Lecture16_IC1_NEW

Non-Deductive Reasoning

• Focus on inductive and causal arguments

• Three important kinds of arguments:

  • Inductive Generalizations: Lead to general knowledge.

  • Causal Arguments: Discuss causes and effects.

  • Applications: Apply general knowledge to specific cases.

Inductive Generalizations

• Involves concluding about a whole category based on information about part of it.

• Example: Expecting a crow to be black based on previous observations.

• Everyday examples:

  • Expecting a bus to be late if it has often been so.

  • Delaying tomato planting until late May due to past cold nights.

• Public Opinion Polls:

  • Polling firms use samples to estimate the opinions of a population, e.g. voting results in the 2018 US elections.

Causal Arguments

• Draw conclusions about causes based on premises about items and their connections.

• Example: Lung cancer is more prevalent in smokers, indicating smoking contributes to lung cancer.

• Details are essential for a strong causal argument:

  • Examining other explanations, e.g., mechanical causes in aircraft crashes.

Applications

• Use of general premises about populations to draw conclusions about specific cases.

• Example:

  • Knowing few men live past 100 leads to not expecting to live that long.

  • Low lung cancer rates among nonsmokers reduce worry for non-smokers.

Structure of Inductive Generalizations

• General format:

  • "X percent of items of kind A have property P.

  • Conclusion: Approximately X percent of all A have property P."

• Example: Polling in Ottawa regarding urban boundaries.

Terminology

• Sample: Items observed.

• Population: The entire collection the conclusion is about.

• Valid inductive generalizations occur when the sample equals the population.

  • Rare; usually samples are part of the population.

Evaluating Inductive Generalizations

• Essential criteria: Quality of data, representativeness of the sample, sample size.

  • Quality of Data:

    • Consider how data was collected, methods, and reliability.

    • Assess potential bias and conflicts of interest.

  • Representativeness of the Sample:

    • Ensure it reflects the population.

    • Random sampling ideal but difficult.

    • Bias examples:

      • Street polls are led by passerby responses, missing many demographics.

      • Phone and internet surveys exclude those without phones or internet access.

  • Sample Size:

    • Small samples less likely to represent the population accurately.

    • Samples around 2000 are considered adequate in Canada.

Margin of Error and Confidence

• Polls come with a margin of error and confidence measure.

• Understanding these reduces misinterpretation of results.

Common Errors in Reasoning

• Predictable World Bias: The incorrect belief that patterns exist without evidence.

• Confirmation Bias: Noticing data that supports preconceptions while ignoring contrary data.

• Availability Bias: Using easily obtained data without ensuring its comprehensive validity.

Common Mistakes in Inductive Reasoning

• Hasty Generalization: Jumping to conclusions based on small data.

• Apriorism: Drawing conclusions without examining data.

• Revisability: An inductive conclusion may change with more data.

Example Evaluations of Inductive Generalizations

• COVID-19 in the Philippines vs. Hong Kong:

  • Weak argument due to sample size and varying testing rates.

• North vs. South Korea COVID-19 Comparisons:

  • Reliable data from North Korea is lacking; conclusion not justified.

• U.S. Senators' Stock Sales:

  • Insufficient sample size to generalize about all politicians.

• Italy vs. Germany COVID-19 Mortality Rates:

  • Unequal testing regimes undermine the comparison accuracy.

Conclusion

• Importance of careful evaluation of problems in inductive reasoning and data quality.

• Reminder to use critical thinking when interpreting polls and data.