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LOGOS


LOGIC
ARGUMENTS

 

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:

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:

 


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