Deductive Logic

S >> St. George Stock >> Deductive Logic

Pages:
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18

In the regressive sorites the proposition which stands first is the
only one which appears as a major premiss in the expanded form.
Each of the others is used in its turn as a minor. If any premiss,
therefore, but the first were negative, we should have a negative
minor in the first figure, which involves illicit process of the
major.

825. The rules above given do not apply to the irregular sorites,
except so far as that only one premiss can be particular and only one
negative, which follows from the general rules of syllogism. But there
is nothing to prevent any one premiss from being particular or any one
premiss from being negative, as the subjoined examples will show. Both
the instances chosen belong to the progressive order of sorites.

(1) Barbara.
All B is A.
All C is B.
All C is A.

All B is A.
All C is B.
Some C is D.
All D is E
.'. Some A is E

[Illustration]

(2) Disamis.
Some C is D.
All C is A.
Some A is D.

(3) Darii.
All D is E
Some A is D.
Some A is E.

(1) Barbara.
All B is C.
All A is B.
All A is C.

All A is B.
All B is C.
No D is C.
All E is D.
.'. No A is E.

[Illustration]

(2) Cesare.
No D is C.
All A is C.
.'. No A is D.

(3) Camestres.
All E is D.
No A is D.
.'. No A is E.

826. A chain argument may be composed consisting
of conjunctive instead of simple propositions. This is
subject to the same laws as the simple sorites, to which
it is immediately reducible.

_Progressive._ _Regressive._
If A is B, C is D. If E is F, G is H.
If C is D, E is F. If C is D, E is F.
If E is F, G is H. If A is B, C is D.
.'. If A is B, G is H. .'. If A is B, G is H.

CHAPTER XXX.

_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 infimae 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: omonumia] 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: amphibolia]) 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: to boulesthai labein me tous polemious]

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: diairesis] 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: diairesis]), on the other hand,
consists in taking words separately which ought to be taken together,
e.g.

[Greek: ego s' eteka doulon ont' eleuteron [Footnote: Evidently the
original of the line in Terence's _Andria_, 37,--feci ex servo
ut esses libertus mihi.],

where the separation of [Greek: doulon] from [Greek: ontra] would lead
to an interpretation exactly contrary to what is intended.

And again--

[Greek: pentekont' andron ekaton lipe dios Achilleus],

where the separation of [Greek: andron] from [Greek: ekaton] 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: prosodia]) 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: to men ou kataputetai ombro] by writing
[Greek: ou] with the circumflex in place of [Greek: ou] 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: to schema tes lexeos]
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: ugiainein] has the
same grammatical form as [Greek: temnein] or [Greek: oikodomein], 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: kapdopos] must be masculine because [Greek: Kleonumos] 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: to
sumbebekos]). 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: to aplos tode e pe legestai kai me
kupios] or, more briefly, [Greek: to aplos e me], or [Greek: to pe kai
aplos], 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: to me on]) is a matter of
opinion, that therefore the non-existent is, or again that because the
existent ([Greek: to on]) 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: pe]), but not absolutely ([Greek: aplos]). 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.

Pages:
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18