BCS 111 Lecture 10

Research of reasoning and its application

• Philosophy

• Psychology

• Computer Science

Deductive vs. Inductive reasoning

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Deductive

• Premises → conclusion

• From broader scope to one (conclusion)

Inductive

• Inference from available information →
  possible outcomes

• From one condition to many (possibilities)

categorical syllogism

• Drawing conclusion from more than one premise

• Each premise is a description of a category.

example

• Some professors are tall. Some tall people are skinny.

  • Is it always true that “Some professors are skinny”?

  • (judging from the premises given above, not by your real-world knowledge)

propositional reasoning

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Proposition

the fact or assertion that you can infer from the sentence

• Ex: How many kids do I have? Do you have enough information to make the conclusion?

Propositional reasoning: Four-card task

If a card has a consonant on one side, it must have an odd number on the other side. Which card(s) would you flip in order to test if the rules are true?

(cont)

• What does flipping “1” tell us?

• What does flipping “8” tell us?

Analogical reasoning

• Inference based on an established relationship between two premises

• Dog: German Shepherd = Bird:

• Car: ground = __ : sky

Hypothesis testing

Why is hypothesis testing a type of inductive reasoning

• Small set of conditions/premises → many possible outcomes

Null hypothesis

Higher IQ test scores is NOT correlated with better reasoning skills

Alternative hypothesis

Higher IQ test scores IS correlated with better reasoning

Type I error

• Reject null hypothesis when it is true (i.e. falsely accept the alternative hypothesis)

  • An accidental finding of correlation between IQ and reasoning from a small (or biased) sample size when there is NO correlation

Type II error

• Fail to reject the null hypothesis when it is NOT true

  • An accidental finding of no-correlation between IQ reasoning when there IS actually a correlation

    • (examples on slides)

Confirmation bias

• Choose the evidence that supports our claims

• Tendency to ignore counter-evidence

• Tendency to remember supportive evidence better than counter-evidence

• Tendency to ignore alternative hypothesis

What else is involved in hypothesis testing?

• What’s the process involved in accepting or rejecting a hypothesis

  • Make a decision

  • Reasoning

  • Problem solving

Spatial reasoning - Raven’s Progressive Matrices

• Which one should you choose to complete the series?

Language can also impact spatial reasoning: evidence from a case study of Raven’s progressive matrices

A case study: “Chelsea” a child with delayed language development

Summary: Problem solving and reasoning 

(cont)