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Arguments, deduction, fallacies, and definitions

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1 Arguments, deduction, fallacies, and definitions

2 Components of arguments
Arguments are composed of premises and conclusions. Premises provide support for conclusions. If the premises are true and the argument is valid, then the conclusion must be true.

3 Premises and conclusions can appear in any order
Interest rates are going to rise. The Federal Reserve is concerned about inflation. Higher interest rates counteract inflation. Conclusion Premise

4 Winston Churchill (pg. 1)
I am an optimist. (conclusion) There does not seem to be much use being anything else. (premise)

5 Sherlock Holmes (pg. 2) A dog was kept in the stables. (premise)
Someone had been in and fetched a horse. (premise) The dog did not bark. (premise) [Dog’s bark at strangers.] (implied premise) Obviously, the visitor was someone whom the dog knew well. (conclusion)

6 Logical structure Form – the way the parts of an arguments are related to each other. When looking at the validity of an argument, consider its form only. Reference – the way words and sentences that make up arguments relate to reality. When considering whether an argument describes reality, we have to consider the truth of its premises in addition to its validity.

7 Now, consider these two arguments. Which of the two is valid?
All apples are delicious. (premise) This is an apple. (premise) So, this is delicious. (conclusion) All human beings are mortal. (premise) Socrates is a human being. (premise) So, Socrates is mortal. (conclusion)

8 They have the same form! All S are P X is an S So, X is a P
That means that if one of them is valid, the other must be valid, too.

9 But it’s obviously not true that any particular apple is going to be delicious. It could be a bad apple.

10 The only thing required for an argument to be valid is for the premises to provide logical support for the conclusion: If the premises were true, the conclusion would have to be true. Validity only assesses the form of the argument, not its content. If we want to assess the content of the argument, we look at whether or not it is sound.

11 Examples: Valid but not sound Sound All horses are green.
All green things are plastic. So, all horses are plastic. All oaks are trees. All trees are plants. So, all oaks are plants.

12 Remember: Valid does not mean sound
Most of the time, we are interested in sound arguments, not just valid ones. If a valid argument has false premises, it may not provide logical support for the conclusion. In order for an argument to support its conclusion, it must be sound. So, we need a theory of truth in order to assess the truth of premises.

13 Four theories of truth:
Correspondence: Something is true if and only if it accurately represents a state of affairs. Coherence: Something is true if and only if it is consistent with a system of beliefs. Pragmatist: Something is true if and only if it is useful or leads to desirable results. Intuitionist: Truths are either intuitively true (though perhaps not obviously true) or they are derived from intuitively true sentences.

14 Some common examples of valid, deductive arguments with their corresponding names.
(Ch. 6)

15 Modus Ponens: If P, then Q. P. So, Q.
If our galaxy has millions of habitable planets, then it seems likely that life has evolved on some planet in our galaxy other than our own. Our galaxy has millions of habitable planets. So, it seems likely that life has evolved on some planet in our galaxy other than our own.

16 Modus Tollens: If P, then Q. Not Q. So, not P.
If the universe is infinitely old, there would be no hydrogen left in the universe. There is hydrogen in the universe. So, the universe is not infinitely old.

17 Hypothetical Syllogism: If P, then Q. If Q, then R. So, if P, then R.
If you make a budget, then you learn how to save money. If you learn how to save money, then you will have money to spend. Therefore, if you make a budget, then you will have money to spend.

18 Disjunctive Syllogism: P or Q. Not P. So, Q.
Either John is a liar or the project is due next week. John isn’t a liar. So, the project is due next week.

19 Dilemma: If P, then Q. If R, then S. P or R. So, Q or S.
Tonight, I can either go to the movies or the party. If I go to the movies, I’ll probably see an action movie. If I go to the party, I’ll probably see my ex-girlfriend Jane. So, tonight I’ll probably either see an action movie or my ex-girlfriend Jane.

20 Reductio ad absurdum To prove X, assume not-X
Reductio ad absurdum To prove X, assume not-X. Then argue from this premise to a false conclusion. Therefore, X must be true, since not-X can’t be true. Every human being has a mother. Assume that some human being has no mother. We no of no other method of human generation than biological reproduction. Biological reproduction requires a mother. So, the human being who has no mother could not exist.

21 Some examples of invalid arguments that may appear valid
Some examples of invalid arguments that may appear valid. They are known as fallacies. (Appendix 1)

22 Ad hominem Joe: I’m what you wouldcall a constitutionalist. I believe that we should restrict federal power from anything beyond what the founding fathers intended in the Constitution. Fred: Are you kidding? Michele Bachmann, Sarah Palin, and Glen Beck believe in that nonsense. And those people are crazy!

23 Appeal to lack of information as proof (ad ignorantiam)
Barack Obama has not produced a copy of his original birth certificate from the hospital he was born. If Obama was not born in the United states, he is not eligible for the presidency. So Barack Obama is not eligible for the presidency of the United States.

24 Appeal to the opinion of the majority (ad populum)
Everybody hates Ke$ha. So, Ke$ha sucks.

25 Begging the question (circular reasoning)
My idea is the best. If everyone would just follow my idea, then we would all be better off. And if everyone were better off, wouldn’t that be the best? So, my idea will lead to a situation that is clearly the best.

26 Definitions Appendix 2

27 A good definition should do the following things:
Include everything that clearly fits the term. Exclude everything that clearly does not fit the term. Draw a clear line or boundary between those things that clearly fit and those that clearly do not fit the term.

28 Example: ‘murder’ Clearly includes: Clearly excludes:
Intentional (premeditated) killing of a human being. Clearly excludes: Accidental death. Killing of enemy soldiers in a war. Self-defense. Controversial cases: Crimes in the heat of passion; negligence; recklessness; honor killing; revenge killing. Abortion. Capital punishment. Animals.


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