Logical Fallacies: Hasty Generalization, Non Sequitur & Slippery Slope

Instructor re-recorded a shorter version (original ran 52 min).
Begins at slide 11; earlier slides (to be posted separately) illustrated experiments showing that:
- Word choice can alter perception and memory.
- People are less rational than they assume.
Immediate goals in the semester:
1. Students are compiling annotated bibliographies largely from peer-reviewed sources (fewer blatant fallacies here, but subtle ones still appear).
2. Students will soon write their own arguments; common student errors include the very fallacies covered today.

A flaw in reasoning that renders a conclusion invalid.
Schematic: \text{Faulty Logic} \Rightarrow \text{Invalid Conclusion}
Frequently arises from:
- Ego – obsession with “winning” or certainty of being right.
- Bias – selective exposure to confirming sources.
- Ignorance – unawareness of misinterpretation/misrepresentation.
- Human need for closure – desire to force a tidy answer on a messy problem.

(Chosen because they recur in student papers and in sources students will soon encounter.)

Drawing a broad conclusion from insufficient or unrepresentative evidence.
Formal outline:
\text{Sample Size } n \ll N \;\; \Longrightarrow \;\; \text{Claim about Entire Population } N
Often based on anecdotal evidence, stereotypes, or single studies with tiny n.

Everyday: “My neighbors own guns and misuse them while drunk; no one has a legitimate reason to own guns.”
Weather: “It’s June and I need a coat → Global warming is a sham.”
Smoking: “My uncle smoked four packs a day and lived to 92 → cigarettes aren’t that bad.”
Literature: Alice in Wonderland passage – Alice had been to the seaside once; therefore any salt water she falls into must have a nearby railway station. (Two separate hasty generalizations.)
Politics 2011 (Herman Cain quote): Used isolated examples of “militant Muslims” & a misreported Oklahoma case to justify excluding all Muslims from a presidential administration.
2016 campaign (Hillary Clinton “basket of deplorables”): Implicitly assigned negative traits to roughly ½ of Trump supporters.

Relying on only sources that already agree with one’s thesis leads to oversimplified, unsupported generalizations when confronting counter-arguments.
Instructor anecdote: student pro-gun paper misunderstood opposing claims because research pool was too narrow.

Latin for “it does not follow.”
Argument pattern:
\text{Claim A} \; \land \; \text{Evidence for A} \; \Rightarrow \; \boxed{C}
where C is logically unrelated to A.

Burger shop: “Buddy Burger is rated #1 in town; therefore owner Phil should be mayor.”
Florida Bar Exam practice item:
- Premise: Aunt wants warm climate + low property taxes; Texas dismissed for high taxes.
- Fallacy: Concludes Florida is therefore ideal, without evaluating other warm, low-tax states.
2011 campaign trail (Mitt Romney): Asked about policy flip-flops → answered by citing 42-year marriage as proof of steadiness; marital longevity ≠ political consistency.

Seen when students pile up research on one sub-topic and then jump to an unrelated thesis statement (“Given these health statistics, the government should ban video games”).

Argument that permitting A will inevitably trigger catastrophic Z.
Form:
A \; \Rightarrow \; B \; \Rightarrow \; C \; \Rightarrow \dots \Rightarrow \; Z \; (\text{dreaded})
\therefore \; \text{Block } A
Leverages fear; steps between A and Z are unsubstantiated or implausible.

Are intermediate steps explained or evidenced?
Is Z truly likely or even possible?
Does the arguer provide any causal mechanism, or simply assert inevitability?

Interracial Marriage (Loving v. Virginia, 1967): Court briefs warned that allowing black/white marriages would open the door to polygamy, incest, and child marriage.
Roe v. Wade (1973): Claims that legal abortion → legalized infanticide “any year now.” (Persistent myth, occasionally traced to satirical Onion article.)
Gay Marriage debates (2003–2015): “If gays can marry, legal incest and bigamy will follow.”
Gun-control discourse: “If we adopt universal background checks, the government will confiscate all guns by the end of the presidential term.”
Cartoons:
- Bully on lawn → on porch → eating your baby in 48 h.
- Comic critique: “Dude, slope isn’t that slippery.”

If small regulatory changes demonstrably raise accident risk (e.g., removing bridge-safety standards in Louisiana), the catastrophic outcome can be probable and evidence-based → not a fallacy.
Test: Evaluate likelihood and causal chain; absence of reasonable mechanism = fallacy.

Diversify sources: consult studies that challenge your stance to avoid narrow evidence pools.
Check sample sizes & representativeness before citing studies.
Trace premises → conclusion line-by-line; if a step jumps topics, inspect for non sequitur.
Map causal chains when predicting consequences; label speculative leaps.
Separate emotion from inference; fear alone is not evidence.

Fallacies fuel prejudice (e.g., religious or racial profiling) and polarize electorates.
They can undermine public health (smoking anecdotes), climate policy (“cold June day” ≠ disproving global warming), or democratic discourse (campaign rhetoric).
Recognizing them supports critical citizenship and scholarly integrity.

Invalid generalization: n{sample} \ll N{population} \; \Rightarrow \; \text{Unjustified Claim}
Non sequitur schema: [Premise\;A \land Evidence\;A] \; \nRightarrow \; C(\not\subseteq A)
Slippery Slope chain: A \to B \to C \to \dots \to Z \; (\text{asserted inevitable})

Additional fallacies will be covered in future sessions.
PowerPoint will be posted for students wanting full experimental background from early slides.