_Of Fallacies_.
§ 827. After examining the conditions on which correct thoughts
depend, it is expedient to classify some of the most familiar forms of
error. It is by the treatment of the Fallacies that logic chiefly
vindicates its claim to be considered a practical rather than a
speculative science. To explain and give a name to fallacies is like
setting up so many sign-posts on the various turns which it is
possible to take off the road of truth.
§ 828. By a fallacy is meant a piece of reasoning which appears to
establish a conclusion without really doing so. The term applies both
to the legitimate deduction of a conclusion from false premisses and
to the illegitimate deduction of a conclusion from any
premisses. There are errors incidental to conception and judgement,
which might well be brought under the name; but the fallacies with
which we shall concern ourselves are confined to errors connected with
inference.
§ 829. When any inference leads to a false conclusion, the error may
have arisen either in the thought itself or in the signs by which the
thought is conveyed. The main sources of fallacy then are confined to
two--
(1) thought,
(2) language.
§ 830. This is the basis of Aristotle's division of fallacies, which
has not yet been superseded. Fallacies, according to him, are either
in the language or outside of it. Outside of language there is no
source of error but thought. For things themselves do not deceive us,
but error arises owing to a misinterpretation of things by the
mind. Thought, however, may err either in its form or in its
matter. The former is the case where there is some violation of the
laws of thought; the latter whenever thought disagrees with its
object. Hence we arrive at the important distinction between Formal
and Material fallacies, both of which, however, fall under the same
negative head of fallacies other than those of language.
| In the language
| (in the signs of thought)
|
Fallacy -| |--In the Form.
|--Outside the language -|
| (in the thought itself) |
|
|--in the Matter.
§ 831. There are then three heads to which fallacies may be
referred-namely, Formal Fallacies, Fallacies of Language, which are
commonly known as Fallacies of Ambiguity, and, lastly, Material
Fallacies.
§ 832. Aristotle himself only goes so far as the first step in the
division of fallacies, being content to class them according as they
are in the language or outside of it. After that he proceeds at once
to enumerate the infimæ species under each of the two main heads. We
shall presently imitate this procedure for reasons of expediency. For
the whole phraseology of the subject is derived from Aristotle's
treatise on Sophistical Refutations, and we must either keep to his
method or break away from tradition altogether. Sufficient confusion
has already arisen from retaining Aristotle's language while
neglecting his meaning.
§ 833. Modern writers on logic do not approach fallacies from the same
point of view as Aristotle. Their object is to discover the most
fertile sources of error in solitary reasoning; his was to enumerate
the various tricks of refutation which could be employed by a sophist
in controversy. Aristotle's classification is an appendix to the Art
of Dialectic.
§ 834. Another cause of confusion in this part of logic is the
identification of Aristotle's two-fold division of fallacies, commonly
known under the titles of In dictione and Extra diotionem, with the
division into Logical and Material, which is based on quite a
different principle.
§ 835. Aristotle's division perhaps allows an undue importance to
language, in making that the principle of division, and so throwing
formal and material fallacies under a common head. Accordingly another
classification has been adopted, which concentrates attention from the
first upon the process of thought, which ought certainly to be of
primary importance in the eyes of the logician. This classification
is as follows.
§ 836. Whenever in the course of our reasoning we are involved in
error, either the conclusion follows from the premisses or it does
not. If it does not, the fault must lie in the process of reasoning,
and we have then what is called a Logical Fallacy. If, on the other
hand, the conclusion does follow from the premisses, the fault must
lie in the premisses themselves, and we then have what is called a
Material Fallacy. Sometimes, however, the conclusion will appear to
follow from the premisses until the meaning of the terms is examined,
when it will be found that the appearance is deceptive owing to some
ambiguity in the language. Such fallacies as these are, strictly
speaking, non-logical, since the meaning of words is extraneous to the
science which deals with thought. But they are called
Semi-logical. Thus we arrive by a different road at the same three
heads as before, namely, (1) Formal or Purely Logical Fallacies, (2)
Semi-logical Fallacies or Fallacies of Ambiguity, (3) Material
Fallacies.
§ 837. For the sake of distinctness we will place the two divisions
side by side, before we proceed to enumerate the infimae species.
|--In the language
| (Fallacy of Ambiguity)
Fallacy-|
| |--In the Form.
|--Outside the language -|
|
|--In the Matter.
|--Formal or purely logical.
|--Logical -|
Fallacy-| |--Semi-logical
| (Fallacy of Ambiguity).
|--Material
838. Of one of these three heads, namely, formal fallacies, it is not
necessary to say much, as they have been amply treated of in the
preceding pages. A formal fallacy arises from the breach of any of the
general rules of syllogism. Consequently it would be a formal fallacy
to present as a syllogism anything which had more or less than two
premisses. Under the latter variety comes what is called 'a woman's
reason,' which asserts upon its own evidence something which requires
to be proved. Schoolboys also have been known to resort to this form
of argument--'You're a fool.' 'Why?' 'Because you are.' When the
conclusion thus merely reasserts one of the premisses, the other must
be either absent or irrelevant. If, on the other hand, there are more
than two premisses, either there is more than one syllogism or the
superfluous premiss is no premiss at all, but a proposition irrelevant
to the conclusion.
839. The remaining rules of the syllogism are more able to be broken
than the first; so that the following scheme presents the varieties of
formal fallacy which are commonly enumerated--
|--Four Terms.
Formal Fallacy-|--Undistributed Middle.
|--Illicit Process.
|--Negative Premisses and Conclusion.
§ 840. The Fallacy of Four Terms is a violation of the second of the
general rules of syllogism (§ 582). Here is a palpable instance of
it--
All men who write books are authors.
All educated men could write books.
.'. All educated men are authors.
Here the middle term is altered in the minor premiss to the
destruction of the argument. The difference between the actual writing
of books and the power to write them is precisely the difference
between one who is an author and one who is not.
§ 841. Since a syllogism consists of three terms, each of which is
used twice over, it would be possible to have an apparent syllogism
with as many as six terms in it. The true name for the fallacy
therefore is the Fallacy of More than Three Terms. But it is rare to
find an attempted syllogism which has more than four terms in it, just
as we are seldom tendered a line as an hexameter, which has more than
seven feet.
§ 842. The Fallacies of Undistributed Middle and Illicit Process have
been treated of under §§ 585, 586. The heading 'Negative Premisses
and Conclusion' covers violations of the three general rules of
syllogism relating to negative premisses (§§ 590-593). Here is an
instance of the particular form of the fallacy which consists in the
attempt to extract an affirmative conclusion out of two negative
premisses--
All salmon are fish, for neither salmon nor fish belong to the class
mammalia.
The accident of a conclusion being true often helps to conceal the
fact that it is illegitimately arrived at. The formal fallacies which
have just been enumerated find no place in Aristotle's division. The
reason is plain. His object was to enumerate the various modes in
which a sophist might snatch an apparent victory, whereas by openly
violating any of the laws of syllogism a disputant would be simply
courting defeat.
§ 843. We now revert to Aristotle's classification of fallacies, or
rather of Modes of Refutation. We will take the species he enumerates
in their order, and notice how modern usage has departed from the
original meaning of the terms. Let it be borne in mind that, when the
deception was not in the language, Aristotle did not trouble himself
to determine whether it lay in the matter or in the form of thought.
§ 844. The following scheme presents the Aristotelian classification
to the eye at a glance:--
| |--Equivocation.
| |--Amphiboly.
|--In the language -|--Composition.
| |--Division.
| |--Accent.
| |--Figure of Speech.
Modes of -|
Refutation. | |--Accident.
| |--A dicto secundum quid.
| |--Ignoratio Elenchi.
|--Outside the language -|--Consequent.
| |--Petitio Principii.
| |--Non causa pro causa.
| |--Many Questions.
[Footnote: for "In the language": The Greek is [Greek: para ten lexin],
the exact meaning of which is; 'due to the statement.']
§ 845. The Fallacy of Equivocation [Greek: òmonumía] consists in an
ambiguous use of any of the three terms of a syllogism. If, for
instance, anyone were to argue thus--
No human being is made of paper,
All pages are human beings,
.'. No pages are made of paper--
the conclusion would appear paradoxical, if the minor term were there
taken in a different sense from that which it bore in its proper
premiss. This therefore would be an instance of the fallacy of
Equivocal Minor.
§ 846. For a glaring instance of the fallacy of Equivocal Major, we
may take the following--
No courageous creature flies,
The eagle is a courageous creature,
.'. The eagle does not fly--
the conclusion here becomes unsound only by the major being taken
ambiguously.
§ 847. It is, however, to the middle term that an ambiguity most
frequently attaches. In this case the fallacy of equivocation assumes
the special name of the Fallacy of Ambiguous Middle. Take as an
instance the following--
Faith is a moral virtue.
To believe in the Book of Mormon is faith.
.'. To believe in the Book of Mormon is a moral virtue.
Here the premisses singly might be granted; but the conclusion would
probably be felt to be unsatisfactory. Nor is the reason far to
seek. It is evident that belief in a book cannot be faith in any sense
in which that quality can rightly be pronounced to be a moral virtue.
§ 848. The Fallacy of Amphiboly ([Greek: ámphibolía]) is an ambiguity
attaching to the construction of a proposition rather than to the
terms of which it is composed. One of Aristotle's examples is this--
[Greek: tò boúlesthai labeîn me toùs polemíous]
which may be interpreted to mean either 'the fact of my wishing to
take the enemy,' or 'the fact of the enemies' wishing to take me.' The
classical languages are especially liable to this fallacy owing to the
oblique construction in which the accusative becomes subject to the
verb. Thus in Latin we have the oracle given to Pyrrhus (though of
course, if delivered at all, it must have been in Greek)--
Aio te, AEacida, Romanos vincere posse.
Pyrrhus the Romans shall, I say, subdue (Whately),
[Footnote: Cicero, De Divinatione, ii. § 116; Quintilian,
Inst. Orat. vii 9, § 6.]
which Pyrrhus, as the story runs, interpreted to mean that he could
conquer the Romans, whereas the oracle subsequently explained to him
that the real meaning was that the Romans could conquer him. Similar
to this, as Shakspeare makes the Duke of York point out, is the
witch's prophecy in Henry VI (Second Part, Act i, sc. 4),
The duke yet lives that Henry shall depose.
An instance of amphiboly may be read on the walls of Windsor
Castle--Hoc fecit Wykeham. The king mas incensed with the bishop for
daring to record that he made the tower, but the latter adroitly
replied that what he really meant to indicate was that the tower was
the making of him. To the same head may be referred the famous
sentence--'I will wear no clothes to distinguish me from my Christian
brethren.'
§ 849. The Fallacy of Composition [Greek: diaíresis] is likewise a
case of ambiguous construction. It consists, as expounded by
Aristotle, in taking words together which ought to be taken
separately, e.g.
'Is it possible for a man who is not writing to write?'
'Of course it is.'
'Then it is possible for a man to write without writing.'
And again--
'Can you carry this, that, and the other?' 'Yes.'
'Then you can carry this, that, and the other,'--
a fallacy against which horses would protest, if they could.
§ 850. It is doubtless this last example which has led to a convenient
misuse of the term 'fallacy of composition' among modern writers, by
whom it is defined to consist in arguing from the distributive to the
collective use of a term.
§ 851. The Fallacy of Division ([Greek: diaíresis]), on the other hand,
consists in taking words separately which ought to be taken together,
e.g.
[Greek: ègó s' êteka doûlon ônt' èleúteron [Footnote: Evidently the
original of the line in Terence's _Andria_, 37,--feci ex servo
ut esses libertus mihi.],
where the separation of [Greek: doûlon] from [Greek: ôntra] would lead
to an interpretation exactly contrary to what is intended.
And again--
[Greek: pentékont' àndrôn èkatòn lípe dîos Àchilleús],
where the separation of [Greek: àndrôn] from [Greek: èkatòn] leads to
a ludicrous error.
Any reader whose youth may have been nourished on 'The Fairchild
Family' may possibly recollect a sentence which ran somewhat on this
wise--'Henry,' said Mr. Fairchild, 'is this true? Are you a thief and
a liar too?' But I am afraid he will miss the keen delight which can
be extracted at a certain age from turning the tables upon
Mr. Fairchild thus--Henry said, 'Mr. Fairchild, is this true? Are
_you_ a thief and a liar too?'
§ 852. The fallacy of division has been accommodated by modern writers
to the meaning which they have assigned to the fallacy of
composition. So that by the 'fallacy of division' is now meant arguing
from the collective to the distributive use of a term. Further, it is
laid down that when the middle term is used distributively in the
major premiss and collectively in the minor, we have the fallacy of
composition; whereas, when the middle term is used collectively in the
major premiss and distributively in the minor, we have the fallacy of
division. Thus the first of the two examples appended would be
composition and the second division.
(1) Two and three are odd and even.
Five is two and three.
.'. Five is odd and even.
(2) The Germans are an intellectual people.
Hans and Fritz are Germans.
.'. They are intellectual people.
§ 853. As the possibility of this sort of ambiguity is not confined to
the middle term, it seems desirable to add that when either the major
or minor term is used distributively in the premiss and collectively
in the conclusion, we have the fallacy of composition, and in the
converse case the fallacy of division. Here is an instance of the
latter kind in which the minor term is at fault--
Anything over a hundredweight is too heavy to lift.
These sacks (collectively) are over a hundredweight.
.'. These sacks (distributively) are too heavy to lift.
§ 854. The ambiguity of the word 'all,' which has been before
commented upon (§ 119), is a great assistance in the English language
to the pair of fallacies just spoken of.
§ 835. The Fallacy of Accent ([Greek: prosodía]) is neither more nor
less than a mistake in Greek accentuation. As an instance Aristotle
gives Iliad xxiii. 328, where the ancient copies of Homer made
nonsense of the words [Greek: tò mèn oú katapútetai ómbro] by writing
[Greek: oû] with the circumflex in place of [Greek: oú] with the acute
accent. [Footnote: This goes to show that the ancient Greeks did not
distinguish in pronunciation between the rough and smooth breathing
any more than their modern representatives.] Aristotle remarks that
the fallacy is one which cannot easily occur in verbal argument, but
rather in writing and poetry.
§ 856. Modern writers explain the fallacy of accent to be the mistake
of laying the stress upon the wrong part of a sentence. Thus when the
country parson reads out, 'Thou shall not bear false witness
_against_ thy neighbour,' with a strong emphasis upon the word
'against,' his ignorant audience leap [sic] to the conclusion that it
is not amiss to tell lies provided they be in favour of one's
neighbour.
§ 857. The Fallacy of Figure of Speech [Greek: tò schêma tês léxeos]
results from any confusion of grammatical forms, as between the
different genders of nouns or the different voices of verbs, or their
use as transitive or intransitive, e.g. [Greek: úgiaínein] has the
same grammatical form as [Greek: témnein] or [Greek: oìkodomeîn], but
the former is intransitive, while the latter are transitive. A sophism
of this kind is put into the mouth of Socrates by Aristophanes in the
Clouds (670-80). The philosopher is there represented as arguing that
[Greek: kápdopos] must be masculine because [Greek: Kleónumos] is. On
the surface this is connected with language, but it is essentially a
fallacy of false analogy.
§ 858. To this head may be referred what is known as the Fallacy of
Paronymous Terms. This is a species of equivocation which consists in
slipping from the use of one part of speech to that of another, which
is derived from the same source, but has a different meaning. Thus
this fallacy would be committed if, starting from the fact that there
is a certain probability that a hand at whist will consist of thirteen
trumps, one were to proceed to argue that it was probable, or that he
had proved it.
§ 859. We turn now to the tricks of refutation which lie outside the
language, whether the deception be due to the assumption of a false
premiss or to some unsoundness in the reasoning.
§ 860. The first on the list is the Fallacy of Accident ([Greek: tò
sumbebekós]). This fallacy consists in confounding an essential with
an accidental difference, which is not allowable, since many things
are the same in essence, while they differ in accidents. Here is the
sort of example that Aristotle gives--
'Is Plato different from Socrates ?' 'Yes.' 'Is Socrates a man ?'
'Yes.' 'Then Plato is different from man.'
To this we answer--No: the difference of accidents between Plato and
Socrates does not go so deep as to affect the underlying essence. To
put the thing more plainly, the fallacy lies in assuming that whatever
is different from a given subject must be different from it in all
respects, so that it is impossible for them to have a common
predicate. Here Socrates and Plato, though different from one another,
are not so different but that they have the common predicate 'man.'
The attempt to prove that they have not involves an illicit process of
the major.
§ 861. The next fallacy suffers from the want of a convenient name. It
is called by Aristotle [Greek: tò áplos tóde ê pê légestai kaì mè
kupíos] or, more briefly, [Greek: tò áplôs ê mé], or [Greek: tò pê kaí
áplôs], and by the Latin writers 'Fallacia a dicto secundum quid ad
dictum simpliciter.' It consists in taking what is said in a
particular respect as though it held true without any restriction,
e.g., that because the nonexistent ([Greek: tò mè ôn]) is a matter of
opinion, that therefore the non-existent is, or again that because the
existent ([Greek: tò ôn]) is not a man, that therefore the existent is
not. Or again, if an Indian, who as a whole is black, has white teeth,
we should be committing this species of fallacy in declaring him to be
both white and not-white. For he is only white in a certain respect
([Greek: pê]), but not absolutely ([Greek: àplôs]). More
difficulty, says Aristotle, may arise when opposite qualities exist in
a thing in about an equal degree. When, for instance, a thing is half
white and half black, are we to say that it is white or black? This
question the philosopher propounds, but does not answer. The force of
it lies in the implied attack on the Law of Contradiction. It would
seem in such a case that a thing may be both white and not-white at
the same time. The fact is--so subtle are the ambiguities of
language--that even such a question as 'Is a thing white or
not-white?' straightforward, as it seems, is not really a fair one. We
are entitled sometimes to take the bull by the horns, and answer with
the adventurous interlocutor in one of Plato's dialogues--'Both and
neither.' It may be both in a certain respect, and yet neither
absolutely.
§ 862. The same sort of difficulties attach to the Law of Excluded
Middle, and may be met in the same way. It might, for instance, be
urged that it could not be said with truth of the statue seen by
Nebuchadnezzar in his dream either that it was made of gold or that it
was not made of gold: but the apparent plausibility of the objection
would be due merely to the ambiguity of language. It is not true, on
the one hand, that it was made of gold (in the sense of being composed
entirely of that metal); and it is not true, on the other, that it was
not made of gold (in the sense of no gold at all entering into its
composition). But let the ambiguous proposition be split up into its
two meanings, and the stringency of the Law of Excluded Middle will at
once appear--
(1) It must either have been composed entirely of gold or not.
(2) Either gold must have entered into its composition or not.
§ 863. By some writers this fallacy is treated as the converse of the
last, the fallacy of accident being assimilated to it under the title
of the 'Fallacia a dicto simpliciter ad dictum secundum quid.' In this
sense the two fallacies may be defined thus.
The Fallacy of Accident consists in assuming that what holds true as a
general rule will hold true under some special circumstances which may
entirely alter the case. The Converse Fallacy of Accident consists in
assuming that what holds true under some special circumstances must
hold true as a general rule.
The man who, acting on the assumption that alcohol is a poison,
refuses to take it when he is ordered to do so by the doctor, is
guilty of the fallacy of accident; the man who, having had it
prescribed for him when he was ill, continues to take it morning,
noon, and night, commits the converse fallacy.
§ 864. There ought to be added a third head to cover the fallacy of
arguing from one special case to another.
§ 865. The next fallacy is Ignoratio Elenchi [Greek: èlégchou
âgnoia]. This fallacy arises when by reasoning valid in itself one
establishes a conclusion other than what is required to upset the
adversary's assertion. It is due to an inadequate conception of the
true nature of refutation. Aristotle therefore is at the pains to
define refutation at full length, thus--
'A refutation [Greek: êlegchos] is the denial of one and the same--not
name, but thing, and by means, not of a synonymous term, but of the
same term, as a necessary consequence from the data, without
assumption of the point originally at issue, in the same respect, and
in the same relation, and in the same way, and at the same time.'
The ELENCHUS then is the exact contradictory of the opponent's
assertion under the terms of the law of contradiction. To establish by
a syllogism, or series of syllogisms, any other proposition, however
slightly different, is to commit this fallacy. Even if the substance
of the contradiction be established, it is not enough unless the
identical words of the opponent are employed in the
contradictory. Thus if his thesis asserts or denies something about
[Greek: lópion], it is not enough for you to prove the contradictory
with regard to [Greek: ìmátion]. There will be need of a further
question and answer to identify the two, though they are admittedly
synonymous. Such was the rigour with which the rules of the game of
dialectic were enforced among the Greeks!
§ 866. Under the head of Ignoratio Elenchi it has become usual to
speak of various forme of argument which have been labelled by the
Latin writers under such names as 'argumentum ad hominem,' 'ad
populum,' 'ad verecundiam,' 'ad ignorantiam,' 'ad baculum'--all of
them opposed to the 'argumentum ad rem' or 'ad judicium.'
§ 867. By the 'argumentum ad hominem' was perhaps meant a piece of
reasoning which availed to silence a particular person, without
touching the truth of the question. Thus a quotation from Scripture
is sufficient to stop the mouth of a believer in the inspiration of
the Bible. Hume's Essay on Miracles is a noteworthy instance of the
'argumentum ad hominem' in this sense of the term. He insists strongly
on the evidence for certain miracles which he knew that the prejudices
of his hearers would prevent their ever accepting, and then asks
triumphantly if these miracles, which are declared to have taken place
in an enlightened age in the full glare of publicity, are palpably
imposture, what credence can be attached to accounts of extraordinary
occurrences of remote antiquity, and connected with an obscure corner
of the globe? The 'argumentum ad judicium' would take miracles as a
whole, and endeavour to sift the amount of truth which may lie in the
accounts we have of them in every age. [Footnote: On this subject see
the author's _Attempts at Truth_ (Trubner & Co.), pp. 46-59.]
§ 868. In ordinary discourse at the present day the term 'argumentum
ad hominem' is used for the form of irrelevancy which consists in
attacking the character of the opponent instead of combating his
arguments, as illustrated in the well-known instructions to a
barrister--'No case: abuse the plaintiff's attorney.'
§ 869. The 'argumentum ad populum' consists in an appeal to the
passions of one's audience. An appeal to passion, or to give it a less
question-begging name, to feeling, is not necessarily amiss. The heart
of man is the instrument upon which the rhetorician plays, and he has
to answer for the harmony or the discord that comes of his
performance.
§ 870. The 'argumentum ad verecundiam' is an appeal to the feeling of
reverence or shame. It is an argument much used by the old to the
young and by Conservatives to Radicals.
§ 871. The 'argumentum ad ignorantiam' consists simply in trading on
the ignorance of the person addressed, so that it covers any kind of
fallacy that is likely to prove effective with the hearer.
§ 872. The 'argumentum ad baculum' is unquestionably a form of
irrelevancy. To knock a man down when he differs from you in opinion
may prove your strength, but hardly your logic.
A sub-variety of this form of irrelevancy was exhibited lately at a
socialist lecture in Oxford, at which an undergraduate, unable or
unwilling to meet the arguments of the speaker, uncorked a bottle,
which had the effect of instantaneously dispersing the audience. This
might be set down as the 'argumentum ad nasum.'
§ 873. We now come to the Fallacy of the Consequent, a term which has
been more hopelessly abused than any. What Aristotle meant by it was
simply the assertion of the consequent in a conjunctive proposition,
which amounts to the same thing as the simple conversion of A (§ 489),
and is a fallacy of distribution. Aristotle's example is this--
If it has rained, the ground is wet.
.'. If the ground is wet, it has rained.
This fallacy, he tells us, is often employed in rhetoric in dealing
with presumptive evidence. Thus a speaker, wanting to prove that a man
is an adulterer, will argue that he is a showy dresser, and has been
seen about at nights. Both these things however may be the case, and
yet the charge not be true.
§ 874. The Fallacy of Petitio or Assumptio Principii [Greek: tò èn
àrchê aìteîstai or lambánein] to which we now come, consists in an
unfair assumption of the point at issue. The word [Greek: aìteîstai],
in Aristotle's name for it points to the Greek method of dialectic by
means of question and answer. This fact is rather disguised by the
mysterious phrase 'begging the question.' The fallacy would be
committed when you asked your opponent to grant, overtly or covertly,
the very proposition originally propounded for discussion.
§ 875. As the question of the precise nature of this fallacy is of
some importance we will take the words of Aristotle himself
(Top. viii. 13. §§ 2, 3). 'People seem to beg the question in five
ways. First and most glaringly, when one takes for granted the very
thing that has to be proved. This by itself does not readily escape
detection, but in the case of "synonyms," that is, where the name and
the definition have the same meaning, it does so more
easily. [Footnote: Some light is thrown upon this obscure passage by a
comparison with Cat. I. § 3, where 'synonym' is defined. To take the
word here in its later and modern sense affords an easy
interpretation, which is countenanced by Alexander Aphrodisiensis, but
it is flat against the usage of Aristotle, who elsewhere gives the
name 'synonym,' not to two names for the same thing, but to two things
going under the same name. See Trendelenberg on the passage.]
Secondly, when one assumes universally that which has to be proved in
particular, as, if a man undertaking to prove that there is one
science of contraries, were to assume that there is one science of
opposites generally. For he seems to be taking for granted along with
several other things what he ought to have proved by itself.
Thirdly, when one assumes the particulars where the universal has to
be proved; for in so doing a man is taking for granted separately what
he was bound to prove along with several other things. Again, when
one assumes the question at issue by splitting it up, for instance,
if, when the point to be proved is that the art of medicine deals with
health and disease, one were to take each by itself for granted.
Lastly, if one were to take for granted one of a pair of necessary
consequences, as that the side is incommensurable with the diagonal,
when it is required to prove that the diagonal is incommensurable with
the side.'
§ 876. To sum up briefly, we may beg the question in five ways--
(1) By simply asking the opponent to grant the point which requires
to be proved;
(2) by asking him to grant some more general truth which involves
it;
(3) by asking him to grant the particular truths which it involves;
(4) by asking him to grant the component parts of it in detail;
(5) by asking him to grant a necessary consequence of it.
§ 877. The first of these five ways, namely, that of begging the
question straight off, lands us in the formal fallacy already spoken
of (§ 838), which violates the first of the general rules of
syllogism, inasmuch as a conclusion is derived from a single premiss,
to wit, itself.
§ 878. The second, strange to say, gives us a sound syllogism in
Barbara, a fact which countenances the blasphemers of the syllogism in
the charge they bring against it of containing in itself a petitio
principii. Certainly Aristotle's expression might have been more
guarded. But it is clear that his quarrel is with the matter, not with
the form in such an argument. The fallacy consists in assuming a
proposition which the opponent would be entitled to deny. Elsewhere
Aristotle tells us that the fallacy arises when a truth not evident by
its own light is taken to be so. [Footnote: [Greek: Ôtan tò mè dí
aùtoû gnostòn dí aùtoû tis èpicheiraê deiknúnai, tót' aìteîtai tò èx
àrchês.]. Anal. Pr. II. 16. § I ad fin.]
§ 879. The third gives us an inductio per enumerationem simplicem, a
mode of argument which would of course be unfair as against an
opponent who was denying the universal.
§ 880. The fourth is a more prolix form of the first.
§ 881. The fifth rests on Immediate Inference by Relation (§ 534).
§ 882. Under the head of petitio principii comes the fallacy of
Arguing in a Circle, which is incidental to a train of reasoning. In
its most compressed form it may be represented thus--
(1) B is A.
C is B.
.'. C is A.
(2) C is A.
B is C.
.'. B is A.
§ 883. The Fallacy of Non causa pro causa ([Greek: tò mè aîtion] or
[Greek: aîtoin]) is another, the name of which has led to a complete
misinterpretation. It consists in importing a contradiction into the
discussion, and then fathering it on the position controverted. Such
arguments, says Aristotle, often impose upon the users of them
themselves. The instance he gives is too recondite to be of general
interest.
§ 884. Lastly, the Fallacy of Many Questions ([Greek: tò tà déo
èrotémata ên poieîn]) is a deceptive form of interrogation, when a
single answer is demanded to what is not really a single question. In
dialectical discussions the respondent was limited to a simple 'yes'
or 'no'; and in this fallacy the question is so framed as that either
answer would seem to imply the acceptance of a proposition which would
be repudiated. The old stock instance will do as well as
another--'Come now, sir, answer "yes" or "no." Have you left off
beating your mother yet?' Either answer leads to an apparent
admission of impiety.
A late Senior Proctor once enraged a man at a fair with this form of
fallacy. The man was exhibiting a blue horse; and the distinguished
stranger asked him--'With what did you paint your horse?'
EXERCISES.
These exercises should be supplemented by direct questions upon the
text, which it is easy for the student or the teacher to supply for
himself.
PART I.
CHAPTER I.
Classify the following words according as they are categorematic,
syncategorematic or acategorematic;--
come peradventure why
through inordinately pshaw
therefore circumspect puss
grand inasmuch stop
touch sameness back
cage disconsolate candle.
CHAPTER II.
Classify the following things according as they are substances,
qualities or relations;--
God likeness weight
blueness grass imposition
ocean introduction thinness
man air spirit
Socrates raillery heat
mortality plum fire.
CHAPTER III.
1. Give six instances each of-attribute, abstract, singular,
privative, equivocal and relative terms.
2. Select from the following list of words such as are terms, and
state whether they are (1) abstract or concrete, (2) singular or
common, (3) univocal or equivocal:--
van table however
enter decidedly tiresome
very butt Solomon
infection bluff Czar
short although Caesarism
distance elderly Nihilist.
3. Which of the following words are abstract terms?--
quadruped event through
hate desirability thorough
fact expressly thoroughness
faction wish light
inconvenient will garden
inconvenience volition grind.
4. Refer the following terms to their proper place under each of the
divisions in the scheme:--
horse husband London
free lump empty
liberty rational capital
impotent reason Capitol
impetuosity irrationality grave
impulsive double calf.
5. Give six instances each of proper names and designations.
6. Give six instances each of connotative and non-connotative terms.
7. Give the extension and intension of--
sermon animal sky
clock square gold
sport fish element
bird student fluid
art river line
gas servant language
CHAPTER IV.
Arrange the following terms in order of extension--carnivorous, thing,
matter, mammal, organism, vertebrate, cat, substance, animal.
* * * * *
PART II.
CHAPTER I.
Give a name to each of the following sentences:--
(1) Oh, that I had wings like a dove!
(2) The more, the merrier.
(3) Come rest in this bosom, my own stricken deer.
(4) Is there balm in Gilead?
(5) Hearts may be trumps.
CHAPTER II.
Analyse the following propositions into subject, copula and
predicate:--
(1) He being dead yet speaketh.
(2) There are foolish politicians.
(3) Little does he care.
(4) There is a land of pure delight.
(5) All's well that ends well.
(6) Sweet is the breath of morn.
(7) Now it came to pass that the beggar died.
(8) Who runs may read.
(9) Great is Diana of the Ephesians.
(10) Such things are.
(11) Not more than others I deserve.
(12) The day will come when Ilium's towers shall perish.
CHAPTER III.
1. Express in logical form, affixing the proper symbol:--
(1) Some swans are not white.
(2) All things are possible to them that believe.
(3) No politicians are unprincipled.
(4) Some stones float on water.
(5) The snow has melted.
(6) Eggs are edible.
(7) All kings are not wise.
(8) Moths are not butterflies.
(9) Some men are born great.
(10) Not all who are called are chosen.
(11) It is not good for man to be alone.
(12) Men of talents have been known to fail in life.
(13) 'Tis none but a madman would throw about fire.
(14) Every bullet does not kill.
(15) Amongst Unionists are Whigs.
(16) Not all truths are to be told.
(17) Not all your efforts can save him.
(18) The whale is a mammal.
(19) Cotton is grown in Cyprus.
(20) An honest man's the noblest work of God.
(21) No news is good news.
(22) No friends are like old friends.
(23) Only the ignorant affect to despise knowledge.
(24) All that trust in Him shall not be ashamed.
(25) All is not gold that glitters.
(26) The sun shines upon the evil and upon the good.
(27) Not to go on is to go back.
(28) The king, minister, and general are a pretty trio.
(29) Amongst dogs are hounds.
(30) A fool is not always wrong.
(31) Alexander was magnanimous.
(32) Food is necessary to life.
(33) There are three things to be considered,
(34) By penitence the Eternal's wrath's appeased.
(35) Money is the miser's end.
(36) Few men succeed in life.
(37) All is lost, save honour.
(38) It is mean to hit a man when he is down.
(39) Nothing but coolness could have saved him.
(40) Books are generally useful.
(41) He envies others' virtue who has none himself.
(42) Thankless are all such offices.
(43) Only doctors understand this subject.
(44) All her guesses but two were correct.
(45) All the men were twelve.
(46) Gossip is seldom charitable.
2. Give six examples of indefinite propositions, and then quantify
them according to their matter.
3. Compose three propositions of each of the following kinds:--
(1) with common terms for subjects;
(2) with abstract terms for subjects;
(3) with singular terms for predicates;
(4) with collective terms for predicates;
(5) with attributives in their subjects;
(6) with abstract terms for predicates.
CHAPTER IV.
1. Point out what terms are distributed or undistributed in the
following propositions:--
(1) The Chinese are industrious.
(2) The angle in a semi-circle is a right angle.
(3) Not one of the crew survived.
(4) The weather is sometimes not propitious.
The same exercise may be performed upon any of the propositions in the
preceding list.
2. Prove that in a negative proposition the predicate must be
distributed.
CHAPTER V.
Affix its proper symbol to each of the following propositions:--
(1) No lover he who is not always fond.
(2) There are Irishmen and Irishmen.
(3) Men only disagree,
Of creatures rational.
(4) Some wise men are poor.
(5) No Popes are some fallible beings.
(6) Some step-mothers are not unjust.
(7) The most original of the Roman poets was Lucretius.
(8) Some of the immediate inferences are all the forms of
conversion.
CHAPTER VI.
1. Give six examples of terms standing one to another as genus to
species.
2. To which of the heads of predicables would you refer the following
statements? And why?
(1) A circle is the largest space that can be contained by one line.
(2) All the angles of a square are right angles.
(3) Man alone among animals possesses the faculty of laughter.
(4) Some fungi are poisonous.
(5) Most natives of Africa are negroes.
(6) All democracies are governments.
(7) Queen Anne is dead.
CHAPTER VII.
1. Define the following terms--
Sun inn-keeper tea-pot
hope anger virtue
bread diplomacy milk
carpet man death
sincerity telescope mountain
poverty Senate novel.
2. Define the following terms as used in Political Economy--
Commodity barter value
wealth land price
money labour rent
interest capital wages
credit demand profits.
3. Criticise the following as definitions--
(1) Noon is the time when the shadows of bodies are shortest.
(2) Grammar is the science of language.
(3) Grammar is a branch of philology.
(4) Grammar is the art of speaking and writing a language with
propriety.
(5) Virtue is acting virtuously.
(6) Virtue is that line of conduct which tends to produce happiness.
(7) A dog is an animal of the canine species.
(8) Logic is the art of reasoning.
(9) Logic is the science of the investigation of truth by means of
evidence.
(10) Music is an expensive noise.
(11) The sun is the centre of the solar system.
(12) The sun is the brightest of those heavenly bodies that move
round the earth.
(13) Rust is the red desquamation of old iron.
(14) Caviare is a kind of food.
(15) Life is the opposite of death.
(16) Man is a featherless biped.
(17) Man is a rational biped.
(18) A gentleman is a person who has no visible means of
subsistence.
(19) Fame is a fancied life in others' breath.
(20) A fault is a quality productive of evil or inconvenience.
(21) An oligarchy is the supremacy of the rich in a state.
(22) A citizen is one who is qualified to exercise deliberative and
judicial functions.
(23) Length is that dimension of a solid which would be measured by
the longest line.
(24) An eccentricity is a peculiar idiosyncrasy.
(25) Deliberation is that species of investigation which is
concerned with matters of action.
(26) Memory is that which helps us to forget.
(27) Politeness is the oil that lubricates the wheels of society.
(28) An acute-angled triangle is one which has an acute angle.
(29) A cause is that without which something would not be.
(30) A cause is the invariable antecedent of a phenomenon.
(31) Necessity is the mother of invention.
(32) Peace is the absence of war.
(33) A net is a collection of holes strung together.
(34) Prudence is the ballast of the moral vessel.
(35) A circle is a plane figure contained by one line.
(36) Superstition is a tendency to look for constancy where
constancy is not to be expected.
(37) Bread is the staff of life.
(38) An attributive is a term which cannot stand as a subject.
(39) Life is bottled sunshine.
(40) Eloquence is the power of influencing the feelings by speech or
writing.
(41) A tombstone is a monument erected over a grave in memory of the
dead.
(42) Whiteness is the property or power of exciting the sensation of
white.
(43) Figure is the limit of a solid.
(44) An archdeacon is one who exercises archidiaconal functions.
(45) Humour is thinking in jest while feeling in earnest.
CHAPTER VIII.
1. Divide the following terms--
Soldier end book
church good oration
apple cause school
ship government letter
vehicle science verse.
2. Divide the following terms as used in Political Economy--
Requisites of production, labour, consumption, stock, wealth,
capital.
3. Criticise the following as divisions--
(1) Great Britain into England, Scotland, Wales, and Ireland.
(2) Pictures into sacred, historical, landscape, and mythological.
(3) Vertebrate animals into quadrupeds, birds, fishes, and reptiles.
(4) Plant into stem, root, and branches.
(5) Ship into frigate, brig, schooner, and merchant-man.
(6) Books into octavo, quarto, green, and blue.
(7) Figure into curvilinear and rectilinear.
(8) Ends into those which are ends only, means and ends, and means
only.
(9) Church into Gothic, episcopal, high, and low.
(10) Sciences into physical, moral, metaphysical, and medical.
(11) Library into public and private.
(12) Horses into race-horses, hunters, hacks, thoroughbreds, ponies,
and mules.
4. Define and divide--
Meat, money, virtue, triangle;
and give, as far as possible, a property and accident of each.
PART III.
CHAPTERS I-III.
1. What kind of influence have we here?
The author of the Iliad was unacquainted with writing.
Homer was the author of the Iliad.
.'. Homer was unacquainted with writing.
2. Give the logical opposites of the following propositions--
(1) Knowledge is never useless.
(2) All Europeans are civilised.
(3) Some monks are not illiterate.
(4) Happy is the man that findeth wisdom.
(5) No material substances are devoid of weight.
(6) Every mistake is not culpable.
(7) Some Irishmen are phlegmatic.
3. Granting the truth of the following propositions, what other
propositions can be inferred by opposition to be true or false?
(1) Men of science are often mistaken.
(2) He can't be wrong, whose life is in the right.
(3) Sir Walter Scott was the author of Waverley.
(4) The soul that sinneth it shall die.
(5) All women are not vain.
4. Granting the falsity of the following propositions, what other
propositions can be inferred by opposition to be true or false?--
(1) Some men are not mortal.
(2) Air has no weight.
(3) All actors are improper characters.
(4) None but dead languages are worth studying.
(5) Some elements are compound.
CHAPTER IV.
1. Give, as far as possible, the logical converse of each of the
following propositions--
(1) Energy commands success.
(2) Mortals cannot be happy.
(3) There are mistakes which are criminal.
(4) All's well that ends well.
(5) Envious men are disliked.
(6) A term is a kind of word or collection of words.
(7) Some Frenchmen are not vivacious.
(8) All things in heaven and earth were hateful to him.
(9) The square of three is nine.
(10) All cannot receive this saying.
(11) P struck Q.
(12) Amas.
2. 'More things may be contained in my philosophy than exist in heaven
or earth: but the converse proposition is by no means true.' Is the
term converse here used in its logical meaning?
CHAPTER V.
Permute the following propositions--
(1) All just acts are expedient.
(2) No display of passion is politic.
(3) Some clever people are not prudent.
(4) Some philosophers have been slaves.
The same exercise may be performed upon any of the propositions in the
preceding lists.
CHAPTER VI.
1. Give the converse by negation of--
(1) All women are lovely.
(2) Some statesmen are not practical.
(3) All lawyers are honest.
(4) All doctors are skilful.
(5) Some men are not rational.
2. Give the contrapositive of--
(1) All solid substances are material.
(2) All the men who do not row play cricket.
(3) All impeccable beings are other than human,
(4) Some prejudiced persons are not dishonest.
3. Prove indirectly the truth of the contrapositive of 'All A is B.'
4. Criticise the following as immediate inferences--
(1) All wise men are modest.
.'. No immodest men are wise.
(2) Some German students are not industrious.
.'. Some industrious students are not Germans.
(3) Absolute difference excludes all likeness.
.'. Any likeness is a proof of sameness.
(4) None but the brave deserve the fair.
.'. All brave men deserve the fair.
(5) All discontented men are unhappy.
.'. No contented men are unhappy.
(6) Books being a source of instruction, our knowledge must come
from our libraries.
(7) All Jews are Semitic.
.'. Some non-Semitic people are not Jews.
5. Show by what kind of inference each of the subjoined propositions
follows from
All discontented men are unhappy.
(1) All happy men are contented.
(2) Some discontented men are unhappy.
(3) Some contented men are happy.
(4) Some unhappy men are not contented.
(5) No discontented men are happy.
(6) Some happy men are contented.
(7) Some contented men are not unhappy.
(8) Some unhappy men are discontented.
(9) No happy men are discontented.
(10) Some discontented men are not happy.
(11) Some happy men are not discontented.
(12) None but unhappy men are discontented.
From how many of these propositions can the original one be derived?
And why not from all?
CHAPTER VII.
What kind of inference have we here?--
(1) None but the ignorant despise knowledge.
.'. No wise man despises knowledge.
(2) A is superior to B.
.'. B is inferior to A.
CHAPTER VIII.
Fill up the following enthymemes, mentioning to which order they
belong, and state which of them are expressed in problematic form--
(1) I am fond of music: for I always like a comic song.
(2) All men are born to suffering, and therefore you must expect
your share.
(3) Job must have committed some secret sins: for he fell into
dreadful misfortunes.
(4) Latin was the language of the Vestals, and therefore no lady
need be ashamed of speaking it.
(5) None but physicians came to the meeting. There were therefore no
nurses there.
(6) The human soul extends through the whole body, for it is found
in every member.
(7) No traitor can be trusted, and you are a traitor.
(8) Whatever has no parts does not perish by the dissolution of its
parts. Therefore the soul of man is imperishable.
Is the suppressed premiss in any case disputable on material grounds?
CHAPTERS IX-XVIII.
Refer the following arguments to their proper mood and figure, or show
what rules of syllogism they violate.
(1) No miser is a true friend, for he does not assist his friend
with his purse.
(2) Governments are good which promote prosperity.
The government of Burmah does not promote prosperity.
.'. It is not a good government.
(3) Land is not property.
Land produces barley.
.'. Beer is intoxicating.
(4) Nothing is property but that which is the product of man's hand.
The horse is not the product of man's hand.
.'. The horse is not property.
(5) Some Europeans at least are not Aryans, because the Finns are
not.
(6) Saturn is visible from the earth, and the moon is visible from
the earth. Therefore the moon is visible from Saturn.
(7) Some men of self-command are poor, and therefore some noble
characters are poor.
(8) Sparing the rod spoils the child: so John will turn out very
good, for his mother beats him every day.
(9) Some effects of labour are not painful, since every virtue is an
effect of labour.
(10) The courageous are confident and the experienced are
confident. Therefore the experienced are courageous.
(11) No tale-bearer is to be trusted, and therefore no great talker
is to be trusted, for all tale-bearers are great talkers.
(12) Socrates was wise, and wise men alone are happy: therefore
Socrates was happy.
II.
1. From the major 'No matter thinks' draw, by supplying the minor, the
following conclusions--
(1) Some part of man does not think.
(2) The soul of man is not matter.
(3) Some part of man is not matter.
(4) Some substance does not think.
Name the figured mood into which each syllogism falls.
2. Construct syllogisms in the following moods and figures, stating
whether they are valid or invalid, and giving your reasons in each
case--
AEE in the first figure; EAO in the second; IAI in the third; AII in
the fourth.
3. Prove that 'Brass is not a metal,' using as your middle term
'compound body.'
4. Construct syllogisms to prove or disprove--
(1) Some taxes are necessary.
(2) No men are free.
(3) Laws are salutary.
5. Prove by a syllogism in Bokardo that 'Some Socialists are not
unselfish,' and reduce your syllogism directly and indirectly.
6. Prove the following propositions in the second figure, and reduce
the syllogisms you use to the first--
(1) All negroes are not averse to education.
(2) Only murderers should be hanged.
7. Prove in Baroko and also in Ferio that 'Some Irishmen are not
Celts.'
8. Construct in words the same syllogism in all the four figures.
9. Invent instances to show that false premisses may give true
conclusions.
III.
1. What moods are peculiar to the first, second, and third figures
respectively?
2. What moods are common to all the figures?
3. Why can there be no subaltern moods in the third figure?
4. What is the only kind of conclusion that can be drawn in all the
figures?
5. Show that IEO violates the special rules of all the figures.
6. In what figures is AEE valid?
7. Show that AEO is superfluous in any figure.
8. Prove that O cannot be a premiss in the first figure, nor a minor
premiss anywhere but in the second.
9. Show that in the first figure the conclusion must have the quality
of the major premiss and the quantity of the minor.
10. Why do the premisses EA yield a universal conclusion in the first
two figures and only a particular one in the last two?
11. Show that AAI is the only mood in the fourth figure in which it is
possible for the major term to be distributed in the premiss and
undistributed in the conclusion.
12. Why are the premisses of Fesapo and Fresison not transposed in
reduction like those of the other moods of the fourth figure?
IV.
1. Why is it sufficient to distribute the middle term once only?
2. Prove that from two affirmative premisses you cannot get a negative
conclusion.
3. Prove that there must be at least one more term distributed in the
premisses than in the conclusion.
4. Prove that the number of distributed terms in the premisses cannot
exceed those in the conclusion by more than two.
5. Prove that the number of undistributed terms in the premisses
cannot exceed those in the conclusion by more than one.
6. Prove that wherever the minor premiss is negative, the major must
be universal.
7. Prove that wherever the minor term is distributed, the major
premiss must be universal.
8. If the middle term be twice distributed, what mood and figure are
possible?
9. If the major term of a syllogism be the predicate of the major
premiss, what do we know about the minor premiss?
10. When the middle term is distributed in both premisses, what must
be the quantity of the conclusion?
11. Prove that if the conclusion be universal, the middle term can
only be distributed once in the premisses.
12. Show how it is sometimes possible to draw three different
conclusions from the same premisses.
CHAPTER XIX.
1. Convert the following propositions--
(1) If a man is wise, he is humble.
(2) Where there is sincerity there is no affectation.
(3) When night-dogs run, all sorts of deer are chased.
(4) The nearer the Church, the further from God.
(5) If there were no void, all would be solid.
(6) Not to go on is sometimes to go back.
2. Express in a single proposition--
If he was divine, he was not covetous; and if he was covetous, he
was not divine.
3. Exhibit the exact logical relation to one another of the following
pairs of propositions--
(1) If the conclusion be false, the premisses are false. If the
conclusion be true, the premisses are not necessarily true.
(2) If one premiss be negative, the conclusion must be negative.
If the conclusion be negative, one of the premisses must be
negative.
(3) The truth of the universal involves the truth of the particular.
The falsity of the particular involves the falsity of the universal.
(4) From the truth of the particular no conclusion follows as to the
universal.
From the falsity of the universal no conclusion follows as to the
particular.
(5) If the conclusion in the fourth figure be negative, the major
premiss must be universal.
If the major premiss in the fourth figure be particular, the
conclusion must be affirmative.
(6) If both premisses be affirmative, the conclusion must be
affirmative.
If the conclusion be negative, one of the premisses must be
negative.
4. 'The Method of Agreement stands on the ground that whatever
circumstance can be eliminated is not connected with the phenomenon by
any law; the Method of Difference stands on the ground that whatever
circumstance cannot be eliminated is connected with the phenomenon by
a law.' Do these two principles imply one another?
CHAPTERS XX-XXVIII.
1. Fill up the following enthymemes, and state the exact nature of the
resulting syllogism--
(1) If Livy is a faultless historian, we must believe all that he
tells us; but that it is impossible to do.
(2) If they stay abroad, the wife will die; while the husband's
lungs will not stand the English climate. It is to be feared
therefore that one must fall a victim.
(3) He is either very good, very bad, or commonplace. But he is not
very good.
(4) Either a slave is capable of virtue or he is not.
.'. Either he ought not to be a slave or he is not a man.
(5) Does not his feebleness of character indicate either a bad
training or a natural imbecility?
(6) Those who ask shan't have; those who don't ask don't want.
(7) If a man be mad, he deviates from the common standard of
intellect.
.'. If all men be alike mad, no one is mad.
(8) 'I cannot dig; to beg I am ashamed.'
2. 'The infinite divisibility of space implies that of time. If the
latter therefore be impossible, the former must be equally so.'
Formulate this argument as an immediate inference.
3. Examine the following arguments--
(1) If we have a dusty spring, there is always a good wheat
harvest. We shall therefore have a poor harvest this year, for the
spring has not been dusty.
(2) Virtues are either feelings, capacities, or states; and as they
are neither feelings nor capacities, they must be states.
(3) Everything must be either just or unjust.
Justice is a thing, and is not unjust.
.'. Justice is just.
Similarly justice is holy.
But the virtues of knowledge, justice, courage, temperance, and
holiness were declared to be different from one another.
.'. Justice is unholy and holiness unjust.
CHAPTER XXIX.
Formulate the following trains of reasoning, resolve them into their
component parts, and point out any violations of the rules of
syllogism which they may contain--
(1) No Church Institutions are useful; for they teach religious
matters, not business matters, which latter are useful, being
profitable.
(2) Mr. Darwin long ago taught us that the clover crop is dependent
on the number of maiden ladies in the district. For the ladies keep
cats, and the cats destroy the field-mice, which prey on the bees,
which, in their turn, are all-important agents in the fertilisation
of the clover flowers.
(3) Athletic games are duties; for whatever is necessary to health
is a duty, and exercise is necessary to health, and these games are
exercise.
(4) The iron-trade leads to the improvement of a new country; for
furnaces require to be fed with fuel, which causes land to be
cleared.
(5) 'Is stone a body?' 'Yes.' 'Well, is not an animal a body?'
'Yes,' 'And are you an animal?' 'It seems so.' 'Then you are a
stone, being an animal.'
(6) If A is B, C is D.
If E is F, G is H.
But if A is B, E is F.
.'. If C is D, G is sometimes H.
(7) The soul is not matter.
My arm is not myself.
(8) Honesty deserves reward and a negro is a
fellow-creature. Therefore an honest negro is a fellow-creature
deserving of reward.
CHAPTER XXX.
1. Point out any ambiguities which underlie the following
propositions--
(1) Every one who has read the book in French will recommend those
who have not to read it in English.
(2) I will not do this because he did it.
(3) These are all my books.
(4) By an old statute of the date of Edward III it was accorded
'that Parliament should be holden every year once or more often if
need be.'
(5) They found Mary and Joseph and the babe lying in a manger.
(6) The king and his minister are feeble and unscrupulous.
(7) Heres meus uxori meae triginta pondo vasorum argenteorum dato,
quae volet.
2. Examine the following arguments, formulating them when sound, and
referring them, when unsound, to the proper head of fallacy--
(1) We know that thou art a teacher come from God; for no man can do
these signs that thou doest, except God be with him. S. John iii. 2.
(2) 'Sir Walter Scott's novels have ceased to be popular.' 'Well,
that's only because nobody reads them.'
(3) What we produce is property.
The sheriff produces a prisoner.
.'. A prisoner is property.
(4) As all metals are not necessarily solid, we may expect some
metals to be liquid.
(5) Moses was the son of Pharaoh's daughter.
.'. Moses was the daughter of Pharaoh's son.
(6) If Aeschines took part in the public rejoicings over the success
of my policy, he is inconsistent in condemning it now; if he did
not, he was a traitor then.
(7) It is wrong to stick knives into people.
.'. Surgeons ought to be punished.
(8) If a thing admits of being taught, there must be both teachers
and learners of it.
.'. If there are neither teachers nor learners of a thing, that
thing does not admit of being taught.
(9) It is unnecessary to lend books, if they are common, and wrong
to lend them, if they are rare. Therefore books should not be lent
from public libraries.
(10) Seeing is believing.
.'. What is not seen cannot be believed.
(11) St. Paul was not of Jewish blood, for he was a Roman citizen.
(12) To call you an animal is to speak the truth.
To call you an ass is to call you an animal.
.'. To call you an ass is to speak the truth.
(13) Pain chastens folly. A life of ease must therefore be one of
folly incurable.
(14) We cannot be happy in this world; for we must either indulge
our passions or combat them.
(15) It must be clear to the most unlettered mind that, as all
things were originally created by the Deity, including the hair on
our heads and the beards on our faces, there can be no such thing as
property.
(16) The crime was committed by the criminal.
The criminal was committed by the magistrate.
.'. The crime was committed by the magistrate.
(17) General councils are as likely to err as the fallible men of
whom they consist.
(18) Dead dogs are heavier than living ones, because vitality is
buoyant.
(19) Deliberation is concerned with actions.
Actions are means.
.'. Deliberation is concerned with means.
(20) 'No beast so fierce but has a touch of pity; But I have none:
therefore I am no beast.'
(21) Practical pursuits are better than theoretical.
.'. Mathematics are better than logic.
(22) Death must be a good. For either the soul, ceasing to be,
ceases ta suffer, or, continuing to be, lives in a better state.
(23) What is right should be enforced by law.
.'. Charity should be so enforced.
(24) All animals were in the Ark.
.'. No animals perished in the Flood.
(25) If he robs, he is not honourable.
If he pays all his dues, he does not rob.
.'. If he pays all his dues, he is honourable.
(26) A dove can fly a mile in a minute.
A swallow can fly faster than a dove.
.'. A swallow can fly more than a mile in a minute.
(27) 'I must soap myself, because it's Sunday.'
'Then do you only soap yourself on Sunday.'
(28) If the charge is false, the author of it is either ignorant or
malicious. But the charge is true. Therefore he is neither.
(29) All the angles of a triangle are equal to two right angles.
The angle at the vertex is an angle of a triangle.
.'. It is equal to two right angles.
(30) Si gravis sit dolor, brevis est; si longus, levis. Ergo
fortiter ferendus.
(31) You are not what I am.
I am a man.
.'. You are not a man.
(32) The extension of the franchise is necessary, for it is
imperative that the right of voting should be granted to classes who
have hitherto not possessed this privilege.
(33) If Hannibal is really victorious, he does not need supplies;
while, if he is deluding us, we ought certainly not to encourage him
by sending them. Livy, xxiii. 13. § 5.
(34) Laws must punish, and punishment hurts.
All laws therefore are hurtful.
(35) The sun is an insensible thing.
The Persians worship the sun.
.'. The Persians worship an insensible thing.
(36) Some ores are not metals; for they are not fluids,
and some metals are not fluids.
(37) All the Grecian soldiers put the Persians to flight.
.'. Every Grecian soldier could rout the Persians.
(38) The resurrection of Jesus Christ is either an isolated fact or
else admits of parallel. But if it be an isolated fact, it cannot be
rendered probable to one who denies the authority of Christianity;
and, if it admit of parallel, it no longer proves what is
required. Therefore it is either incapable of being substantiated or
else makes nothing for the truth of Christianity.
(39) The resurrection of Christ in the flesh and his ascension into
heaven were events either intrinsically incredible in their nature
or not. If the former, the prevalent belief in them can only be
accounted for by miracles; if the latter, they ought to be believed
even without miracles. St. Aug. De Civ. Dei, xxii. 8.
(40) Only contented people are wise. Therefore the tramp contented
in his rags is necessarily a wise man.
(41) Four-legged things are brutes.
Tables are four-legged things.
.'. Tables are brutes.
(42) The apparent volcanoes in the moon are not volcanoes; for
eruptions are produced by gases only, and there are no gases in the
moon.
(43) To read the Scriptures is our duty. Therefore the Captain was
wrong in punishing the helmsman for reading the Bible at the time
when the ship struck.
(44) The divine law orders that kings should be honoured.
Louis Quatorze is a king.
.'. The divine law orders that Louis Quatorze should be honoured.
(45) Those who desire the same object are unanimous.
Caesar and Pompey both desire the same object, namely, supreme
power.
.'. They are unanimous.
(46) Either the ministers left at home will be ciphers or they will
not be ciphers. If they are ciphers, cabinet government, which is
equivalent to constitutional government, will receive a rude blow.
If they are not ciphers, the cabinet will be considering matters of
the utmost importance in the absence, and the gratuitous absence, of
two of its most important members. 'The Standard,' Wed. June 5,
1878.
(47) One patent stove saves half the ordinary amount of
fuel. Therefore two would save it all.
(48) One number must win in the lottery.
My ticket is one number.
.'. It must win.
(49) All good shepherds are prepared to lay down their lives for the
sheep.
Few in this age are so prepared.
.'. Few in this age are good shepherds.
(50) You cannot define the sun; for a definition must be clearer
than the thing defined, and nothing can be clearer than the source
of all light.
(51) To give the monopoly of the home market to the produce of
domestic industry ... must in almost all cases be either a useless
or a hurtful regulation. If the produce of domestic can be brought
there as cheap as that of foreign industry, the regulation is
evidently useless; if it cannot, it is generally hurtful. Adam
Smith, Wealth of Nations, Bk. iv. ch. 2.
(52) Verberare est actio.
Ergo et vapulare.
(53) The ages of all the members of this family are over 150.
The baby is a member of this family.
.'. Its age is over 150.
(54) Romulus must be an historical person; because it is not at all
likely that the Romans, whose memory was only burdened with seven
kings, should have forgotten the most famous of them, namely, the
first.
(55) All scientific treatises that are clear and true deserve
attention.
Few scientific treatises are clear and true.
.'. Few scientific treatises deserve attention.
(56) The Conservative Government is an expensive one; for, on their
going out of Office, there was a deficit.
(57) A man is forbidden to marry his brother's wife, or, in other
words, a woman is forbidden to marry her husband's brother, that is,
a woman is directly forbidden to marry two brothers. Therefore a man
may not marry two sisters, so that a man may not marry his wife's
sister.
INDEX.
The references refer to the sections.
Abstraction, 97.
Acategorematic words, 71.
Accent, Fallacy of, 855.
Accident, 318.
Accident, Fallacy of, 860.
A dicto secundum quid, Fallacy of, 861.
Amphiboly, Fallacy of, 848.
Antecedent
of a complex proposition, 212.
of an inference, 428.
A posteriori Truth, 232.
A priori Truth, 231.
'A' Propositions, 260.
conversion of, 489.
Arguing in a circle, 882.
Argumentum ad hominem, etc., 867.
Art, 20.
Attribute, 81 sqq.
Essential and non-essential, 320.
Attributives, 88 sqq.
Basis of Division, 391.
Categorematic words, 71.
Circulus in definiendo, 382.
Common Terms, 105.
how formed, 99.
nature of, 48.
Complex Proposition, 209.
conversion of, 709.
conversion by contraposition of, 728.
conversion by negation of, 721.
divided into conjunctive and disjunctive, 214.
permutation of, 718.
Complex Syllogism, 731.
mixed form of, 778.
Composition, Fallacy of, 849.
Concept, 36, 40 sqq.
Conception, 33.
Conceptualists, 51.
Conclusion, 540.
predicate of, 542.
subject of, 542.
Conjunctive Syllogisms, 733.
canon of, 742.
reduction of partly, 744.
partly conjunctive syllogisms as an immediate inference, 753.
Connotation of Terms, 148.
Consequent of a complex proposition, 213.
of an inference, 428.
Consequent, Fallacy of, 873.
Contingent, 17.
Contradiction, Law of, 25 sqq.
Contradictory Propositions, 458.
Terms, 129.
Contrary Propositions, 458.
Terms, 130.
Converse, 480.
Conversion, 479.
of complex propositions, 709.
by contraposition, 516.
illative, 481.
by negation, 504.
per accidens, 487.
simple, 486.
rules of, 482.
Convertend, 480.
Copula, 58, 64, 186 sqq.
modality of, 196.
Correlatives, 142.
Deduction and Induction, difference of, 431 sqq.
Deductive Inference, 442.
Deductive Logic, definition of, 4.
Definition of Terms, 347 sqq.
of Aristotle ([Greek: òrismós]), 336.
final, 374.
nominal, 375.
provisional, 374.
real, 375.
rules of, 378.
Denotation of Terms, 152.
Description, 360.
Designations, 112.
Determination, 167.
Dictum de omni et nullo, 569.
de diverso, 641.
de exemplo et excepto, 642.
Difference, 318, 358.
generic, 410.
specific, 409.
Dilemma, 732, 779.
rebutted, 792.
reduction of, 796.
regarded as an immediate inference, 798.
Disjunctive Syllogism, 760.
canon of, 765.
reduction of, 766.
regarded as an immediate inference, 770.
Distinction, 424.
Distribution of Terms, 274.
four rules for, 293.
Divided whole, 393.
Dividing members, 394.
Division, 385 sqq.
by dichotomy, 412.
rules of, 395.
Division, Fallacy of, 851.
Division of Propositions, 206.
of terms, 86.
of things, 77.
Enthymeme, incorrectly so-called, 557.
Enumeration, 387, 422.
Epicheirema, 803.
Episyllogism, 802.
'E' Propositions, 260.
conversion of, 490.
Equivocation, Fallacy of, 845.
Excluded Middle, Law of, 25 sqq., 502.
Extension of Terms, 149 sqq., 166 sqq.
Fallacy, 827 sqq.
of ambiguity, 831.
definition of, 828.
formal, 838.
logical, 836.
material, 831, 836.
of undisturbed middle, 585.
Figure of Speech, Fallacy of, 857.
Figures, of a Syllogism, 558.
special canons of, 633.
special rules of, 606.
special uses of, 648.
Formal Logic, 16.
Four Terms, Fallacy of, 840.
Fundamentum Divisionis, 391.
Generalisation, 168.
Genus, 318.
as used by Aristotle, 336.
cognate, 408.
proximate, 420.
subaltern, 406.
summum, 167, 404.
Heads of Predicables, 313.
as given by Aristotle, 336.
'Ideas' of Plato, 52.
Identity, Law of, 25 sqq.
Ignoratio Elenchi, Fallacy of, 865.
Ignotum per ignotius, 383.
Illicit Process, Fallacy of, 586.
Immediate Inference, 442 sqq.
by added determinants, 535.
by complex conception, 537.
applied to complex propositions, 701.
Immediate Inference, compound forms of, 503.
partly conjunctive syllogisms regarded as, 753.
by conversion, 479.
disjunctive syllogisms regarded as, 770.
by opposition, 462.
by permutation, 496.
Induction, differing from Deduction, 430 sqq.
Inductive Logic, 2, 204.
Inferences in general, 426.
classification of, 441.
deductive, 442.
inductive, 430.
Intimae species, 405.
Intension of Terms, 150, 166.
Intuition, 232.
Inverse Variation, Law of, 166.
'I' Propositions, 260.
conversion of, 490.
'Judgement,' various meanings of, 32, 36.
'Law,' ambiguities of the word, 7 sqq.
Major Premiss, 544.
Major Term, 542.
Many Questions, Fallacy of, 884.
Mediate Inferences or Syllogisms, 444, 540 sqq.
axioms of, 576.
Membra Dividentia, 394.
Middle Term, 541.
position of, in a syllogism, 563.
Minor Premiss, 545.
Minor Term, 542.
Modality, Question of, 196.
Mode, the, 196.
Moods of a Syllogism, 558.
determination of the legitimate, 599.
subaltern, 628.
valid in the Four Figures, 621.
mnemonics of, valid in Four Figures, 629.
Name, definition of, 61.
Negative Premisses and Conclusion, Fallacy of, 842.
Nominalists, 50, 54.
Non causa pro causa, Fallacy of, 883.
Nouns, 62.
Opposition, 449 sqq.
contradictory, 457.
contrary, 454.
laws of, 464.
subaltern, 456.
sub-contrary, 455.
'O' Propositions, 260.
conversion of, 491.
Partition, 423.
Permutation, 496 sqq.
of Complex Propositions, 718.
Petitio Principii, Fallacy of, 874.
Predicable, 314.
Predicate of a Proposition, 58, 184.
read in extension, 307.
quantification of, 295 sqq.
quantity of, 281, 494.
Predication, 194.
in quid or in quale, 332.
Premisses, 540.
major, 544.
minor, 545.
Primary Existences, 55.
Problema, the, 556.
Proper Names, 113.
Property, 318.
generic, 411.
specific, 411.
Proposition, 172 sqq.
accidental, 238.
affirmative, 258.
complex or conditional, 209.
conjunctive or hypothetical, 214, 704.
conversion of, 479.
definition of, 178.
disjunctive, 214.
divisions of, 206.
essential, 238.
exceptive, 270.
exclusive, 266.
extensive, 264.
general, 251.
indefinite, 244.
intensive, 264.
modal, 205.
negative, 258.
particular, 240.
pure, 205.
quality of, 258.
quantity of, 246.
real or synthetical, 227.
simple or categorical, 207.
singular, 250.
tautologous or identical, 273.
universal, 239.
verbal or analytical, 224.
Proprium, 336.
Pro-syllogism, 802.
Quaestio, the, 556.
Quality, a, 82.
Quality of the matter, 204.
of propositions, 258.
Quantification of the Predicate, 295 sqq., 493.
Quantity of propositions, 258.
of terms, 148.
Realists, 49.
Real Kinds, 371.
Reasoning or Inference, 35.
the canon of, 560.
trains of, 800.
Reduction of propositions, 667.
of the dilemma, 796.
of disjunctive syllogisms, 766.
indirect, 691.
mnemonics for, 697.
ostensive or direct, 673.
of partly conjunctive syllogisms, 744.
Relation, a, 83, 144.
Relation, immediate inference by, 462.
compatible and incompatible, 462.
Science, 20.
Secondary Existences, 55.
Simple Apprehension, 33.
Sorites, the, 807 sqq.
Specialisation, 167.
Species, 318.
cognate, 407.
infimae, 405.
subaltern, 406.
Subalternant, 458.
Subalternate, 458.
Subalternation, 458.
Subalterns, 458.
Sub-contraries, 458.
Sub-division, 401.
Subject, 58, 183.
how used, 264.
quantity of, 279.
Substance, 80, 84.
Summum Genus, 167, 404.
Suppositio Materialis, 76.
Syllogism, 546 sqq.
complex, 731.
in common discourse, 557.
conjunctive, 733.
definition of, 552.
disjunctive, 760.
general rules of, 582.
figures of, 560, 563.
with three figures, 656.
legitimate moods of, 599 sqq.
mnemonics for, 598.
moods of, 559, 562.
Syncntegorematic words, 70.
Synonym, 345.
Term, 57 sqq.
absolute, 140.
abstract, 95.
analogous, 139.
attributive, 88.
collective, 118.
common, 105.
concrete, 96.
connotative, 147.
contradictory, 129.
contrary, 130.
definition of, 347.
Terms, distribution of, 275.
distributive and collective use of, 119.
division of, 86.
equivocal, 137.
incompatible, 135.
individual, 121.
major, middle, and minor, 542.
negative, 126.
non-connotative, 147.
positive, 126.
privative, 126.
quantity of, 148.
Terms, relative, 141.
repugnant, 135.
singular, 43, 104.
subject, 87.
undistributed, 277.
univocal, 137.
Universals, nature of, 48, 55.
'U' Propositions, 297.
Verb, 64.
Words, their relation to terms, 65 sqq,
THE END.