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The Logic of Arguments |
An
argument is a connected series of statements or propositions, some of which are
intended to provide support, justification, or evidence for the truth of
another statement or proposition.
Arguments
consist of one or more premises and a conclusion.
The premises are those statements that are taken to provide the support or
evidence; the conclusion is that which the premises allegedly support. For
example, the following is an argument:
Taxes should be increased only if the increase results in better public services. However, public services can improve only if there is a new management, and since the current management will not change until the new elections –which will take place in four years- we must reject the increase in taxes for the coming fiscal year.
The
conclusion of this argument is the final statement: "we must reject the
increase in taxes". The other statements are the premises; they are
offered as reasons or justification for this claim.
Some
important elements of an argument might be left implicit or unstated. For example,
Dr. Ivan Vlasic is an outstanding scholar. He was appointed Professor Emiritus
at McGill University.
In
the following example, the author takes it for granted that the reader
understands that McGill University only appoints recognized scholars as
Professor Emiritus. Therefore, the argument is best understood as an
abbreviated form of the full argument: "McGill University has a very
rigorous selection process for appointing Professors Emiritus. Only those
internationally recognized scholars over 65 years of age, who have
significantly contributed to the advancement of their disciplines may be
appointed Professor Emeritus. Dr. Ivan Vlasic, who has published numerous books
and journal articles, has a Ph.D. from Yale, supervised numerous doctoral and
master's theses, and contributed to many International Law debates and
pioneered in the development of Space Law, was appointed as McGill University's
Professor Emeritus in Law. He is an outstanding scholar."
o
A premise of an
argument is something that is put forward as a truth, but which is not proven.
It is not proven and hence is assumed to be true (although how universally
accepted this truth is may be another matter). If you want to attack another
person's argument, you can challenge the truth of their premises. If you are
making an argument, you should be ready to defend any of your own premises.
o
The conclusion (or claim)
is the statement with which you want the other person to agree. It is drawn
from the premises of the argument, of which there may be many. A useful way of
spotting a conclusion is that may well be a statement of necessity, saying what
must or should happen. It may well be framed to persuade the other person to do
something or make some decision.
o
Between the
conclusion and the premises are further statements which translate the premises
into the conclusion. This is the reasoning process, and in a formal argument the
author uses careful logic (in informal arguments, emotional reasoning and
assumptive leaps may well be used).
Formalized
arguments can be broadly grouped into two categories: deductive and inductive.
The relationship between the premises and conclusion that holds in each case
serves to distinguish them:
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DEDUCTIVE |
INDUCTIVE |
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I.
If all of the premises are
true, the conclusion must be true. II.
All of the information or
factual content was already contained, at least implicitly, in the premises. |
I.
If all of the premises are
true, the conclusion is probably true but not necessarily true. II.
The conclusion contains
information not present, even implicitly, in the premises.
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|
Example: (P1) All men are human beings. \Socrates is a human being. |
Example: (P1) Every emerald yet discovered
has been green. \All emeralds are green. |
Deductive
arguments are assessed in terms of their validity or invalidity.
An argument’s validity deals only with the inferential relation between its
premises and its conclusion. That is, the premises need not be true for an
argument to be valid. For example:
(C) My
mother is evil. If we assume
that P1 and P2 are true, then the conclusion inexorably follows. (The premises
aren't true in this case, though—my mother happens to be perfectly nice). If
the premises of a valid deductive argument are indeed true, the conclusion must
be true, and the argument is considered sound. Inductive
arguments, in contrast, inhabit a spectrum from weak to strong.
Conclusions to arguments of this type go beyond their premises and hence cannot
be guaranteed true, regardless of the truth of the premises, and even if its
premises are true, an inductive argument’s conclusion is at best probably true.
Consider the following example:
(C) Beethoven
had little musical ability. P1 and P2 are both true, yet the conclusion is certainly
false. Hence, though inductive arguments are a primary source of our beliefs,
they remain a tentative source of knowledge. Logical fallacies are mistakes in reasoning. They may be
intentional or unintentional, but in either case they undermine the strength of
an argument. Some common fallacies are defined below. 1. Hasty Generalization: A generalization based on too little
evidence, or on evidence that is biased. Example: All men are
testosterone-driven idiots. Or: After being in New York for a week, I can tell
you: all New Yorkers are rude. 2.
Either/Or Fallacy:
Only two possibilities are presented when in fact several exist. Example:
America: love it or leave it. Or: Shut down all nuclear power plants, or watch
your children and grandchildren die from radiation poisoning. 3.
Non Sequitur: The conclusion does not follow logically from the premise.
Example: My teacher is pretty; I'll learn a lot from her. Or: George Bush was a
war hero; he'll be willing to stand tough for America. 4.
Ad Hominem: Arguing against the man instead of against the issue.
Example: We can't elect him mayor. He cheats on his wife! Or: He doesn't really
believe in the First Amendment. He just wants to defend his right to see porno
flicks. 5.
Red Herring:
Distracting the audience by drawing attention to an irrelevant issue. Example:
How can he be expected to manage the company? Look at how he manages his wife! 6.
Circular Reasoning:
Asserting a point that has just been made. Sometimes called "begging the
question." Example: She is ignorant because she was never educated. Or: We
sin because we're sinners. 7.
False Analogy:
Wrongly assuming that because two things are alike in some ways, they must be
alike in all ways. Example: An old grandmother's advice to her granddaughter,
who is contemplating living with her boyfriend: "Why should he buy the cow
when he can get the milk for free?" 8.
Post Hoc, Ergo
Propter Hoc: The mistake of
assuming that, because event a is followed by event b, event a
caused event b. Example: It rained today because I washed my car. Or:
The stock market fell because the Japanese are considering implementing an
import tax. 9.
Equivocation: Equates
two meanings of the same word falsely. Example: Christianity teaches that faith
is necessary for salvation. Faith is irrational, it is belief in the absence of
or contrary to evidence. Therefore: Christianity teaches that irrationality is
rewarded. 10.
Middle Ground: The
fallacy of the middle ground is based on the assertion that a proposition is
true simply because it falls between two more extreme propositions. The
principle of moderation is however not necessarily fallacious. Example: Some
people claim that God is all powerful, all knowing, and all good. Other people
claim that God does not exist at all. Now, it seems reasonable to accept a
position somewhere in the middle. So, it is likely that God exists, but that he
is only very powerful, very knowing, and very good. That seems right to me Non-arguments These
are only common non-arguments. That is not to say that some instances of them
will not be arguments. Remember, if an inferential claim is being made between
the evidence and conclusion, then there is an argument. In order to establish
this, the reader must make a subjective deduction about the author's
intentions. Non-inferential
passages: passages in which
there is no inference being made that the premises support or entail a
conclusion. Warning: Ex:
“Stop!” or “Duck so you do not hit your head on the pipe” *
For one, these are not statements as they have no truth value. Further, there
are no premises which support the conclusions in these examples. Piece
of advice: Ex:
“I suggest you slow down while driving. * Again, no truth vale for the statement and no evidence
(premises). Opinion: Ex:
“I think you should buy a bullet proof vest to ensure your safety.” *No
evidence is used to support opinion; therefore, it is not an argument. Loosely associated statements: These are statements that are
perhaps loosely related but there is no inferential claim being made between
the statements. Therefore, there is nothing being proved in such a passage. Ex: Water is wet. Swimming pools are filled with water. Many
colleges and universities have collegiate water sports. Water is fun to play
in. Report: A passage which conveys information about a subject
(topic). Reports are not used to prove anything. The facts are simply reported
without any inferences being made. Ex: See report example on the previous page of the notes. Expository
passages: These are passages
of which one offers a topic sentence and then expounds upon the topic. The key
to these passages is deciding if the author provides proof for his topic
sentence or just expounds upon it in more detail. If the author only intends
his exposition to expound upon the topic sentence then there is no argument
because he is offering no proof for the conclusion (the topic sentence).
However, if the author provides reason for the reader to believe his exposition
proves that the topic sentence is true, then the exposition is an argument. Illustrations: These are passages in which a statement is made about a
certain subject and then specific instances are used to illustrate this
statement. Ex: Elements can be represented by atomic symbols. Thus,
oxygen is represented by O and potassium is represented by K. *
This is not an argument because the author makes no claim that he is proving
that Elements can be represented. All he is doing is illustrating how it is
done. At best, all he can say is “If elements can be represented by atomic
symbols, this is how it would be done. It
is important to remember that the author has to make a claim that her premises
entail her conclusion. Illustrating her conclusion, or showing how it is done,
is usually not enough to establish entailment. However, again, there is a large
amount of subjectivity in just what the author is trying to prove. Explanations:
These are passages which intend to shed light on a specific fact. In
an explanation the author usually relates an excepted fact and then tries to
make sense of it. That is, he tries to explain why it might have happed or some
of the causes for the fact. However, the author is not intending for his
explanations to prove that the fact is in fact true. All he is trying to do is
make sense of it or explain it. These types of passages are easily mistaken for
arguments. One has to ask, though, is the author trying to prove the conclusion
or is he trying to explain what happed (make sense of it). Conditional
Statements: The statements are
if/then statements. Ex: If
I go to the store then I will buy chocolate. I
will buy chocolate if I go to the store. If
I win my match then I will go on to regional. These
seem to be arguments; however, at best they can only be parts of an argument.
Again, to be an argument, there must be at least one statement which gives us reason
(evidence) to believe the conclusion (another statement). However, conditional
statements are only one statement. If
these statements are broken up into antecedent (taken as evidence) and
consequent (conclusion) there is still no argument because there is no truth
value to the resulting claims. Remember,
conditional statements alone are not arguments. Example of an
argument: If I go to the
store then I will buy chocolate. I will go to
the store. Therefore, I
will buy chocolate. Stephen Toulmin
identified the following elements of an argument: 1. Claim
(assertion, proposition): A statement affirming or denying something. 2. Evidence:
Material which will convince audience 3.
Warrant: what links
support evidence to claim, e.g., a principle of logic or reasoning, a recipe or
license, a formal rule, generally unstated, an assumption that both rhetor and
audience implicitly accept. EXAMPLE: ·
Claim: Joe
Smith is a good choice for the position of Appellate Court Judge ·
Grounds: The
American Bar Association recommended Smith as well qualified. ·
Warrant:
(usually unspoken) The ABA is an authority source known as
competent to determine who is a good choice for appellate judge positions.
(P2) My mother is Russian.
(P2) Beethoven was deaf.
Common
Fallacies
The basic
elements of the argument