|Many of the important points of this section are covered in the section on writing Argumentative Essays: Being Logical. You might want to review that section first and then come back here for a more thorough review of the principles of logic.|
|This document is part of a collection of instructional materials used in the Purdue University Writing Lab. The on-line version is part of OWL (On-line Writing Lab), a project of the Purdue University Writing Lab, funded by the School of Liberal Arts at Purdue.|
We use logic every day to figure out test questions, plan our budgets, and decide who to date. We borrow from the vocabulary of logic when we say, "Brilliant deduction" or even "I don't want to argue about it." In the study of logic, however, each of these terms has a specific definition, and we must be clear on these if we are to communicate.
- Proposition --
- T or F in an argument, but not alone. Can be a premise or conclusion. Is not equal to a sentence.
- Premise --
- Proposition used as evidence in an argument.
- Conclusion --
- Proposition used as a thesis in an argument.
- Argument --
- A group of propositions of which one is claimed to follow from the others.
- Induction --
- A process through which the premises provide some basis for the conclusion
- Deduction --
- A process through which the premises provide conclusive proof for the conclusion.
|Argument Indicators:||Premise Indicators:||Conclusion Indicators:|
When dealing with persuasive writing, it will be helpful for you to outline the argument by premises and conclusions. By looking at the structure of the argument, it is easy to spot logical error.
"Universities are full of knowledge. The freshmen bring a little in, and the seniors take none away, and knowledge accumulates.
-- Harvard President A. L. Lowell
|Freshmen bring a little (knowledge) in|
Seniors take none away
Universities are full of knowledge
(Here, the conclusion of one argument is used as a premise in another. This is very common.)
Even though there may be a deceiver of some sort, very powerful and very tricky, who bends all his efforts to keep me perpetually deceived, there can be no slightest doubt that I exist, since he deceives me; and let him deceive me as much as he will, he can never make me be nothing as long as I think I am something. Thus, after having thought well on this matter, and after examining all things with care, I must finally conclude and maintain that this proposition: I am, I exist, is necessarily true every time that I pronounce it or conceive it in my mind.
-- Rene Descartes, *Meditations*
|Argument 1 Premise 1:|
Conclusion of Argument 1
|To be deceived ... I must exist |
When I think that I exist I cannot be
I am, I exist, is necessarily true ... .
Find the Arguments and Outline them in These Statements:
1. Ask the same for me, for friends should have all things in common.
-- Plato, Phaedrus
2. Matter is activity, and therefore a body is where it acts; and because every particle of matter acts all over the universe, every body is everywhere.
-- Collingwood, The Idea of Nature
3. The citizen who so values his "independence" that he will not enroll in a political party is really forfeiting independence, because he abandons a share in decision©making at the primary level: the choice of the candidate.
-- Felknor, Dirty Politics
Reaching Logical Conclusions
This article is reprinted from pages 78-79 of Pearson-Allen: Modern Algebra , Book One. In the book it is one of several between-chapter articles that add interest and provike thought on subjects related to the topics discussed in the text.
Consider the two statements:
1. Any member of a varsity squad is excused from physical education.
2. Henry is a member of the varsity football squad.
Our common sense tells us that if we accept these two statement as true, then we must accept the following third statement as true:
3. Henry is excused from physical education.
We say that the third statement follows logically from the other two.
In drawing logical conclusions it does not matter whether the statements we accept as true are reasonable or sensible. This is because we depend entirely upon the form of the statements and not upon what we are talking about. Thus, if we accept the following statements as true:
1. All whales are mammals;
2. All mammals are warm-blooded animals;
3. All warm-blooded animals are subject to colds;
then we must conclude that
4. All whales are subject to colds. Do you see that statements 1, 2, and 3 are arranged in logical order ?
|In the diagram at the right the set of whales is represented|
by W, the set of mammals by M, the set of warm-blooded
animals by B, the set of animals by B, the set of animals
subject to colds by C, and the set of all animals by A. The
diagram shows that W is a subset of M as required by
statement 1, that M is a subset of B as required by statement
2, and that B is a subset of C as required by statement 3. The
only conclusion that uses all of our given statements is that
W is a subset of C, as asserted by statement 4.
|Had our third statement been "no warm-blooded animals are subject to colds," our diagram would have been the one shown at the right and our conclusion would have been "no whales are subject to colds."|
If you have read Alice's Adventures in Wonderland or Through the Looking-Glass , you know that their author, Lewis Carroll, delighted in giving sets of nonsense statements which lead to logical conclusions. One such set is the following:
- Babies are illogical;
- Nobody is despised who can manage a crocodile;
- Illogical persons are despised.
When these statements are arranged in logical order we have:
1. Babies are illogical;
2. Illogical persons are despised;
3. Nobody is despised who can manage a crocodile.
From these we can draw the logical conclusion:
4. Babies cannot manage crocodiles.
Other sets of statements written by this author follow. To draw a conclusion from each set of statements, first arrange the statements in logical order. A diagram such as those in the preceding column may help you. The correct conclusions are given at the bottom of the page, but do not look at them until you have written your conclusion.
1. Everyone who is sane can do Logic;
2. No lunatics are fit to serve on a jury;
3. None of your sons can do Logic.
1. No ducks waltz;
2. No officers ever decline to waltz;
3. All my poultry are ducks.
1. No kitten that loves fish is unteachable;
2. No kitten without a tail will play with a gorilla;
3. Kittens with whiskers always love fish;
4. No teachable kitten has green eyes;
5. No kittens have tails unless they have whiskers.
1. There is no box of mine here that I dare open;
2. My writing-desk is a box made of rose-wood;
3. All my boxes are painted except what are here;
4. There is no box of mine that I dare not open, unless
it is full of live scorpions;
5. All my rose-wood boxes are unpainted.
I. None of your sons are fit to serve on the jury.
II. My poultry are not officers.
III. No kitten with green eyes will play with a gorilla.
IV. My writing-desk is full of live scorpions.
With this brief introduction to Lewis Carroll type problems, you will find it worthwhile and interesting to construct your own problems of this type.
(The fun part)
A fallacy is an error of reasoning. It can be used against you in an argument, but if you are familiar with them, you will be able to refute the fallacious argument. Likewise, if you are clever, you can use them to convince others.
Fallacies fall into two major categories:
- Fallacies of Relevance
- -- Premises are irrelevant to the conclusion.
- Fallacies of Ambiguity
- -- Ambiguous, changeable wording in the propositions
Here are examples of each of the major fallacies. You figure out and write in a definition which makes sense to you.
Fallacies of Relevance
- 1. Argumentum ad Bacculum (appeal to force) --
- "Pay back the loan and 10 % daily interest by Thursday, or be sure that you have you hospital insurance paid up."
- 2. Argumentum ad Hominem (abusive) --
- "Don't believe anything John says; he's a nerd."
- 3. Argumentum ad Hominem (circumstantial) -- "Of course he thinks fraternities are great. He's a Phi Delta."
- 4. Argumentum ad Ignorantiam (argument from ignorance) --
- There is no proof that witches exist; therefore, they do not.
- 5. Argumentum ad Misericordiam (appeal to pity) --
- "Your honor, how can the prosecution dare try to send this poor, defenseless child to jail for the murder of his father and mother. Have a heart; the boy is now an orphan."
- 6. Argumentum ad Populum --
- "Don't be left out! Buy your Chevette today!"
- 7. Argumentum ad Vericundiam (appeal to authority) --
- Joe Namath selling pantyhose; Joe DiMaggio selling Mr. Coffee.
- 8. Accident --
- "What you bought yesterday, you eat today; you bought raw meat yesterday; therefore, you eat raw meat today."
- 9. Converse Accident (hasty generalization) --
- "That man is an alcoholic. Liquor should be banned."
- 10. False cause (Post hoc ergo propter hoc) (Many of our superstitions stem from use of this fallacy.) --
- "a black cat crossed Joe's path yesterday, and he died last night." or "Put your money where your mouth is. Whiter teeth and fresh breath will win Susie."
- 11. Petitio Principii (begging the question) --
- "It's time to come in the house now, Billy."
"Because I said so!"
"Because it's time, and I said so."
- 12. Complex Question --
- "Have you given up cheating on exams?"
- 13. Ignoratio Elenchi (irrelevant conclusion) --
- In a law court, in attempt to prove that the accused is guilty of theft, the prosecution may argue that theft is a horrible crime for anyone to commit.
Fallacies of Ambiguity
- 1. Equivocation --
- Some dogs have fuzzy ears. My dog has fuzzy ears. My dog is some dog!
- 2. Amphibole (grammatical construction) --
- "Woman without her man would be lost." or "Save Soap and Waste Paper."
- 3. Accent --
- "We should not speak ill of our friends."
- 4. Composition--
- "Each part of this stereo weighs under one pound. This is a very light stereo."
or " ... ONLY $1.97 plus processing and postage."
- 5. Division--
- "Purdue is a great engineering school. Mike went there; he must be a great engineer."
Listen to your roommate, the T.V., and even your profs. You'll be amazed how many fallacies we encounter each day.
More important, check your papers. Does your argument have premisses and conclusions stated properly? Have you been guilty of fallacious reasoning?
(from Copi, Introduction to Logic pp. 85-87)
Identify the Fallacies in the Following Passages and Explain how each Specific Passage Involves that Fallacy or Fallacies:
1. It is necessary to confine criminals and to lock up dangerous lunatics. Therefore there is nothing wrong with depriving people of their liberties.
2. How much longer are you going to waste your time in school when you might be doing a man's work in the world, and contributing to society? If you had any sense of social responsibility, you would leave immediately.
3. The army is notoriously inefficient, so we cannot expect Major Smith to do an efficient job.
4. God exists because the Bible tells us so, and we know that what the Bible tells us must be true because it is the revealed word of God.
5. Congress shouldn't bother to consult the Joint Chiefs-of-Staff about the military appropriations. As members of the armed forces, they will naturally want as much money for military purposes as they think they can get.
6. Mr. Brown: I will give no more money to your cause next year.
Solicitor: That's all right, sir, we'll just put you down for the same amount that you gave this year.
7. When we had got to this point in the argument, and every one saw that the definition of justice had been completely upset, Thrasymachus, instead of replying to me, said:
"Tell me, Socrates, have you got a nurse?"
"Why do you ask such a question," I said, "when you ought rather to be answering?"
"Because she leaves you to snivel, and never wipes your nose: she has not even taught you to know the shepherd from the sheep."
-- Plato, Republic
8. Narcotics are habit-forming. Therefore if you allow your physician to ease your pain with an opiate, you will become a hopeless drug addict.
9. You can't prove that he was to blame for the misfortune, so it must actually have been someone else who was responsible.
10. You can't park here. I don't care what the sign says. If you don't drive on, I'll give you a ticket.
11. But lest you think, that my piety has here got the better of my philosophy, I shall support my opinion, if it needs my support, by a very great authority. I might cite all the divines almost, from the foundation of Christianity, who have ever treated of this or any other theological subjects: but I shall confine myself, at present, to one equally celebrated for piety and philosophy. It is Father Malebranche...
-- David Hume, Dialogues Concerning Natural Religion
(from Copi, *Introduction to Logic* pp. 87-88)
16. Cooks have been preparing food for generations, so our cook must be a real expert.
17. More young people are attending high schools and colleges than ever before in the history of our nation. But there is more juvenile delinquency than ever before. This makes it clear that to eliminate delinquency among the youth we must abolish the schools.
18. You say we ought to discuss whether or not to buy a new car now. All right, I agree. Let's discuss the matter. Which should we get, a Ford or a Chevy?
19. Our nation is a democracy and dedicated to the proposition that all men are created equal. We believe in equality of opportunity for everyone, so our colleges and universities should admit every applicant, regardless of his economic or educational background.
20. Anyone who deliberately strikes another person should be punished. Therefore the middleweight boxing champion should be severely punished, for he assaults all of his opponents.
21. We should reject Mr. Watkins' suggestions for increasing the efficiency of our colleges. As a manufacturer he cannot be expected to realize that our aim is to educate the youth, not to make a profit. His recommendations can have no value for us.
22. Everyone said that the soup had a very distinctive taste, so they must all have found it very tasty.
23. If we want to know whether a state is brave we must look at its army, not because the soldiers are the only brave people in the community, but because it is only through their conduct that the courage or cowardice of the community can be manifested.
-- R. L. Nettleship, Lectures on the Republic of Plato
24. My client is the sole support of his aged parents. If he is sent to prison, it will break their hearts, and they will be left homeless and penniless. You surely cannot find it in your hearts to reach any other verdict than "not guilty."
25. There is no proof that the secretary "leaked" the news to the papers, so she can't have done it.
26. Diamonds are seldom found in this country, so you must be careful not to mislay your engagement ring.
27. Was it through stupidity of through deliberate dishonesty that the Administration has hopelessly botched its foreign policy? In either case, unless you are in favor of stupidity or dishonesty, you should vote against the incumbents.
28. Since all men are mortal, the human race must some day come to an end.
Try these for Fun!
Exercises in Reasoning
I. Four men, whom we shall call Robert, Ralph, Ronald, and Rudolph, were playing cards one evening. As a result of a quarrel during the course of the game, one of these men shot and killed another. From the facts below determine the murder and the victim.
- Rudolph had known Ronald for only five days prior to the murder.
- Robert will not expose his brother's guilt.
- Rudolph has been released from jail on the day of the murder, after serving a three day sentence.
- Ralph met Robert's father only once.
- Robert had wheeled Ralph, a cripple, to the card game at Ronald's home.
- The host is about to give evidence against the murderer, whom he dislikes.
- The murdered man had eaten dinner on the previous evening with one of the men who did not customarily bowl with Ronald.
II. Five men are in a poker game: Brown, Perkins, Turner, Jones, and Reilly. Their brands of cigarettes are Luckies, Camels, Kools, Old Golds, and Chesterfields, but not necessarily in that order. At the beginning of the game, the number of cigarettes possessed by each player was 20, 15, 8, 6, and 3, but not necessarily in that order.
During the game, at a certain time when no one was smoking, the following obtained:
- Perkins asked for three cards.
- Reilly had smoked half of his original supply, or one less than Turner had smoked.
- The Chesterfield man originally had as many more, plus half as many more, plus 2 1/2 more cigarettes than he has now.
- The man who was drawing to an inside straight could taste only the menthol in his fifth cigarette, the last one he smoked.
- The man who smokes Luckies had smoked at least two more than anyone else, including Perkins.
- Brown drew as many aces as he originally had cigarettes.
- No one had smoked all his cigarettes.
- The Camel man asks Jones to pass Brown's matches.
How many cigarettes did each man have to begin with, and of what brand?
A functional impropriety is the use of a word as the wrong part of speech. The wrong meaning for a word can also be impropriety.
Mark improprieties in the following phrases and correct them in the blanks at the right. If you find none, write C in the blank. Example: (occupation) hazards -- occupational
1. reforming institution policies
2. percentaging students by grades
3. dead trees as inhabitants for birds
4. an initiate story about a young girl
5. a recurrence theme in literature
6. a wood chisel
7. a wood baseball bat
8. a frivolity conversation on the weather
9. a utopia hideaway of alpine villas
10. a utilize room complete with workbench
11. the unstabled chemical compounds
12. the unschooled labor force
13. the vandals who rapined Rome
14. an erupting volcano crevassing the hills
15. criticism writing which is often abstract
16. abstracted beyond understanding
17. classified as an absorbent
18. a handwriting letter
19. banjoed their way to the top ten
20. a meander stream
21. hoboing across the country
22. holidayed the time away
23. the redirective coming from the officer
24. grain-fed slaughter cattle
25. ivy tendoned to the walls
The term "logic" refers to the science that studies the principles of correct reasoning. Logic requires the act of reasoning by humans in order to form thoughts and opinions, as well as classifications and judgments. The foundation of a logical argument is its proposition, or statement. The proposition is either accurate (true) or not accurate (false). The argument is then built on premises. The premises are the propositions used to build the argument. Then an inference is made from the premises. Finally, a conclusion is drawn.
Understanding Logic Through Examples
There are two types of logical arguments - deductive and inductive. Examples of these are:
- Deductive – This type of reasoning provides complete evidence of the truth of its conclusion. It uses a specific and accurate premise that leads to a specific and accurate conclusion. With correct premises, the conclusion to this type of argument is verifiable and correct.
- Inductive - This type of reasoning is "bottom up," meaning that it takes specific information and makes a broad generalization that is considered probable, allowing for the fact that the conclusion may not be accurate. This type of reasoning usually involves a rule being established based on a series of repeated experiences.
Examples of Deductive and Inductive Logic
- All squares are rectangles. All rectangles have four sides. Logic, therefore, tells you that all squares have four sides.
- It is dangerous to drive when it is snowing. It is snowing now. Logic tells you that it would be dangerous to drive right now.
- All dogs have a good sense of smell. Bailey is a dog. Therefore, deductive reasoning logic tells you that Bailey has a good sense of smell.
- All seniors are bad drivers. Mr. Jones is 70 years old and you won't let him drive your car because you think he is an unsafe driver.
- When it rains the trees get wet. The trees are wet this morning, so it rained last night.
- All trees have trunks. An oak tree is a tree. Therefore, deductive reasoning tells you that the oak tree has a trunk.
- An umbrella prevents you from getting wet in the rain. Ashley took her umbrella and she did not get wet. In this case, you could use inductive reasoning to offer an opinion that it was probably raining. Your concluson, however, would not necessarily be accurate because Ashley would have remained dry whether it rained and she had an umbrella, or whether it did not rain at all.
- Every three year old you see at the park every afternoon spends most of their time crying and screaming. Your conclusion is that all three year olds spend their afternoon screaming.
- Every house that burned down on the block was caused by faulty wiring. You conclusion is that all homes on the block have faulty wiring.
- Red lights prevent accidents. Mike did not have an accident, therefore Mike stopped at a red light. This is an example of inductive reasoning; but, it is faulty reasoning because Mike might not have encountered any traffic signals at all. Therefore, he might have been able to avoid accidents even without stopping at a red light.
As these examples show, you can use logic to solve problems and to draw conclusions. Sometimes those conclusions are correct conclusions and sometimes they are inaccurate. When you use deductive reasoning, you arrive at correct logical arguments while inductive reasoning may or may not provide you with a correct outcome.