3.6: Common Valid and Invalid Arguments
- Page ID
- 89967
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
Students will be able to:
- Identify common valid and invalid arguments.
It would be difficult to take the time to draw a Venn Diagram to check the validity of every argument you come across. People who argue for a living such as lawyers and judges already know certain argument structures that are always valid, then use them often. Also, they study arguments that are invalid so that they know when they are perhaps being tricked. In this section, you will see valid and invalid argument structures that are quite common. Remember, to be a valid argument, the conclusion must follow from the premises. The premises do not have to be true!
1) Modus Pones: All A is/are B.
A.
Therefore, B.
For example: All lawyers study logic.
Zala is a lawyer.
Therefore, Zala studies logic.
2) Modus Tollens: All A is/are B.
Not B.
Therefore, not A.
For example: All lawyers study logic.
Patrick has not studied logic.
Therefore, Patrick is not a lawyer.
3) Hypothetical Syllogism: All A is/are B.
All B is/are C.
Therefore, All A are C.
For example: All lawyers study logic.
All who study logic are paid well.
Therefore, All lawyers are paid well.
I am sure you will all make valid arguments, especially now that you know some of the basic forms. Be careful however, not everybody has taken a class like this and they will often argue, yet their arguments are invalid. Here are a couple of the most common invalid arguments.
1. Denying the antecedent: All A is/are B.
Not A.
Therefore, not B.
For example: All lawyers study logic.
Zala is not a lawyer.
Therefore, Zala does not study logic.
2. Affirming the consequent: All A is/are B.
B.
Therefore, A
For example: All lawyers study logic.
Patrick studies logic.
Therefore, Patrick is a lawyer