4: Logic
- Page ID
- 306932
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Inquiry proceeds by formulating, clarifying and evaluating arguments. An argument is a reason for thinking that something is true. The basic anatomy of arguments is straightforward, though learning to identify and clarify arguments in the wild is a skill that takes a good deal of practice. An argument consists of a set of premises which work together to provide a reason for accepting a conclusion as true. In this chapter we will get introduced to the basic standards and procedures for formulating, clarifying and evaluating arguments.
We’ve introduced the idea of an argument as a reason for believing something and most this chapter will focus on this primary function of arguments. But arguments are multifunction tools in inquiry and we will also want to discuss their various other uses along the way. Here are a few: Arguments can be useful for
- Providing a reason for thinking their conclusions are true
- Teasing out false premises
- Clarifying our own conceptual understanding
- Recognizing gaps on our own reasoning
- Understanding the views of others
We’ll consider how to clarify and evaluate arguments before explaining these points.
- 4.1: Arguments
- This page discusses the evaluation of claims through their supporting arguments, which consist of premises leading to conclusions. The strength of an argument is determined by the truthfulness of its premises and their logical support. Evaluating arguments can be complex due to interdependent reasoning chains where the strength depends on interconnected premises.
- 4.2: Evidence
- This page explores the intricate relationship between evidence and belief, positing that some foundational beliefs are self-justified. It argues that scientific knowledge, while rooted in sense experience, is shaped by prior biases and contextual understanding. Accurate perception requires an appropriate framework beyond mere observation.
- 4.3: Support
- This page discusses the evaluation of premises and their support for conclusions in arguments, emphasizing the distinction between truth assessment and support quality. It warns against confirmation bias and provides two examples: one with strong but not guaranteed support concerning cooking skills, and another offering guaranteed support about Boston's location. It also defines deductive validity and inductive strength as essential criteria for evaluating reasoning.
- 4.4: Deductive Validity
- This page discusses deductive validity as the highest standard of argument support, where true premises guarantee a true conclusion. It outlines that an argument is valid if false conclusions can't arise from true premises. Validity emphasizes logical possibility over actual truth. A sound argument contains true premises and a valid conclusion. While intuitive in some cases, many deductive arguments demand a deeper understanding of logic.
- 4.5: Logical Form
- This page discusses deductive validity, highlighting that it is based on logical form rather than the truth of premises or conclusions. It uses symbolic representation to illustrate valid arguments, showing that valid conclusions can arise from false premises. The "if-then" format is used to exemplify this. Additionally, it explains that identifying the validity of an argument can reveal false premises, thereby enhancing logical reasoning skills.
- 4.6: Validity’s Multiple Functions
- This page explores the role of arguments in inquiry, focusing on identifying false premises, hidden assumptions, and biases. It discusses the reductio ad absurdum technique using moral relativism as an example and emphasizes the need for clarity in argumentation. The text advocates for charitable interpretation of opposing views to enhance critical thinking and underlines the importance of deductive validity in addressing complex issues and uncovering truth.
- 4.7: Inductive Strength
- This page explores inductive reasoning, contrasting it with deductive reasoning. It defines inductively strong arguments as those where true premises lead to probable conclusions, unlike deductive arguments, which provide guaranteed conclusions. The author discusses how factors like sample size and representativeness influence inductive strength and introduces various forms of inductive reasoning, such as analogy, to illustrate its broader applicability.
- 4.8: Inference to the Best Explanation
- This page discusses inference to the best explanation as a method to assess inductive strength, exemplified by detective work like Sherlock Holmes deducing Moriarty's guilt. It highlights Charles Sanders Peirce's Surprise Principle, which focuses on explanations that reduce the element of surprise.