???? (The Problem of Logic)
(Ke Ping [Ed.],
2002-2021)
2.1.1.1 Hypothetical syllogism (?????)
2.1.1.2 Disjunctive syllogism (?????)
2.1.1.3 Categorical syllogism (?????)
2.1.2 Fallacy of the consequent (??????)
2.1.2.1 Denial of the antecedent (????)
2.1.2.2 Affirmation of the consequent (????)
2.1.3 Fallacy of illicit major (or minor) premise
(????????)
2.1.3.1 The formation of a categorical syllogism
2.1.3.2 Five basic rules governing the validity of categorical syllogisms
2.1.3.3 Distribution of terms (??)
2.1.4 Extended discussion on
correct forms of or rules for syllogistic reasoning
2.1.4.1 Distinction between a
valid deduction (??) and a valid argument (??)
2.1.4.2 Verification (??) vs falsification (??)
2.2 Informal Logical
Fallacies
(1) Non sequitur (< Latin: “it does not follow” ???)
(2) Oversimplification (?????)
(3) Hasty generalization (?????????)
(4) Argument from dubious authority (??????)
(5) Begging the question (????????????????????????????????????also called “Circular Argument” ????)
(6) Argument ad hominem (< Latin, “against the man” ????)
(7) Argument from ignorance (??????????)
(8) Post hoc ergo propter hoc (< Latin, “after this, therefore because of
this” ????????????)
(10) Card-stacking (?????????)
(11) Arguing by analogy (?????)
2.2.2 Fallacies of ambiguity (verbal fallacies)
?
(which should be
?/
Logic is no guarantee that we will not make mistakes in argument. But it will help us to avoid making obvious or absurd mistakes because some ways of reasoning are evidently more fallible than others.
?
In Aristotle’s formal logic, two ways of reasoning are distinguished, i.e. deductive reasoning or deduction, and inductive reasoning or induction.
A classic form of deductive reasoning is syllogism, that is, (a reasoned argument in which there are two statements which must
lead to a third statement). A typical syllogism is a three-step form like this:
? All trees have roots. (Major premise)
A plane is a tree. (Minor premise)
Therefore, a plane has roots. (Conclusion)
Few
writers arrange their statements in this strict form, favored by Aristotle in
his Rhetoric, a classical
guide to argument so brilliant that it remains useful today. And yet all of us
still employ, at times, the same method of reasoning found in a syllogism: deductive
reasoning. This kind of
reasoning begins with a statement of general truth (“All trees have roots”) and
moves to a statement about an individual (“A plane has roots”).
But you might argue the other way around. If instead of starting with a general statement (“All trees have roots.”), you were to study a score of different trees, find them all having roots, and then conclude that trees have roots, you would follow the opposite method: inductive reasoning. Inductive reasoning is (sometimes called “scientific method.”) Scientists commonly work in this way: by observing particulars and then drawing general conclusions. In this way new knowledge is acquired about nature.
Either method of
reasoning is only as trustworthy as the observations on which it is based.
Case: Anselmus’ ontological proof of the existence of God
11?????????????????????
1. ???????????????????????
2. ?????“??”??????????????????????????“????”?
3. ????????? {??} ?????
??????????????????????????????????????????????????????????????????????
?????????????????????????????????????????????????????·????
Test yourself:
If you were Kant, how would you challenge Anselmus’
ontological proof of God’s existence and what might be your way of proving the
existence of God?
Answer:
?
?/
In modern times, a simple, practical method of reasoning has been devised by the British philosopher Stephen Toulmin in The Uses of Argument (Cambridge University Press, 1969). Helpfully, Toulmin has divided a typical argument into three parts:
1. The data, or evidence to prove something
2. The claim, what you are proving with the data
3. The warrant, the thinking that leads from data to claim
Any clear, explicit argument has to have all three parts. Toulmin’s own example of such an argument is this:
Tommy was born in
(Data) | (Claim)
|
Since
Bermuda is a British colony in NW
(Warrant)
(Toulmin, 1969. [The Uses of Argument]. Cambridge University Press)
In arguments we hear or read, we often detect logical fallacies, i.e. common mistakes in thinking or reasoning, or more precisely, a mistake made in the process of moving from the premises of an argument to the conclusion. When we argue by ourselves, we may also inadvertently commit logical fallacies from time to time. As a result of the fallacy, the premises do not justify the conclusion. (Kennedy, X.J. & Dorothy M. Kennedy, 1987, p. 280. [The Bedford Guide for College Writers. NY: St Martin’s Press.])
In the following we list some most frequently committed logical fallacies with a view to helping you to recognize them when you read or hear them and to guard against them when you make arguments in your own speech and writing. (Some arguments can exhibit more than one fallacy at once.)
Basically, there are three types of logical fallacy:
1. Formal Logical Fallacies (????????)
2. Informal Logical Fallacies (????????)
3. Mixed Logical Fallacies
Formal logical fallacies are mistakes in which the argument violates a rule of the logical system of which that argument is a part. They are classified into:
1. Fallacy of the consequent
a Denial of the antecedent
b Affirmation of the consequent
2. Fallacy of illicit major (or minor) premise
Formal
logical fallacies occur when an inference maker violates any rule governing the
validity of a syllogism, so before characterizing formal logical fallacies, we
need to take a closer look at syllogism.
Syllogism
is a mode of argument that forms the core of the body of Western logical
thought. Aristotle defined syllogistic logic, and his formulations were thought
to be the final word in logic; they underwent only minor revisions in the
subsequent 2,200 years. Every syllogism is a sequence of three propositions
such that the first two imply [(of a fact or occurrence) suggest (something) as a logical
consequence: The
forecasted traffic increase implied more roads and more air pollution. (NOECD) ????; ??……?????] the third, the conclusion.
There are three basic types of syllogism: hypothetical, disjunctive, and
categorical.
The hypothetical
syllogism (modus ponens) has as
its first premise a conditional hypothesis:
If p then q; it continues: p, therefore q, e.g.
? If there is life on Mars [p],
then Mars has an atmosphere [q].
It is the case that there is
life on Mars [p].
Therefore, it is the case that
Mars has an atmosphere [q].
It should
be noted that in the conditional hypothesis, term p presupposes [To require or
involve necessarily as an antecedent condition (AHD4)] term q. Only when this condition is met, can the syllogism be
true in both its positive form and negative form. The negative form and its
example are displayed in the following:
If p, then q;
it is not the case that q; therefore, it is not the
case that p, e.g.
? If there is life on Mars [p],
then Mars has an atmosphere [q].
It is not the case that Mars has
an atmosphere [q].
Therefore, it is not the case
that there is life on Mars [p].
The disjunctive
syllogism (modus tollens)
has as its first premise a statement of alternatives:
Either p or q; it continues: not
q,
therefore p.
The categorical
syllogism comprises three categorical propositions, which must be
statements of the form
all S’s are P’s,
no S is P,
some S is P, or
some S is not P.
(Based on Syllogism.
[2004]. In Columbia Encyclopaedia
[)
This fallacy (also known as “Aristotle’s fallacy of the
consequent”) occurs when the inference maker violates the rule for making a
hypothetical syllogism (If
p then q;
it continues: p, therefore q). It has two forms:
Mistakenly arguing from the premises “If p, then q” and “not p” (symbolized ~ p1) to
the conclusion “not q”, e.g.
? *If George is a man of good faith, he can be entrusted with this office; but George is not a man of good faith; therefore, George cannot be entrusted with this office.
{Comment: “Not p, then not q” cannot be deduced from “If p,
then q” because in the conditional hypothesis in a
hypothetical syllogism, term p is one of the many possible
conditions conducive to, instead of a necessary precondition for, term q. Cannot see what is wrong with that? Look at a more
obvious example:
*???????????????
?????????
?????????}
Mistakenly arguing from the premises “If p, then q” and “q” to the
conclusion “p”, e.g.
? *If Amos was a prophet, then he had a social conscience;
Amos had a social
conscience; hence, Amos was a prophet.
{Comment: “If q, then p” cannot be deduced from “If p, then q” because in the conditional hypothesis in a hypothetical syllogism, term p, as we noted above, is one of the many possible conditions conducive to, instead of a necessary precondition for, term q.}
This fallacy occurs when the inference maker violates any
one of the five basic rules governing the validity of categorical
syllogisms.
Traditional Aristotelian logic is
concerned with syllogistic reasoning, a form of deductive argument. A syllogism
is an argument made up of propositions [statements ??] in one of four forms:
“Every S is P”. (universal affirmative);
“No S is P”. (universal negative);
“Some S is P”. (particular affirmative); or
“Some S is not P”. (particular negative).
The letters stand for common nouns, such
as “dog”, “four-footed animal”, “living thing”, which are called the terms of the
syllogism. “S” is called the subject term (S, [???] ??/??), and “P”, the predicate (P, [???] ??/??), of the syllogism.
A categorical syllogism contains
precisely three terms: the major term (??), which is the predicate of the conclusion; the minor term (??), the subject of the conclusion; and the middle term (??), which appears in both premises but not in the
conclusion. Thus:
? All men [middle term] are
mortal [major term], [Major
premise]
all
philosophers [minor
term] are men [middle term]; therefore [Minor
premise]
all philosophers [minor term] are mortal [major term]. [Conclusion]
The premises containing the major and
minor terms are named the major and
minor premises (???????), respectively.
Aristotle discovered five
basic rules governing the validity of categorical syllogisms:
(1) The middle term must be distributed at least once (a term is said to be distributed [??] when it refers to all members of the denoted class, as in “All S are P” and “No S is P”; see 2.1.3.3 in the following for a more detailed explanation).
(2) A
term distributed in the conclusion must be distributed in the premise in which
it occurs.
(3) Two negative premises imply no valid conclusion.
(4) If one premise is negative, then the conclusion must be negative.
(5) Two affirmatives imply an affirmative.
(Based on Syllogism.
[2004]. In Columbia Encyclopaedia
[)
In syllogistics [????], the application of a term of a proposition to
the entire class that the term denotes. A term is said to be distributed
when reference is made to all members of the class.
Briefly, only universal propositions distribute their subject
term (S,
[???]??), and only
negative propositions distribute their predicate (P, [???] ??). {?????????????????????????????????}
Naturally, singular terms [singular: Logic Of or
relating to the specific as distinguished from the general; individual.???????? (AHD)] (including proper names used as singular terms)
are always distributed, for they refer only to one object and cannot refer to
fewer.
Test yourself: What terms are distributed and
what are not?
What terms in
the following forms of proposition are distributed and what are not?
1) Every S
is P.
2) No S is P.
3) Some S
is P.
4) Some S
is not P.
Discuss both the subject term (??) and the predicate (??) in each proposition.
Answer:
?
?/
The importance of distribution lies in
its being a principle of formal inference (specifically, the second rule governing the well-formedness
of a categorical syllogism) that no term may be distributed in the conclusion unless it
was distributed in the premises. (Based on “Distribution”. In BCD 2002)
The illicit major (or minor) premise
fallacy arises when a major (or minor) term that is undistributed in the
premise is distributed in the conclusion, e.g.
? *All tubers are high-starch foods;
no squashes are tubers;
therefore,
no squashes are high-starch foods.
Analysis:
? *All tubers are high-starch foods; [undistributed: reference is made to high-starch foods in terms of their quality of having much starch, not of their totality.] [Cf. Every S is P.]
no squashes are tubers;
therefore, no squashes are high-starch foods. [distributed: reference is made to any kind of high-starch food (no squash is high-starch food of whatever kind).] [Cf. No S is P.]
(Based on Distribution. In Blackburn, Simon 2000.
[Oxford Dictionary of Philosophy. ?????????. ix + 418 pp.]; Distribution. In BCD 2002,
and MERL 2004.)
Test yourself: What is it that makes Twain’s “apology” funny?
Mark Twain once remarked to the press that “some American congressmen are bastards.” That, of course, made some congressmen mad. They pressured Twain to make a public apology. By way of apology, Twain said: “some American congressmen are not bastards.” What is it that makes Twain’s “apology” funny?
Analysis:
?
?/
Conclusion:
?
?/
Test yourself: What would have Twain said if he had sincerely wished to
apologize?
What form of syllogistic reasoning would Twain
have used if he had sincerely wished to apologize to the congressmen he had
cursed earlier?
Answer:
?
?/
Deduction A ?
? All the planets in our solar system are equipped with an atmosphere.
Pluto is a planet in our solar system.
× Therefore, Pluto is equipped with an atmosphere. {Valid deduction, but wrong argument.}
Whether an argument is a valid argument is determined by
the truth or falsity of the content of its premises. Deduction A is
invalid, but Argument A is false because its major premise is false. It is one
of the informal logical fallacies (Fallacies of relevance?the
claims made by the premises are wrong or irrelevant to the truth of the
conclusion), which we will discuss later.
Deduction B ×
? *Some animals [middle term, undistributed; Cf. Some S is P.] are two-footed.
All people are animals [middle term, undistributed; Cf. Every S is P.].
? Therefore, all people are two-footed. {Sound argument, but invalid deduction.}
Whether an argument is a valid deduction is determined by
its form. This deduction is invalid because it violated the first basic rule governing
the validity of categorical syllogism, i.e.
(1) The middle term must be distributed at least once.
An experiment in scientific research (in
principle) allows the researcher to check against the hypothesis and say “this hypothesis
is right”. If so, the experiment supports (or verifies) the
hypothesis and the researcher is justified in adding the idea behind the
hypothesis to their theoretical base.
If, on the other hand, the experiment
says “this hypothesis is wrong”, this would be falsifying the
hypothesis.
Case: What is the logical basis of Popper’s famous argument that one can
never totally verify a theory?
The importance that scientists have attached to falsification (as opposed to verification) goes back to the 1930s, when Karl Popper [1902-1994. Austrian-born British philosopher of science, known for his theory of scientific method and for his criticism of historical determinism] developed our current view of how theories are created and re-created.
According to Popper, it is possible to overturn a theory, but it is impossible to make it absolutely correct. In Popper’s terms you can never totally verify (“prove”) a theory—but you can falsify it with one conflicting observation.
What is the logical basis of Popper’s famous argument that one can never totally verify a theory?
(Based on Goodman,
Albert. [School of Computing and Mathematics, Deakin
University, Australia] [1996]. Introduction to Data Collection and Analysis.)
Test yourself: What is wrong with verification?
Analysis:
?
?/
Test yourself: How should we find out the scientific validity of the
theory of translation universals?
The theory of translation universals developed by Mona Baker and others has concerned a number of scholars in the international translation community in the past decade or so. How should we find out the scientific validity of this theory?
Analysis:
?
?/
Informal logical fallacies are mistakes caused by wrong, irrelevant or ambiguous evidence. They are classified into:
1. Fallacies of
relevance
2. Fallacies of
ambiguity (verbal fallacies)
Fallacies of relevance are those arguments in which the truth of the conclusion does not depend on the claims made by the premises; in other words, the claims made by the premises are wrong or irrelevant to the truth of the conclusion. The following are some familiar fallacies of relevance:
? Non sequitur
? Oversimplification
? Hasty generalization
? Argument from dubious authority
? Begging the question
? Argument ad hominem
? Argument from ignorance
? Post hoc ergo propter hoc
? Stereotypes
? Card-stacking
? Arguing by analogy
Stating a claim that doesn’t follow from the (minor) premise (or the statement you begin with), because the major premise is false.
? Jergus will make an excellent husband for Marge. Why, in high school he got all A’s.
? In order to greet National Day,
Beijing is carrying out various renovations. Many renovated buildings belong to
the so-called "bean dregs” or shoddy project. Because of the limited time,
those projects have to be finished in a hurry. So though the government calls
on the builders to pay attention to quality, many new or renewed bean dregs
projects still kept appearing “irresistibly.” (Students’ essay)
? The cover of a 1997 Beijing Youth Weekly has “Chinese Defeat Kasparov!” splashed across a picture of the downcast grand master. Two of the six members of the IBM research group that programmed “Deep Blue,” it turns out, were Chinese-Americans. “It was the genius of these two Chinese,” one article asserts, “that allowed ‘Deep Blue’ to defeat Mr. Kasparov.” (Peter Hays Gries. 2003. China's New Nationalism: Pride, Politics, and Diplomacy. A Philip E. Lilienthal Book in Asian Studies. The University of California Press. Retrieved December 22, 2004, from http://www.ucpress.edu/books/pages/9662/9662.intro.html)
? ??????????????????
?????????????????“??”???????????“???70???????????????????????‘????’?????????????????????????????????????????????????????”
(Retrieved October 16, 2006, from http://blog.sina.com.cn/u/48670cb20100062a)
A special kind of non-sequitur fallacy?reversing cause and effect or taking cause for effect [????]):
? Bob is well trained, therefore Bob is an astronaut.
? ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? (?????????????????)
Supplying neat and easy explanations for large and complicated phenomena (Cf. Albert Einstein’s famous quote—paying special attention to the second half of this quote: “everything should be made as simple as possible, but not one bit simpler.”).
? We have a lot of unemployment now in this country because people are too lazy to work.
? If we want to do away with drug abuse, let’s get tough: let’s sentence every drug user to death.
A special kind of oversimplified thinking—Either/or reasoning [assuming that a reality may be divided into only two parts, that there are only two sides to a question, that all statements are either true or false, that all questions demand either a yes or a no answer.]:
? What are we going to do about acid rain? Either we shut down all the factories that cause it, or we just forget about acid rain and learn to live with it. We’ve got no choice, right?
? ?????????????
??????????????????????21??????????????????“??”???
???????????25???????40????????15???25??
??????????????????????????“??”???95???????????????????????????????????10????????????????????????????????????????????????????????
(??????2002?11?29?1?)
The assumption that what is true of a few cases is true in general.
Example 1.
? Bertrand Russell’s “cruel”
example: the chicken’s hasty generalization that the farmwife’s coming means
food.
Example 2.
? … “But that’s not my dog.”
The practice of defending a conclusion by appealing to force, pity, authority, or popular belief.
? According to some of the most
knowing scientists in America, smoking two packs a day is as harmless as eating
a couple of oatmeal cookies.
? According to some of the most famous scientists in
China, eating our pills will help short men to grow taller within a few days.
? ???????——?????????——????8????48?????{Who were they?} 100??????10???????????????——???????
????????
????????????
??????????????????????????????????
?????????????????????????????????????????????
Defending a conclusion by appealing to popular belief is known as “Bandwagon appeals,” i.e. using the desire to “go along with the crowd” as fact:
? Surveys show that a majority of the people want only “family oriented” programming on television. Therefore, this must be our goal.
Setting out to prove a statement that is already taken for granted (or, in other words, assuming in the premises what is to be proved).
This fallacy sometimes takes the form of tautology or arguing in a circle (i.e. stating or believing a fact to be its own reason).
? He is a liar because he simply is not telling the truth.
? Most people like gardening because it is something they enjoy.
? It’s wet because it has water on it.
? I know because I know.
Attacking people’s opinions by attacking their character.
? Jack may argue that we need to save the whales, but Jack is the kind of person who always gets excited over nothing.
? Jack would have us spend millions to save whales, but I happen to know that he owns a yacht from which he selfishly enjoys watching whales.
? ?????????????????????? [????] ???“?????????????????????”(??????2002??2??5?)
{Comment: ????????????????????????????????????????????“????”?“????”????}
Maintaining that, because a conclusion has not been disproved, it has to be accepted or, because a conclusion has not been proved, it should be rejected.
? Despite years of effort, no one has conclusively proved that ghosts don’t exist; therefore, we should expect to see them at any time.
? No one has ever shown that there is intelligent life on any other planet. Evidently the notion of visitors from other planets in the universe is unthinkable.
Confusing cause and effect.
? Because the new Premier of
Russia sent a rose to every woman member of the Duma as a token of his
gratitude for their support of the work of his government, he was soon
dismissed from office by President Yeltzin.
? The devastating earthquake which
struck Taiwan recently was a warning sent by Heaven to Li Denghui,
since it occurred shortly after Li made another attempt to split China by
claiming statehood for Taiwan.
Both positive and negative ones should be avoided.
? Being a woman meant she was smaller than a man.
? Being a woman meant she was more compassionate than a man.
Ignoring an issue’s contrary evidence.
? A “pro-gun” paper that cites only people who have used guns to protect themselves from danger, or an “anti-gun” paper that cites only accidental deaths caused by guns.
Using a metaphor as though it were evidence.
In logic, analogy is the name of an inductive form of argument which asserts that if two or more entities are similar in one or more respects, then a probability exists that they will be similar in other respects.
An analogy explains a complicated idea in terms of something familiar: for instance, shooting a spacecraft to another planet is like placing a golf ball with uncanny accuracy into a hole half a mile away and a risky action is analogized to “???????????” in Chinese.
? People were born as free as the birds. It’s wrong and cruel to expect them to work.
? [In 1633, Scipio Chiaramonti, professor of philosophy at the University of Pisa, argued against Galileo:] “Animals, which move, have limbs and muscles. The earth has no limbs and muscles, hence it does not move.”
? [????????????????????????]“?????????????????????????”
? [????]“?X???????/??!”
Fallacies of ambiguity (verbal fallacies) are erroneous conclusions based on the equivocal use of language.
? All laws are the product of legislative activity. Newton discovered several laws; therefore, Newton discovered several products of legislative activity.
? [CCTV-1 advertisement featuring ???]
Shot 1 ????“????????”
Shot 2 Slogan?????????
(Partly based on Kennedy,
X.J. & Dorothy M. Kennedy [1987] [The
Bedford Guide for College Writers. NY: St Martin’s Press.])
Mixed logical fallacies refer to cases in which formal and informal fallacies co-exist in an inference.
Case: ??????????????
2003???????????????????????????????????????????????????????6??????????????????“????”?????????????????????????????????????2004???????????????????????????????????????????2004?????????????????2004?10?20????????????????????????????????????????????????????????????????????????????????“?????????????????????????????”
What logical fallacies can you identify in the student’s bewildering
question?
Analysis:
?
?/
Case: ?????????????
???????????????????
“????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????” (Retrieved October 16, 2006, from http://blog.sina.com.cn/u/48670cb20100062a)
What logical fallacies can you identify in Li Ao’s argument?
Analysis:
?
?/
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