Crossfire: Fundamentals of Reasoning

This week our test will be about BOTH deductive and inductive argumentation, and focus on the first two types of induction: Inductive Generalizations and Statistical Arguments. This will give you a chance to review deduction (which we did last week) and see what you've been able to learn about induction

So, review everything you did for last week (see below, "Preparing for Test#3") plus

Be able to define:

• strong argument
• weak argument
• cogent argument
• uncogent argument
• reliable
• unreliable
• Inductive Generalization
• Statistical Argument
• sample population
• random
• double blind
• reference class

Be able to

• distinguish an inductive argument from a deductive argument
• list the inductive argument indicator words
• identify and evaluate inductive arguments from a given text
• tell whether an argument given to you is strong or weak; cogent or uncogent, reliable or unreliable
• show how an inductive argument can be strengthened by adding more evidence (premises).
• Identify and evaluate Inductive Generalizations.
• Identify and evaluate Statistical Arguments.

Inductive Generalizations

In understanding inductive generalizations, you should . . .
1) be able to identify the sample population and the population as a whole (i.e. the population that the generalization is about) in an inductive generalization.

2) understand that a good inductive argument should reach a conclusion that is appropriate to the evidence offered in the premises.

3) A more moderate conclusion makes the inference stronger.

4) An overstated conclusion makes the inference weaker.

5) In evaluating inductive generalizations you should ask the following questions:
--Are the premises true?
--Is the sample population large enough?
--Is the sample population representative of the population as a whole?

6) You should understand that a representative sample is similar to the population as a whole in all relevant respects.

In evaluating generalizations that are generated through opinion polls, you should . . .

1) understand that opinion polls operate under the same basic standards as other inductive generalizations insofar as the sample must be large enough and representative of the population as a whole;

2) The size of the sample should be large enough to reach an acceptable margin of error.

3) The sample is best generated randomly (where each member of the population has an equal chance of being selected) so as to avoid bias.

4) recognize the weaknesses in self-selecting samples;

5) understand

--how the tendency of people to respond to polls dishonestly, and the tendency of agencies with vested interests to ask slanted questions, can bias a poll sample;
--recognize the merits of a double-blind poll for generating objective results.

Statistical Arguments

In evaluating statistical arguments, students should . . .

1) understand the distinction between inductive strength and statistical reliability in statistical arguments;

2) understand how the specificity of the reference class in a statistical argument can impact the strength and reliability of the inference

Be able to:

1) define:

• deduction


• induction


• syllogism


• hypothetical syllogism


• chain argument


• antecedent


• consequent


• categorical syllogism


• valid (WARNING: remember, "valid" doesn't mean "true!")


• invalid


• sound


• unsound

2) distinguish deductive arguments from inductive arguments, and non-arguments like reports, opinions, illustrations, explanations, and conditional statements.

3) able to identify and evaluate (valid/invalid?) common patterns of deductive reasoning from a text:

a) be able to identify and evaluate hypothetical syllogisms

• chain argument


• affirming the antecedent (valid)


• denying the consequent (valid )


• affirming the consequent (invalid)


• denying the antecedent (invalid)

b) categorical syllogisms

4) Be able to tell whether an argument given to you is sound or unsound.

5) Know and be able to apply the common test for for deductive validity: "If you assumed the premises were all true, would the conclusion have to be true? If so, the argument is valid. If not, the argument is invalid."

5) Know that it is impossible to have true premises and a false conclusion if you have a valid deductive argument.

6) Know and be able to apply:

Indicator Word Test
Strict Necessity Test
Common Pattern Test

Be sure that you are able to..

1) List, identify and give examples of the different types of sentences
2) List, identify and give examples of the different types of statements
3) Pick out statements from non-statements
4) Define what an argument is
5) Define what a premise is; what a conclusion is
6) Be able to identify what statements are premises and what statement is the conclusion in a variety of arguments I will give you
7) Be able to list which words are Premise Identifiers
8) Be able to list which words are Conclusion Identifiers
9) List and be able to identify the five types of texts which are not arguments: reports, unsupported assertions (opinions), conditional statements, illustrations, explanations.

The test will be 20 questions: some TF, some multiple choice, some listing, and one short answer.

Be sure you are able to:

1) Define critical thinking, and discuss why it is important, especially for Christians.

2) compare and contrast right and left brain thinking

3) List and explain the barriers to critical thinking. Be able to identify examples of each of those barriers.

4) List and explain the standards for critical thinking

6) Give an example of a biblical character who, in your opinion, demonstrates:
a. left brain thinking
b. one of the barriers to critical thinking
c. one of the standards for critical thinking
Explain your answer.