8: Reasoning
- Page ID
- 54105
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Reasoning in cognitive psychology refers to the mental processes used to draw conclusions, make judgments, or infer information from available facts, evidence, or premises. It involves the ability to think logically and systematically to arrive at decisions. There are two primary types of reasoning studied in cognitive psychology: (1) Deductive Reasoning: This is a process where conclusions are drawn from general principles or premises. If the premises are true and the reasoning is valid, the conclusion must also be true. For example, in syllogisms, a form of deductive reasoning, if "All humans are mortal" and "Socrates is human," the conclusion "Socrates is mortal" logically follows. and (2) Inductive Reasoning: This involves making generalizations based on specific observations or evidence. It is probabilistic, meaning the conclusions are likely but not guaranteed to be true. For instance, after observing that the sun has risen every day, one might reason inductively that it will rise again tomorrow.
- 8.1: Formal Reasoning
- Reasoning and decision-making are essential cognitive abilities used daily to form opinions and make choices. This text uses an example from Knut's life to illustrate these concepts as he prepares for a trip to Spain. The reasoning involves taking premises, such as Spain being warm in summer, and drawing conclusions beyond these premises. The text further distinguishes between inductive and deductive reasoning and hints at the link between brain lesions and cognitive impairments in reasoning.
- 8.2: Deductive Reasoning + Inductive Reasoning
- This page explores deductive and inductive reasoning. Deductive reasoning involves deriving specific conclusions from general premises, exemplified by syllogisms. Categorical and conditional syllogisms are discussed, along with normative and descriptive approaches to syllogisms. Inductive reasoning involves forming generalizations from specific instances; its forms, strong and weak induction, determine conclusion reliability.
- 8.3: Propositional Reasoning
- The page highlights a podcast by Cindy Sifonis, a psychology professor at Oakland University, focusing on propositional reasoning and its significance in cognitive psychology. The podcast runs for 4 minutes and 44 seconds, offering insights into this area of study.
- 8.4: Venn Diagrams
- Venn diagrams, introduced by John Venn in 1880, represent sets with overlapping circles inside a box that signifies the universal set. These diagrams highlight the common and distinct elements among the sets. For instance, \(A \cup B\) encompasses elements in either set, \(A \cap B\) includes shared elements, and \(A^c \cap B\) covers elements in \(B\) absent in \(A\). They also explain complex interactions like \((H \cap F)^c \cap W\), depicting elements outside \(H \cap F\) but within \(W\).
- 8.5: Syllogisms
- Syllogisms exemplify deductive reasoning, a method of deriving specific conclusions from known premises, widely employed by ancient rhetoricians like Aristotle. A syllogism consists of major and minor premises supporting a conclusion, exemplified by "All humans are mortal; Socrates is a human; Socrates is mortal." Valid conclusions depend on true premises. Faulty syllogisms arise from incorrect premises or unrelated truths, leading to false conclusions.