This resource covers using logic within writing—logical vocabulary, logical fallacies, and other types of logos-based reasoning.
Contributors: Ryan Weber, Allen Brizee
Last Edited: 2011-04-03 07:43:41
Before using logic to reach conclusions, it is helpful to know some important vocabulary related to logic.
Premise: Proposition used as evidence in an argument.
Conclusion: Logical result of the relationship between the premises. Conclusions serve as the thesis of the argument.
Argument: The assertion of a conclusion based on logical premises.
Syllogism: The simplest sequence of logical premises and conclusions, devised by Aristotle.
Enthymeme: A shortened syllogism which omits the first premise, allowing the audience to fill it in. For example, "Socrates is mortal because he is a human" is an enthymeme which leaves out the premise "All humans are mortal."
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.
Reaching Logical Conclusions
Reaching logical conclusions depends on the proper analysis of premises. The goal of a syllogism is to arrange premises so that only one true conclusion is possible.
Consider the following premises:
Premise 1: Non-renewable resources do not exist in infinite supply.
Premise 2: Coal is a non-renewable resource.
From these two premises, only one logical conclusion is available:
Conclusion: Coal does not exist in infinite supply.
Often logic requires several premises to reach a conclusion.
Premise 1: All monkeys are primates.
Premise 2: All primates are mammals.
Premise 3: All mammals are vertebrate animals.Conclusions: Monkeys are vertebrate animals.
Logic allows specific conclusions to be drawn from general premises. Consider the following premises:
Premise 1: All squares are rectangles.
Premise 2: Figure 1 is a square.
Conclusion: Figure 1 is also a rectangle.
Notice that logic requires decisive statements in order to work. Therefore, this syllogism is false:
Premise 1: Some quadrilaterals are squares.
Premise 2: Figure 1 is a quadrilateral.
Conclusion: Figure 1 is a square.
This syllogism is false because not enough information is provided to allow a verifiable conclusion. Figure 1 could just as likely be a rectangle, which is also a quadrilateral.
Logic can also mislead when it is based on premises that an audience does not accept. For instance:
Premise 1: People with red hair are not good at checkers.
Premise 2: Bill has red hair.
Conclusion: Bill is not good at checkers.
Within the syllogism, the conclusion is logically valid. However, it is only true if an audience accepts Premise 1, which is very unlikely. This is an example of how logical statements can appear accurate while being completely false.
Logical conclusions also depend on which factors are recognized and ignored by the premises. Therefore, different premises could lead to very different conclusions about the same subject. For instance, these two syllogisms about the platypus reveal the limits of logic for handling ambiguous cases:
Premise 1: All birds lay eggs.
Premise 2: Platypuses lay eggs.
Conclusion: Platypuses are birds.
Premise 1: All mammals have fur.
Premise 2: Platypuses have fur.
Conclusion: Platypuses are mammals.
Though logic is a very powerful argumentative tool and is far preferable to a disorganized argument, logic does have limitations. It must also be effectively developed from a syllogism into a written piece.
LESSON # 1
Arguments, Premises And Conclusions
Reading Assignment: 1.1 (pp. 1-7)
Click here to bypass the following discussion and go straight to the assignments.
Logic is the science that evaluates arguments.
An argument is a group of statements including one or more premises and one and only one conclusion.
A statement is a sentence that is either true or false, such as "The cat is on the mat." Many sentences are not statements, such as "Close the door, please" , "How old are you?"
A premise is a statementin an argument that provides reason or support for the conclusion. There can be one or many premises in a single argument.
A conclusion is a statement in an argument that indicates of what the arguer is trying to convince the reader/listener. What is the argument trying to prove? There can be only one conclusion in a single argument.
In this lesson you will need to be able to distinguish premises and conclusions:
The foolproof way to do this is to ask yourself what the author of the argument is trying to get you to believe. The answer to this question is the conclusion.
There must also be at least one reason and possibly many. These are your premises.
Your common sense will be of great help here.
You should also study very carefully the lists of premise and conclusion indicator words on page 3 in the text. There will not always be indicator words, though more often than not there are. You should note as well that the conclusion can often be identified as the statement directly before a premise indicator. Remember that these are general rules only. Think of indicator words as "red flags." They are positioned in the argument to signal the author's intent, but always check yourself by asking what's being proven, and what the proof is.
When you feel confident that you have mastered these concepts, do the True/False exercise on p. 13 in the textbook. (section IV) You can check your answers in the appendix of this study guide.
Then do exercises 1.1 I 1-22 on your Logic Coach Software. If you need more practice, feel free to do more. If you use up all the exercises in section I, you may do problems from II and send the answers to me to get checked (this section of the text isn't on Logic Coach)
When you are ready, complete the following assignments, using the book as little as possible. Hand in both of the following assignments together with a copy of your logic coach record screen. For more detailed instructions on doing this click here.
Rewrite the following arguments listing the premise(s) first and the conclusion last. Each line should be a single statement written as a complete sentence. Feel free to modify the sentences as you deem necessary, without changing their basic meaning. (after all you want to be restating this argument, not writing a new one!) Label the premise(s) P¹, P², P³, etc. and the conclusion C. Leave out any indicator words and any fluff (i.e., sentences which are neither the conclusion nor a premise). 10 points each.
Cats with long hair shed all over the house so you should not get a long-haired cat.
I have heard that they also have lots of fleas.
|Long-haired cats shed all over the house|
|Long-haired cats have a lot of fleas|
|You should not get a long haired cat|
1. Fairdale will win the championship because they have the best team.
2. Since the housing market is depressed and interest rates are low, it's a good time to buy a home.
3. China is guilty of extreme human rights abuses. Further, they refuse to implement democratic reforms. Thus, the U.S. should refuse to deal with the present Chinese government.
4. The revocation of the 55 mph speed limit has resulted in an increased number of auto fatalities. We must alleviate this problem with stricter speed limit enforcement.
5. We may infer that the U. S. military is both capable and competent from the results of the Persian Gulf War.
6. Scientific discoveries are continually debunking religious myths. Further, science provides the only hope for solving the many problems faced by humankind. Hence, science provides a more accurate view of human life than does religion.
7. Jesse is one year old. Most one-year-olds can walk. It follows that Jesse can walk.
8. I deserve a raise. I'm very good at my job.
Write out two arguments you have encountered in the course of your day. First write them as you encountered them, then re-write in the format you practiced in assignment 1. Make sure they are arguments, with premises and conclusions. You'll get more practice distinguishing between arguments and other passages in the next lesson. For now just make sure there is a conclusion and at least one premise and you'll do fine. (10 points each.)
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