How Do We Reason and Solve Problems?

From drawing conclusions to finding a new way forward

Level: Intermediate
Reading load: 10 core readings in 6 units
Prerequisites: No formal logic or programming course is required. Familiarity with comparing a theory's predictions with evidence will help. How Can We Study the Mind? provides a useful introduction. How Do We Organize Knowledge? develops the role of prior knowledge in inference.
Last reviewed: September 2026

Introduction

Thought can be led astray by what feels most convincing. A plausible conclusion need not follow; an apparently unhelpful test may reveal the decisive fact; a stubborn problem may yield when seen in another form. These contrasts are the substance of an explanation of reasoning. A verdict of rational or irrational is too brief to tell us how the mind arrived there.

This path follows two connected questions: how do we draw and evaluate conclusions, and how do we find a solution when the next step is unclear? It moves from asking what follows from a claim and how to test an explanation, to drawing broader conclusions from examples and interpreting causes. It then examines how we search for solutions, use analogies, and find a new way to understand a problem. Conceptual papers specify what a process would have to do; experiments and model comparisons test the resulting claims.

The ten readings span six units and 157 journal pages. This is an intermediate path: the hypothesis-testing and probabilistic-model papers are technically demanding. The guidance introduces the vocabulary and connects formal claims to concrete examples. By the end, you should be able to specify a task, compare explanations of performance, and propose evidence that would distinguish them.

Unit 1 of 6

What follows—and what merely seems believable?

Deduction asks what must follow if the premises hold. Start with a proposal about how people represent possibilities, then examine a task in which logical validity and everyday belief point in different directions. Keep the standard for a valid conclusion separate from the process that produces a response.

Reading
1 of 10
Mental Models and Human Reasoning
Johnson-Laird, P. N. (2010). Mental models and human reasoning. Proceedings of the National Academy of Sciences, 107(43), 18243–18250. https://doi.org/10.1073/pnas.1012933107
Foundational argument · Major synthesis · Moderate · Full work: 8 pages
Follow how considering another possible situation changes a conclusion, and how the model account differs from applying an inference rule.
Why you're reading it. Establish a representational explanation that makes predictions about error and difficulty.
A question to consider. If a conclusion fits one interpretation of the premises but not another, what would an added counterexample reveal about the reasoner's first response?
Reading
2 of 10
On the Conflict Between Logic and Belief in Syllogistic Reasoning
Evans, J. St. B. T., Barston, J. L., & Pollard, P. (1983). On the conflict between logic and belief in syllogistic reasoning. Memory & Cognition, 11(3), 295–306. https://doi.org/10.3758/BF03196976
Landmark empirical study · Methodological contribution · Moderate · Full work: 12 pages
Use the crossed validity/believability design to separate an answer pattern from the proposed explanation of it. Compare the evidence from choices and verbal reports.
Why you're reading it. Apply the distinction between logical standards, prior knowledge, and response processes to an experiment.
A question to consider. Would accepting many believable conclusions uniquely support failure to search for counterexamples, or could a response preference produce a similar pattern?

Unit 2 of 6

Which evidence should we seek?

Evaluating a supplied conclusion differs from choosing what to observe next. First distinguish positive testing from protecting a belief; then examine a probabilistic proposal about informative observations. Both readings ask what a test can accomplish under specified assumptions.

Reading
3 of 10
Confirmation, Disconfirmation, and Information in Hypothesis Testing
Klayman, J., & Ha, Y.-W. (1987). Confirmation, disconfirmation, and information in hypothesis testing. Psychological Review, 94(2), 211–228. https://doi.org/10.1037/0033-295X.94.2.211
Critical reappraisal · Foundational argument · Challenging · Full work: 18 pages
Keep the choice of a test separate from whether its outcome confirms or contradicts a hypothesis. Compare environments in which the same strategy succeeds or fails.
Why you're reading it. Replace a broad bias label with an account of information search and its conditions.
A question to consider. After three successful deliveries, someone hypothesizes that a route is always reliable. What rival explanations should determine the next delivery conditions to investigate?
Reading
4 of 10
A Rational Analysis of the Selection Task as Optimal Data Selection
Oaksford, M., & Chater, N. (1994). A rational analysis of the selection task as optimal data selection. Psychological Review, 101(4), 608–631. https://doi.org/10.1037/0033-295X.101.4.608
Foundational argument · Critical reappraisal · Challenging · Full work: 24 pages
Compare the model's information-gain objective with the logical rule-checking interpretation of the selection task. Trace the role of assumed property frequencies.
Why you're reading it. Evaluate a probabilistic explanation against both its data fit and its assumptions about the task.
A question to consider. What observation would distinguish people responding to expected information from people simply choosing cards that repeat the words in the rule?

Unit 3 of 6

How does knowledge shape an inference?

Induction extends what is known to an unobserved case; causal reasoning uses a proposed structure to interpret evidence. These shared readings now serve a new comparison: changing a property or a causal interpretation can change which information matters, even when much of the task stays the same.

Reading
5 of 10
Similarity and Property Effects in Inductive Reasoning
Heit, E., & Rubinstein, J. (1994). Similarity and property effects in inductive reasoning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 20(2), 411–422. https://doi.org/10.1037/0278-7393.20.2.411
Landmark empirical study · Methodological contribution · Moderate · Full work: 12 pages
Compare the same animal relationships under different property questions. Ask what a fixed similarity ranking would predict and where it fails.
Why you're reading it. Distinguish extending a plausible pattern from deriving a necessary conclusion.
A question to consider. If two arguments reverse their apparent strength when the property changes, what has changed about the inference despite the animals staying the same?
Reading
6 of 10
Predictive and Diagnostic Learning Within Causal Models: Asymmetries in Cue Competition
Waldmann, M. R., & Holyoak, K. J. (1992). Predictive and diagnostic learning within causal models: Asymmetries in cue competition. Journal of Experimental Psychology: General, 121(2), 222–236. https://doi.org/10.1037/0096-3445.121.2.222
Landmark empirical study · Foundational argument · Moderate · Full work: 15 pages
Draw the common-cause and common-effect structures implied by the instructions. Track the direction of reasoning separately from the direction of causation.
Why you're reading it. Show how an assumed causal structure can organize learning and inference beyond a list of associations.
A question to consider. Would observing both an alarm and a warning light mean the same thing if they were effects of one fault as if they were independent causes of it? Specify what the experiment would need to hold constant.

Unit 4 of 6

What makes a problem searchable?

We now move from evaluating claims to constructing a solution. The symbolic account makes states, moves, and goals explicit. Its broader claims about intelligence should remain separate from the narrower question of how a particular solver finds a useful next step.

Reading
7 of 10
Computer Science as Empirical Inquiry: Symbols and Search
Newell, A., & Simon, H. A. (1976). Computer science as empirical inquiry: Symbols and search. Communications of the ACM, 19(3), 113–126. https://doi.org/10.1145/360018.360022
Foundational argument · Historical turning point · Challenging · Full work: 14 pages
Identify how representation defines the available problem space and how knowledge guides search. Examine the article's recognition and representation examples alongside its search account.
Why you're reading it. Build an explicit process explanation that the later analogy and insight papers can extend or challenge.
A question to consider. For a puzzle with many possible moves, how would you tell whether improvement came from searching more efficiently or from representing the problem differently?

Unit 5 of 6

When can an old solution help with a new problem?

Prior knowledge can reduce the need to search from scratch, but surface resemblance is an unreliable guide. Pair a theory of relational mapping with experiments that compare how people study examples. Understanding a comparison, retrieving it later, and applying it successfully are distinct achievements.

Reading
8 of 10
Structure-Mapping: A Theoretical Framework for Analogy
Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. Cognitive Science, 7(2), 155–170. https://doi.org/10.1207/s15516709cog0702_3
Foundational argument · Moderate · Full work: 16 pages
Identify the relational structure transferred by an analogy and the attributes left behind. Compare relational mapping with the property-dependent similarity examined earlier.
Why you're reading it. Explain how a comparison can suggest a solution without proving that the solution works.
A question to consider. Can two problems with different objects share the same solution structure while two visually similar problems do not? Construct one example of each.
Reading
9 of 10
Learning and Transfer: A General Role for Analogical Encoding
Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. Journal of Educational Psychology, 95(2), 393–408. https://doi.org/10.1037/0022-0663.95.2.393
Landmark empirical study · Methodological contribution · Moderate · Full work: 16 pages
Follow how the successive experiments isolate the contribution of comparing cases. Distinguish learning a principle from recognizing when it applies.
Why you're reading it. Connect a theory of analogy to an intervention and a measurable transfer outcome.
A question to consider. What would successful transfer to a new negotiation show beyond accurate recall of the training stories, and what would it leave unresolved about mechanism?

Unit 6 of 6

What changes when we get unstuck?

Knowledge can also impose an unhelpful constraint. End by testing whether the obstacle lies in searching within the current representation or in the representation itself. Changes in difficulty and transfer can inform that distinction, while the subjective feeling of insight remains a separate measurement problem.

Reading
10 of 10
Constraint Relaxation and Chunk Decomposition in Insight Problem Solving
Knoblich, G., Ohlsson, S., Haider, H., & Rhenius, D. (1999). Constraint relaxation and chunk decomposition in insight problem solving. Journal of Experimental Psychology: Learning, Memory, and Cognition, 25(6), 1534–1555. https://doi.org/10.1037/0278-7393.25.6.1534
Landmark empirical study · Foundational argument · Moderate · Full work: 22 pages
Compare constraint relaxation with chunk decomposition and trace their different predictions across problem types and prior-exposure conditions.
Why you're reading it. Bring search, prior knowledge, and representational change together in a testable account of impasse.
A question to consider. Design a hint that changes the representation without revealing the final move. What pattern of performance would support your explanation, and would an Aha! report alone be enough?

Scope and omissions

This path examines explanations of inference and problem solving, principally in adult laboratory tasks. It includes deduction, hypothesis testing, property-based induction, causal interpretation, search, analogy, and representational change. It does not rank people's intelligence or treat an error as evidence of a general personal deficit.

Probability appears here as an account of inference and information search. Preferences, value, risk, time, confidence calibration, and choosing between consequential options require a fuller treatment of judgment and decision making. Formal logic, mathematical cognition, neural mechanisms, scientific expertise, and collaborative reasoning receive limited coverage.

The core draws heavily on Western university samples, symbolic tasks, and well-defined problems. Cultural and developmental differences, embodied interaction, ill-defined real-world problems, and creative production constrain its generality. The selected experiments and historical theories do not establish a universal architecture of thought or a general recipe for becoming more creative.

Synthesis

Reasoning depends on the form in which a problem is understood, the purpose pursued, and the possibilities that become available. Logical rules offer standards for conclusions; probabilistic models describe inference under uncertainty; process accounts seek to explain how a person reaches a response. These approaches can illuminate one another, provided we remember which question each answers.

Across the readings, prior knowledge is both a resource and a possible obstacle. It selects relevant properties, supplies causal structure, supports analogies, and guides search. It can also make an unsupported conclusion seem necessary or hide a legal move. Progress sometimes requires a better search strategy and sometimes a different representation. Neither an error, a successful solution, nor a report of insight uniquely identifies the process.

For a final exercise, imagine a team trying to explain why a machine fails and devise a repair. Specify two hypotheses, an informative observation, a causal interpretation, a possible analogy, and a constraint the team may have assumed without justification. Choose one competing explanation of their performance and describe evidence that would distinguish it. Separate an explanation of how they think from an assessment of whether the repair is well supported.

To explore how practice and examples change later performance, continue to How Does Practice Build Skill?. To revisit the knowledge structures on which these inferences depend, return to How Do We Organize Knowledge?.

To examine how we evaluate uncertain outcomes, form preferences, and choose between alternatives, continue to How Do We Judge and Decide?.