Reasoning

Reasoning connects what we know to what we conclude.

We reason when we ask:

• What follows?
• What probably happened?
• What should I do?
• What explanation best fits the evidence?

Formal logic gives standards.

Human cognition supplies the actual machinery.

The two are related but not identical.

Inference

An inference moves from:

premises

to:

a conclusion.

The move may be:

• deductive,
• inductive,
• abductive,
• probabilistic.

Reasoning is broader than deduction.

Deduction

Deductive reasoning aims at necessity.

If the premises are true and the argument valid, the conclusion must be true.

Example:

All mammals are warm-blooded.

Whales are mammals.

Therefore:

whales are warm-blooded.

Induction

Induction generalizes from evidence.

Example:

Every observed sample of this metal expanded when heated.

Therefore:

this metal probably expands when heated in general.

The conclusion is not logically guaranteed.

Abduction

Abduction seeks a plausible explanation.

Observation:

the ground is wet.

Possible explanation:

it rained.

Abduction is central to:

• diagnosis,
• science,
• everyday reasoning.

Probabilistic Reasoning

When uncertainty can be quantified, probability provides a formal framework.

Bayesian reasoning updates beliefs as evidence arrives.

Human reasoning often approximates this imperfectly.

Normative vs Descriptive

A normative theory says how reasoning should work.

A descriptive theory asks how people actually reason.

Logic is normative.

Psychology studies descriptive behavior.

Confusing the two creates mistakes.

Humans Are Not Theorem Provers

People do not usually derive every conclusion through explicit formal rules.

We use:

• heuristics,
• examples,
• mental models,
• analogy.

This can be efficient.

It can also create bias.

Mental Models

One theory proposes that people reason by constructing possible situations satisfying the premises.

If a conclusion holds across the represented possibilities, we accept it.

Failure to consider alternatives produces error.

Confirmation Bias

People preferentially seek or interpret evidence supporting existing beliefs.

This is confirmation bias.

Reasoning is shaped by motivation and prior models.

Wason Selection Task

The Wason selection task shows that people often struggle with abstract conditional logic.

Performance improves when the same logical structure is embedded in familiar social or practical contexts.

Reasoning is context-sensitive.

Conditional Reasoning

From:

[ P\rightarrow Q ]

and P,

we may infer Q.

This is modus ponens.

But people often make invalid moves such as:

affirming the consequent.

Belief Bias

People may judge an argument by whether its conclusion seems believable rather than whether the inference is valid.

A valid argument with an implausible conclusion can feel wrong.

Belief and logic interact.

Syllogistic Reasoning

Classic syllogisms test relations among categories.

Humans perform better when:

• content is familiar,
• working-memory demands are low.

Formal competence is constrained by cognition.

Working Memory

Complex reasoning requires maintaining:

• premises,
• intermediate steps,
• alternatives.

Limited working memory can explain many errors.

Logical capacity depends on cognitive resources.

Cognitive Load

Add distraction or time pressure.

Reasoning often becomes more heuristic.

This suggests rationality is resource-dependent.

Bounded Rationality

Herbert Simon argued that real agents have limited:

• information,
• time,
• computation.

They cannot optimize globally.

They satisfice.

Satisficing

A satisficing agent seeks an option good enough.

This can be rational when exhaustive search is too expensive.

Perfect optimization is often irrational under resource constraints.

Heuristics

Heuristics are shortcuts.

Examples include:

• availability,
• representativeness,
• anchoring.

They reduce effort.

They can systematically fail.

Availability Heuristic

Events easier to recall feel more probable.

Dramatic accidents may be overestimated.

Common but invisible risks may be underestimated.

Memory accessibility influences judgment.

Representativeness

People may judge probability by similarity to a stereotype.

This can neglect:

• base rates,
• sample size.

Similarity is not probability.

Anchoring

An initial number can influence later estimates even when irrelevant.

Reasoning is path-dependent.

Base-Rate Neglect

People often underuse prior probabilities.

A vivid case can dominate statistical background.

This creates errors in:

• medicine,
• law,
• diagnosis.

Conjunction Fallacy

People may judge:

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

even though this is impossible by probability rules.

Narrative coherence can overpower formal probability.

Framing Effects

Equivalent choices can produce different decisions depending on wording.

“90% survival”

may feel different from:

“10% mortality.”

Representation shapes reasoning.

Loss Aversion

Losses often influence choice more strongly than equivalent gains.

Prospect theory models this asymmetry.

Human decision making deviates systematically from expected-utility ideals.

Motivated Reasoning

Reasoning can serve goals other than truth.

A person may unconsciously defend:

• identity,
• status,
• prior commitments.

Intelligence can become a tool for rationalization.

Intelligence Does Not Eliminate Bias

Greater reasoning capacity can sometimes produce more sophisticated justifications for preferred conclusions.

Ability and epistemic virtue are different.

Open-Mindedness

Good reasoning requires willingness to revise beliefs.

This includes:

• seeking disconfirming evidence,
• considering alternatives.

Reasoning quality is partly a disposition.

Steelmanning

To evaluate an opposing view, construct its strongest reasonable version.

This reduces straw-man reasoning.

It improves comparison.

Falsification

Ask:

What evidence would change my mind?

If no possible observation counts against a belief, reasoning has become insulated.

This connects individual reasoning to scientific method.

Bayesian Updating

A rational agent should update beliefs in proportion to evidence.

Bayes’ theorem gives:

[ P(H\mid D)=\frac{P(D\mid H)P(H)}{P(D)} ]

The challenge is assigning realistic probabilities.

Likelihood Ratios

Evidence is informative when it is more expected under one hypothesis than another.

The likelihood ratio:

[ \frac{P(D\mid H_1)}{P(D\mid H_2)} ]

captures comparative support.

This is often more useful than raw probability.

Causal Reasoning

Correlation does not imply causation.

Reasoning about cause requires questions such as:

What would happen under intervention?

Counterfactual models are important.

Confounding

A third variable can create an apparent relation between two others.

Causal reasoning must identify alternative paths.

Statistical association alone is insufficient.

Analogical Reasoning

Analogy transfers structure from a familiar domain.

Example:

electric circuit

as analogous to:

fluid flow.

Analogies aid discovery.

They can also mislead when irrelevant similarities dominate.

Structural Similarity

A good analogy preserves relational structure.

Surface similarity is less important.

This is why mathematics can apply across different domains.

Case-Based Reasoning

Experts often solve new problems by retrieving similar past cases.

Medicine and law rely heavily on this.

Memory becomes a reasoning engine.

Expertise

Experts do not simply know more facts.

They organize knowledge differently.

Their mental models support:

• faster recognition,
• better inference.

Representation shapes reasoning quality.

Metacognition

Good reasoners monitor:

• confidence,
• uncertainty,
• error.

They ask:

How sure am I?

What assumption am I making?

Metacognition regulates inference.

Calibration

A calibrated reasoner is correct about as often as their confidence predicts.

Statements assigned 80% confidence should be right roughly 80% of the time across many cases.

Calibration connects belief to probability.

Overconfidence

Humans are often too confident.

Confidence can exceed accuracy.

Strong feeling is not strong evidence.

Collective Reasoning

Groups can outperform individuals by combining:

• diverse knowledge,
• independent perspectives.

But groups can also amplify:

• conformity,
• polarization.

Collective intelligence depends on structure.

Groupthink

If disagreement is socially punished, groups may converge prematurely.

Consensus can be evidence.

It can also be a product of pressure.

Markets and Aggregation

Prediction markets and other mechanisms can aggregate dispersed beliefs.

Under some conditions, collective estimates become accurate.

Institution design influences reasoning quality.

Scientific Reasoning

Science institutionalizes correction through:

• replication,
• peer review,
• public criticism.

It does not rely on scientists being unbiased individually.

It builds processes around human fallibility.

Machine Reasoning

AI systems can perform:

• theorem proving,
• probabilistic inference,
• planning.

They also inherit biases from:

• training data,
• objectives,
• model structure.

Formal machinery does not guarantee epistemic virtue.

Hybrid Reasoning

Humans and machines can complement one another.

Machines provide:

• speed,
• consistency,
• search.

Humans provide:

• goals,
• context,
• representation changes.

The division is evolving.

Rationality as Resource Management

A mature view treats reasoning as allocation of limited cognitive resources.

The agent must decide:

• what to think about,
• how deeply,
• when to stop.

Meta-reasoning becomes part of rationality.

The Philosophical Lesson

Reasoning is not one formal procedure.

It is a family of inference processes operating under:

• limited memory,
• incomplete information,
• goals,
• emotion,
• context.

Logic gives standards.

Human cognition negotiates reality.

The Next Question

The same sentence can mean different things in different situations.

The same action can be rational in one environment and foolish in another.

What changes?

Context.

That is the next topic.