13: Inductive Reasoning
- Page ID
- 22033
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)If it looks like a duck, walks like a duck, and quacks like a duck, then it's a duck. This is usually good reasoning. It’s probably a duck. Just don't assume that it must be a duck for those reasons. The line of reasoning is not sure-fire. It is strong inductive reasoning, but it is not strong enough to be deductively valid. Deductive arguments are arguments intended to be judged by the deductive standard of, "Do the premises force the conclusion to be true?" Inductive arguments are arguments intended to be judged by the inductive standard of, "Do the premises make the conclusion probable?" So, the strengths of inductive arguments range from very weak to very strong. This chapter focuses specifically on the nature of the inductive process because inductive arguments play such a central role in our lives. We will begin with a very important and very common kind of inductive argument, generalizing from a sample. Then later we will consider the wide variety of inductive arguments. As we shall see, inductive reasoning is about seeing patterns and making claims that extend beyond the data at hand.
- 13.1: Generalizing from a Sample
- This page discusses how scientists gather data to recognize patterns and make broader generalizations about populations from samples. It emphasizes the importance of representative samples to prevent biased conclusions and explains that inductive generalizations can be statistical or non-statistical.
- 13.2: Obstacles to Collecting Reliable Data
- This page highlights the challenges in obtaining reliable statistics from representative samples, including self-selection bias, misrepresentation of behaviors, and difficulties in obtaining diverse data. Busy individuals may decline to participate, and methodological errors can compromise reliability, ultimately undermining the significance of statistical conclusions.
- 13.3: Varieties of Inductive Arguments
- This page explores the complexities of inductive logic relative to deductive logic, indicating that inductive logic includes various independent areas dedicated to different inductive argument types. It notes that the study of inductive arguments is less developed and introduces several inductive argument types, emphasizing that some arguments may incorporate multiple types.
- 13.4: How New Information Affects an Argument’s Strength
- This page explores the assessment of inductive arguments through the Principle of Total Information, highlighting how new relevant information affects their strength. It uses examples to show how modifications can change argument strength, especially concerning future predictions based on past data.
- 13.5: Statistics and Probability
- This page emphasizes the significance of critical thinking in interpreting statistics and probabilities, noting that misleading presentations can arise, as shown with examples like fat content in drinks. It defines probability, explaining the range from 0 to 1 and its basis in equally likely outcomes. The gambler's fallacy is analyzed through the perspectives of different individuals regarding a biased coin flip.
- 13.6: Review of Major Points
- This page explores the complexities and risks of inductive arguments compared to deductive ones, noting their variability in quality and the potential for false conclusions. It highlights the significance of representative samples for generalization and critiques analogical reasoning.
- 13.7: Glossary
- This page covers key concepts in sampling and statistics, including biased samples and confidence levels. It describes various sample types, such as random, representative, and stratified, and addresses errors in reasoning like hasty generalization. The importance of the principle of total information in evaluating arguments is emphasized, alongside definitions of essential terms like population, parameter, sample, and variable.
- 13.8: Exercises
- This page covers statistical survey techniques, emphasizing the importance of generalization, random and stratified sampling, and biases. It analyzes case studies, such as the impact of gender distribution on sampling and logical reasoning fallacies. The text delves into inductive reasoning, particularly its application in experimental scenarios and real-life implications, such as hiring decisions based on past behavior.