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LOGOS |
One unerring mark of the love of truth is not entertaining any proposition with greater assurance than the proofs it is built upon warrant.
—John Locke
A. DEFINITION
An argument is any group of propositions in which one proposition (conclusion) is claimed to logically follow from, or be derived from, one or more other propositions (premises) that are accepted and affirmed as supporting grounds for the truth of the conclusion (See Hurley diagram, p. 3).
Examples
1. Every law is an evil, for every law is an
infraction of liberty.
—Jeremy Bentham, Principles of
Legislation, 1802.
2. All humans are mortal.
Socrates is a human.
Therefore, Socrates is mortal.
3. Every squirrel in my back yard is grey. So squirrels are
grey.
—4 year-old child
4. In an infinite universe, every point can be regarded as the
center, because every point has an infinite number of stars on each side of it.
—Stephen Hawking,
A Brief History of Time
5. 90% of New York City residents are Yankee fans.
Kurt lives in New York City.
Hence, Kurt is probably a Yankee fan.
6. Archimedes will be remembered when
Aeschylus is forgotten, because languages die and mathematical ideas do not.
—G. H. Hardy, A Mathematician’s
Apology, 1940.
7. A child who has received no religious instruction and has
never heard about God, is not an atheist—for he is not denying any theistic
claims.
—Ernest Nagel, “Philosophical
Concepts of Atheism,” 1959.
8. He would not take the crown;
Therefore ‘tis certain he was not ambitious.
—William Shakespeare, Julius
Caesar, act 3, scene 2.
9. Marriage is the chief cause of divorce, since everyone who
gets divorced is already married.
—adapted from Groucho Marx
10. The fact that an opinion has been widely held
is no evidence whatever that it is not utterly absurd; indeed, in view of the
silliness of the majority of mankind, a wide-spread belief is more likely to be
foolish than sensible.
—Bertrand Russell, Marriage and
Morals, 1929.
The terms argument and inference are often used synonymously or interchangeably, as basically equivalent in meaning. However, they should be distinguished in the following manner:
Therefore, arguments exhibit the following logical traits:
PREMISE INDICATOR TERMS | CONCLUSION INDICATOR TERMS |
since | therefore |
because | thus |
for | hence |
as | so |
follows from | accordingly |
inasmuch as | consequently |
as shown by | for this reason |
in view of the fact that | as a result |
for the reason that | proves that |
as indicated by | it follows that |
may be inferred from | which shows that |
may be derived from | which implies that |
may be deduced from | which entails that |
NOTE: The
indicator terms above, when used in an argument, have a logical
meaning. But they may also function in non-logical
ways (cf. Hurley, p. 15). For example:
Since Joe graduated from college there
have been many changes in college life. (temporal use)
Since Joe graduated from college he probably knows how to read. (logical
use)
Since Joe graduated from college he has a well-paying job. (explanatory
use)
C. TYPES OF INFERENTIAL CLAIMS
D. GENERAL TYPES OF ARGUMENTS
Example:
We haven’t been outside all week.
(premise)
Hence, some outdoor exercise will be good for us. (subconclusion)
So, we should go for a hike in the canyon this weekend. (final conclusion)
E.
DISTINGUISHING ARGUMENTS FROM NON-ARGUMENTS
In order to recognize arguments accurately, they must be distinguished from
other linguistic passages that lack an inferential claim (cf. Hurley, pp.
16-25):
Common Obstacles in Identifying Arguments
Steps in Identifying Arguments
F. DEDUCTIVE AND INDUCTIVE ARGUMENTS
1. Distinguishing Deductive and Inductive Arguments
DEDUCTIVE | INDUCTIVE |
1. Claims conclusion follows from premises with strict necessity (Logical implication) | 1. Claims conclusion follows from premises with probability only (Probable inference) |
2. Either valid or invalid; not a matter of degrees | 2. Strength or weakness: a matter of degrees of probability |
3. Additional information is irrelevant to the validity or invalidity of a deductive argument | 3. Additional information is relevant to the strength or weakness of an inductive argument |
4. Premises provide joint or dependent support for the conclusion | 4. Premises provide independent or joint support for the conclusion |
5. The conclusion of a valid deductive argument is already contained in, or strictly implied by, the premises. Francis Bacon analogy: the spider | 5. The conclusion of any inductive argument goes beyond the information contained in the premises. Francis Bacon analogy: the bee |
6. Not restricted to reasoning from general premises to a particular conclusion | 6. Not restricted to reasoning from particular premises to a general conclusion |
7. Valid=If the premises are assumed to be true, then the conclusion must be true also | 7. Strong=the conclusion follows from the premises with probability. |
8. Sound=valid + true premises | 8. Cogent=strong + true premises |
Note well: Neither argument type is true or false (only propositions are T/F) |
Note well:
Neither argument type is true or false (only propositions are T/F).
Deductive arguments are logically evaluated as valid/invalid and sound/unsound;
inductive arguments are logically evaluated as strong/weak and cogent/uncogent
(cf. Hurley, p. 51).
2. Types of Deductive and Inductive Arguments
a) Deductive arguments
Examples
1. X = 5 because 2 + X = 7. (mathematics)
2. Since Peter is a bachelor, he is an unmarried male. (definition)
3. All humans are mortal.
Socrates is a human.
Therefore, Socrates is mortal. (categorical
syllogism)
4. If it’s Monday, then I have logic class tonight.
It is Monday.
So I have logic class tonight. (mixed
hypothetical syllogism)
5. Either New England or St. Louis will win the Super Bowl.
But St. Louis will not win the Super Bowl.
Therefore, New England will win the Super Bowl. (disjunctive
syllogism)
Types of Deductive Syllogism
1. Categorical syllogism:
All M is P
All S is M
Therefore, all S is P
2. Disjunctive syllogism:
Either P is true or Q is true
P is not true
Therefore, Q is true
3. Hypothetical syllogism:
If P is true then Q is true
P is true
Therefore, Q is true (mixed hypothetical syllogism)
If P is true then Q is true
If Q is true then R is true
Therefore, if P is true then R is true (pure hypothetical syllogism)
b) Inductive arguments
Examples
1. David will probably excel in his current logic
course because he’s always excelled academically. (prediction)
2. Gloria-Jean has demonstrated her ability to apply
CPR (cardiopulmonary resuscitation) to a dummy in simulated cases of cardiac
arrest. Therefore, she can be expected to apply CPR to actual cardiac patients
effectively as well. (argument from analogy)
3. Western religions (Judaism, Christianity, Islam) are monotheistic. Therefore,
all the major world religions are monotheistic. (inductive generalization)
4. Alan Greenspan, the chairman of the
Federal Reserve, recently stated that the economy should improve in the fall.
Given Mr. Greenspan’s wisdom in such matters, the economy probably will improve
in the fall. (argument from authority)
5. The sign we just passed said there’s an accident up ahead, so it probably is
the case. (argument based on signs)
6. My roommate woke up this morning feeling nauseous and with a terrible
headache. He must have been downing mudslides at Babylon last night. (causal
inference)
7. Most CCRI students are interested in improving their
critical-thinking skills. Daniel is a student at CCRI. Therefore, Daniel is
probably interested in improving his critical-thinking skills. (statistical
syllogism)
8. Observant toddler: The cardinal I saw last month was red, and the one
I saw last week was red, and the one I saw yesterday was red. So the next
cardinal I see will be red. (simple enumeration)
Inductive Argument Forms
1. Inductive Generalization:
A form of inductive reasoning that proceeds from
particular premises (a sampling of X, a statistical percentage of X)
to a general conclusion (universal, statistical).
a) Terminology:
b) Types of Inductive Generalization:
Universal Generalization: Concludes that something is
true about all members of X (population) on the
basis of what is observed (target characteristic) about some of them (sample).
Hence, universal inductive generalizations reason from a sample of X
(class or category) to a generalization about all members of X.
General form: X¹ is p.
X² is p.
X³ is p.
All X’s are p.
Example: The students I’ve met in my logic class are personable and interesting (X¹, X², X³ are p.). So, probably all the students in my logic class are personable and interesting (All X’s are p.).
Statistical Generalization:
Concludes that something is true about a
statistical percentage of X (population) on the basis
of what is observed (target characteristic) about a statistical
percentage of them (sample). Hence, statistical inductive
generalizations reasons from a statistical percentage of observed members of X
(class or category) to a statistical percentage of X itself (entire class or
category).
General form: X percent of
observed As are F.
Thus, probably X percent of all As are F.
Example: 75 % of the
professional wrestlers we interviewed admitted taking anabolic steroids.
Consequently, probably 75 % of all professional wrestlers are taking anabolic
steroids.
d) Assessing the Inductive Strength of Inductive
Generalizations:
representative sample: a sample is representative of a population if it reflects the variety internal to the population; and if the target characteristic(s) observed in the sample occurs with the same frequency or in the same proportion as they occur in the population. The size and diversity of the sample must be adequate.
2. Causal Inference/Argument
a) Causal concepts:
b) Types of Causal Inference/Argument:
3. Argument from Analogy
a) General Form
A and B are similar in that both possess features f, g, and h.
(similarity, resemblance, analogous)
A also possesses feature j.
Thus, B probably possesses feature j also.
Example
Professor Leclerc and Minuto are in the CCRI
Department of Social Sciences, are males, drive automobiles, are critical of
contemporary culture, and enjoy intellectual discussion.
Professor Leclerc also likes cats.
Therefore, Professor Minuto probably
likes cats.
b) Terminology: utilizing the above example, we may distinguish the following terms.
c) Assessing the Inductive Strength of Arguments from Analogy:
4. Argument from Authority
a) General Form
Expert X argues that
p
Accordingly, P is
probably the case
Example
My primary care physician claims that
poison ivy is contagious when it is oozing.
Therefore, poison ivy is probably
contagious when it is oozing.
b) Assessing the Inductive Strength of Arguments from Authority: