2.14: Glossary
- Page ID
- 36045
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)argument A conclusion plus one or more basic premises.
basic premises The basic premises for a conclusion are those premises that directly support the conclusion rather than indirectly support it. Indirect premises are premises in support of other premises, such as those in support of the basic premises.
conclusion indicators Words or phrases that signal the presence of conclusions but not premises. Examples: So, therefore, thus, it follows that.
conditional statement An if-then statement. An assertion that the then-clause holds on the condition that the if-clause holds.
counterexample to an argument a possible situation that makes the premises true and the conclusion false. A possible situation is a logically possible one. A situation in which half of my ancestors died childless is not a possible situation.
deductive argument An argument intended to meet the standard of being deductively valid. [Later chapters are devoted to deductive and inductive argumentation.]
deductively valid An argument is deductively valid if its conclusion follows with certainty from its basic premises. [This chapter introduced four other, equivalent definitions.]
description A statement or sequence of statements that characterize what is described. Descriptions state the facts, report on states of mind, make value judgments or explain the situation. A pure description does not argue.
discount indicator A term in an argument that indicates the presence of a claim that discounts or de-emphasizes a relevant factor. That claim is neither a premise nor a conclusion.
equivocating Changing the reference of a term from one occurrence to another within an argument.
explanation A statement or sequence of statements designed to show the cause, the motivation, or the sequence of events leading up to the event that is being explained. Pure explanations do not describe. Nor are they designed to convince you that something is so or that something should be done.
final conclusion In a chain of arguments, the last conclusion, the conclusion that isn’t used as a premise.
implicit premise A statement that does not appear explicitly in an argument but that is intended by the arguer to be a premise to help make the conclusion follow from the premises.
imply A statement P logically implies a statement Q if Q has to be true whenever P is. Informally, speakers might say “P means Q” instead of “P implies Q.”
indicator term A conclusion indicator term is a word or phrase in an argument that is usually followed by the conclusion; a premise indicator term is usually followed by a premise.
inductive argument An argument intended to meet the standard of being inductively strong.
inductively strong An argument is inductively strong if the conclusion would be very probably true if the premises were to be true. Inductive strength is a matter of degree.
invalid Not deductively valid. Even strong inductive arguments are deductively invalid.
multiple argumentation A passage containing more than one argument.
premise A claim that is used as a reason in an argument.
premise indicators Words or phrases that signal the presence of premises but not conclusions. Examples: Because, since, for the reason that.
standard form A single argument rewritten with its basic premises above the line and its conclusion below the line. The premises and conclusion should be expressed as complete sentences. Pronouns should be replaced with their antecedents (the nouns themselves) wherever possible. The order of the premises is not important. Indicator words and other fluff words are stripped away. When an argument is in standard form, it is supposed to stand alone with everything significant stated explicitly so that the reader can view the whole argument and understand what it is without needing additional information from the context.
sub-conclusion The conclusion of an argument that occurs among other arguments.