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1Critical Thinking: An Introduction to
Logic and Logical Fallacies
Lecture II
Fall 2008
2Truth Tables and Logical Operators
Truth Tables and Logical Operators
zFace it…some things are either true or false (specifying this formally is called “propositional calculus”)
zA “proposition” is a meaningful statement
zLimited number of operators: (not, and, or, if…then, if and only if)
zTruth tables chart truth value of proposition by laying out state-of-world possibilities
zUse of conditional logic (if certain conditions are met, then a proposition is true)
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4Forms of Conditional Reasoning,
Forms of Conditional Reasoning,
based on
based on “
“If P then Q
If P then Q”
”
zValid Forms
–Modus Ponens: P, ∴Q
–Modus Tollens: not Q, ∴not P
zInvalid Forms
–Affirming the Consequent: Q, ∴P
–Denying the Antecedent: not P, ∴not Q
5Logical Fallacies
zIt is important to identify common ways of thinking falsely so that you can sharpen your own
logical analyses
zIdentifying source of fallacious reasoning often helps clarify ideas you are trying to
communicate
zTA’s will call you on logical errors (in public)
6Fallacies of Distraction
zFallacy lies in that you are distracted from “true” premises and led to assume something
faulty
zIllegitimate use of a logical operator is key
zYou can identify these fallacies by showing that the main premise doesn’t accurately reflect
what’s really going on
7False Dilemma (misuse of “or”)
zA limited number of options (usually two) is given, while in reality there are more options. A false dilemma is
an illegitimate use of the "or" operator.
zPutting issues or opinions into "black or white" terms is a common instance of this fallacy
zExamples:
–You’re either for me or against me.
–America: Love it or leave it.
–If you ain’t a Gator, you’re Gator bait (this one’s true).
8Slippery Slope (misuse of ‘if-then’)
zIf the first step in a “possible” series of events occurs, the other possible steps in the series must inevitably
occur.
zExamples
–If you drink alcohol once, then you’ll want to drink it again, and pretty soon you’ll be an alcoholic and lose your job.
–If we pass laws against fully-automatic weapons, then it won't be long before we pass laws on all weapons, and then we
will begin to restrict other rights, and finally we will end up living in a communist state. Thus, we should not ban fully-
automatic weapons.
