Module 1, Lesson 3 - SkeletalOutline
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Apr 3, 2024
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PHI 1100
MODULE 1, LESSON 3 SKELETAL OUTLINE
INTRODUCTION TO DEDUCTIVE ARGUMENTS
Important Concepts:
Deductive Arguments
Inductive Argument
Fallacy
Indirect Proof
Valid Argument
Sound Argument
Notes on Text (Salmon’s Introduction to Logic and Critical Thinking
, sixth edition)
I.
Chapter 3, I: Introduction (78-79)
1.
When trying to evaluate an argument, which two things must you consider?: Are the premisses true? Is the argument logical?
2.
How can you determine if an argument is logical?: We can analyze structures, or forms, of arguments in a general way, without reference to specialized factual knowledge.
3.
What are the three (general) types of arguments that we will cover in this course? Deductive Arguments, Inductive Arguments, and Fallacies
4.
What is a deductive argument? What kind of support is needed for a deductive argument to be considered a good argument? An argument is deductive when its premisses and conclusion are related in such a way that the truth of the premisses guarantees the truth of the conclusion.
In a deductive argument, if the premisses are all true, then the conclusion must be true
.
5.
What is an inductive argument? What kind of support is needed for it to be considered a good argument? In an inductive argument, if the premisses are all true, then probably the conclusion is true, but it might be false. Inductive support provides good reasons but not conclusive reasons to accept the conclusion.
6.
What is a sound argument? What is a cogent argument? Arguments (either deductive or inductive) that provide the proper kind of support for their conclusions and also have all true premisses are called sound arguments. Cogent argument refers to an inductive argument with all true premisses.
7.
What is a fallacy, or fallacious argument
?
In a fallacy, or fallacious argument, the alleged evidence offers only very weak support or is irrelevant to the conclusion. Fallacies also occur when the premisses make some irrelevant appeal to our emotions instead of providing evidence for the truth of the conclusion.
2
8.
Other Notes:
II.
Chapter 3, II: Deductive Arguments (pp. 80-90)
1.
What does it mean to say that a deductive argument is truth-preserving? Deductive arguments preserve truth because they recombine and restate information that is contained at least implicitly in the premisses. In a deductive argument, if all the premisses are true, the conclusion cannot be false. The conclusion of a deductive argument puts together or restates information that is contained in the premisses without adding new information about the world.
2.
What kind of reasoning does Salmon state is a “primary example” of deductive reasoning? Mathematical
3.
Give an example of a deductive argument that you have experience with in your life or in school (Salmon talks about several kinds of arguments that tend to be deductive):
Premise 1: All school athletes practice on the football field. Premise 2: A cheerleader is a school athlete. Conclusion: Therefore, cheerleaders report to the football field for practice. 4.
What is an indirect proof?: Proof by contradiction. Indirect proof is a type of argument that shows that a contradiction or an obviously false sentence follows deductively from an assumption that a statement to be proved is false.
5.
What is a valid argument? A valid argument is a correct, successful, or genuine deductive argument—that is, an argument in which the premisses, if true, guarantee
the truth of the conclusion. 6.
What are two common, but different, ways to define “deductive arguments?” What is the difference and what are the plusses/minuses to each definition?
___________
_____________________________________________________________________
_____________________________________________________________________
7.
Other Notes:
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Practice Exercises Complete the following problems from Exercise Sets 3.1 & 3.3 for your own practice. These will not be graded. Similar problems will appear on Assignment 3 and the Module 1 Test. (The answers to these problems can be found in the back of your textbook.)
From Exercise Set 3.1 (p. 83)
For each of the following sets of premises, think of a conclusion that follows deductively. Then, write the argument (with that conclusion) in standard form.
2. Each cake requires five eggs. We need to make four cakes.
We need to make four cakes
Each cake requires five eggs
----------------------------------------------------
We need 20 eggs to make four cakes.
If four cakes need to be made and each cake needs 5 eggs, 5x4=20. Therefore, you need 20 eggs to make four cakes.
4. The probability of rolling an ace with a fair die is 1/6. The probability of rolling two aces with a pair of fair die is the probability of rolling an ace on the first die times the probability of rolling
an ace on the second.
From Exercise Set 3.3, Pt I (p. 89)
If we define a deductive argument as one in which it is impossible for the conclusion to be false if all the premises are true, which of the following sentences are true?*
*Some texts and logicians would refer to this as a
valid deductive argument
2. A deductive argument can have a false conclusion. False
in a valid deductive argument, if the premises are true, the conclusion must also be true. However, the conclusion can be false if either the premises are false or if the argument is invalid.
4. A deductive argument can have all false premises and a true conclusion. False
In a deductive argument, if all the premises are false, it would not logically support a true conclusion.
6. A deductive argument can have one true premise, several false premises, and a true conclusion. True
In a deductive argument, as long as the logical structure is valid, it is possible for there to be one true premise, several false premises, and a true conclusion
.
8. A deductive argument can have the same sentence as one of its premises and as its conclusion. True
a deductive argument can have the same sentence as one of its premises and as its conclusion.
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From Exercise Set 3.3, Pt II (p. 89)
For each of the following arguments, indicate in a general way the definitional or structural features that make it deductive. If the argument requires the addition of an obviously true but unstated premise, say what that premise is.
2. Mary is Michael’s mother. Therefore, Michael is Mar’s son.
4. Every senior owns a smart phone. Carolos does not own a smart phone. Therefore, Carlos is not a senior. 8. A person should not be judged guilty of murder if he was certified as insane at the time of the
act of killing another person. The court has accepted the doctor’s certification of Smith’s insanity at the time of killing. Therefore, Smith should not be judged guilty of murder.
From Exercise Set 3.3, Pt III (p. 90)
None of the following arguments is deductive (i.e. valid deductive argument). Describe a situation in which the conclusion of each of the following arguments could turn out to be false even though the premises are all true.
2. Every senior can register for this class. Sally is not a senior. Sally cannot register for this class.
6. In Shakespeare’s Hamlet
, Polonius gives the following advice to his son Laertes:
This above all, to thine own self be true, And it must follow, as the night the day,
Thou canst not then be false to any man.