Logical Fallacies

* independent
[2025-10-11 Sat]

1. What are logical fallacies?

A logical fallacy is an error in an argument that invalidates or weakens an argument. They sound persuasive, but fail logically

2. Formal fallacies–Errors in the structure of an argument(violating logic rules)

  • These occur when the argument's form is invalid, even if the premise is true.

2.1. Affirming the consequent

2.1.1. Structure

P → Q. Q. ∴ P

If P then Q. Q is true. Therefore P is true.

  1. Example:

    If it rains, the ground is wet. The ground is wet, so it must have rained.

2.1.2. Why It's Wrong:

Other causes might make the ground wet.

2.2. Denying the Antecedent

2.2.1. Structure

P → Q. ¬ P. ∴ ¬ Q

If P then Q. Not P. Therefore not Q

  1. Example

    If I’m human, I’m mortal. I’m not human, so I’m not mortal.

2.2.2. Why It's Wrong

False–Some non-humans are mortal

2.3. Undistributed Middle

2.3.1. Structure

\begin{align*} &\quad \forall x (A(x) \rightarrow B(x)) \\ &\quad B(C) \\ \therefore &\quad A(C) \end{align*}
  1. Example

    All cats are mammals. Dogs are mammals. Therefore dogs are cats.

2.3.2. Why It's Wrong

Middle term not linked properly.

2.4. Invalid syllogism

3. Informal fallacies–Errors in the content or assumptions of an argument, not necessarily the structure

  • These are much more common in real life.

3.1. Relevance Fallacies

Using irrelevant info to distract or persuade.

3.1.1. Ad Hominem

Attacking the person instead of his argument

  1. Example

    you cant trust his opinion on science–Hes not even a doctor

3.1.2. Tu Qoque("You Too")

Claiming Hypocrisy invalidates an argument

  1. Example

    You smoke, so you cant tell me smoking is bad.

3.1.3. Genetic Fallacy

Judging an idea based on its origin

  1. Example

    That idea came from a communist, so it must be false

3.1.4. Appeal to Authority

Using authority where expertise isnt relevant or missaplied

  1. Example

    A famous actor says this diet works, so it must.

3.1.5. Appeal to Emotion

Using fear, pity, or flattery instead of logic.

  1. Example

    If you don’t believe this, you’re heartless.

3.1.6. Appeal to Popularity(Ad Populum)

Assuming something is true because many believe it.

  1. Example

    Everyone knows this product

3.1.7. Appeal to Tradition

Assuming something is right because it is old or tradition

  1. Example

    We’ve always done it this way.

3.1.8. Appeal to Novelty

Assuming something is better because it’s new.

  1. Example

    This app must be great — it’s brand new.

3.1.9. Red Herring

Diverting attention from the issue

  1. Example

    Sure, pollution is bad, but what about crime?

3.1.10. Straw Man

Misrepresenting an opponent’s view to make it easier to attack.

  1. Example

    You want to regulate guns? So you want to ban all self-defense?

3.2. Ambiguity Fallacies

Relying on unclear language or shifting menaings

3.2.1. Equivocation

Using a word with two meanings in the same argument.

  1. Example

    “A feather is light. What is light cannot be dark. So a feather cannot be dark.”

3.2.2. Amphiboly

Grammatical ambiguity

  1. Example

    “The police shot the rioters with guns.” (Who had the guns?)

3.2.3. Accent/Emphasis

Changing meaning by stressing different words.

  1. Example

    He didn’t steal the money” vs “He didn’t steal the money.”

3.3. Presumption Fallacies

3.3.1. Begging the Question(Circular Reasoning)

Assuming what you’re trying to prove.

  1. Example

    The Bible is true because it’s the word of God.

3.3.2. Complex Question (Loaded Question)

A question with a hidden assumption

  1. Example

    Have you stopped cheating on tests?

3.3.3. False Cause(Post Hoc)

Assuming causation from correlation.

  1. Example

    I wore lucky socks and we won — they caused it.

3.3.4. Slippery Slope

Claiming one step will lead to extreme outcomes.

  1. Example

    If we allow this, soon everything will be banned.

3.3.5. False Dillema(Either Or)

Presenting only two options when more exist

  1. Example

    You’re either with us or against us.

3.3.6. False Analogy

Comparing two things that aren’t actually alike.

  1. Example

    Employees are like nails — they work best when hit on the head.

3.3.7. Composition

Assuming what’s true of parts is true of the whole.

  1. Example

    Each part of the machine is light, so the machine is light.

3.3.8. Division

Assuming what’s true of the whole is true of its parts.

  1. Example

    The team is the best, so each player must be the best

3.3.9. Hasty Generalization

Drawing a broad conclusion from too little evidence.

  1. Example

    Two rude drivers — all New Yorkers are rude.

3.3.10. No True Scotsman

Redefining a category to dismiss counterexamples.

  1. Example

    No Scotsman puts sugar on porridge.” “But Angus does.” “Then he’s no true Scotsman.

3.4. Epistemic/Evidential Fallacies

Errors in how we justify or weigh evidence.

3.4.1. Appeal to Ignorance (Ad Ignorantiam)

Claiming something is true because it hasn’t been proven false.

  1. Example

    No one’s proven aliens don’t exist, so they must.

3.4.2. Burden of Proof

Demanding others disprove your claim.

  1. Example

    Prove ghosts don’t exist.

3.4.3. Cherry Picking

Selecting only evidence that supports your claim.

  1. Example

    These 3 studies say it works (ignoring 20 that don’t).

3.4.4. Suppressed Evidence

Leaving out info that changes interpretation.

  1. Example

    The medicine worked for 90% (ignores 10% died).

3.4.5. Texas Sharpshooter

Finding patterns after the fact.

  1. Example

    Shooting a barn then painting a target around the bullet holes.

3.5. Moral/Pyschological Fallacies

Relying on feelings instead of logic

3.5.1. Moralistic Fallacy

Assuming what is must be what ought to be.

  1. Example

    People cooperate, so selfishness is wrong.

3.5.2. Naturalistic Fallacy

Assuming what ought to be from what is.

  1. Example

    It’s natural, so it’s good.

3.5.3. Appeal to Consequences

Arguing truth based on desired outcomes.

  1. Example

    God must exist, because life would be meaningless otherwise.

3.5.4. Appeal to Force(Ad Baculum)

Using threats to prove a point.

  1. Example

    Agree with me or you’ll regret it.

4. Glossary & Acronyms

5. Elsewhere

5.1. References

5.2. In my garden

Notes that link to this note (AKA backlinks).

Glossary

syllogism
Deductive reasoning in which a conclusion is derived from two premises ↑
epistemic
Of relating to the nature, origin, and scope of knowledge ↑

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