Section 10.2 Reasoning Taxonomy
Understanding these reasoning patterns allows us to diagnose our own cognitive processes when building Eigenotes. We employ deductive reasoning to derive consequences from axioms, abductive reasoning to generate hypotheses from anomalous data, and spatial reasoning to visualize geometric structures.
- Deductive Reasoning
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Drawing specific conclusions from general laws or principles.Example: “Given this mechanism, what must follow?”
- Inductive Reasoning
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Generalizing from patterns or experimental observations.Example: “Given this data, what can we infer about X?”
- Temporal Reasoning
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Predicting events or states based on order in time.Example: “If A happens before B, and B affects C, what is the downstream effect?”
- Spatial Reasoning
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Understanding structures, orientation, or symmetry.Example: “What is the normal force on an object sliding down a ramp inclined at angle X?”
- Causal Reasoning
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Identifying cause-and-effect relationships.Example: “What arrangement of three electrons causes zero electric field at the center-of-mass location?”
- Comparative Analysis
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Judging between alternatives or evaluating differences across conditions.Example: “What is the percent difference in the ground-state energy of an atom trapped in a harmonic potential versus a quartic potential?”
- Abstract Reasoning
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Working with non-concrete or theoretical ideas.Example: “What is the entropy change in a hypothetical closed system with constraint X?”
- Pattern Recognition
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Spotting and interpreting regularities in data or sequences.Example: “The amounts of a radioactive isotope at times \(t_1\text{,}\) \(t_2\text{,}\) and \(t_3\) are \(N_1\text{,}\) \(N_2\text{,}\) and \(N_3\text{.}\) What is the half-life?”
- Statistical Reasoning
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Using data, probabilities, and distributions to reach conclusions.Example: “Determine the uncertainty in the extracted value of X given the experimental data.”
- Abductive Reasoning
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Inferring the most likely explanation from incomplete evidence.Example: “As the temperature changes from \(T_1\) to \(T_2\text{,}\) the spatial correlation length increases exponentially. What is likely true about the material’s location in phase space?”
- Hypothetical Reasoning
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Predicting outcomes under hypothetical or counterfactual scenarios.Example: “What would be the fractional change in Earth’s gravitational field if the gravitational constant were doubled?”
