Informal Fallacies and Logical Reasoning Principles

Definition: The introduction of an irrelevant point into an argument to distract from the real question or topic at hand.
Intent and Illusion: A speaker may believe, or attempt to make the audience believe, that the introduced point proves their side of the argument, even though it does not.
Truth Value of Irrelevant Points: When someone introduces a red herring, the statement made may actually be true, but it remains fallacious because it is completely irrelevant to the main point.
Quality of Argument: A red herring can be a logically valid or strong argument in isolation; its failure stems entirely from the fact that it fails to prove the specific position being debated.
Contextual Example: Demonstrations such as the dialogue between Jenny and Bert highlight how an irrelevant point can derail the focus of a discussion.

Etymology: Derived from the Latin phrase meaning "to the man."
Definition: An argument that attacks a person's character or motives directly rather than disproving the logical validity of their actual argument.
Distinction Regarding Truthfulness: It is not an ad hominem fallacy to question whether someone is telling the truth. Questioning credibility based on past evidence discredits their capacity for truthfulness rather than attacking their opinion, which can be a valid point if the individual is a known liar or has reason to be untrustworthy.
Comparative Examples:
- Ad Hominem Attack: "Your cousin's a liar, so I'm not believing anything he says." (This attacks the person's character to dismiss their argument or opinion).
- Valid Credibility Assessment (Not Ad Hominem): "I don't know if I can trust what your cousin says; he's been known to lie before." (This questions the person's ability to tell the truth based on established past evidence).

Etymology: Derived from the Latin phrase meaning "you, too."
Definition: Dismissing someone's viewpoint on an issue simply because that person acts in a manner inconsistent with their own argument.
Mechanism: The accused person responds to an allegation by turning the exact same allegation back on the accuser.
Psychological Underpinnings: Individuals committing this fallacy often act out of a guilty conscience, attempting to relieve their own guilt by shifting blame onto another person.
Relation to Logical Fallacies: Frequently manifests in the rationale that "two wrongs make a right."

General Appeal to Authority: Claiming that a statement is true simply because an authoritative figure asserted that it was true.
- Proper Usage: Appealing to authority is legitimate when referencing a legitimate expert in the relevant field (e.g., a parent instructing a child not to drive a vehicle because a qualified mechanic advised against it).
Definition of Faulty Appeal: Occurs when an appeal is made to an individual who lacks specialized knowledge or expertise in the specific area under discussion.
Intimidation Factor: Used strategically to overawe an opponent and make them reluctant or intimidated to challenge the authority's stance.
Controversial Topics: When a topic is actively debated or controversial among respected authorities within a field, appealing solely to the isolated opinion of a single authority constitutes a faulty appeal to authority.
Logical Status: A faulty appeal to authority inherently results in a bad argument.

Definition: An argument that attacks the origin or source of a claim rather than addressing the claim itself.
Mechanism: Condemns and rejects an argument strictly based on how or why the person came to hold that belief (their underlying reason or background).

Etymology: Known by the Latin phrase argumentum ad populum.
Definition: Asserting that a claim or viewpoint must be correct simply because a large number of people agree with it.

Definition: A broad assertion made about an entire group of people or a category of items.
Composition: Formed by evaluating samples drawn from a specific "class" (a group of people or objects sharing common characteristics).
- Class: All jelly beans.
- Sample: Green jelly beans.
- Generalization: $31.7\%$ of all jelly beans are green.
Epistemological Nature: Generalizations possess no absolute certainty. They are categorized as either strong or weak, rather than strictly true or false. A strong generalization is one that carries a higher probability of being accurate.
Sampling vs. Fact: Generalizations rely entirely on representative samples of a class. A study that evaluates every single individual member of a class yields a factual claim, not a generalization.
Adjustment Rule: A generalization must be modified or entirely abandoned upon the discovery of a single counterexample.
- Example: The statement "All crows are black" is disproved by observing a single white crow. The generalization must then be revised to "Almost all crows are black."
Strength Conditions: A generalization gains strength as its underlying sample size increases and becomes more representative of the overall class.

Definition: Reaching a general conclusion about an entire class based on a sample that is either too small or unrepresentative.
Primary Modes of Failure:
- Inadequate Sample Size: Tossing a coin produces heads $50\%$ of the time and tails $50\%$ of the time on average. However, tossing a coin only four times will not reliably yield two heads and two tails; the expected ratio only emerges over many repeated trials.
- Unrepresentative Sample: Selecting a sample that fails to accurately reflect the diversity and characteristics of the broader class.

Definition: Misrepresenting, exaggerating, or altering an opponent's actual argument to make it appear significantly weaker than it is, thereby making it easier to attack and disprove.
Etymology: Termed a "straw man" because a figure made of straw is fragile and effortless to knock down.

Logical Structure: Assertion $P$ is argued to be true because assertion $Q$ is true, while assertion $Q$ is simultaneously argued to be true because assertion $P$ is true.
Mechanism: Begs the question by assuming as a premise the very conclusion that the argument is attempting to prove.

Definition: Shifting or changing the definition of a key word or term in the middle of an argument.
Practical Application: Demonstrates the necessity of clearly defining terms and asking clarifying questions such as "What do you mean by $x$ ?" during formal or informal debate.