Pattern, rule, proof

Three ways to go beyond the evidence

Philosophers and psychologists split inference into three kinds. The split is not academic tidiness. Each kind has a different standard of proof, and most wrong answers in reasoning tests come from applying the standard of one kind to a problem of another.

Deduction

Reasoning from rules to a case, where the truth of the premises guarantees the truth of the conclusion. If every symbol appears once per row, and a row already holds a circle, the blank in that row is not a circle. No further evidence could change that.

Induction

Reasoning from cases to a rule. The conclusion goes beyond what the premises strictly contain, so it can be wrong. Three striped cards that belong and one solid card that does not suggest "striped belongs", but the next card could break it.

Abduction

Reasoning to the best explanation: choosing the hypothesis that would, if true, make the evidence least surprising. Charles Sanders Peirce named it; debugging, diagnosis and detective work run on it.

The Stanford Encyclopedia of Philosophy puts the core distinction in one line: in deduction the truth of the premises guarantees the conclusion, while induction and abduction are ampliative, meaning their conclusions go beyond what is logically contained in the premises. That is why a deduction item has exactly one defensible answer and an induction item has one best answer among the options offered. Test writers make the induction items fair by building the options so that only one survives the rule. The item is closed, even though induction in general is open.

What happens in your head

Psychologists call the capacity to solve new problems without relying on stored knowledge fluid intelligence, a term Raymond Cattell set against crystallised intelligence, the knowledge and skills you have already built up. A figure matrix is the textbook fluid task. You cannot have memorised the answer, and vocabulary will not help you.

Three findings explain what fluid reasoning actually consists of.

It is rule-finding plus bookkeeping. Carpenter, Just and Shell took apart Raven's Advanced Progressive Matrices and found that a small set of rule types describes almost every item: a value constant across a row, a quantity that progresses, figures that add or subtract, and a set of three values distributed across a row. What separated high from low scorers was less the ability to see any one rule than the ability to keep several rules and their sub-goals in order at once. Hard items are hard mainly because three things change at the same time.

It leans on working memory, but is not the same thing. A meta-analysis of 86 samples by Ackerman, Beier and Boyle put the correlation between working memory and general intelligence at about .48. That is substantial, and it explains why reasoning collapses when you try to hold too much in your head. It is also well short of 1, which is why strategy matters so much (lesson 4 returns to this).

It recruits a specific control system. In a brain-imaging study, Duncan and colleagues compared tasks that load heavily on general intelligence with matched easier ones. The harder tasks did not light up the whole brain. They selectively recruited lateral frontal cortex, the same regions involved in controlling many kinds of behaviour. Reasoning looks less like a special module and more like disciplined control of attention and memory.

The four facets this app measures

The reasoning score on your profile is built from ten games, grouped into four facets. Each facet is a different demand, and you will usually find one clearly stronger than another.

Reasoning carries the largest weight of the seven dimensions in your overall profile, a little over a quarter. Within it, Matrix Logic counts most (15 per cent), followed by Symbol Grid and Rule Learning (13 per cent each) and Rule Sorter (12 per cent). Sequence Transformer lives on the Memory shelf because it also loads heavily on holding a sequence in mind, but it feeds the pattern facet too.

A few distinctions inside the facets are worth knowing now.

• Pattern recognition versus rule learning. In a pattern task the rule is visible in the structure of the item: a row of panels, a pair of figures. In a rule-learning task you only see outcomes (this card belongs, that one does not) and must reconstruct the rule that produced them. The first is about transformations, the second about categories.
• Rule learning versus flexibility. Some rule games give you a fresh rule on every trial. Object Sorting changes the rule inside a trial, so it also measures how quickly you let go of a rule that has stopped working. That is the family of the Wisconsin Card Sorting Test, where the sorting rule changes without warning after a run of correct sorts.
• Deduction versus guessing. In Symbol Grid the answer is always forced by the clues. Every trial is generated so that exactly one symbol fits the target cell. If you are guessing, you have stopped reasoning too early.

Where you already do this

You reason every day without calling it that. Workplace reasoning simply has higher stakes and less time.

• A failing build is abduction. Something changed; you list candidate causes and pick the one that best explains the pattern of failures, then test it.
• A spreadsheet that looks wrong is induction. You notice that every bad row came from the same region, form a rule, and check it against rows you have not looked at yet.
• A meeting schedule with six people, three rooms and fixed constraints is deduction. It is a Latin-square problem wearing a calendar.
• A client's data request is often numerical reasoning: which combination of the figures you have answers the question they asked?

Placement tests compress these into two-minute items with abstract content, so that prior knowledge of any particular job does not decide the result.

1. 1938

   John C. Raven publishes the Progressive Matrices: 60 items in five sets of twelve, black figures on white.

2. 1948

   Grant and Berg introduce the Wisconsin Card Sorting Test, a measure of concept formation and shifting.

3. 1956

   Bruner, Goodnow and Austin publish A Study of Thinking, the classic account of how people discover a concept from examples.

4. 1960

   Peter Wason's 2-4-6 task shows how rarely people try to disprove their own hypothesis.

5. 1963

   Raymond Cattell's critical experiment on fluid and crystallised intelligence.

6. 1967

   Mikhail Bongard publishes 100 visual concept puzzles, two groups of six figures split by a rule.

7. 1990

   Carpenter, Just and Shell show that a handful of rule types and good goal management explain Raven performance.

8. 2006

   Birney, Halford and Andrews publish the Latin Square Task, a pure test of relational deduction.

Three ways reasoning goes wrong

Knowing the failure modes is half of the defence against them.

Take these into the next lesson

• Deduction guarantees its conclusion; induction and abduction propose the best-supported one. Know which kind an item is.
• Fluid reasoning is rule-finding plus bookkeeping. Hard items are hard because several rules change at once.
• Working memory supports reasoning (correlation of about .48 with general intelligence) but strategy decides how far it gets you.
• This app splits reasoning into pattern recognition, rule learning, deduction and numerical reasoning, measured by ten games.
• The classic errors are confirming rather than testing, holding on to an old rule, and stopping at the first partial fit.

Next, why reasoning matters: what the research says it predicts, and how much.

Sources

1. Douven, I. (2025 revision). Abduction. In E. N. Zalta (Ed.), Stanford Encyclopedia of Philosophy. plato.stanford.edu/entries/abduction
2. Cattell, R. B. (1963). Theory of fluid and crystallized intelligence: A critical experiment. Journal of Educational Psychology, 54(1), 1–22. doi:10.1037/h0046743
3. Carpenter, P. A., Just, M. A., & Shell, P. (1990). What one intelligence test measures: A theoretical account of the processing in the Raven Progressive Matrices Test. Psychological Review, 97(3), 404–431. doi:10.1037/0033-295X.97.3.404
4. Verguts, T., & De Boeck, P. (2002). The induction of solution rules in Raven's Progressive Matrices Test. European Journal of Cognitive Psychology, 14(4), 521–547. doi:10.1080/09541440143000230
5. Ackerman, P. L., Beier, M. E., & Boyle, M. O. (2005). Working memory and intelligence: The same or different constructs? Psychological Bulletin, 131(1), 30–60. doi:10.1037/0033-2909.131.1.30
6. Duncan, J., Seitz, R. J., Kolodny, J., Bor, D., Herzog, H., Ahmed, A., Newell, F. N., & Emslie, H. (2000). A neural basis for general intelligence. Science, 289(5478), 457–460. doi:10.1126/science.289.5478.457
7. Wason, P. C. (1960). On the failure to eliminate hypotheses in a conceptual task. Quarterly Journal of Experimental Psychology, 12(3), 129–140. doi:10.1080/17470216008416717
8. Luchins, A. S. (1942). Mechanization in problem solving: The effect of Einstellung. Psychological Monographs, 54. doi:10.1037/h0093502
9. Nyhus, E., & Barceló, F. (2009). The Wisconsin Card Sorting Test and the cognitive assessment of prefrontal executive functions: A critical update. Brain and Cognition, 71(3), 437–451. doi:10.1016/j.bandc.2009.03.005
10. Raven's Progressive Matrices. Wikipedia. en.wikipedia.org/wiki/Raven's_Progressive_Matrices
11. Bongard problem. Wikipedia. en.wikipedia.org/wiki/Bongard_problem
12. Birney, D. P., Halford, G. S., & Andrews, G. (2006). Measuring the influence of complexity on relational reasoning: The development of the Latin Square Task. Educational and Psychological Measurement, 66(1), 146–171. doi:10.1177/0013164405278570
13. Bruner, J. S., Goodnow, J. J., & Austin, G. A. (1956). A Study of Thinking. Wiley.
14. AMCAT syllabus: Logical Ability. myamcat.com/amcat-syllabus