Fallacies

A fallacy is a pattern of reasoning that appears stronger than it really is.

Some fallacies are formally invalid.

Others misuse:

• evidence,
• relevance,
• language,
• probability.

The important goal is not memorizing labels.

It is learning to see where support fails.

Formal Fallacies

A formal fallacy arises from invalid logical structure.

The error can be identified without examining the subject matter.

Example:

If P, then Q.

Q.

Therefore P.

This is affirming the consequent.

Affirming the Consequent

If it rains, the road is wet.

The road is wet.

Therefore it rained.

The conclusion may be true.

The reasoning is invalid.

Other causes could explain the wet road.

Denying the Antecedent

Another formal fallacy:

If P, then Q.

Not P.

Therefore not Q.

Example:

If I am in Istanbul, I am in Türkiye.

I am not in Istanbul.

Therefore I am not in Türkiye.

The conclusion does not follow.

Informal Fallacies

Informal fallacies depend on content and context.

They involve failures such as:

• irrelevant evidence,
• distorted opponents,
• hidden assumptions.

These cannot always be diagnosed by symbolic form alone.

Ad Hominem

An ad hominem attack targets a person instead of addressing the argument.

Example:

“Her climate argument is wrong because she is arrogant.”

Her personality may be unpleasant.

That does not refute the evidence.

When Personal Information Is Relevant

Not every statement about a speaker is fallacious.

If the issue is credibility, relevant conflicts of interest may matter.

The fallacy occurs when personal attack substitutes for argument.

Context matters.

Straw Man

A straw man misrepresents an opponent’s position into an easier target.

Instead of answering:

“What was actually claimed?”

the critic attacks a weaker substitute.

This is common because caricatures are easier to defeat.

Steelmanning

A useful counterpractice is steelmanning:

state the strongest reasonable version of the opposing position before evaluating it.

This improves disagreement.

It also reduces accidental straw men.

False Dilemma

A false dilemma presents too few alternatives.

“You either support this policy or you do not care about safety.”

There may be many intermediate positions.

Binary framing can hide the real option space.

Slippery Slope

A slippery-slope argument says one step will lead to a chain of increasingly extreme outcomes.

Some slopes are real.

The fallacy occurs when the intermediate causal links are merely asserted.

A good slope argument needs mechanism and evidence.

Appeal to Authority

Experts can provide legitimate evidence.

The fallacy appears when authority is treated as decisive outside relevant expertise or against stronger evidence.

“An expert said it” is not automatically fallacious.

The quality and domain of expertise matter.

Appeal to Popularity

Many people believing something does not make it true.

This is appeal to popularity.

Popularity can indicate:

• social convention,
• widespread experience.

It does not settle factual truth by itself.

Appeal to Ignorance

A claim is not true merely because it has not been disproved.

Nor false merely because it has not been proven.

Example:

“No one has shown aliens are not here, therefore they are here.”

Absence of refutation is not positive proof.

Burden of Proof

The person making a claim normally bears some burden to support it.

Shifting that burden improperly creates bad reasoning.

Extraordinary claims generally require appropriately strong evidence.

Circular Reasoning

Circular reasoning uses the conclusion as support for itself.

“The book is reliable because everything in it is true.”

“How do we know everything is true?”

“Because the book is reliable.”

No independent support is added.

Begging the Question

Begging the question is closely related.

The premise assumes what the argument is supposed to establish.

The reasoning may be formally valid but epistemically useless.

Equivocation

Equivocation changes the meaning of a word during an argument.

Example:

“A feather is light.”

“What is light cannot be dark.”

“Therefore a feather cannot be dark.”

The word “light” changes meaning.

Language ambiguity creates invalidity.

Amphiboly

An amphiboly exploits grammatical ambiguity.

A sentence has multiple parses.

The argument shifts between them.

Syntax itself becomes the source of error.

Composition

The fallacy of composition assumes that what is true of parts must be true of the whole.

Each player is excellent.

Therefore the team must be excellent.

Sometimes this works.

Sometimes interaction changes the result.

Division

The fallacy of division reverses the error.

The company is wealthy.

Therefore every employee is wealthy.

Whole-level properties need not transfer to parts.

This connects directly to emergence.

Hasty Generalization

A hasty generalization draws a broad conclusion from too little evidence.

“I met two rude tourists from country X; people from X are rude.”

The problem is sampling.

Induction requires representative evidence.

Cherry-Picking

Cherry-picking selects evidence that supports a preferred conclusion while ignoring relevant counterevidence.

The dataset is not merely small.

It is selectively filtered.

This creates a false impression of support.

Survivorship Bias

We often study visible successes while ignoring failures.

This is survivorship bias.

For example, studying only successful companies can hide common reasons businesses fail.

What is missing from the sample matters.

Post Hoc

The fallacy:

post hoc ergo propter hoc

means roughly:

after this, therefore because of this.

Event B follows event A.

Therefore A caused B.

Temporal order alone does not establish causation.

Correlation and Causation

Two variables may correlate because:

• A causes B,
• B causes A,
• C causes both,
• coincidence.

Causal claims require more than association.

We encountered this earlier in scientific reasoning.

Gambler’s Fallacy

After several heads in a row, someone may think tails is “due.”

If coin tosses are independent, past outcomes do not change the probability of the next toss.

This is the gambler’s fallacy.

Human intuition often misreads randomness.

Base-Rate Neglect

People sometimes focus on vivid evidence while ignoring prior probability.

A diagnostic test may be highly accurate.

But if the condition is extremely rare, many positive results can still be false positives.

Reasoning must include base rates.

Conjunction Fallacy

People may judge a detailed conjunction as more probable than one of its components.

But:

[ P(A \land B) \leq P(A) ]

The conjunction cannot be more probable than either event alone.

Narrative detail can overpower probability.

Availability Heuristic

Events that are vivid or easy to recall may feel more probable.

Airplane crashes receive intense coverage.

They may therefore feel more common than they are.

Memory accessibility can distort risk judgment.

Confirmation Bias

People tend to seek, remember, and interpret evidence in ways that support existing beliefs.

This is not a formal fallacy in the narrow sense.

It is a cognitive bias that produces fallacious argument patterns.

Motivated Reasoning

Reasoning can become goal-directed toward a desired conclusion.

The mind then functions less like an impartial evaluator and more like a lawyer.

Intelligence does not automatically eliminate bias.

It can sometimes strengthen rationalization.

False Balance

Giving equal weight to unequal evidence can also mislead.

Fairness does not require pretending all positions have equal support.

Reasoning should track evidence quality.

Fallacy Fallacy

Even if an argument contains a fallacy, its conclusion may still be true.

Bad reasoning does not prove the opposite.

Reject the argument.

Do not automatically reject the conclusion.

Labels Are Not Refutations

Saying:

“That’s an ad hominem”

does not finish the analysis.

We still need to explain:

• what inference failed,
• why the information is irrelevant.

Fallacy labels should compress reasoning, not replace it.

Context Changes Classification

The same argumentative move can be legitimate in one context and fallacious in another.

Expert testimony matters in medicine.

Popularity matters for defining slang usage.

Personal credibility matters in eyewitness testimony.

Critical thinking needs context.

Fallacies in Science

Science reduces fallacies through:

• controls,
• replication,
• statistical methods,
• peer review.

But scientists are still human.

Methodology exists partly because intuition is unreliable.

Fallacies in Machine Reasoning

AI systems can also produce fallacious arguments.

Fluent language does not guarantee valid inference.

A model may:

• hallucinate premises,
• reverse causation,
• ignore alternatives.

Reasoning quality must be evaluated independently of style.

The Philosophical Lesson

A fallacy is not simply a wrong conclusion.

It is a failure in the route from evidence to conclusion.

Learning fallacies means learning to ask:

• What exactly supports what?
• Is the support relevant?
• Is the probability handled correctly?
• Has the language shifted?

The Next Question

Some arguments are wrong because they are fallacious.

Some puzzles are more interesting.

They begin from plausible assumptions and lead to conclusions that seem impossible, contradictory, or deeply counterintuitive.

These are:

paradoxes.