Deductive and Inductive Arguments - OLDHAM'S HOUSE

Deductive and Inductive

Arguments

Monday, January 9, 2012

Deduction and Induction

• Arguments can be broken down into two categories:

• Deductive = necessity

• Inductive = probability


Deductive

• In a deductive argument it is claimed that the premises provide necessary support for the conclusion

• 2 + 2 = 4 - necessary

• Indicator words: necessarily, certainly, absolutely, definitely

• Arguments based on laws, rules, or widely held principles


Inductive

• In an inductive argument it is claimed that the premises provide probable support for the conclusion

• It is likely the sun will rise again tomorrow

• Indicator words: probably, plausible, likely, reasonable to conclude

• Arguments based on experience and observation


All bats are mammals.All mammals are warm-blooded.So, all bats are warm-blooded.

Is the argument above deductive or inductive?


All bats are mammals.All mammals are warm-blooded.So, all bats are warm-blooded.

If the premises are true, the conclusion,

logically, must also be true.

Deductive.


Tess: Are there any good Italian restaurants in town? Don: Yeah, Luigi's is pretty good. I've had their Neapolitan rigatoni, their lasagne col pesto, and their mushroom ravioli. I don't think you can go wrong with any of their pasta dishes.

Based on what you've learned, is this argument deductive or inductive? How can you tell?


Don: Yeah, Luigi's is pretty good. I've had their Neapolitan rigatoni, their lasagne col pesto, and their mushroom ravioli. I don't think you can go wrong with any of their pasta dishes.

The argument is an inductive generalization, which is a common pattern of inductive reasoning. Also, the conclusion does not follow with strict necessity from the premises.

Inductive.


I wonder if I have enough cash to buy my psychology textbook as well as my biology and history textbooks. Let's see, I have $200. My biology textbook costs $65 and my history textbook costs $52. My psychology textbook costs $60. With taxes, that should come to about $190. Yep, I have enough.

Is this argument deductive or inductive? How can you tell?


I wonder if I have enough cash to buy my psychology textbook as well as my biology and history textbooks. Let's see, I have $200. My biology textbook costs $65 and my history textbook costs $52. My psychology textbook costs $60. With taxes, that should come to about $190. Yep, I have enough.

This argument is an argument based on mathematics, which is a common pattern of deductive reasoning. Plus, the conclusion follows necessarily from the premises.

Deductive.


Mother: Don't give Billy that brownie. It contains walnuts, and I think Billy is allergic to walnuts. Last week he ate some oatmeal cookies with walnuts and he broke out in a severe rash. Father: Billy isn't allergic to walnuts. Don't you remember he ate some walnut fudge ice cream at Melissa's birthday party last spring? He didn't have any allergic reaction then.

Is the father's argument deductive or inductive? How can you tell?


Mother: Don't give Billy that brownie. It contains walnuts, and I think Billy is allergic to walnuts. Last week he ate some oatmeal cookies with walnuts, and he broke out in a severe rash. Father: Billy isn't allergic to walnuts. Don't you remember he ate some walnut fudge ice cream at Melissa's birthday party last spring? He didn't have any allergic reaction then.

The father's argument is a causal argument, which is a common pattern of inductive reasoning. Also, the conclusion does not follow necessarily from the premises. (Billy might have developed an allergic reaction to walnuts since last spring.)

Inductive.


John is an agnostic. It follows that he doesn't believe in God.



John is an agnostic. It necessarily follows that he doesn't believe in God.

This argument is an argument by definition, which is a common pattern of deductive inference. Also, the phrase "it necessarily follows that" is a deduction indicator phrase. Also, the conclusion follows from the premises.

Deductive.


Larry: Do you think Representative Porkmeister will be re-elected? Norman: I doubt it. Porkmeister's district has become more conservative in recent years. Porkmeister is a liberal Democrat, and 63% of the registered voters in his district are now Republicans.



Larry: Do you think Representative Porkmeister will be re-elected? Norman: I doubt it. Porkmeister's district has become more conservative in recent years. Porkmeister is a liberal Democrat, and 63% of the registered voters in his district are now Republicans.

This argument is both a statistical argument and a predictive argument, which are two common patterns of inductive reasoning. Also, the conclusion does not follow necessarily from the premises.

Inductive.


If Buster walked to the game, then he didn't drive to the game. Buster didn't drive to the game. Therefore, Buster walked to the game.



If Buster walked to the game, then he didn't drive to the game. Buster didn't drive to the game. Therefore, Buster walked to the game.

Note, however, that the conclusion does not follow logically from the premises. (Maybe Buster rode his bike to the game, for example.)

This argument is a hypothetical syllogism, which is a common pattern of deductive reasoning.

Deductive.


Validity, Truth, Soundness, Cogency

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Overview• Deductive arguments

– Valid versus invalid– Soundness

• Inductive arguments– Strong versus weak– Cogency

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Traits of deductive arguments

• Validity• A deductive argument is an argument where it’s impossible

to have true premises and a false conclusion.• This is called a valid deductive argument.• An invalid deductive argument is one where it is possible

to have true premises and a false conclusion. The conclusion doesn’t follow from the premises, even though it claims to do so.

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Testing for validity

• Assume its premises are true (whether they are or not), and see if the conclusion follows forth from it falsely. If it does, then the argument is invalid. If not, then it passes the test and is valid.

Example:• “All television networks are media companies. (True)• NBC is a television network. (True)• Therefore, NBC is a media company” (True)

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• “All automakers are computer manufacturers. (False, but assumed true)

• United Airlines is an automaker. (False, but assumed true)

• Therefore, United Airlines is a computer manufacturer” (True, if the premises are true)

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• “All banks are financial institutions. (True)• Wells Fargo is a financial institution. (True)• Therefore, Wells Fargo is a bank. (Not

necessarily true)• INVALID

Why did it fail? Because some financial institutions are not banks. Stock brokerages, credit unions, etc.

• The conclusion is true under these conditions, but it can be made false under different conditions.

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Soundness

• A sound argument is a deductive argument that is valid and has all true premises.

• Soundness: (Valid) + (True premises)• These conditions will also lead to a true

conclusion as well.

• This is considered a truly good deductive argument.

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Soundness• Sound:

– “All television networks are media companies. (True)– NBC is a television network. (True)– Therefore, NBC is a media company” (True)

• Unsound– “All automakers are computer manufacturers. (False,

but assumed true)– United Airlines is an automaker. (False, but assumed

true)– Therefore, United Airlines is a computer

manufacturer” (True, if the premises are true)26


Strong and Weak• Inductive arguments are those where it’s

improbable for there to be true premises and a false conclusion.

• If that claim is true, then it’s said to be a strong inductive argument.

• If it’s not improbable to have true premises/false conclusion, it’s said to be a weak inductive argument. 27


Testing for Strength• Assume the premises are true, and see if the

conclusion is probably true, based on that.Example:

• “All dinosaur bones discovered to this day have been at least 50 million years old.

• Therefore, probably the next dinosaur bone to be found will be at least 50 million years old”.

• The premises are true and lead to a conclusion that is probably true, so it’s a strong argument. 28


Example:• All meteorites found to this day have

contained sugar. • Therefore, probably the next meteorite to be

found will contain sugar”.• The premises are false in this argument, but

if we assume they’re true, then the conclusion is probably true too, so this is also a strong argument.

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• Example:• “When a lighted match is slowly dunked into

water, the flame is snuffed out. • But gasoline is a liquid, just like water. • Therefore, when a lighted match is slowly

dunked into gasoline, the flame will be snuffed out”.

• In this argument, the premises are true, but the conclusion is false. Thus, it is not difficult to assume the premises to be true. We merely check to see if they support the conclusion. We find they do not, so the argument is weak.

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• Truth or falsity when testing an argument (validity or strength) are relevant, but only to an extent.

• First you must assume the premises are true, and check to see if the conclusion is well supported. If it is well supported, then the argument is valid (deductive) or strong (inductive).

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Cogency

• An inductive argument is said to be cogent when it is both strong and has all true premises.

• Cogency: (Strong) + (True premises)

• A cogent argument is considered to be the ideal “good” inductive argument.

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• Cogent• “All dinosaur bones discovered to this day have been at

least 50 million years old. • Therefore, probably the next dinosaur bone to be found

will be at least 50 million years old”.

• Not Cogent• All meteorites found to this day have contained sugar. • Therefore, probably the next meteorite to be found will

contain sugar”.

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Quick Review

• Deductive or Inductive• Valid or Invalid• Sound or Unsound• Strong or Weak• Cogent or Not

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Deductive and Inductive Arguments - OLDHAM'S HOUSE