplete divisions, conclusions which suppose them to
be perfect.
A division
is a repository which the philosopher frames for holding his ware in convenient
order. The philosopher maintains, that
such or such a thing is not good ware, because there is no place in his
wareroom that fits it. We are apt to
yield to this argument in philosophy, but it would appear ridiculous in any
other traffic. Peter Ramus,
who had the spirit of a reformer in philosophy, and who had a force of genius sufficient
to shake the Aristotelian fabric in many parts, but insufficient to erect
anything more solid than in its place, tried to remedy the imperfection of
philosophical divisions by introducing a new manner of dividing. His divisions always consisted of two
members, one of which was the contradictory of the other, as if one should
divide England into Middlesex and what is not Middlesex. It is evident that these two members
comprehend all England; for the Logicians observe, that a term along with its contradictory
comprehend all things. In the same
manner, we may divide what is not Middlesex into Kent and what is not Kent. Thus one may go on by divisions and
subdivisions that are absolutely complete.
This example may serve to give an idea of the spirit of Ramean
divisions, which were in no small reputation about two hundred years ago.
Aristotle was not ignorant of this kind of division. But he used it only as a touchstone to prove by induction the perfection
of some other division, which indeed is the best use that can be made of
it. When applied to the common purpose of division, it is both inelegant and burdensome to the memory; and, after it
has put one out of breath by endless subdivisions, there is still a negative
term left behind, which shews you that you are no nearer the end of your
journey than when you began. Until some more effectual remedy be found for the imperfection of divisions, I beg leave
to propose one more simple than that of Ramus.
It is this - When you meet with a division of any subject imperfectly
comprehended, add to the last member an et caetera. That this et caetera
makes the division complete, is undeniable; and therefore it ought to hold its place as a member,
and to be always understood, whether expressed or not, until clear and positive proof be
brought that the division is complete without it. And this same et caetera shall be the
repository of all members that may in future time shew a good and valid right to a property in the subject.
Section III ON DISTINCTIONS Having said so much of
logicial divisions, we shall next make some remarks upon distinctions.
Since the philosophy of Aristotle fell into disrepute, it
has benn a common topic of wit and raillery to inveigh against
metaphysical distinctions. INdeed the abuse of them, in the
scholastic ages, sems to justify a general prejudice against them; and
shallow thinkers and writers have good reason to be jealous of
distinctions, because they make sad work when applied to their flimsy
compositions. But every man of true judgment, while he condemns
distinctions that have no foundation in the nature of things, must
perceive, that indiscriminately to descry distinctions, is to renounce
all pretensions to just reasoning: for, as false reasoning commonly
proceeds from confounding things that are different, so, without
distinguishing such things, it is impossible to avoid error or detect
sophistry. The authority of Aquinas, or Suarez, or even of Aristotle,
can neither stamp a real value upon distinctions of base metal, nor
hinder the currency of those that havve intrinsic value.
Some distinctions are verbal, others are real. The first
kind distinguish the various meanings of a word, whether proper or
metaphorical. Distinctions of this kind make a part of the grammar of
a language, and are often absurd when translated into another
language. Real distinctions are equally good in all languages, and
suffer no hurt by translation. They distinguish the different species
contained under some general notion, or the different parts contained
in one whole.
Many of Aristotle's distinctions are verbal
merely, and therefore more proper materials for a dictionary of the
Greek language, than for a philosophical treatise. At least, they
ought never to have been translated into other languages, when the
idiom of the language will not justify them: for this is to adulterate
the language, to introduce foreign idioms into it without necessity or
use, and to make it ambiguous where it was not. The distinctions in
the end of categories of the four words, prius, simul, motus,
and habere, are all verbal.
The modes or species of Prius, according to Aristotle, are five.
One thing may be prior to another - first, in point of time; secondly,
in point of dignity; thirdly, in point of order; and so forth. The
modes of simul are only three. It seems this word was not used
in the Greek with so great latitude as the other, although they are
relative terms. The modes or species of Motion he makes to be
six - viz., generation, corruption, increase, decrease, alteration
, and change of place. The modes or species of
Having are principally eight. 1. Having a quality or
habit, as having wisdom. 2. Having quantity or magnitude. 3.
Having things adjacent, as having a sword. 4. Having things
as parts, as having hands or feet. 5. Having in a part or on a
part, as having a ring on one's finger. 6. Containing, as
a cask is said to contain wine. 7. Possessing, as having
lands or houses. 8. Having a wife or husband.
Another distinction of this kind is Aristotle's distinction of
Causes; of which he makes four kinds, efficient, material,
formal, and final. These distinctions may deserve a place
in a dictionary of the Greek language; but in English or Latin, they
adulterate the language. Yet so fond were the schoolmen of
distinctions of this kind, that they added to Aristotle's enumeration
an impulsive cause, an exemplary cause, and I don't know
how many more. We seem to have adopted into English a final
cause; but it is merely a term of art, borrowed from the Peripatetic
philosophy, without necessity or use; for the English word end
is as good as final cause, though not so long nor so
learned.
Section IV ON DEFINITIONS It
remains that we make some remarks on Aristotle's Definitions, which
have exposed him to much censure and ridicule. Yet I think it must be
allowed, that, in things which need definition, and admit of it, his
definitions are commonly judicious and accurate; and, had he attempted
to define such things only, his enemies had wanted great matter or
triumph. I believe it may likewise be said in his favour, that, until
Locke's essay was wrote, there was nothing of importance delivered by
philosophers with regard to definition, beyond what Aristotle has said
on that subject. He considers a Definition as a speech
declaring what a thing is. Every thing essential to the
thing defined, and nothing more, must be contained in the definition.
Now, the essence of a thing consists in these two parts: first,
What is common to it with other things of the same kind; and,
secondly, What distinguishes it from other things of the same kind
. The first is called the Genus of the thing, the second
its Specific Difference. The definition, therefore, consists
of these two parts. And, for finding them, we must have recourse to
the ten categories; in one or other of which everything in nature is
to be found. Each category is a genus, and is divided into so
many species, which are distinguished by their specific differences.
Each of these species is again subdivided into so many species, with
regard to which it is a genus. This division and subdivision co
ntinues until we come to the lowest species, which can only be divided
into individuals distinguished from one another, not by any specific
difference, but by accidental differences of time, place, and other
circumstances. The category itself, being the highest genus,
is in no respect a species, and the lowest species is in no respect a
genus; but every intermediate order is a genus compared with those
that are below it, and a species compared with those above it. To
find the definition of anything, therefore, you must take the genus
which is immediately above its place in the category, and the specific
difference by whcih it is distinguished from other species of the same
genus. These two make a perfect definition. This I take to be the
substance of Aristotle's system, and probably the system of the Py
thagorean school, before Aristotle, concerning definitions.
But, notwithstanding the specious appearance of this system, it has
its defects. Not to repeat what was before said of the imperfection
of the division of things into ten categories, the subdivisions of
each category are no less imperfect. Aristotle has given some
subdivisions of a few of them; and, as far as he goes, his followers
pretty unaminously take the same road. But, when they attempt to go
farther, they take very different roads. It is evident, that, if the
series of each category could be completed, and the division of things
into categories could be made perfect, still the highest genus in each
category could not be defined, because it is not a species; nor could
individuals be defined, because they have no specific difference.
There are also many species of things, whose specific difference
cannot be expressed in language, even when it is evident to sense, or
to the understanding. Thus, green, red, and blue, are very distinct
species of colour; but who can express in words wherein green differs
from red or blue? Without borrowing light from the ancient
system, we perceive that every definition must consist of words that
need no definition; and that to define the common words of a language
that have no ambiguity is trifling, if it could be done; the only
clear use of a definition being to give a clear and adequate
conception of the meaning of a word. The logicians indeed
distinguish between the definition of a word and the
definition of a thing; considering the former as the mean office
of a lexicographer, but the last as the grand work of a philosopher.
But what they have said about the definition of a thing, if it has a
meaning, is beyond my comprehension. All the rules of definition
agree in the definition of a word: and if they mean, by the definition
of a thing, the giving an adequate conception of the nature and
essence of anything that exists, this is impossible, and is the vain
boast of men unconscious of the weakness of human understanding.
The works of God are all imperfectly known by us. We see their
outside, or perhaps we discover some of their qualities and relations,
by observation and experiment, assisted by reasoning: but we can give
no definition of the meanest of them which comprehends its real
essence. It is justly observed by Locke, that nominal essences
only, which are the creatures of our own minds, are perfectly
comprehended by us, or can be properly defined; and even of these
there are many too simple in their nature to admit of definition.
When we cannot give precision to our notions by a definition, we must
endeavour to do it by attentive reflection upon them, by observing
minutely their agreements and differences, and especially by a right
understanding of the powers of our own minds by which such notions are
formed. The principles laid down by Locke, with regard to
definition, and with regard to the abuse of words, carry conviction
along with them: and I take them to be one of the most important
improvements made in logic since the days of Aristotle; not so much
because they enlarge our knowledge, as because they make us sensible
of our ignorance, and shew that a great part of what speculative men
have admired as profound philosophy, is only a darkening of knowledge
by words without understanding.
Section V. ON THE
STRUCTURE OF SPEECH
The few hints contained in the beginning
of the book concerning Interpretation relating to the structure of
speech, have been left out in treatises of logic, as belonging rather
to grammar; yet I apprehend this is a rich field of philosophical
speculation. Language being the express image of human thought, the
analysis of the one must correspond to that of the other. Nouns
adjective and substantive, verbs active and passive, with their
various moods, tenses, and persons, must be expressive of a like
variety in the modes of thought. Things that are distinguished in all
languages, such as substance and quality, action and passion, cause
and effect, must be distinguished by the natural powers of the human m
ind. The philosophy of grammar, and that of the human understanding,
are more nearly allied than is commonly imagined. The
structure of language was pursued to a considerable extent by the
ancient commentators upon this book of Aristotle. Their speculations
on this subject, which neither the least ingenious nor the least
useful part of the Peripatetic philosophy, were neglected for many
ages, and lay buried in ancient manuscripts, or in books little known,
till they were lately brought to light by the learned Mr Harris, in
his 'Hermes'. The definitions given by Aristotle of a noun
, of a verb, and of speech, will hardly bear
examination. It is easy in practice to distinguish the various parts
of speech; but very difficult, if at all possible, to give accurate
definitions of them. He observes justly, that, besides that
kind of speech called a proposition, which is always either
true or false, there are other kinds which are neither true nor false,
such as a prayer or a wish; to which we may add, a question, a
command, a promise, a contract, and many others. These Aristotle pro
nounces to have nothing to do with his subject, and remits them to
oratory or poetry; and so they have remained banished from the regions
of philosophy to this day; yet I apprehend that an analysis of such
speeches, and of the operations of mind which they express, would be
of real use, and perhaps would discover how imperfect an enumeration
the logicians have given of the powers of human understanding, when
they reduce them to Simple Apprehension, Judgment, and Reasoning.
Section VI. ON PROPOSITIONS Mathematicians use
the word Proposition in a larger sense than Logicians. A
problem is called a proposition in mathematics, but in logic it
is not a proposition; it is one of those speeches which are not
enunciative, and which Aristotle remits to oratory or poetry.
A Proposition, according to Aristotle, is a speech wherein
one thing is affirmed or denied of another. Hence, it is easy to
distinguish the thing affirmed or denied, which is called the
Predicate, from the thing of which it is affirmed or denied, which
is called the Subject; and these two are called the Terms of
the proposition. Hence, likewise, it appears that propositions
are either affirmative or negative; and this is called
their Quality. All affirmative propositions have the same
quality, so likewise have all negative; but an affirmative and a
negative are contrary in their quality. When the subject of
the proposition is a general term, the predicate is affirmed or denied
either of the whole, or of a part. Hence propositions are
distinguished into universal and particular. 'All men
are mortal,' is an universal proposition; 'Some men are learned,' is a
particular; and this is called the Quantity of the proposition.
All universal propositions agree in quantity, as also all particular;
while an universal and a particular are said to differ in quantity. A
proposition is called indefinite when there is no mark of
either of universality or particularity annexed to the subject: thus,
'Man is of few days,' is an indefinite proposition; but it must be
understood either as universal or particular, and therefore is not a
third species, but, by interpolation, is brought under one of the
other two. There are also singular propositions, which
have not a general term, but an individual, for their subject; as,
'Alexander was a great conqueror.' These are considered by logicians
as universal, because the subject being indivisible, the predicate is
affirmed or denied of the whole, and not of a part only. Thus, all
propositions, with regard to quality, are either affirmative or
negative; and, with regard to quantity, are universal or particular;
and, taking in both quantity and quality, they are universal
affirmatives, or universal negatives, or particular affirmatives or
particular negatives. These four kinds, after the days of Aristotle,
came to be named by the names of the four first vowels, A, E, I, O,
according to the following distich: - Asserit A, negat E, sed
universaliter ambae, When the young Logician is thus far instructed in the
nature of propositions, he is apt to think there is no difficulty in
analysing any proposition, and shewing its subject and predicate, its
quantity and quality; and, indeed, unless he can do this, he will be
unable to apply the rules of logic to use. Yet he will find there are
some difficulties in this analysis, which are overlooked by Aristotle
altogether; and although they are sometimes touched, they are not rem
oved by his followers. For, 1. There are propositions in which it is
difficult to find a subject and a predicate; as in these, 'It rains,'
'It snows.' 2. In some propositions, either term may be made the
subject or the predicate, as you like best; as in this, 'Virtue is the
road to happiness.' 3. The same example may serve to shew that it is
sometimes difficult to say, whether a proposition is universal or
particular. 4. The quality of some propositions is so dubious that
Logicians have never been able to agree whether they be affirmative or
negative; as in this proposition, 'Whatever is insentient is not an
animal.' 5. As there is one class of propositions which have only two
terms, viz., one subject and one predicate, which called
Categorical Propositions, so there are many classes that have more
than two terms. What Aristotle delivers in this book is applicable
only to categorical propositions; and to them only the rules
concerning the conversion of propositions, and concerning the figures
and modes of syllogisms, are accommodated. The subsequent writers of
logic have taken notice of some of the many classes of complex
propositions, and hve given rules adapted to them; but, finding this
work endless, they have left us to manage the rest by the rules of
common sense. CHAPTER III ACCOUNT OF THE FIRST
ANALYTICS
Section I ON THE CONVERSION OF
PROPOSITIONS In attempting to give some account of the
Analytics and of the Topics of Aristotle, ingenuity requires me to
confess, that, though I have often purposed to read the whole with
care, and to understand what is intelligible, yet my courage and
patience always failed before I had done. Why should I throw away so
much time and painful attention upon a thing of so little real use?
If I had lived in those ages when the knowledge of Aristotle's Organon
entitled a man to the highest rank in philosophy, ambition might have
induced me to employ upon it some years of painful study; and less, I
conceive, would not be sufficient. Such reflections as these always
got the better of my resolution, when the first ardout began to cool.
All I can say is, that I have read some parts of the different books
with care, some slightly, and some, perhaps, not at all. I have
glanced over the whole often, and, when anything attracted my
atention, have dipped into it till my appetite was satisfied. Of all
reading, it is the most dry and the most painful, empoying an infinite
labour of demonstration, about things of the most abstract nature,
delieverd in a laconic style, and often, I think, with affected
obscurity; and all to prove general propositions, which, when applied
to particular instances, appear self-evident. There is
probably but little in the Categories, or in the book of
Interpretation, that Aristotle could claim as his own invention; but
the whole theory of syllogisms he claims as his own, and as the fruit
of much time and labour. And indeed it is a stately fabric, a
monument of a great genius, which we could wish to have been more
usefully employed. There must be something, however, adatped to
please the human understanding, or to flatter human pride, in a work
which occupied men of speculation for more than a thousand years.
These books are called Analytics, because the intention of them
is to resolve all reasoning into its simple ingredients. The
first book of the First Analytics, consisting of
forty-six chapters, may be divided into four parts; the
first [A] trreating of the conversion of propositions; the
second, [B,] of the structure of syllogisms, in all the
different figures and modes; the third, [C,] of the invention of a
middle term; and the last, [D,] of the resolution of syllogisms
. We shall give a brief account of each. [A] To
convert a proposition is to infer from it another proposition, whose
subject is the predicate of the first, and whose predicate is the
subject of the first. This is reduced by Aristotle to three
rules:- 1. An universal negative may be converted into an universal
negative: thus, 'No man is a quadruped;'therefore 'No quadruped is a
man.' 2. An universal affirmative can be converted only into a
particular affirmative: thus, 'All men are mortal;' therefore 'Some
mortal beings are men.' 3. A particular affirmative may be converted
into a particular affirmative: as, 'Some men are just;' therefore
'Some just persons are men.' When a proposition may be converted
without changing its quantity, this is called simple conversion
; but when the quantity is diminished, as in the universal
affirmative, it is called conversion per accidens.
There is another kind of conversion omitted in this place by
Aristotle, but supplied by all his followers, called conversion by
contraposition, in which the term that is contradictory to the
predicate is put for the subject, and the quality of the proposition
is changed; as, 'All animals are sentient;' therefore, 'What is not
sentient is not an animal.' A fourth rule of conversion, therefore
is, That an universal affirmative, and a particular negative, may be
converted by contraposition.
Section II OF THE
FIGURES AND MODES OF PURE SYLLOGISMS [B] A SYLLOGISM is
an argument, or reasoning, consisting, always explicitly or
implicitly, of three propositions, the last of which, called the
CONCLUSION, is necessarily inferred from the very statement of the two
preceding, which are called the PREMISES. The conclusion having
two terms, a subject and a predicate, its predicate is called the
major term, and its subject the minor term. In order to
prove the conclusion, each of its terms is, in the premises, compared
with the third term, called the middle term. By this means one
of the premises will have for its two terms the major term and the
middle term; and this premise is called the major premise, or
the major proposition of the syllogism. The other premise must
have for its two terms the minor term and the middle term, and it is
called the minor proposition. Thus the syllogism consists of
three propositions, distinguished by the names of the major,
the minor, and the conclusion; and, although each of
these has two terms, a subject and a predicate, yet there are only
three different terms in all. The major term is always the predicate
of the conclusion, and is also either the subject or predicate of the
major proposition. The minor term is slways the subject of the
conclusion, and is also either the subject or predicate of the minor
proposition. The middle term never enters into the conclusion, but
stands in both premises, either in the position of subject or
predicate.
According to the various positions which
the Middle Term may have in the premises, syllogisms are said to be of various
Figures. Now, all the possible positions of the
middle term are only four; for, first, it may be the subject of the
major proposition, and the predicate of the minor, and then the syllogism is of
the first figure; or it may be the predicate of both premises, and then the
syllogism is of the second figure; or it may be the subject of both, which
makes a syllogism of the third figure; or it may be the predicate of the major
proposition, and the subject of the minor, which makes the fourth figure.
Aristotle takes no notice of the fourth figure. It was added by the famous
Galen, and is often called the Galenical Figure.
There is another division of syllogisms
according to their Modes. The Mode of a syllogism is determined by
the Quality and Quantity of the propositions of which it consists. Each of
the three propositions must be either an universal affirmative, or an universal
negative, or a particular affirmative, or a particular negative. These four
kinds of propositions, as was before observed, have been named by the four
vowels A, E, I, O; by which means the mode of a syllogism is marked by any
three of those vowels. Thus, A, A, A, denotes that mode in which the major,
minor and conclusion, are all universal affirmatives; E, A, E, denotes that
mode in which the major and conclusion are universal negatives and the minor is
an universal affirmative.
To know all the possible modes of
syllogism, we must find how many different combinations may be made of three
out of the four vowels; and from the art of combination the number is found to
be sixty four. So many possible modes are there in every figure, consequently
in the three figures of Aristotle there are one hundred and ninety-two, and in
all the four figures two hundred and fifty six.
Now, the theory of syllogism requires that
we shew what are the particular modes in each figure, which do or do not form a
just and conclusive syllogism, that so the legitimate may be adopted, and the
spurious rejected. This Aristotle has shewn in the first three figures,
examining all the modes one by one, and passing sentence upon each; and from
this examination he collects some rules which may aid the memory in
distinguishing the false from the true, and point out the properties of each
figure.
The first figure has only four
legitimate modes. The major proposition in this figure must be universal, and
the minor affirmative; and it has this property, that it yields conclusions of
all kinds, affirmative and negative, universal and particular.
The second figure has also four
legitimate modes. Its major proposition must be universal, and one of the
premises must be negative. It yields conclusions both universal and
particular, but all negative.
The third figure has six legitimate
modes. Its minor must always be affirmative; and it yields conclusions both
affirmative and negative, but all particular.
Besides the rules that are proper to each
figure, Aristotle has given some that are common to all, by which the
legitimacy of syllogisms may be tried. These may, I think, be reduced to
five. 1. There must be only three terms in a syllogism. As each term occurs
in two of the propositions, it must be precisely the same in both: If it be
not, the syllogism is said to have four terms, which makes a vitious
syllogism. 2. The middle term must be taken universally in one of the
premises. 3. Both premises must not be particular propositions, nor both
negative. 4. The conclusion must be particular, if either of the premises be
particular; and negative, if either of the premises be negative. 5. No term
can be taken universally in the conclusion, if it not be taken universally in
the premises.
For understanding the second and fifth of
these rules, it is necessary to observe, that a term is said to be taken
universally, not only when it is the subject of an universal proposition, but
when it is the predicate of a negative proposition; on the other hand, a term
is said to be taken particularly, when it is either the subject of a
particular, or the predicate of an affirmative proposition.
Section III
OF THE INVENTION OF A MIDDLE TERM
[C.] The third part of this book contains
rules, general and special, for the invention of a middle term; and this
the author conceives to be of great utility. The general rule amounts to this
- That you are to consider well both terms of the proposition to be proved; their
definition, their properties, the things which may be affirmed or denied of
them, and those of which they may be affirmed or denied; these things,
collected together, are the materials from which your middle term is to be
taken.
The special rules require you to consider
the quantity and quality of the proposition to be proved, that you may discover
in what mode and figure of syllogism the proof is to proceed. Then, from the
materials before collected, you must seek a middle term which has that relation
to the subject and predicate of the proposition to be proved, which the nature
of the syllogism requires. Thus, suppose the proposition I would prove is an
universal affirmative, I know, by the rules of syllogisms, that there is only
one legitimate mode in which an universal affirmative proposition can be
proved; and that is the first mode of the first figure. I know likewise that,
in this mode, both the premises must be universal affirmatives; and that the
middle term must be the subject of the major, and the predicate of the minor.
Therefore, of the terms collected according to the general rule, I seek out one
or more which have these two properties; first, That the predicate of the
proposition to be proved can be universally be affirmed of it; and, secondly,
That it can be universally affirmed of the subject of the proposition to be
proved. Every term you can find, which has these two properties, will serve
you as a middle term, but no other. In this way, the author gives special
rules for all the various kinds of propositions to be proved; points out the
various modes in which they may be proved, and the properties which the middle
term must have to make it fit for answering that end. And the rules are
illustrated, or rather, in my opinion, purposely darkened, by putting letters
of the alphabet for the several terms.
Section IV
OF THE REMAINING PART OF THE FIRST BOOK
The resolution of syllogisms requires no
other principles but those before laid down for constructing them. However, it
is treated of largely, and rules laid down for reducing reasoning to
syllogisms, by supplying one of the premises when it is understood, by
rectifying inversions, and putting the propositions in the proper order.
Here he speaks also of hypothetical
syllogisms; which he acknowledges cannot be resolved into any of the figures,
although there be many kinds of them that ought diligently to be observed, and
which he promises to handle afterwards. But this promise is not fulfilled, as
far as I know, in any of his works that are extant.
Section V
OF THE SECOND BOOK OF THE FIRST ANALYTICS
The second book treats of the powers
of syllogisms, and shews, in twenty-seven chapters, how we may perform
many feats by them, and what figures and modes are adapted to each. Thus, in
some syllogisms, several distinct conclusions may be drawn from the same
premisses; in some, true conclusions may be drawn from false premises; in some,
by assuming the conclusion and one premise, you may prove the other; you may
turn a direct syllogism into one leading to an absurdity.
We have likewise precepts given in this
book, both to the assailant in a syllogistical dispute, how to carry on his
attack, with art, so as to obtain the victory, and to the defendant, how to keep
the enemy at such a distance as that he shall never be obliged to yield. From
which we learn, that Aristotle introduced in his own school the practice of
syllogistical disputation, instead of the rhetorical disputations which the
Sophists were wont to use in more ancient times.
CHAPTER IV
REMARKS
Section I
OF THE CONVERSION OF PROPOSITIONS
We have given a summary view of the theory
of pure syllogisms as delivered by Aristotle, a theory of which he claims the
sole invention. And I believe it will be difficult, in any science, to find so
large a system of truths of so very general and abstract a nature, all
fortified by demonstration, and all invented and perfected by one man. It
shews a force of genius, and labour of investigation, equal to the most arduous
attempts. I shall now make some remarks upon it.
As to the conversion of propositions, the
writers on logic commonly satisfy themselves with illustrating each of the
rules by an example, conceiving them to be self-evident, when applied to particular
cases. But Aristotle has given demonstrations of the rules he mentions. As a
specimen, I shall give his demonstration of the first rule. 'Let A B be an
universal negative proposition; I say, that if A is in no B, it will follow
that B is in no A. If you deny this consequence, let B be in some A, for
example, in C; then the first supposition will not be true; for C is of the
Bs.' In this demonstration, if I understand it, the third rule of conversion
is assumed, that, if B is in some A, then A must be in some B, which
indeed is contrary to the first supposition. If the third rule be assumed for
want of proof of the first, the proof of all the three goes round in a circle;
for the second and third rules are proved by the first. This is a fault in
reasoning which Aristotle condemns, and which I would be very unwilling to
charge him with, if I could find any better meaning in his demonstration. But
it is indeed a fault very difficult to be avoided, when men attempt to prove
things which are self-evident.
The rules of conversion cannot be applied
to all propositions, but only to those that are categorical, and we are left to
the direction of common sense in the conversion of other propositions. To give
an example: 'Alexander was the son of Philip;' therefore, 'Philip was the
father of Alexander:' 'A is greater than B;' therefore 'B is less than A.'
These are conversions which, as far as I know, do not fall within any rule in
logic; nor do we find any loss for want of a rule in such cases.
Even in the conversion of categorical
propositions, it is not enough to transpose the subject and predicate. Both
must undergo some change, in order to fit them for their new station; for, in
every proposition, the subject must be a substantive, or have the force of a
substantive; and the predicate must be an adjective, or have the force of an
adjective. Hence it follows, that when the subject is an individual, the
proposition admits not of conversion. How, for instance, shall we convert this
proposition, 'God is omniscient'?
These observations shew, that the doctrine
of the conversion of propositions is not so complete as it appears. The rules
are laid down without any limitation; yet they are fitted only to one class of
propositions - viz., the categorical; and of these only to such as have a
general term for their subject.
Section II
ON ADDITIONS MADE TO ARISTOTLE'S LOGIC
Although the logicians have enlarged the
first and second parts of logic, by explaining some technical words and
distinctions which Aristotle had omitted, and by giving names to some kinds of
propositions which he overlooks, yet, in what concerns the theory of
categorical syllogisms, he is more full, more minute and particular, than any
of them; so that they seem to have thought this capital part of the Organon
rather redundant than deficient.
It is true that Galen added a fourth figure
to the three mentioned by Aristotle. But there is reason to think that
Aristotle omitted the fourth figure, not through ignorance or inattention, but
of design, as containing only some indirect modes, which, when properly
expressed, fall into the first figure.
It is true also that Peter Ramus, a
professed enemy of Aristotle, introduced some new modes that are adapted to
singular propositions; and that Aristotle takes no notice of singular
propositions, either in his rules of conversion, or in the modes of syllogism.
But the friends of Aristotle have shewn that this improvement of Ramus is more
specious than useful. Singular propositions have the force of universal
propositions, and are subject to the same rules. The definition given by
Aristotle of an universal proposition applies to them; and therefore he might
think, that there was no occasion to multiply the modes of syllogism upon their
account.
These attempts, therefore, shew rather
inclination than power to discover any material defect in Aristotle's theory.
The most valuable addition to the theory of
categorical syllogisms seems to be the invention of those technical names given
to the legitimate modes, by which they may easily be remembered, and which have
been comprised in these barbarous verses: -
Barbara, Celarent, Darii, Ferioque, dato primae; In these verses, every legitimate modes
belonging to the three figures has a name given to it, by which it may be
distinguished and remembered. And this name is so contrived as to denote its
nature; for the name has three vowels, which denote the kind of each of its
propositions.
Thus, a syllogism in Bocardo must be
made up of the propositions denoted by the three vowels O, A, O; that is, its
major and conclusion must be particular negative propositions, and its minor an
universal affirmative; and, being in the third figure, the middle term must be
the subject of both premises.
This is the mystery contained in the vowels
of these barbarous words. But there are other mysteries contained in their
consonants; for, by their means, a child may be taught to reduce any syllogism
of the second or third figure to one of the first. So that the four modes of
the first figure being directly proved to be conclusive, all the modes of the
other two are proved at the same time, by means of this operation of
reduction. For the rules and manner of this reduction, and the different
species of it, called direct or ostensive, and indirect or
per impossible, I refer to the Logicians, that I may not disclose all
their mysteries.
The invention contained in these verses is
so ingenious, and so great an adminicle to the dexterous management of
syllogisms, that I think it very probable that Aristotle had some contrivance
of this kind, which was kept as one of the secret doctrines of his school, and
handed down by tradition, until some person brought it to light. This is
offered only as a conjecture, leaving it to those who are better acquainted
with the most ancient commentators on the Analytics, either to refute it or
confirm it.
Section III
ON EXAMPLES USED TO ILLUSTRATE THIS THEORY
We may observe, that Aristotle hardly ever
gives examples of real syllogisms to illustrate his rules. In demonstrating
the legitimate modes, he takes A, B, C, for the terms of the syllogism. Thus,
the first mode of the first figure is demonstrated by him in this manner:-
'For,' says he, 'if A is attributed to every B, and B to every C, it follows
necessarily, that A may be attributed to every C.' For disproving the
illegitimate modes, he uses the same manner; with this difference, that he
commonly, for an example, gives three real terms, such as bonum, habitus,
prudentia: of which three terms you are to make up a syllogism of the
figure and mode in question, which will appear to be inconclusive.
The commentators and systematical writers
in logic have supplied this defect, and given us real examples of every
legitimate mode in all the figures. We acknowledged this to be charitably
done, in order to assist the conception in matters so very abstract; but whether
it was prudently done for the honour of the art, may be doubted. I am afraid
this was to uncover the nakedness of the theory. It has undoubtedly
contributed to bring it into contempt; for when one considers the silly and
uninstructive reasonings that have been brought forth by this grand organ of
science, he can hardly forbear crying out
'Parturiunt montes; nascetur ridiculus
mus
Many of the writers of logic are acute and
ingenious, and much practised in the syllogistical art; and there must be some reason
why the examples they have given of syllogisms are so lean.
We shall speak of the reason afterwards;
and shall now give a syllogism in each figure as an example.
No work of God is bad; In this syllogism, the middle term, 'work
of God,' is the subject of the major, and the predicate of the minor; so that
the syllogism is of the first figure. The mode is that called Celarent;
the major and conclusion being both universal negatives, and the minor and
universal affirmative. It agrees to the rules of the figure, as the major is
universal, and the minor affirmative; it is also agreeable to all the general
rules; so that it maintains its character in every trial. And to shew of what
ductile material syllogisms are made, we may, by converting simply the major
proposition, reduce it to a good syllogism of the second figure, and of the
mode Cesare, thus:-
Whatever is bad is not the work of God; Another example:
Every thing virtuous is praiseworthy; Here the middle term 'praiseworthy,' being
the predicate of both premises, the syllogism is of the second figure; and
seeing it is made of the propositions A, O, O, the mode is Baroco. It
will be found to agree both with the general and special rules; and it may be
reduced into a good syllogism of the first figure, upon converting the major by
contraposition, thus:-
What[ever] is not praiseworthy is not
virtuous; That this syllogism is conclusive, common
sense pronounces, and all Logicians must allow; but it is somewhat unpliable to
rules, and requires a little straining to make it tally with them.
That it is of the first figure is beyond
dispute; but to what mode of that figure shall we refer it?
This is a question of some difficulty, for,
in the first place, the premises seem to be both negative, which contradicts
the third general rule; and, moreover, it is contrary to a special rule of the
first figure, That the minor should be negative. These are the difficulties to
be removed.
Some logicians think that the two negative
particles in the major are equivalent to an affirmative; and that, therefore,
the major proposition, 'What[ever] is not praiseworthy is not virtuous,' is to
be accounted an affirmative proposition. This, if granted, solves one
difficulty; but the other remains. The most ingenious solution, therefore, is
this, Let the middle term be 'not-praiseworthy.' Thus, making the negative
particle a part of the middle term, the syllogism stands thus:-
Whatever is not-praiseworthy is not
virtuous; By this analysis, the major becomes an
universal negative, the minor a particular affirmative, and the conclusion a
particular negative, and so we have a just syllogism in Ferio.
We see, by this example, that the quality
of propositions is not so invariable, but that, when occasion requires, an
affirmative may be degraded into a negative, or a negative exalted into an
affirmative.
Another example:
All Africans are black; This is of the third figure, and of the
mode Darapti; and it may be reduced to Darii in the first figure,
by converting the minor.
All Africans are black; By this time I apprehend the reader had got
as many examples of syllogisms as will stay his appetite for that kind of
entertainment.
Section IV
ON THE DEMONSTRATION OF THE THEORY
Aristotle and all his followers have
thought it necessary, in order to bring this theory of categorical syllogisms
to a science, to demonstrate both that the fourteen authorised modes conclude
justly, and that none of the rest do. Let us now see how this has been
executed.
As to the legitimate modes, Aristotle and
those who follow him the most closely, demonstrate the four modes of the first
figure directly from an axiom called the Dictum de omni et nullo. The
amount of the axiom is this, That what is affirmed of a whole genus may by
affirmed of all the species and individuals belonging to that genus; and that
what is denied of the whole genus may be denied of all its species and
individuals. The four modes of the first figure are evidently included in
this axiom. And as to the legitimate modes of the other figures, they are
proved by reducing them to some mode of the first. Nor is there any other
principle assumed in these reductions but the axioms concerning the conversion
of propositions, and, in some cases, the axioms concerning the opposition of
propositions.
As to the illegitimate modes, Aristotle has
taken the labour to try and condemn them one by one in all the three figures:
But this is done in such a manner that it is very painful to follow him. To
give a specimen: In order to prove that those modes of the first figure, in
which the major is particular do not conclude, he proceeds thus:- 'If A is, or
is not, in some B, and B in every C, no conclusion follows. Take for the terms
in the affirmative case, good, habit, prudence; in the negative, good
habit, ignorance.' This laconic style, the use of symbols not familiar,
and, in place of giving an example, his leaving us to form one from three
assigned terms, give such embarrassment to a reader, that he is like one
reading a book of riddles.
Having thus ascertained the true and false
modes of a figure, he subjoins the particular rules of that figure, which seem
to be deduced from the particular cases before determined. The general rules
come last of all, as a general corollary from what goes before.
I know not whether it is from a diffidence
of Aristotle's demonstrations, or from an apprehension of their obscurity, or
from a desire of improving upon his method, that almost all the writers I have
met with have inverted his order, beginning where he ends, and ending where he
begins. They first demonstrate the general rules, which belong to all the
figures, from three axioms; then, from the general rules and the nature of each
figure, they demonstrate the special rules of each figure. When this is done,
nothing remains but to apply these general and special rules, and to reject
every mode which contradicts them.
This method has a very scientific
appearance; and when we consider that, by a few rules once demonstrated, and
hundred and seventy-eight false modes are destroyed at one blow, which
Aristotle had the trouble to put to death one by one, it seems to be a great
improvement. I have only one objection to the three axioms.
The three axioms are these: 1. Things
which agree with the same third agree with one another. 2. When one agrees
with the third, and the other does not, they do not agree with one another. 3.
When neither agrees with the third, you cannot thence conclude, either that
they do, or do not agree with one another. If these axioms are applied to
mathematical quantities, to which they seem to relate when taken literally,
they have all the evidence of that an axiom ought to have; but the Logicians
apply them in an analogical sense to things of another nature. In order,
therefore, to judge whether they are truly axioms, we ought to strip them of their
figurative dress, and to set them down in plain English, as the Logicians
understand them. They amount, therefore, to this:- 1. If two things be
affirmed of a third, or the third be affirmed of them; or if one be affirmed of
the third, and the third be affirmed of the other; then they may be affirmed
one of the other. 2. If one is affirmed of the third, or the third of it, and
the other denied of the third, and the other denied of the third, or the third
of it, they may be denied one of the other. 3. If both are denied of the
third, or the third of them, or if one is denied of the third, and the third
denied of the other, nothing can be inferred.
When the three axioms are thus put in plain
English, they seem not to have that degree of evidence which axioms ought to
have; and, if there is any defect of evidence in the axioms, this defect will
be communicated to the whole edifice raised upon them.
It may even be suspected, that an attempt,
by any method, to demonstrate that a syllogism is conclusive, is an impropriety
somewhat like that of attempting to demonstrate an axiom. In a just syllogism,
the connection between the premises and the conclusion is not only real, but
immediate; so that no proposition can come between them to make their
connection more apparent. The very intention of a syllogism is to leave
nothing to be supplied that is necessary to a complete demonstration.
Therefore, a man of common understanding, who has a perfect comprehension of
the premises, finds himself under a necessity of admitting the conclusion,
supposing the premises to be true; and the conclusion is connected with the
premises with all the force of intuitive evidence. In a word, an immediate
conclusion is seen in the premises by the light of common sense; and, where
that is wanting, no kind of reasoning will supply its place.
Section V
ON THIS THEORY, CONSIDERED AS AN ENGINE OF
SCIENCE
The slow progress of useful knowledge,
during the many ages in which the syllogistic art was most highly cultivated as
the only guide to science, and its quick progress since that art was disused,
suggest a presumption against it; and this presumption is strengthened by the
puerility of the examples which have always been brought to illustrate its
rules.
The ancients seem to have had too high
notions, both of the force of the reasoning power in man, and of the art of
syllogism as its guide. Mere reasoning can carry us but a very little way in
most subjects. By observation, and experiments properly conducted, the stock
of human knowledge may be enlarged without end; but the power of reasoning
alone, applied with vigour through a long life, would only carry a man round
like a horse in a mill, who labours hard but makes no progress. There is
indeed an exception to this observation in the mathematical sciences. The
relations of quantity are so various, and so susceptible of exact mensuration,
that long trains of accurate reasoning on that subject may be formed, and
conclusions drawn, very remote from the first principles. It is in this
science, and those which depend upon it, that the power of reasoning triumphs;
in other matters, its trophies are inconsiderable. If any man doubt this, let
him produce, in any subject unconnected with mathematics, a train of reasoning
of some length, leading to a conclusion which, without this train of reasoning,
would never have been brought within human sight. Every man acquainted with
mathematics can produce thousands of such trains of reasoning. I do not say
that none such can be produced in other sciences; but I believe they are few,
and not easily found; and that, if they are found, it will not be in subjects
that can be expressed by categorical propositions, to which alone the theory of
figure and mode extends.
In matters to which that theory extends, a
man of good sense, who can distinguish things that differ, who can avoid the
snares of ambiguous words, and who is moderately practised in such matters,
sees at once all that can be inferred from such premises, or finds that there
is but a very short step to the conclusion.
When the power of reasoning is so feeble by
nature, especially in subjects to which this theory can be applied, it would be
unreasonable to expect great effects from it. And hence we see the reason why
the examples brought to illustrate it by the most ingenious Logicians have
rather tended to bring it into contempt.
If it should be thought that the
syllogistic art may be an useful engine in mathematics, in which pure reasoning
has ample scope: First, it may be observed, that facts are unfavourable to this
opinion: For it does not appear that Euclid, or Apollonius, or Archimedes, or
Huygens, or Newton, ever made the least use of this art; and I am even of
opinion that no use can be made of it in mathematics. I would not wish to
advance this rashly, since Aristotle has said, that most mathematicians reason
in the first figure. What led him to think so was, that the first figure only
yields conclusions that are universal and affirmative, and the conclusions of
mathematics are commonly of that kind. But it is to be observed, that the
propositions of mathematics are not categorical propositions, consisting of one
subject and one predicate. They express some relation which one quantity bears
to another, and on the account must have three terms. The quantities compared
make two, and the relation between them is a third. Now, to such propositions
we can neither apply the rules concerning the conversion of propositions, nor
can they enter into a syllogism of any of the figures or modes. We observed
before, that this conversion, A is greater than B, therefore B is
less than A, does not fall within the rules of conversion given by
Aristotle or the Logicians; and we now add, that this simple reasoning, A is
equal to B, and B to C, therefore A is equal to C, cannot be brought
into any syllogism in figure and mode. There are indeed syllogisms into which
mathematical propositions may enter, and of such we shall afterwards speak: but
they have nothing to do with the system of figure and mode.
When we go without the circle of the
mathematical sciences, I know nothing in which there seems to be so much
demonstration as in that part of logic which treats of the figures and modes of
syllogism; but the few remarks we have made, shew that it has some weak places;
and, besides, this system cannot be used as an engine to rear itself.
The compass of the syllogistic system, as
an engine of science, may be discerned by a compendious and general view of the
conclusion drawn, and the argument used to prove it, in each of the three
figures.
In the first figure, the conclusion affirms
or denies something of a certain species or individual; and the argument to
prove the conclusion is this, That the same thing may be affirmed or denied
of the whole genus to which that species or individual belongs.
In the second figure, the conclusion is,
That some species or individual does not belong to such a genus; and the
argument is, That some attribute common to the whole genus does not belong
to that species or individual.
In the third figure, the conclusion is,
That such an attribute belongs to part of a genus; and the argument is, That
the attribute in question belongs to a species or individual which is part of
that genus.
I apprehend that, in this short view, every
conclusion that falls within the compass of the three figures, as well as the
mean of proof, is comprehended. The rules of all the figures might be easily
deduced from it; and it appears that there is only one principle of reasoning
in all the three; so that it is not strange that a syllogism of one figure
should be reduced to one of another figure.
The general principle in which the whole
terminates, and of which every categorical syllogism is only a particular
application, is this, That what is affirmed or denied of the whole genus may
be affirmed or denied of every species and individual belonging to it This
is a principle of undoubted certainty indeed, but of no great depth. Aristotle
and all the Logicians assume it as an axiom, or first principle, from which the
syllogistic system, as it were, takes its departure; and, after a tedious
voyage, and great expense of demonstration, it lands at last in this principle,
as its ultimate conclusion.
"O curas hominum! O quantum est in
rebus inane!"
Section VI
ON MODAL
SYLLOGISMS
Categorical propositions, besides their quantity and quality, have another affection, by
which they are divided into pure and modal. In a pure
proposition, the predicate is barely affirmed or denied of the subject; but, in
a modal proposition, the affirmation or negation is modeified, by being
declared to be necessary, or contingent, or impossible.
These are the four modes observed by Aristotle, from which he denominates a
proposition modal. His genuine disciples maintain, that these are all the
modes that can affect an affirmation or negation, and that the enumeration is
complete. Others maintain, that this enumeration is incomplete; and that, when
an affirmation or negation is said to be certain or uncertain, probable or
improbable, this makes a modal proposition, no less than the four modes of
Aristotle. We shall not enter into this dispute, but proceed to observe, that
the epithets of pure and modal are applied to syllogisms as well
as to propositions. A pure syllogism is that in which both premises are pure
propositions. A modal syllogism is that in which either of the premises is a
modal proposition. The syllogismsof which we have already said so much, are those only which are pure as well as
categorical. But, when we consider, that, through all the figures and modes, a
syllogism may have one premise modal of any of the four modes, while the other
is pure, or it may have both premises modal, and that they may be either of the
same mode, or of different modes, what prodigious variety arises from all these
combinations? Now, it is the business of a Logician to shew how the conclusion
is affected in all this variety of cases. Aristotle has done this in his first
Analytics with immense labour; and it will not be thought strange that, when he
had employed only four chapters in discussing one hundred and ninety-two modes,
true and false, of pure syllogisms, he should employ fifteen upon modal
syllogisms.
I am very willing to excuse myself from entering upon this great branch of logic, by the
judgment and example of those who cannot be charged either with want of respect
to Aristotle, or with a low esteem of the syllogistic art. Keckermann, a famous Dantiscan professor, who spent his life in teaching and writing logic,
in his huge folio system of that science, published anno 1600, calls the
doctrine of the modals the crux Logicorum. With regard to the
scholastic doctors among whom this was a proverb, De modali non gustabit
asinus, he thinks it very dubious whether they tortured most the modal
syllogisms, or were tortured by them. But those crabbed geniuses, says he,
made this doctrine so very thorny that it is fitter to tear a man's wits in
pieces than to give them solidity. He desires it to be observed, that the doctrine
of the modals is adapted to the Greek language. The modal terms were
frequently used by the Greeks in their disputations, and, on that account, are
so fully handled by Aristotle; but, in disputations in the Latin tongue, you
shall hardly ever meet with them. Nor do I remember, in all my experience,
says he, to have observed any man in danger of being foiled in a dispute,
through his ignorance of the modals.
This author,
however, out of respect to Aristotle, treats pretty fully of modal
propositions, shewing how to distinguish their subject and predicate, their
quantity and quality. But the modal syllogism he passes over altogether.
Ludovicus
Vives, whom I mention, not as a devotee of Aristotle, but on account of his own
judgment and learning, thinks that the doctrine of modals ought to be banished
out of logic, and remitted to grammar; and that, if the grammar of the Greek
tongue had been brought to a system in the time of Aristotle, that most acute
philosopher would have saved the great labour he has bestowed on this subject.
Burgersdyke,
after enumerating five classes of modal syllogisms, observes, that they require
many rules and cautions, which Aristotle hath handled diligently; but that, as
the use of them is not great, and their rules difficult, he thinks it not worth
while to enter into the discussion of them; recommending to those who would
understand them, the most learned paraphrase of Johannes Monlorius upon the
first book of the First Analytics.
All the writers
of logic for two hundred years back, that have fallen into my hands, have
passed over the rules of modal syllogisms with as little ceremony. So that
this great branch of the doctrine of syllogisms, diligently handled by
Aristotle, fell into neglect, if not contempt, even while the doctrine of pure
syllogisms continued in the highest esteem. Moved by these authorities, I
shall let this doctrine rest in peace, without giving the least disturbance to
its ashes.
ON SYLLOGISMS
THAT DO NOT BELONG TO FIGURE AND MODE
Aristotle gives
some observations upon imperfect syllogisms; such as the Enthymeme, in
which one of the premises is not expressed, but understood; Induction,
wherein we collect an universal from a full enumeration of particulars; and Example,
which is an imperfect induction. The Logicians have copied Aristotle, upon
these kinds of reasoning, without any considerable improvement. But, to
compensate the modal syllogisms, which they have laid aside, they have given
rules for several kinds of syllogism, of which Aristotle takes no notice.
These may be reduced to two classes.
The first
class comprehends the syllogisms into which any exclusive, restrictive,
exceptive, or reduplicative proposition enters. Such propositions
are by some called Exponible, by others Imperfectly (or
Secondarily) Modal. The rules given with regard to these are
obvious, from a just interpretation of the propositions.
The second
class is that of Hypothetical syllogisms, which take that
denomination from having a hypothetical proposition for one or both premises.
Most logicians give the name of hypothetical to all complex propositions
which have more terms than one subject and one predicate. I use the word in
this large sense, and mean, by hypothetical syllogisms, all those in which
either of the premises consists of more terms than two. How many various kinds
there may be of such syllogisms, had never been ascertained. The Logicians
have given names to some; such as the copulative, the conditional,
(by some called hypothetical,) and the disjunctive.
Such syllogisms
cannot be tried by the rules of figure and mode. Every kind would require
rules peculiar to itself. Logicians have given rules for some kinds; but there
are many that have not so much as the name.
The Dilemma
is considered by most Logicians as a species of the disjunctive syllogism. A
remarkable property of this kind is, that it may sometimes by happily retorted:
it is, it seems, like a hand-grenade, which, by dextrous management, may be
thrown back, so as to spend its force upon the assailant. We shall conclude
this tedious account of syllogisms with a dilemma mentioned by Aulus Gellius,
and from him by many Logicians, as insoluble in any other way.
'Euathlus, a rich
young man, desirous of learning the art of pleading, applied to Protogoras, a
celebrated sophist, to instruct him, promising a great sum of money as his
reward; one half of which was paid down; the other half he bound himself to pay
as soon as he should plead a cause before the judges and gain it. Protogoras
found him a very apt scholar; but, after he had made good progress, he was in
no haste to plead causes. The master, conceiving that he intended by this
means to shift off his second payment, took, as he thought, a sure method to
get the better of his delay. He sued Euathlus before the judges; and, having
opened his cause at the bar, he pleaded to this purpose:- 'O most foolish young
man, do you not see that, in any event, I must gain my point? - for, if the
judges give sentence for me, you must pay by their sentence; if against me, the
condition of your bargain is fulfilled, and you have no plea left for you
delay, after having pleaded and gained a cause.' To which Euathlus answered:-
'O most wise master, I might have avoided the force of your argument, by not
pleading my own cause. But, giving up this advantage, do you not see that,
whatever sentence the judges pass, I am safe? If they give sentence for me, I
am acquitted by their sentence; if against me, the condition of our bargain is
not fulfilled, by my pleading a cause, and losing it.' The judges, thinking
the arguments unanswerable on both sides, put off the cause to a long day.'
CHAPTER V
ACCOUNT OF THE REMAINING BOOKS OF THE
ORGANON
Section I
OF THE LAST ANALYTICS
In the first analytics, syllogisms are
considered in respect of their form; they are now to be considered in
respect of their matter. The form lies in the necessary connection
between the premises and the conclusion; and, where such a connection is
wanting, they are said to be informal, or vicious in point of form.
But, where there is no fault in the form,
there may be in the matter - that is, in the propositions of which they are
composed, which may be true or false, probable or improbable.
When the premises are certain, and the
conclusion drawn from them on due form, this is demonstration, and
produces science. Such syllogisms are called apodeictical, and
are handled in the two books of the Last Analytics. When the premises are not
certain, but probable only, such syllogisms are called dialectical; and
of them he treats in the eight books of the Topics. But there are some
syllogisms which seem to be perfect both in matter and form, when they are not
really so; as, a face may seem beautiful which is but painted. There being apt
to deceive, and produce a false opinion, are called sophistical; and
they are the subject of the book concerning Sophisms.
To return to the Last Analytics, which
treat of demonstration and of science: We shall not pretend to
abridge those books, for Aristotle's writings do not admit of abridgement; no
man, in fewer words, can say what he says; and he is not often guilty of
repetition. We shall only give some of his capital conclusions, omitting his
long reasoning and nice distinctions, of which his genius was wonderfully
productive.
All demonstration must be built upon
principles already known, and these upon others of the same kind; until we come
at last to first principles, which neither can be demonstrated, nor need to be,
being evident of themselves.
We cannot demonstrate things in a circle,
supporting the conclusion by the premises, and the premises by the conclusion.
Nor can there be an infinite number of middle terms between the first principle
and the conclusion.
In all demonstration, the first principles,
the conclusion, and all the intermediate propositions, must be necessary,
general and eternal truths; for , of things fortuitous, contingent, or mutable,
or of individual things, there is no demonstration.
Some demonstrations prove only, that
the thing is thus affected; others prove, why it is thus affected. The
former may be drawn from a remote cause, or from an effect; but the latter must
be drawn from an immediate cause, and are the most perfect.
The first figure is best adapted to
demonstration, because it affords conclusions universally affirmative; and this
figure is commonly used by the mathematicians.
The demonstration of an affirmative
proposition is preferable to that of a negative; the demonstration of an
universal to that of a particular; and direct demonstration to that ad absurdum.
The principles are more certain than the
conclusion.
There cannot be opinion and science of the
same thing at the same time.
In the second book, we are taught, that the
questions that may be put with regard to any thing are four: 1. Whether
the thing be thus affected. 2. Why it is thus affected. 3. Whether
it exists. 4. What it is.
The last of these questions, Aristotle, in
good Greek, calls the What is it of a thing. The schoolmen, in very
barbarous Latin, called this the quiddity of a thing. This quiddity, he
proves by many arguments, cannot be demonstrated, but must be fixed by a
definition. This gives occasion to treat of definition, and how a right
definition should be formed. As an example, he gives a definition of the number
three, and defines it to be the first odd number.
In this book he treats also of the four
kinds of cause - efficient, material, formal, and final.
Another thing treated of in this book is,
the manner in which we acquire first principles, which are the foundations of
all demonstration. These are not innate, because we may be, for a great part
of life, ignorant of them: nor can they be deduced demonstratively from any
antecedent knowledge, otherwise they would not be first principles. There he
concludes, that first principles are got by induction, from the informations of
sense. The senses give us informations of individual things, and from these by
induction we draw general conclusions; for it is a maxim with Aristotle, That
there is nothing in the understanding which was not before in some sense.
The knowledge of first principles, as it is
not acquired by demonstration, ought not to be called science; and therefore he
calls in intelligence.
Section II
OF THE TOPICS
The professed design of the Topics is, to
shew a method by which a man may be able to reason with probability and
consistency upon every question that can occur.
Every question is either about the genus
of the subject, or its specific difference, or something proper
to it, or something accidental.
To prove that this division is complete,
Aristotle reasons thus: Whatever is attributed to a subject, it must either be,
that the subject can be reciprocally attributed to it, or that it cannot. If
the subject and attribute can be reciprocated, the attribute either declares
what the subject is, and then it is a definition; or it does not declare what
the subject is, and then it is a property. If the attribute cannot be
reciprocated, it must be something contained in the definition, or not. If it
be contained in the definition of the subject, it must be the genus of the
subject, or its specific difference; for the definition consists of these two.
If it be not contained in the definition of the subject, it must be an
accident.
The instruments by which we may supply
ourselves with the furniture proper to fit a man for arguing dialectically may
be reduced to these four heads: 1. To make choice of probable propositions of
all sorts, which may on occasion be assumed in an argument. 2. To take
distinctions of words which are nearly of the same signification. 3. To mark
the distinctions of things which are not so far asunder but that they may be
taken for one and the same. 4. To consider similitudes.
The second and the five following books are
taken up in enumerating the topics or heads of argument that may be used
in questions about the genus, the definition, the properties, and the accidents
of a thing; and occasionally he introduces the topics for proving things to be
the same or different, and the topics for proving one thing to be better or
worse than another.
In this enumeration of topics, Aristotle
has shewn more the fertility of his genius than the accuracy of method. The
writers of logic seem to be of this opinion; for I know none of them that has
followed him closely upon this subject. They have considered the topics of
argumentation as reducible to certain axioms. For instance, when the question
is about the genus of a thing, it must be determined by some axiom about genus
and species; when it is about a definition, it must be determined by some axiom
relating to definition, and things defined; and so of other questions. They
have therefore reduced the doctrine of the topics to certain axioms or canons,
and disposed these axioms in order under certain heads.
This method seems to be more commodious and
elegant than that of Aristotle. Yet it must be acknowledged that Aristotle has
furnished the materials from which all the logicians have borrowed their
doctrine of topics; and even Cicero, Quintilian, and other rhetorical writers,
have been much indebted to the topics of Aristotle.
He was the first, as far as I know, who
made an attempt of this kind; and in this he acted up to the magnanimity of his
own genius, and that of ancient philosophy. Every subject of human thought had
been reduced ten categories; everything that can be attributed to any subject,
to five predicables; he attempted to reduce all the forms of reasoning to fixed
rules of figure and mode, and to reduce all the topics of argumentation under
certain heads; and by that means to collect, as it were, into one store, all
that can be said on one or the other of every question, and to provide a grand
arsenal, from which all future combatants might be furnished with arms,
offensive and defensive, in every cause, so as to leave no room to future
generations to invent anything new.
The last books of the Topics is a code of
the laws according to which a syllogistical disputation ought to be managed,
both on the part of the assailant and defendant. From which it is evident, that
this philosopher trained his disciples to contend, not for truth merely, but
for victory.
Section III
OF THE BOOK CONCERNING SOPHISMS
A syllogism which leads to a false
conclusion must be vicious, either in matter or form; for, from true
principles, nothing but truth can be justly deduced. If the matter be faulty -
that is, if either of the premises be false, that premise must be denied by the
defendant. If the form be faulty, some rule of syllogism is transgressed; and
it is the part of the defendant to shew what general or special rule it is that
is transgressed; so that, if he be an able logician, he will be impregnable in the
defence of truth, and may resist all the attacks of the sophist. But, as there
are syllogisms which may seem to be perfect both in matter and form, when they
are not really so, as piece of money may seem to be good coin when it is
adulterate, such fallacious syllogisms are considered in this treatise, in
order to make a defendant more expert in the use of his defensive weapons.
And here the author, with his usual
magnanimity, attempts to bring all the Fallacies that can enter into a
syllogism under thirteen heads; of which six lie in the
diction or language, and seven not in the diction.
The Fallacies in diction are, 1.
When an ambiguous word is taken at one time in one sense, and at another time
in another. 2. When an ambiguous phrase is taken in the same manner. 3. and
4. are ambiguities in syntax; when words are conjoined in syntax that ought to
be disjoined, or disjoined when they ought to be conjoined. 5. is an ambiguity
in prosody, accent, or pronunciation. 6. An ambiguity arising from some figure
of speech.
When a sophism of any of these kinds is
translated into another language, or even rendered into unambiguous expressions
in the same language, the fallacy is evident, and the syllogism appears to have
four terms.
The seven fallacies which are said not to
be in the diction, but in the thing, have their proper names in Greek and in
Latin, by which they are distinguished. Without minding their names, we shall
give a brief account of their nature.
1. The first is, Taking an accidental
conjunction of things for a natural or necessary connection: as, when from an
accident we infer a property; when from an example we infer a rule; when from a
single act we infer a habit.
2. Taking that absolutely which ought to be
taken comparatively, or with a certain limitation. The constitution of
language often leads into this fallacy; for, in all languages it is common to
use absolute terms to signify things that carry in them some secret comparison;
or, to use unlimited terms, to signify what from its nature must be limited.
3. Taking that for a cause of a thing which
is only an occasion, or concomitant.
4. Begging the question. This is done when
the thing to be proved, or something equivalent, is assumed in the premises.
5. Mistaking the question. When the
conclusion of the syllogism is not the thing that ought to be proved, but
something else that is mistaken for it.
6. When that which is not a consequence is mistaken
for a consequence; as if, because all Africans are black, it were taken for
granted that all blacks are African.
7. The last fallacy lies in propositions
that are complex and imply two affirmations, whereof one may be true, and the
other false; so that, whether you grant the proposition or deny it, you are
entangled; as when it is affirmed that such a man has left off playing the fool.
If it be granted, it implies that he did play the fool formerly; if it be
denied, it implies, or seems to imply, that he plays the fool still.
In this enumeration, we ought, in justice
to Aristotle, to expect only the fallacies incident to categorical syllogisms.
And I do not find that the Logicians have made any additions to it when taken
in this view, although they have given some other fallacies that are incident
to syllogisms of the hypothetical kind, particularly the fallacy of an
incomplete enumeration in disjunctive syllogisms and dilemmas.
The different species of sophisms above
mentioned are not so precisely defined by Aristotle, or by subsequent
logicians, but that they allow of great latitude in the application; and it is
often dubious under what particular species a sophistical syllogism ought to be
classed. We even find the same example brought under one species by one author,
and under another species by another. Nay, what is more strange, Aristotle
himself employs a long chapter in proving, by a particular induction, that all
the seven may be brought under that which we have called mistaking the
question, and which is commonly called ignoratio elenchi. And,
indeed, the proof of this is easy, without that laborious detail which
Aristotle uses for the purpose; for if you lop off from the conclusion of a
sophistical syllogism all that is not supported by the premises, the conclusion
in that case will always be found different from that which ought to have been
proved; and so it falls under the ignoratio elenchi.
It was probably not Aristotle's aim to
reduce all the possible variety of sophisms, as he had attempted to do of just
syllogisms, to certain definite species; but he seems to be sensible that he
had fallen short in this last attempt. When a genus is properly divided into
its species, the species should not only, when taken together, exhaust the
whole genus, but every species should have its own precinct so accurately
defined that one wall not encroach upon another. And when an individual can be
said to belong to two or three different species, the division is imperfect;
yet this is the case of Aristotle's division of the sophisms, by his own
acknowledgment. It ought not, therefore, to be taken for a division strictly
logical. It may rather be compared to the several species or forms of action
invented in law for the redress of wrongs. For every wrong there is a remedy
in law by one action or another; but sometimes a man may take his choice among
several different actions. So every sophistical syllogism may, by a little
art, be brought under one or other of the species mentioned by Aristotle, and
very often you may take your choice of two or three.
Besides the enumeration of the various kinds of sophisms, there are many other things
in this treatise concerning the art of managing a syllogistical dispute with an
antagonist. And indeed, if the passion for this kind of litigation, which
reigned for so many ages, should ever again lift up its head, we may predict,
that the Organon of Aristotle will then become a fashionable study; for it
contains such admirable materials and documents for this art, that it may be
said to have brought it to a science.
The conclusion of this treatise ought not to be overlooked; it manifestly relates,
not to the present treatise only, but also to the whole analytics and topics of
the author. I shall therefore give the substance of it:-
'Of those who may be called inventors, some have made important additions to things
long before begun and carried on through a course of ages; others have given a
small beginning to things which, in succeeding times, will be brought to
greater perfection. The beginning of a thing, though small, is the chief part
of it, and requires the greatest degree of invention; for it is easy to make
additions to inventions once begun.
'Now, with regard to the dialectical art, there was not something done, and something
remaining to be done. There was absolutely nothing done; for those who
professed the art of disputation had only a set of orations composed, and of
arguments, and of captious questions, which might suit many occasions. These,
their scholars soon learned, and fitted to the occasion. This was not to teach
you the art, but to furnish you with the materials produced by the art; as if a
man professing to teach you the art of making shoes should bring you a parcel
of shoes of various sized and shapes, from which you may provide those who want.
This may have its use; but is not to teach the art of making shoes. And
indeed, with regard to rhetorical declamation, there are many precepts handed
down from ancient times; but, with regard to the construction of syllogisms,
not one.
'We have, therefore, employed much time and labour upon this subject; and if our
system appear to you not to be in the number of those things which, being
before carried a certain length, were left to be perfected, we hope for your
favourable acceptance of what is done, and your indulgence in what is left
imperfect.
CHAPTER VI.
REFLECTIONS ON THE UTILITY OF LOGIC, AND THE MEANS OF ITS IMPROVEMENT
Section I
OF THE UTILITY OF LOGIC
Men rarely leave one extreme without running into the contrary. It is no wonder,
therefore, that the excessive admiration of Aristotle, which continued for so
many ages, should end in an undue contempt; and that the high esteem of logic,
as the grand engine of science, should at last make way for too unfavourable an
opinion, which seems now prevalent, of its unworthy of a place in a liberal
education. Those who think according to the fashion, as the greatest part of
men do, will be as prone to go into this extreme as their grandfathers were to
go into the contrary.
Laying aside prejudice, whether fashionable or unfashionable, let us consider whether
logic is, or may be made, subservient to any good purpose. Its professed end
is, to teach men to think, to judge, and to reason, with precision and
accuracy. No man will say that this is a matter of no importance; the only
thing, therefore, that admits of doubt is, whether it can be taught.
To resolve this doubt, it may be observed, that our rational faculty is the gift
of God, given to men in very different measure. Some have a larger portion,
some a less; and where there is a remarkable defect of the natural power, it
cannot be supplied by any culture. But this natural power, even where it is
the strongest, may lie dead for want of the means of improvement: a savage may
have been born with as good faculties as a Bacon or a Newton: but his talent
was buried, being never put to use; while theirs was cultivated to the best
advantage.
It may be likewise observed, that the chief mean of improving our rational power,
is the vigorous exercise of it, in various and in different subjects, by which
the habit is acquired of exercising it properly. Without such exercise, and
good sense over and above, a man who has studied logic all his life may, after
all, be only a petulant wrangler, without true judgment or skill of reasoning
in any science.
I take this to be Locke's meaning, when, in his 'Thoughts on Education,' he says,
'If you would have your son to reason well, let him read Chillingworth.' The
state of things is much altered since Locke wrote. Logic has been much
improved, chiefly by his writings; and yet much less stress is laid upon it,
and less time consumed in it. His counsel, therefore, was judicious and
seasonable - to with, That the improvement of our reasoning power is to be
expected much more from an intimate acquaintance with the authors who reason
the best, than from studying voluminous systems of logic. But if he had meant
that the study of logic was no use, nor deserved any attention, he surely would
not have taken the pains to have made so considerable an addition to it by his
'Essay on the Human Understanding' and by his 'Thoughts on the Conduct of the
Understanding.' Nor would he have remitted his pupil to Chillingworth, the
acutest logician as well as the best reasoner of his age; and one who, in
innumerable places of his excellent book, without pedantry even in that
pedantic age, makes the happiest application of the rules of logic, for
unravelling the sophistical reasoning of his antagonist.
Our reasoning power makes no appearance in infancy; but as we grow up, it unfolds
itself by degrees, like the bud of a tree. When a child first draws an
inference, or perceives the force of an inference drawn by another, we may call
this the birth of his reason; but it is yet like a newborn babe, weak
and tender; it must be cherished, carried in arms, and have food of easy
digestion, till it gathers strength.
I believe no man remembers the birth of his reason: but it is probable that his
decisions are at first weak and wavering; and, compared with that steady
conviction which he acquires in ripe years, are like the dawn of the morning
compared with noon-day. We see that the reason of children yields to
authority, as a reed to the wind; nay, that it clings to it, and leans upon it,
as if conscious of its own weakness.
When reason acquires such strength as to stand on its own bottom, without the aid of
authority, or even in opposition to authority, this may be called its manly
age. But, in most men, it hardly ever arrives at this period. Many, by
their situation in life, have not the opportunity of cultivating their rational
powers. Many, from the habit they have acquired of submitting their opinions
to the authority of others, or from some other principle which operates more
powerfully than the love of truth, suffer their judgment to be carried along to
the end of their days, either by the authority of a leader, or of a party, or
of the multitude, or by their own passions. Such persons, however learned,
however acute, may be said to be all their days children in understanding.
They reason, they dispute, and perhaps write; but it is not that they may find
the truth, but that they may defend opinions which have descended to them by
inheritance, or into which they have fallen by accident, or been led by
affection.
I agree with Mr Locke, that there is no study better fitted to exercise and
strengthen the reasoning powers, than that of the mathematical sciences - for
two reasons: first, Because there is no other branch of science which gives
such scope to long and accurate trains of reasoning; and, secondly, Because, in
mathematics, there is no room for authority, nor for prejudice of any kind,
which may give a false bias to the judgment.
When a youth of moderate parts begins to study Euclid, everything at first is new to
him. His apprehension is unsteady; his judgment is feeble, and rests partly
upon the evidence of the thing, and partly upon the authority of his teacher.
But, every time he goes over the definitions, the axioms, the elementary
propositions, more light breaks in upon him; the language becomes familiar, and
conveys clear and steady conceptions; the judgment is confirmed; he begins to
see what demonstration is; and it is impossible to see it without being charmed
with it. He perceives it to be a kind of evidence that has no need of
authority to strengthen it. He finds himself emancipated from that bondage,
and exults so much in this new state of independence, that he spurns at
authority, and would have demonstration for everything, until experience
teaches him that this is a kind of evidence which cannot be had in most things;
and that, in his most important concerns, he must rest contented with
probability.
As he goes on in mathematics, the road of demonstration becomes smooth and easy;
he can walk in it firmly, and take wider steps; and at last he acquires the
habit, not only of understanding a demonstration, but of discovering and
demonstrating mathematical truths.
Thus a man, without rules of logic, may acquire a habit of reasoning justly in
mathematics; and I believe he may, by like means, acquire a habit of reasoning
justly in mechanics, in jurisprudence, in politics, or in any other science.
Good sense, good examples, and assiduous exercise, may bring a man to reason
justly and acutely in his own profession, without rules.
But if any man think, that, from this concession, he may infer the inutility of
logic, he betrays a great want of that art by this inference; for it is no
better reasoning than this, That because a man may go from Edinburgh to London
by the way of Paris, therefore any other road is useless.
There is perhaps no practical art which may not be acquired, in a very considerable
degree, by example and practice, without reducing it to rules. But practice,
joined with rules, may carry a man in his art farther, and more quickly, than
practice without rules. Every ingenious artist knows the utility of having his
art reduced to rules, and by that means made a science. He is thereby
enlightened in his practice, and works with more assurance. By rules, he
sometimes corrects his own errors, and often detects the errors of others; he
finds them of great use to confirm his judgment, to justify what is right, and
to condemn what is wrong.
Is it of no use reasoning to be well acquainted with the various powers of the
human understanding, by which we reason? Is it of no use to resolve the
various kinds of reasoning into their simple elements, and to discover, as far
as we are able, the rules by which these elements are combined in judging and
in reasoning? Is it of no use to mark the various fallacies in reasoning, by
which even the most ingenious men have been led into error? It must surely
betray great want of understanding, to think these things useless or
unimportant. These are the things which Logicians have attempted, and which
they have executed; not, indeed, so completely as to leave no room for
improvement, but in such a manner as to give very considerable aid to our
reasoning powers. That the principles laid down with regard to definition and
division, with regard to the conversion and opposition of propositions, and the
general rules of reasoning, are not without use, is sufficiently apparent from
the blunders committed by those who disdain any acquaintance with them.
Although the art of categorical syllogism is better fitted for scholastic litigation
than for real improvement in knowledge, it is a venerable piece of antiquity,
and a great effort of human genius. We admire the pyramids of Egypt, and the
wall of China, though useless burdens upon the earth; we can bear the most
minute description of them, and travel hundreds of leagues to see them: if any
person should, with sacrilegious hands, destroy or deface them, his memory
would be had in abhorrence. The predicaments and predicables, the rules of
syllogism, and thye topics, have a like title to our veneration as antiquities;
they are uncommon efforts, not of human power, but of human genius; and they
make a remarkable period in the progress of human reason.
The prejudice against logic has probably been strengthened by its being taught too
early in life. Boys are often taught logic as they are taught their creed,
when it is an exercise of memory only, without understanding. One may as well
expect to understand grammar before he can speak, as to understand logic before
he can reason. It must even be acknowledged, that commonly we are capable of
reasoning in mathematics more early than in logic. The objects presented to
the mind in this science are of a very abstract nature, and can be distinctly
conceived only when we capable of attentive reflection upon the operations of
our own understanding, and after we have been accustomed to reason. There may
be an elementary logic, level to the capacity of these who have been but little
exercised in reasoning; but the most important parts of this science require a
ripe understanding, capable of reflecting upon its own operations. Therefore,
to make logic the first branch of science that is to be taught, is an old error
that ought to be corrected.
Section II
OF THE IMPROVEMENT OF LOGIC.
In compositions of human thought, expressed by speech or by writing, whatever is
excellent and whatever is faulty fall within the province, either of grammar,
or of rhetoric, or of logic. Propriety of expression is the province of
grammar; grace, elegance, and force, in thought and in expresssion, are the
province of rhetoric; justness and accuracy of thought are the province of
logic.
The faults in composition, therefore, which fall under the censure of logic, are
obscure and indistinct conceptions, false judgment, inconclusive reasoning, and
all improprieties in distinctions, definitions, division, or method. To aid
our rational powers in avoiding these faults, and in attaining the opposite
excellencies, is the end of logic; and whatever there is in it that has no
tendency to promote this end, ought to be thrown out.
The rules of logic being of a very abstract nature, ought to be illustrated by a
variety of real and striking examples taken from the writings of good authors.
It is both instructive and entertaining to observe the virtues of accurate
composition in writers of fame: we cannot see them without being drawn to the
imitation of them, in a more powerful manner than we can by dry rules. Nor are
the faults of such writers less insructive or less powerful monitors. A wreck
left upon a shoal, or upon a rock, is not more useful to the sailor than the
faults of good writers, when set up to view, are to those who come after them.
It was a happy thought in a late ingenious writer of English grammar, to
collect under the several rules examples of bad English found in the most
approved authors. It were to be wished that the rules of logic were
illustrated in the same manner. By this means, a system of logic would become
a repository, wherein whatever is most acute in judging and in reasoning,
whatever is accurate in dividing, distinguishing, and defining, should be laid
up and disposed in order for our imitation, and wherein the false steps of
eminent authors should be recorded for our admonition.
After men had laboured in the search of truth near two thousand years by the help of
syllogisms, Lord Bacon proposed the method of induction, as a more effectual
engine for that purpose. His 'Novum Organum' gave a new turn to the thoughts
and labours of the inquisitive, more remarkable and more useful than that which
the 'Organon' of Aristotle had given before, and may be considered as a second
grand era in the progress of human reason.
The art of syllogism produced numberless disputes, and numberless sects who fought
against each other with much animosity, without gaining or losing ground, but
did nothing considerable for the benefit of human life. The art of induction,
first delineated by Lord Bacon, produced numberless laboratories and
observatories, in which nature has been put to the question by thousands of experiments,
and forced to confess many of her secrets that before were hid from mortals:
and, by these, arts have been improved, and human knowledge wonderfully
increased.
In reasoning by syllogism from general principles, we descend to a conclusion
virtually contained in them. The process of induction is more arduous, being
an ascent from particular premises to a general conclusion. The evidence of
such general conclusions is probable only, not demonstrative: but when the
induction is sufficiently copious and carried on according to the rules of art,
it forces conviction no less than demonstration itself does.
The greatest part of human knowledge rests upon evidence of this kind. Indeed we
can have no other for general truths which are contingent in their nature, and
depend upon the will and ordination of the Maker of the world. He governs the
world he has made by general laws: The effects of these laws in particular
phaenomena are open to our observation; and, by observing a train of uniform
effects with due caution, we may at last decipher the law of nature by which
they are regulated.
Lord Bacon has displayed no less force of genius in reducing to rules this method
of reasoning, than Aristotle did in the method of syllogism. His 'Novum Organon' ought
therefore to be held as a most important addition to the ancient logic. Those who understand it,
and enter into its spirit, will be able to distinguish the chaff from the wheat in philosophical
disquisitions into the works of God. They will learn to hold in due contempt all
hypotheses and theories, the creatures of human imagination, and to respect nothing but facts
sufficiently drawn from them by a fair and chaste interpretation of nature.
Most arts have been reduced to rules, after they had been brought to a considerable
degree of perfection by the natural sagacity of artists; and the rules have been drawn
from the best examples of the art that had been before exhibited; but the art of
philosophical induction was delineated by Lord Bacon in a very ample manner, before the
world had seen any tolerable example of it. This, although it adds greatly to the merit
of the author, must have produced some obscurity in the work, and a defect of proper examples
for illustration. This defect may now easily be supplied from those authors who, in their
philosophical disquisitions, have the most strictly pursued the path pointed out in the
'Novum Organon'. Among these, Sir Isaac Newton appears to hold the first rank; having,
in the third book of his 'Principia', and in his 'Optics', had the rules of the
'Novum Organon' constantly in his eye.
I think Lord Bacon was also the first who endeavoured to reduce to a system the
prejudices or biasses of the mind, which are the causes of false judgment, and which he
calls the idols of the human understanding. Some late writers of logic have very
properly introduced this into their system; but it deserves to be more copiously handled,
and to be illustrated by real examples.
It is of great consequences to accurate reasoning to distinguish first principles which are
to be taken for granted, from propositions which require proof. All the real knowledge of
mankind may be divided into two parts: The first consisting of self-evident propositions;
the second, of those which are deduced by just reasoning from self-evident propositions.
The line that divides these two parts ought to be marked as distinctly as possible; and the
principles that are self-evident reduced, as far as can be done, to general axioms. This
has been done in mathematics from the beginning, and has tended greatly to the emolument
of that science. It has lately been done in natural philosophy: and by this means
that science has advanced more in an hundred and fifty years, than it had done before in
two thousand. Every science is in an unformed state until its first principles are
ascertained; after which, it advances regularly, and secures the ground it has gained.
Although first principles do not admit of direct proof, yet there must be certain marks
and characters by which those that are truly such may be distinguished from counterfeits.
These marks ought to be described and applied to distinguish the genuine from the spurious.
In the ancient philosophy, there is a redundance, rather than a defect, of first principles.
Many things were assumed under that character without a just title. That nature abhors a
vacuum; that bodies do not gravitate in their proper place; that the heavenly bodies
undergo no change; that they move in perfect circles, and with an equable motion: such principles
as these were assumed in the Peripatetic philosophy without proof, as if they were self-evident.
Des Cartes, sensible of this weakness in the ancient philosophy, and desirous to guard
against it in his own system, resolved to admit nothing until his assent was forced by
irresistible evidence. The first thing which he found to be certain and evident was,
that he thought, and reasoned, and doubted. He found himself under a necessity of
believing the existence of those mental operations of which he was conscious; and having
thus found sure footing in this one principle of consciousness, he rested satisfied with
it, hoping to be able to build the whole fabric of his knowledge upon it; like Archimedes,
who wanted one fixed point to move the whole earth. But the foundation was too narrow;
and in his progress he unawares assumes many things less evident than those which he
attempts to prove. Althought he was not able to suspect the testimony of consciousness,
yet he thought the testimony of sense, of memory, and of every other faculty, might be
suspected, and ought not to be received until proof was brought that they are not fallacious.
Therefore he applies these faculties, whose character is yet in question, to prove, That there is an
infinitely perfect Being, who made him, and who made his senses, his memory, his reason, and all
his faculties; that this Being is not deceiver, and therefore could not give him faculties that
are fallacious; and that on this account they deserve credit.
It is strange that this philosopher, who found himself under a necessity of yielding
to the testimony of consciousness, did not find the same necessity of yielding to the testimony
of his senses, his memory, and his understanding; and that, while he was certain that he doubted
and reasoned, he was uncertain whether two and three made five, and whether he was dreaming or
awake. It is more strange that so acute a reasoner should not perceive that his whole
train of reasoning, to prove that his faculties were fallacious, was mere sophistry; for, if his faculties
were fallacious, they might deceive him in this train of reasoning; and so the conclusion, That
they were not fallacious, was only the testimony of his faculties in their own favour, and might
be a fallacy.
It is difficult to give any reason for distrusting our other faculties, that will not reach
consciousness itself. And he who distrusts the faculties of judging and reasoning which God
hath given him, must even rest in his scepticism till he come to a sound mind, or until God
give him new faculties to sit in judgment upon the old. If it be not a first principle,
that our faculties are not fallacious, we must be absolute sceptics; for this principle
is incapable of proof; and if it is not certain, nothing else can be certain.
Since the time of Des Cartes, it has been fashionable with those who dealt in abstract
philosophy, to employ their invention in finding philosophical arguments, either to prove
those truths which ought to be received as first principles, or to overturn them: and it
is not easy to say, whether the authority of first principles is more hurt by the first of these
attempts, ot by the last; for such principles can stand secure only upon their own bottom; and
to place them upon any other foundation than that of their intrinsic evidence, is in effect to
overturn them.
I have lately met with a very sensible and judicious treatise, wrote by Father Buffier
about fifty years ago, concerning first principles and the source of human judgments, which, with great
propriety, he prefixed to his treatise of logic. And indeed I apprehend it is a subject of such
consequence, that, if inquisitive men can be brought to the same unanimity in the first principles
of the other sciences as in those of mathematics and natural philosophy, (and why should we despair
of a general agreement in things that are self-evident?) this might be considered as a third
grand era in the progress of human reason
James Harris (1709–80) was the author of Hermes: or,
A Philosophical Inquiry concerning Language and Universal Grammar,
which appeared in 1751.
Reid admired his work,
and thought that he was one of the only writers who properly understood the word 'idea'.
Section I OF THE AUTHOR
Section II OF PORPHRY'S INTRODUCTION
Section III OF THE CATEGORIES
Section IV OF THE BOOK CONCERNING INTERPRETATION
Chapter II
Section I OF THE FIVE PREDICABLES
Section II OF THE TEN CATEGORIES, AND ON DIVISIONS IN GENERAL
Section III ON DISTINCTIONS
Section IV ON DEFINITIONS
Section V ON THE STRUCTURE OF SPEECH
Section VI ON PROPOSITIONS
Chapter III
Section I ON THE CONVERSION OF PROPOSITIONS
Section II OF THE FIGURES AND MODES OF PURE SYLLOGISMS
Section III OF THE INVENTION OF A MIDDLE TERM
Section IV OF THE REMAINING PART OF THE FIRST BOOK
Section V OF THE SECOND BOOK OF THE FIRST ANALYTICS
Chapter IV
Section I OF THE CONVERSION OF PROPOSITIONS
Section II ON ADDITIONS MADE TO ARISTOTLE'S LOGIC
Section III ON EXAMPLES USED TO ILLUSTRATE THIS THEORY
Section IV ON THE DEMONSTRATION OF THE THEORY
Section V ON THIS THEORY, CONSIDERED AS AN ENGINE OF SCIENCE
Section VI ON MODAL SYLLOGISMS
Section VII ON SYLLOGISMS THAT DO NOT BELONG TO FIGURE AND MODE
Chapter V
Section I OF THE LAST ANALYTICS
Section II OF THE TOPICS
Section III OF THE BOOK CONCERNING SOPHISMS
CHAPTER VI
Section I OF THE UTILITY OF LOGIC
Section II OF THE IMPROVEMENT OF LOGIC
Asserit I, negat O, sed particulariter
ambo.
Cesare, Camestres, Festino, Baroco, secundae;
Tertia grande sonans recitat Darapti, Felapton
Adjugens Disamis, Datisi, Felapton,Bocardo, Ferison.
The natural passions and appetites of men
are the works of God;
Therefore, none of them is bad.
All the natural passions and appetites of
men are the works of God;
Therefore, they are not bad.
Some pleasures are not praiseworthy;
Therefore, some pleasures are not virtuous.
Some pleasures are not praiseworthy;
Therefore, some pleasures are not virtuous.
Some pleasures are not-praiseworthy;
Therefore, some pleasures are not virtuous.
All Africans are men;
Therefore, some men are black.
Some men are Africans;
Therefore, some men are black.
THE LOGIC MUSEUM