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CRITICAL THINKING – BASIC TERMS AND CONCEPTS:

Notes © Dwayne Mulder

Last Updated: 3/12/09

Go Back to Deductive – Inductive

ASSESSING THE QUALITY OF AN ARGUMENT:

Valid Argument: A good deductive argument. Not capable of having all true premises and a false conclusion.

Invalid Argument: A bad deductive argument. Capable of having true premises and a false conclusion.

Strong Argument: A good inductive argument. Premises make the conclusion more than 50% likely.

Weak Argument: A bad inductive argument. Premises do not make the conclusion more than 50% likely (i.e., 50% or less).

(You can SKIP the terms sound, unsound, cogent, and uncogent)

NOTICE that logical assessment of an argument is independent of factual assessment.

· An argument can be logically correct while being factually incorrect (all false).

o Deductive Example: “All college students are older than 80” and “George W. Bush is a college student” deductively imply “George W. Bush is older than 80” even though these statements are all false (factually incorrect).

o Inductive Example: “Only 1% of college students are white” and “George W. Bush is a college student” inductively imply “George W. Bush is probably not white” even though these statements are all false (factually incorrect).

· An argument can be logically incorrect while being factually correct (all true).

o Deductive Example: “All billionaires are rich” and “Bill Gates is rich” do NOT imply (either deductively or inductively) “Bill Gates is a billionaire” (being rich does not necessarily mean being a billionaire) even though these statements are all true (factually correct).

o Inductive Example: “Almost all college graduates are high school graduates (there are some exceptions)” and “Dwayne Mulder is a high school graduate” do NOT imply (either deductively or inductively) “Dwayne Mulder is a college graduate” even though these statements are all true (factually correct).

NOTICE ALSO that the difference between a valid and invalid argument is totally objective. Likewise, the difference between a strong and weak inductive argument is totally objective. It depends entirely on the facts in the world, not on subjective intention or opinion.

Proving (deductive) Invalidity, Three Methods:

1) Check – If a deductive argument actually has true premises + a false conclusion, then it is obviously invalid. Example: “All birds have wings (True). A mosquito has wings (True). Therefore, a mosquito is a bird (False).”

2) Conceive (“What if…”) – If you can imagine a case in which the argument would have true premises + a false conclusion, then it is invalid. Example: “If it rained, then the streets are wet. I see that the streets are wet. Therefore, it rained.” What if the streets got wet from sprinklers, or from a street cleaner, and it didn’t rain? In that case, this argument would have true premises (wet streets) + a false conclusion (no rain), proving it invalid.

3) Counterexample – If you can substitute some other content into the logical form of your argument to make an argument with obviously true premises + a false conclusion, then the arguments are invalid (the more obvious the counterexample is, the better). The logical form is like the “logical skeleton / structure / pattern” of a deductive argument. Example: “Some fruits are apples. Some fruits are green. Therefore, some fruits are green apples.” These statements are all true, but the argument is invalid because we can substitute: “Some animals are cats. Some animals are dogs. Therefore, some animals are cat-dogs.” This substitution argument (counterexample) clearly has true premises + a false conclusion, so it and all arguments with the same form are invalid.

[Move on to Language Issues: Unclear Language (chap 4)]