Logic from Stephen's Guide

vagrant

False Dilemma

Definition:

A limited number of options (usually two) is given, while in reality there are more options. A false dilemma is an illegitimate use of the "or" operator.
Putting issues or opinions into "black or white" terms is a common instance of this fallacy.


Examples:
(i) Either you're for me or against me.

(ii) America: love it or leave it.

(iii) Either support Meech Lake or Quebec will separate.

(iv) Every person is either wholly good or wholly evil.


Proof:
Identify the options given and show (with an example) that
there is an additional option.

applebees

thanks1

baby11

thanks, though in English

vagrant

From Stephen's Guide (11)
Fallacies of Ambiguity

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The fallacies in this section are all cases where a word or phrase is used unclearly.
There are two ways in which this can occur.


(i) The word or phrase may be ambiguous, in which case it has more than
one distinct meaning.

(ii) The word or phrase may be vague, in which case it has no distinct
meaning.

The following are fallacies of ambiguity:

1. Equivocation

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Definition:
The same word is used with two different meanings.

Examples:
(i) Criminal actions are illegal, and all murder trials are
criminal actions, thus all murder trials are illegal. (Here the
term "criminal actions" is used with two different meanings.
Example borrowed from Copi.)
(ii) The sign said "fine for parking here", and since it was
fine, I parked there.
(iii) All child-murderers are inhuman, thus, no child-
murderer is human. (From Barker, p. 164; this is called
"illicit obversion")
(iv) A plane is a carpenter's tool, and the Boeing 737 is a
plane, hence the Boeing 737 is a carpenter's tool. (Example
borrowed from Davis, p. 58)

Proof:
Identify the word which is used twice, then show that a
definition which is appropriate for one use of the word would
not be appropriate for the second use

2.Amphiboly

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Definition:

An amphiboly occurs when the construction of a sentence
allows it to have two different meanings.

Examples:
(i) Last night I shot a burglar in my pyjamas.
(ii) The Oracle of Delphi told Croseus that if he pursued the
war he would destroy a mighty kingdom. (What the Oracle
did not mention was that the kingdom he destroyed would
be his own. Adapted from Heroditus, The Histories.)
(iii) Save soap and waste paper. (From Copi, p. 115)

Proof:
Identify the ambiguous phrase and show the two possible
interpretations.

3. Accent

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Definition:

Emphasis is used to suggest a meaning different from the
actual content of the proposition.

Examples:
(i) It would be illegal to give away
Free Beer!
(ii) The first mate, seeking revenge on the captain, wrote in
his journal, "The Captain was sober today." (He suggests, by
his emphasis, that the Captain is usually drunk. From Copi,
p. 117)

vagrant

From Stephen's Guide (12)
Category Errors

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These fallacies occur because the author mistakenly assumes that the whole is
nothing more than the sum of its parts. However, things joined together may have
different properties as a whole than any of them do separately.
The following fallacies are category errors:

1. Composition

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Definition

Because the parts of a whole have a certain property, it is argued
that the whole has that property. That whole may be either an object
composed of different parts, or it may be a collection or set of
individual members.

Examples:
(i) The brick wall is six feet tall. Thus, the bricks in the wall are six
feet tall.
(ii) Germany is a militant country. Thus, each German is militant.
(iii) Conventional bombs did more damage in W.W. II than nuclear
bombs. Thus, a conventional bomb is more dangerous than a
nuclear bomb. (From Copi, p. 118)


Proof:
Show that the properties in question are the properties of the whole,
and not of each part or member or the whole. If necessary, describe
the parts to show that they could not have the properties of the
whole.

2. Division

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Definition:

Because the whole has a certain property, it is argued that the parts
have that property. The whole in question may be either a whole
object or a collection or set of individual members.

Examples:
(i) Each brick is three inches high, thus, the brick wall is three
inches high.
(ii) Because the brain is capable of consciousness, each neural cell
in the brain must be capable of consciousness.

Proof:
Show that the properties in question are the properties of the parts,
and not of the whole. If necessary, describe the parts to show that
they could not have the properties of the whole.

vagrant

From Stephen's Guide (13)
Non-Sequitur

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The term non sequitur literally means "it does not follow". In this section we
describe fallacies which occur as a consequence of invalid arguments.
The following fallacies are non sequiturs:

1. Affirming the Consequent

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Definition:

Any argument of the following form is invalid:
If A then B
B
Therefore, A

Examples:
(i) If I am in Calgary, then I am in Alberta. I am in Alberta,
thus, I am in Calgary. (Of course, even though the premises
are true, I might be in Edmonton, Alberta.)
(ii) If the mill were polluting the river then we would see an
increase in fish deaths. And fish deaths have increased. Thus,
the mill is polluting the river.

Proof:
Show that even though the premises are true, the conclusion
could be false. In general, show that B might be a
consequence of something other than A. For example, the fish
deaths might be caused by pesticide run-off, and not the mill

2. Denying the Antecedent

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Definition:

Any argument of the following form is invalid:
If A then B
Not A
Therefore, Not B

Examples:
(i) If you get hit by a car when you are six then you will die
young. But you were not hit by a car when you were six.
Thus you will not die young. (Of course, you could be hit by
a train at age seven, in which case you still die young.)
(ii) If I am in Calgary then I am in Alberta. I am not in
Calgary, thus, I am not in Alberta.

Proof:
Show that even though the premises are true, the conclusion
may be false. In particular, show that the consequence B may
occur even though A does not occur.

3. Inconsistency

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Definition:

The author asserts more than one proposition such that the
propositions cannot all be true. In such a case, the
propositions may be contradictories or they may be
contraries.

Examples:
(i) Montreal is about 200 km from Ottawa, while Toronto is
400 km from Ottawa. Toronto is closer to Ottawa than
Montreal.
(ii) John is taller than Jake, and Jake is taller than Fred,
while Fred is taller than John.

Proof:
Assume that one of the statements is true, and then use it as
a premise to show that one of the other statements is false

vagrant

From Stephen's Guide (9)
Causal Fallacies

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It is common for arguments to conclude that one thing causes another. But the
relation between cause and effect is a complex one. It is easy to make a mistake.
In general, we say that a cause C is the cause of an effect E if and only if:

(i) Generally, if C occurs, then E will occur, and

(ii) Generally, if C does not occur, then E will not occur ether.

We say "generally" because there are always exceptions. For example:
We say that striking the match causes the match to light, because:

(i) Generally, when the match is struck, it lights (except when the match
is dunked in water), and

(ii) Generally, when the match is not struck, it does not light (except when
it is lit with a blowtorch).

Many writers also require that a causal statement be supported with a natural law.
For example, the statement that "striking the match causes it to light" is supported
by the principle that "friction produces heat, and heat produces fire".
The following are causal fallacies:

1. Coincidental Correlation
(post hoc ergo propter hoc )

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Definition:
The name in Latin means "after this therefore because of this".
This describes the fallacy. An author commits the fallacy when
it is assumed that because one thing follows another that the
one thing was caused by the other.

Examples:
(i) Immigration to Alberta from Ontario increased. Soon
after, the welfare rolls increased. Therefore, the increased
immigration caused the increased welfare rolls.
(ii) I took EZ-No-Cold, and two days later, my cold
disappeared.


Proof:
Show that the correlation is coincidental by showing that: (i)
the effect would have occurred even if the cause did not
occur, or (ii) that the effect was caused by something other
than the suggested cause.

2. Joint Effect

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Definition:
One thing is held to cause another when in fact both are the
effect of a single underlying cause. This fallacy is often
understood as a special case of post hoc ergo prompter hoc.

Examples:
(i) We are experiencing high unemployment which s being
caused by a low consumer demand. (In fact, both may be
caused by high interest rates.)
(ii) You have a fever and this is causing you to break out in
spots. (In fact, both symptoms are caused by the measles.)

Proof:
Identify the two effects and show that they are caused by the
same underlying cause. It is necessary to describe the
underlying cause and prove that it causes each symptom

3. Genuine but Insignificant Cause

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Definition:
The object or event identified as the cause of an effect is a
genuine cause, but insignificant when compared to the other
causes of that event.
Note that this fallacy does not apply when all other
contributing causes are equally insignificant. Thus, it is not a
fallacy to say that you helped cause defeat the Tory
government because you voted Reform, for your vote had as
much weight as any other vote, and hence is equally a part of
the cause.

Examples:
(i) Smoking is causing air pollution in Edmonton. (True, but
the effect of smoking is insignificant compared to the effect
of auto exhaust.)
(ii) By leaving your oven on overnight you are contributing
to global warming.

Proof:
Identify the much more significant cause.

4. Genuine but Insignificant Cause

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Definition:
The object or event identified as the cause of an effect is a
genuine cause, but insignificant when compared to the other
causes of that event.
Note that this fallacy does not apply when all other
contributing causes are equally insignificant. Thus, it is not a
fallacy to say that you helped cause defeat the Tory
government because you voted Reform, for your vote had as
much weight as any other vote, and hence is equally a part of
the cause.

Examples:
(i) Smoking is causing air pollution in Edmonton. (True, but
the effect of smoking is insignificant compared to the effect
of auto exhaust.)
(ii) By leaving your oven on overnight you are contributing
to global warming.

Proof:
Identify the much more significant cause.

5. Wrong Direction

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Definition:
The relation between cause and effect is reversed.

Examples:
(i) Cancer causes smoking.
(ii) The increase in AIDS was caused by more sex education.
(In fact, the increase in sex education was caused by the
spread of AIDS.)

Proof:
Give a causal argument showing that the relation between
cause and effect has been reversed.

6. Complex Cause

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Definition:
The effect is caused by a number of objects or events, of
which the cause identified is only a part. A variation of this is
the feedback loop where the effect is itself a part of the cause.

Examples:
(i) The accident was caused by the poor location of the bush.
(True, but it wouldn't have occurred had the driver not been
drunk and the pedestrian not been jaywalking.)
(ii) The Challenger explosion was caused by the cold
weather. (True, however, it would not have occurred had the
O-rings been properly constructed.)
(iii) People are in fear because of increased crime. (True, but
this has lead people to break the law as a consequence of
their fear, which increases crime even more.)

Proof:
Show that all of the causes, and not just the one mentioned,
are required to produce the effect.

vagrant

From Stephen's Guide (10)
Missing the Point

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These fallacies have in common a general failure to prove that the conclusion is
true.
The following fallacies are cases of missing the point

1. Begging the Question
( petitio principii )

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Definition:
The truth of the conclusion is assumed by the premises.
Often, the conclusion is simply restated in the premises in a
slightly different form. In more difficult cases, the premise is
a consequence of the conclusion.

Examples:
(i) Since I'm not lying, it follows that I'm telling the truth.

(ii) We know that God exists, since the Bible says God exists.
What the Bible says must be true, since God wrote it and
God never lies. (Here, we must agree that God exists in order
to believe that God wrote the Bible.)

Proof:
Show that in order to believe that the premises are true we
must already agree that the conclusion is true

2. Irrelevant Conclusion
( ignoratio elenchi )

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Definition:
An argument which purports to prove one thing instead
proves a different conclusion.

Examples:
(i) You should support the new housing bill. We can't
continue to see people living in the streets; we must have
cheaper housing. (We may agree that housing s important
even though we disagree with the housing bill.)
(ii) I say we should support affirmative action. White males
have run the country for 500 years. They run most of
government and industry today. You can't deny that this
sort of discrimination is intolerable. (The author has proven
that there is discrimination, but not that affirmative action
will end that discrimination.)

Proof: <./b>
Show that the conclusion proved by the author is not the
conclusion that the author set out to prove

3. Straw Man

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Definition:
The author attacks an argument which is different from, and
usually weaker than, the opposition's best argument.

Examples:
(i) People who opposed the Charlottown Accord probably just
wanted Quebec to separate. But we want Quebec to stay in
Canada.
(ii) We should have conscription. People don't want to enter
the military because they find it an inconvenience. But they
should realize that there are more important things than
convenience.

Proof:
Show that the opposition's argument has been
misrepresented by showing that the opposition has a stronger
argument. Describe the stronger argument

vagrant

From Stephen's Guide (6)
Changing the Subject

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The fallacies in this section change the subject by discussing the person making
the argument instead of discussing reasons to believe or disbelieve the conclusion.
While on some occasions it is useful to cite authorities, it is almost never
appropriate to discuss the person instead of the argument.
The fallacies described in this section are:

1. Attacking the Person
(argumentum ad hominem)

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Definition:
The person presenting an argument is attacked instead of the
argument itself. This takes many forms. For example, the
person's character, nationality or religion may be attacked.
Alternatively, it may be pointed out that a person stands to
gain from a favourable outcome. Or, finally, a person may be
attacked by association, or by the company he keeps.
There are three major forms of Attacking the Person:
(1) ad hominem (abusive): instead of attacking an assertion,
the argument attacks the person who made the assertion.
(2) ad hominem (circumstantial): instead of attacking an
assertion the author points to the relationship between the
person making the assertion and the person's circumstances.
(3) ad hominem (tu quoque): this form of attack on the
person notes that a person does not practise what he
preaches.


Examples:
(i) You may argue that God doesn't exist, but you are just
following a fad. (ad hominem abusive)
(ii) We should discount what Premier Klein says about
taxation because he won't be hurt by the increase. (ad
hominem circumstantial)
(iii) We should disregard Share B.C.'s argument because they
are being funded by the logging industry. (ad hominem
circumstantial)
(iv) You say I shouldn't drink, but you haven't been sober for
more than a year. (ad hominem tu quoque)

Proof:
Identify the attack and show that the character or
circumstances of the person has nothing to do with the truth
or falsity of the proposition being defended.

2. Appeal to Authority
(argumentum ad verecundiam)

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Definition:
While sometimes it may be appropriate to cite an authority to
support a point, often it is not. In particular, an appeal to
authority is inappropriate if:
(i) the person is not qualified to have an expert
opinion on the subject,
(ii) experts in the field disagree on this issue.
(iii) the authority was making a joke, drunk, or
otherwise not being serious
A variation of the fallacious appeal to authority is hearsay. An
argument from hearsay is an argument which depends on
second or third hand sources.


Examples:
(i) Noted psychologist Dr. Frasier Crane recommends that
you buy the EZ-Rest Hot Tub.
(ii) Economist John Kenneth Galbraith argues that a tight
money policy s the best cure for a recession. (Although
Galbraith is an expert, not all economists agree on this
point.)
(iii) We are headed for nuclear war. Last week Ronald
Reagan remarked that we begin bombing Russia in five
minutes. (Of course, he said it as a joke during a
microphone test.)
(iv) My friend heard on the news the other day that Canada
will declare war on Serbia. (This is a case of hearsay; in
fact, the reporter said that Canada would not declare war.)
(v) The Ottawa Citizen reported that sales were up 5.9
percent this year. (This is hearsay; we are not n a position to
check the Citizen's sources.)

Proof:
Show that either (i) the person cited is not an authority in the
field, or that (ii) there is general disagreement among the
experts in the field on this point.

3. Anonymous Authorities

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Definition:
The authority in question is not named. This is a type of
appeal to authority because when an authority is not named
it is impossible to confirm that the authority is an expert.
However the fallacy is so common it deserves special
mention.
A variation on this fallacy is the appeal to rumour. Because
the source of a rumour is typically not known, it is not
possible to determine whether to believe the rumour. Very
often false and harmful rumours are deliberately started n
order to discredit an opponent.


Examples:
(i) A government official said today that the new gun law
will be proposed tomorrow.
(ii) Experts agree that the best way to prevent nuclear war
is to prepare for it.
(iii) It is held that there are more than two million needless
operations conducted every year.
(iv) Rumour has it that the Prime Minster will declare
another holiday in October.

Proof:
Argue that because we don't know the source of the
information we have no way to evaluate the reliability of the
information.

4. Style Over Substance

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Definition:
The manner in which an argument (or arguer) is presented is
taken to affect the likelihood that the conclusion is true.

Examples:
(i) Nixon lost the presidential debate because of the sweat on
his forehead.
(ii) Trudeau knows how to move a crowd. He must be right.
(iii) Why don't you take the advice of that nicely dressed
young man?

Proof:
While it is true that the manner in which an argument is
presented will affect whether people believe that its
conclusion is true, nonetheless, the truth of the conclusion
does not depend on the manner in which the argument is
presented. In order to show that this fallacy is being
committed, show that the style in this case does not affect the
truth or falsity of the conclusion.

vagrant

From Stephen's Guide (7)
Inductive Fallacies

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Inductive reasoning consists of inferring from the properties of a sample to the
properties of a population as a whole.
For example, suppose we have a barrel containing of 1,000 beans. Some of the
beans are black and some of the beans are white. Suppose now we take a sample
of 100 beans from the barrel and that 50 of them are white and 50 of them are
black. Then we could infer inductively that half the beans in the barrel (that is,
500 of them) are black and half are white.

All inductive reasoning depends on the similarity of the sample and the
population. The more similar the same is to the population as a whole, the more
reliable will be the inductive inference. On the other hand, if the sample is
relevantly dissimilar to the population, then the inductive inference will be
unreliable.

No inductive inference is perfect. That means that any inductive inference can
sometimes fail. Even though the premises are true, the conclusion might be false.
Nonetheless, a good inductive inference gives us a reason to believe that the
conclusion is probably true.

The following inductive fallacies are described in this section

1.Hasty Generalization

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Definition:
The size of the sample is too small to support the conclusion.

Examples:
(i) Fred, the Australian, stole my wallet. Thus, all Australians
are thieves. (Of course, we shouldn't judge all Australians on
the basis of one example.)
(ii) I asked six of my friends what they thought of the new
spending restraints and they agreed it is a good idea. The
new restraints are therefore generally popular.

Proof:
Identify the size of the sample and the size of the population,
then show that the sample size is too small. Note: a formal
proof would require a mathematical calculation. This is the
subject of probability theory. For now, you must rely on
common sense

2. Unrepresentative Sample

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Definition:
The sample used in an inductive inference is relevantly
different from the population as a whole.

Examples:
(i) To see how Canadians will vote in the next election we
polled a hundred people in Calgary. This shows conclusively
that the Reform Party will sweep the polls. (People in
Calgary tend to be more conservative, and hence more likely
to vote Reform, than people in the rest of the country.)
(ii) The apples on the top of the box look good. The entire
box of apples must be good. (Of course, the rotten apples are
hidden beneath the surface.)

Proof:
Show how the sample is relevantly different from the
population as a whole, then show that because the sample is
different, the conclusion is probably different

3. False Analogy

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Definition:
In an analogy, two objects (or events), A and B are shown to
be similar. Then it is argued that since A has property P, so
also B must have property P. An analogy fails when the two
objects, A and B, are different in a way which affects whether
they both have property P.

Examples:
(i) Employees are like nails. Just as nails must be hit in the
head in order to make them work, so must employees.
(ii) Government is like business, so just as business must be
sensitive primarily to the bottom line, so also must
government. (But the objectives of government and business
are completely different, so probably they will have to meet
different criteria.)

Proof:
Identify the two objects or events being compared and the
property which both are said to possess. Show that the two
objects are different in a way which will affect whether they
both have that property.


4. Slothful Induction

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Definition:
The proper conclusion of an inductive argument is denied
despite the evidence to the contrary.

Examples:
(i) Hugo has had twelve accidents n the last six months, yet
he insists that it is just a coincidence and not his fault.
(Inductively, the evidence is overwhelming that it is his fault.
This example borrowed from Barker, p. 189)
(ii) Poll after poll shows that the N.D.P will win fewer than
ten seats in Parliament. Yet the party leader insists that the
party is doing much better than the polls suggest. (The N.D.P.
in fact got nine seats.)

Proof:
About all you can do in such a case is to point to the strength
of the inference.

5. Slothful Induction

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Definition:
The proper conclusion of an inductive argument is denied
despite the evidence to the contrary.

Examples:
(i) Hugo has had twelve accidents n the last six months, yet
he insists that it is just a coincidence and not his fault.
(Inductively, the evidence is overwhelming that it is his fault.
This example borrowed from Barker, p. 189)
(ii) Poll after poll shows that the N.D.P will win fewer than
ten seats in Parliament. Yet the party leader insists that the
party is doing much better than the polls suggest. (The N.D.P.
in fact got nine seats.)

Proof:
About all you can do in such a case is to point to the strength
of the inference.

6. Fallacy of Exclusion

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Definition:
Important evidence which would undermine an inductive
argument is excluded from consideration. The requirement
that all relevant information be included is called the
"principle of total evidence".

Examples:
(i) Jones is Albertan, and most Albertans vote Tory, so Jones
will probably vote Tory. (The information left out is that
Jones lives in Edmonton, and that most people in Edmonton
vote Liberal or N.D.P.)
(ii) The Leafs will probably win this game because they've
won nine out of their last ten. (Eight of the Leafs' wins came
over last place teams, and today they are playing the first
place team.)

Proof:
Give the missing evidence and show that it changes the
outcome of the inductive argument. Note that it is not
sufficient simply to show that not all of the evidence was
included; it must be shown that the missing evidence will
change the conclusion.