Comprehensive Guide to Erroneous Logic and Fallacies

Ambiguous Reasoning and Circular Logic

• Ambiguous Reasoning (Homonym Fallacy)

  • This error involves the use of the exact same term in exactly two different senses within an argument.

  • It relies on ambiguous reasoning and is considered a relatively rare occurrence in logical discourse.

• Circular Reasoning Type 1 (Erroneous)

  • This occurs when an argument uses the premise to justify the conclusion itself.

  • Verbatim Example: "If you're a firefighter you wear a red hat. John wears a red hat. Therefore, he's a firefighter."

  • In this erroneous form, the logic loops back on itself without providing external validation for the move from premise to conclusion.

• Circular Reasoning Type 2 (Not Erroneous)

  • This is defined as a tautology.

  • It is not logically "wrong," but it is considered uninteresting because it stakes out no new logical ground.

Formal Logic Errors: Reversal, Negation, and Transitivity

• Reverse Without Negating

  • This error occurs when one assumes that because $B$ does not exist without $A$ first, then $A$ must lead to $B$.

  • Logical Relationships:

  • Every single time you have $B$, you have $A$.

  • $A$ is sufficient to bring about $B$.

  • $B$ is necessary to bring about $A$.

  • The Error: This falsely implies that the condition under which a conclusion follows is the only way in which that conclusion follows.

• Negate Without Reversing

  • This is an invalid logical move. One cannot negate a conditional statement without also reversing it.

• Reverse Transitive

  • An error in transitive logic where one attempts to go from $C \rightarrow A$.

  • Correct Procedure: One can only "reverse and negate" (the contrapositive) to maintain logical validity.

Errors of Scale, Quantity, and Generalization

• Some to All

  • It is logically fallacious to assume that "some" means "all."

• Some to Many

  • This cannot be assumed because of the specific numerical definitions assigned to these terms:

  • "Some" can mean as few as $1$.

  • "Many" is defined as meaning $3$ or more.

• Anything to "Most"

  • This involves making a conclusion using the word "most" based on words like "many."

  • Numerical Definition: "Most" specifically means $51\%$ or more of something.

• Mixing Claims Involving "Most"

  • The word "most" should never be used in a transitive argument.

  • This is because "most" involves specific numerical values ($51\%$ or more) that do not reliably transfer through transitive steps.

Fallacies of Authority, Composition, and Personal Attack

• Appealing to a Person as an Authority Outside the Scope of Their Expertise

  • One cannot rely on a professional's opinion if the subject is outside their specific field of knowledge.

  • Example: Asking a mechanic about car colors. Technically, this is outside their scope of expertise, which is mechanical function rather than aesthetics or design.

• Composition Fallacy (Part to Whole)

  • This error claims that if a part of a whole possesses a specific trait, then the entire whole must also possess that trait.

  • Verbatim Example: If red bricks are rectangular, that does not mean the wall (the whole) must also be rectangular; the wall could be square.

• Ad Hominem

  • This involves attacking the person making the argument instead of addressing the actual substance of the argument itself.

Fallacies of Evidence, Probability, and Statistics

• False Dilemma (Assuming Only Two Options)

  • This error occurs when an argument assumes there are only two options for something when, in fact, there are at least three:

  1. More

  2. Less

  3. The same

  • Verbatim Example: "Sarah doesn't have more traffic tickets than Charles. Therefore, she has fewer traffic tickets than Charles." (This ignores the possibility that they have the same number of tickets).

• Absence of Evidence vs. Evidence of Absence

  • This is the claim that if there is no evidence (or only weak evidence), then the conclusion must be false.

  • Key Maxim: "Absence of evidence is not evidence of absence."

• "Most Likely" vs. "Likely"

  • This error occurs when claiming that if something is the "most likely" outcome among options, it is then "likely" (probable) to happen in an absolute sense.

  • Verbatim Example: "The Lakers are the team most likely to win the NBA next year. So the Lakers will probably be next year's NBA champions."

• Drawing Specific Conclusions from an Average

  • This involves applying a general mean to a specific, singular instance incorrectly.

  • Verbatim Example: "On average, Claire studies $5$ hours a day. She did study yesterday, so today she is going to study for $10$ hours."

• Confusing a Fact for the Reporting of a Fact

  • This error assumes that because something is being reported more frequently in the media or elsewhere, it is actually occurring more often in reality. Increased reporting frequency is not synonymous with increased actual frequency.