Deductive Logic
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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: elegchou
agnoia]. 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: elegchos] 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: lopion], it is not enough for you to prove the contradictory
with regard to [Greek: imation]. 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: to en
arche aiteistai or lambanein] to which we now come, consists in an
unfair assumption of the point at issue. The word [Greek: aiteistai],
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: Otan to me di
autou gnoston di autou tis epicheirae deiknunai, tot' aiteitai to ex
arches.]. 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: to me aition] or
[Greek: aitoin]) 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: to ta deo
erotemata en poiein]) 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.
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