Unit 5 - Logic & The Essay

5.1 Objectives
5.2 Discussion
5.3 Summary
5.4 Lab
5.5 Exercises

 


 

5.1 Objectives

 


 

5.2 Discussion

"People who like this sort of thing will find this the sort of thing they like."
Abraham Lincoln [On Logic?]


 

5.2.1 INDUCTION

Inductive Reasoning moves from specific to general. From the specific of what I have observed I make an inductive leap and arrive at one of two types of inductive inference: a generalization or a hypothesis. See the Huxley article below for some good examples of Inductive logic. The green apples and silver spoons examples will help you to remember the difference between a generalization and a hypothesis. Generally a thesis or a topic sentence is either a hypothesis or a generalization.

The STANFORD ENCYCLOPEDIA OF PHILOSOPHY has a very good discussion of Inductive Logic at http://plato.stanford.edu/entries/logic-inductive/

 



5.2.2 DEDUCTION

Deductive logic moves from general to specific. The basic deductive argument consists of a Syllogism, containing a Major Premise, a Minor Premise, and a Conclusion.

From a generality such as Today is Thursday, we conclude that today is a school day. Deductive arguments (even if-then inferences) can be expressed as categorical propositions that name the relationship between two classes of things. Here are two examples of categorical propositions, the first of which is called a Major Premise and the second of which (note that it is more specific--and less debatable) is called a minor premise.

MAJOR PREMISES: All Thursdays are School Days

MINOR PREMISE: (All) Today is Thursday

We most commonly encounter deductive arguments as enthymemes, deductive arguments that are missing one or more parts. When we arose this morning, we immediately concluded "Today is a school Day." Here is an enthymeme in which only the conclusion is stated--BOTH premises are missing. See also the summary below of Huxley's (Unit 5.2.4) "The Method of Scientific Investigation."

An excellent discussion of deductive logic may be found at Dr. David Mesher's logic page at San Jose State University.

5.2.3 Thomas Huxley, "The Method of Scientific Investigation."

SUMMARY-from memory

This essay, published in the nineteenth century, contains the thesis that scientists and the common man (sexist language, but acceptable then) each use logic the same way.

Huxley then discusses two types of INDUCTIVE INFERENCES, the GENERALIZATION and the HYPOTHESIS. In INDUCTIVE LOGIC, we go from specific observations to more general, not necessarily observed, conclusions.

Following that he discusses DEDUCTIVE LOGIC, in which we move from general to specific. The basic form of a DEDUCTIVE argument is a SYLLOGISM which consists of a MAJOR PREMISE (which may be a GENERALIZATION or a HYPOTHESIS), a MINOR PREMISE which is more specific, and a CONCLUSION, which, in a VALID deductive argument, is forced from the Major and Minor premises.

(Note: Huxley does not discuss the term "RELIABILTY," but we shall be much concerned with it. A RELIABLE argument is one which you believe to be sufficiently true to believe, or act upon. You should commit this definition, and the capitalized terms, to memory, for the sake of the quiz, and for life.)

Back to Huxley: In defining GENERALIZATIONS, Huxley discusses the example of the green apples. On going to a store and purchasing a green apple, he observes that it is sour. He goes to another apple in the same store and finds the same thing. He then goes to another store and buys a green apple and it is sour. From the observation of those three apples, he GENERALIZES that "All Green Apples are Sour Things." He believes he has sufficient EVIDENCE to make this GENERALIZATION. He then passes by a field and finds a green apple under a tree; it is green and sour. He then travels to America where he goes to a store and buys agreen apple which is also sour. He now believes his argument to be even more RELIABLE. So, when he wishes to have an apple pie made of sour apples, he always buys green ones. He then goes to Molokai where he finds a guava. . .no, I made that up. But, the RELIABILITY of a GENERALIZATION depends on SAMPLE SIZE and the BREADTH of the sample. A GENERALIZATION relates and explains LIKE items of information, in this case, green apples.

Huxley next discusses HYPOTHESES which relate and explain UNLIKE items of information. He uses the example of the missing spoons and teapot. A woman awakes and proceeds one morning to her dining room, where she discovers that her silver teapot and teaspoons are missing. She races to an open window which she had closed the night before. She sees a handprint on the windowsill and muddy shoeprints in her garden. She formulates a HYPOTHESIS that a robber has stolen her silver; believing this a RELIABLE hypothesis, she calls the police. Her hypothesis--which is not necessarily true, but which is reliable, relates and explains UNLIKE items of information: missing spoons, missing teapot, open window, handprint, and shoe prints. As usual the RELIABILITY of the argument depends upon the EVIDENCE.

Huxley then discusses DEDUCTIVE logic including SYLLOGISMS. A sample is the best example:

MAJOR PREMISE: All persons are mortal

MINOR PREMISE: Socrates is a person.

CONCLUSION: Socrates is mortal.

In order for the conclusion of a Deductive argument to be reliable, the argument must be VALID, i.e. the conclusion must be forced from the premises, and the Premises must be RELIABLE. The debate is usually centered around the MAJOR PREMISE, since it is more general, and is apt to be a GENERALIZATION or HYPOTHESIS.
Another example:

MP: All A is B
mp: All C is A
Conc: All C is B

Another example:

MP: No D is E
mp: All F is D
Conc: No F is E

Another Example:

MP: Most Asians are slow drivers.
mp: Nguyen is Asian
Concl: Nguyen is a slow driver.

The example immediately above is an example of a FALLACY, an error in reasoning. It is a sad example of stereotyping. What other kind of fallacy is this? The fallacy section, immediately following, may help you determine the correct answer.



 

5.2.4 FALLACIES

A fallacy is an error in reasoning. Generally, we should avoid fallacies, but that is not entirely correct, for often, as arguers, we make use of fallacies. The key to a critical thinking course is to be able to identify fallacies as they occur. The Nizkor WEB SITE , below, contains the following formal definition of fallacies, using terminology that is fairly similar to that which we shall use in class:

"In order to understand what a fallacy is, one must understand what an argument is. Very briefly, an argument consists of one or more premises and one conclusion. A premise is a statement (a sentence that is either true or false) that is offered in support of the claim being made, which is the conclusion (which is also a sentence that is either true or false).

There are two main types of arguments: deductive and inductive. A deductive argument is an argument such that the premises provide (or appear to provide) complete support for the conclusion. An inductive argument is an argument such that the premises provide (or appear to provide) some degree of support (but less than complete support) for the conclusion. If the premises actually provide the required degree of support for the conclusion, then the argument is a good one. A good deductive argument is known as a valid argument and is such that if all its premises are true, then its conclusion must be true. If all the argument is valid and actually has all true premises, then it is known as a sound argument. If it is invalid or has one or more false premises, it will be unsound. A good inductive argument is known as a strong (or "cogent") inductive argument. It is such that if the premises are true, the conclusion is likely to be true.

A fallacy is, very generally, an error in reasoning. This differs from a factual error, which is simply being wrong about the facts. To be more specific, a fallacy is an "argument" in which the premises given for the conclusion do not provide the needed degree of support. A deductive fallacy is a deductive argument that is invalid (it is such that it could have all true premises and still have a false conclusion).

An inductive fallacy is less formal than a deductive fallacy. They are simply "arguments" which appear to be inductive arguments, but the premises do not provided enough support for the conclusion. In such cases, even if the premises were true, the conclusion would not be more likely to be true. "

A good example of an inductive fallacy is a hasty generalization, a generalization that does not rest on a sample that is sufficiently large or have the breadth to support the inference. Perhaps that will answer the question about Nguyen, above. Other inductive fallacies include the Post Hoc fallacy, or post hoc ergo propter hoc, latin for "because of this, therefore that," also known as false causation.

While there are hundreds of fallacies, and you could easily spend an entire quarter studying the ones you will find in the following lists, ensure that, in addition to the inductive fallacies already mentioned that you know:

LISTS OF FALLACIES:

http://www.earlham.edu/~peters/courses/inflogic/inflinks.htm

 


 

5.2.5 TESTING FOR RELIABILITY

Technically, reliability is the degree of confidence that is placed in the truth of a proposition. When the evidence supports the conclusion in question to the extent that we are sufficiently convinced of its truth to act upon it, we say that the conclusion is reliable. For our purposes, a conclusion is simply reliable or not reliable. There are no pat mechanical rules for appraising conclusions for reliability, but there is a skill that can be learned and a systematic process that can be mastered which will help in making a reliable judgment. The analysis of any inductive prose argument should include the following steps:

Identify the conclusion (thesis) and the main supporting points (topic sentences)

Consider the inductive process

Identify any fallacies present in the evidence

Evaluate the evidence or the lack of evidence

Organize a defense for the judgment rendered

A. Identify the conclusion (thesis) and the main supporting points (topic sentences)

In the past you may have experienced difficulty identifying theses despite the fact that you have felt reasonably assured that these theses were stated somewhere in the introductory paragraphs. We will be concerned with identifying thesis statements and main supporting points in assigned readings. Additionally, we will be confronted with the problem of determining the theses in much of our research source material. Fortunately, in many cases, there are words and phrases called logical indicators which indicate that the writer has made an inference. These logical indicators focus on the inference and help to identify the conclusion. Each of the following words or phrases usually shows that the statement following it is a conclusion:

 therefore  which shows that
 proves that   hence
 indicates that  consequently
 you see that  implies that
 entails  allows us to infer that
 points to the conclusion that  suggests very strongly that
 leads me to believe that  bears out my point that
 from which it follows that  thus it can be seen that

Main supporting points are not always so easily identified; there are generally no indicator words. The structure of the argument is most often the key. Except in rather long essays or in those that are subtly sophisticated, the topic sentence of each paragraph is in fact a premise, and the information in the paragraph is the evidence which the writer has offered in support of that premise.

This first step in the systematic process can best be accomplished by diagramming the argument. The diagram provides a convenient pictorial representation of the argument which facilitates completion of the remaining four steps of the evaluation.

   THESIS  
 TOPIC SENTENCE 1  TOPIC SENTENCE 2  TOPIC SENTENCE 3
 Evidence in Body Para 1  Evidence in Body Para 2  Evidence in Body Para 3


Testing for Reliability is the critical task in our study of logic. Are we sufficiently convinced of an argument to believe it or act upon it? The rules of argumentation, evidence, and logic are all are key here.


Your final task, having considered all of this, is to articulate your own well-organized argument as to whether an argument is reliable.

Below, you will find two favorites of mine, reliability evaluation of Andrew Marvell's poetic argument contained in "To His Coy Mistress," and the reliability of just one of Martin Luther King's eight arguments in "Letter from Birmingham Jail," namely, King's claim that he is not an outsider. As you write this paper, you will see how key it is that you RESTRICT yourself to a portion of an argument that you can manage.

See also Exercise 4.5.3, evaluating the Reliability of Haunani Kay Trask's (activist in the Hawaii Separatist movement) argument in her essay, "From a Native Daughter."

 

5.3 Summary

Summary INDUCTIVE LOGIC moves from specific observations to more general, not necessarily observed conclusions, called INFERENCES. The two types of INDUCTIVE INFERENCES are GENERALIZATIONS and HYPOTHESES. GENERALIZATIONS relate and explain LIKE ITEMS. HYPOTHESES relate and explain UNLIKE items.

DEDUCTIVE LOGIC moves from GENERAL OBSERVATIONS (which may be Hypotheses or Generalizations) to more SPECIFIC CONCLUSIONS. The basic form of the Deductive argument is the SYLLOGISM, which consists of three parts:

The MAJOR PREMISE
The MINOR PREMISE
The CONCLUSION

If a Syllogism follows the rules of logic--which we shall not go into here--but, basically, if the Conclusion is forced from (or already contained within) the premises, the deductive argument is VALID.

We most commonly do not go around speaking in Syllogisms; rather we give only parts of a deductive argument. A deductive argument with one or more missing parts, is known as an ENTHYMEME. We also use chains of enthymemes.

RELIABILITY DEFINITION

When we are sufficiently convinced of the truth of an argument to BELIEVE it or ACT UPON it, that argument is, to us, RELIABLE. RELIABILITY does not necessarily equal truth.


 

5.4 Lab

LAB EXERCISE 5.4.1


STUDENT LOGIC CLASS, INDUCTION, DEDUCTION, and FALLACIES. In your assigned groups, be prepared to respond to the following questions, using your text (s), and the Huxley essay, "The Method of Scientific Investigation." The use of handouts or material written on the board is strongly encouraged.

GROUP A: Explain Inductive Logic and the Inductive inference known as the Generalization. On what does the reliability of a generalization depend? What is a hasty generalization? Where might you find a generalization in an argumentative essay?

GROUP B: Explain the Inductive Inference known as a Hypothesis. On what does the reliability of an hypothesis depend? Where do you normally find a hypothesis in an argumentative essay? What is the "Inductive Leap"?

GROUP C: Explain Deductive Logic including the Syllogism. Find examples from everyday life to support the notion that we routinely use deductive logic. What does validity mean? What is the difference between reliability and validity? On what does the reliability of a valid deductive argument depend?

GROUP D: Explain Enthymemes and Fallacies. Why are enthymemes important, particularly since you went your entire life until now without hearing the word? If a fallacy is an error in logic, why might you want to employ one, or more?

GROUPS E & F: Explain Specific Fallacies, as assigned. In each case, try to come up with at least one example from outside your text. Also bring in any fallacy you might find from media advertising, such as an ad for women's cigarettes.


 

5.5 Exercises

EXERCISE 5.5.1 EVALUATING THE RELIABILITY OF AN ARGUMENT IN ANDREW MARVELL'S POEM: "To His Coy Mistress."

ALL: When assigned, bring to class, a response to the following questions. You are encouraged to work together within your groups if possible:

A. What is the thesis of the poem, the main line of argument? Be precise. Look for indicator words, and see if structure is of any help also.

B. What are at least two of the main supporting points (or Topic Sentences) and what evidence is introduced to support those?

C. Do you feel the evidence is strong and why?

D. Put yourself in the place of the person to whom the argument is addressed. Is the argument RELIABLE? Why or Why Not?

EXERCISE 5.5.2

Reliability of Dr. Martin Luther King's argument in "Letter from Birmingham Jail." The letter contains eight arguments in response to the eight arguments raised by the clergy in their letter of 12 April. The first of these arguments is King's response to the Clergy's claim that he is an "outsider." HIs evidence for this argument appears primarily in the second and third paragraph of his letter., though later in the essay you may also find material evidence. Evaluate the reliability of King's argument that he is not an outsider.

alternate: Evaluate the reliability of ONE of Dr. King's arguments in his powerful anti-Viet Nam sermon, "A Time to Break Silence," delivered on 3 April, 1967, in the pulpit of the Riverside Church in New York City.


EXERCISE 5.5.3

See Reliability Evaluation of arguments advanced by Haunani Kay Trask, Hawaiian Separatist and UH Professor, from her book FROM A NATIVE DAUGHTER .


 

Last Updated: 9/18/09