rigorous-reasoning

--- name: rigorous-reasoning description: "Rigorous reasoning using philosophical theories and scientific methods. Use this skill when analyzing logic, evaluating arguments, constructing proofs, critiquing opinions, or solving complex problems requiring critical thinking. Triggers - debate, proof, critique, logical analysis, argument evaluation, fallacy detection, inference, argumentation, logical fallacy, critical thinking." --- # Rigorous Reasoning This skill provides a rigorous reasoning framework based on philosophy and scientific methods to analyze, evaluate, and construct arguments. ## Core Principles ### 1. Socratic Method Ask continuous questions to clarify and challenge assumptions: ``` Clarifying definitions → Challenging assumptions → Questioning evidence → Exploring consequences → Considering alternatives ``` **Application:** - "When you say X, how do you define X?" - "What assumptions underlie this argument?" - "What evidence supports this conclusion?" - "If this is true, what are the logical consequences?" ### 2. Standard Argument Structure Every argument must have: ``` PREMISES ├── Premise 1: [Verifiable claim] ├── Premise 2: [Verifiable claim] └── ... ↓ INFERENCE RULE └── [Modus ponens / Modus tollens / Syllogism / ...] ↓ CONCLUSION └── [Claim logically derived from premises] ``` ### 3. Valid Inference Rules | Rule | Form | Example | |------|------|---------| | **Modus Ponens** | P → Q, P ⊢ Q | If it rains, the road is wet. It rains. → The road is wet. | | **Modus Tollens** | P → Q, ¬Q ⊢ ¬P | If it rains, the road is wet. The road is not wet. → It's not raining. | | **Syllogism** | ∀x(P(x)→Q(x)), P(a) ⊢ Q(a) | All men are mortal. Socrates is a man. → Socrates is mortal. | | **Disjunctive Syllogism** | P ∨ Q, ¬P ⊢ Q | Either A or B. Not A. → B. | | **Hypothetical Syllogism** | P → Q, Q → R ⊢ P → R | If A then B. If B then C. → If A then C. | ## Identifying Logical Fallacies ### Formal Fallacies | Fallacy | Description | Invalid Example | |---------|-------------|-----------------| | **Affirming the Consequent** | P→Q, Q ⊢ P (INVALID) | If rain, then wet. Wet → Rain (INVALID: could be other causes) | | **Denying the Antecedent** | P→Q, ¬P ⊢ ¬Q (INVALID) | If study hard, then pass. Don't study hard → Don't pass (INVALID) | ### Informal Fallacies | Fallacy | Description | How to Identify | |---------|-------------|-----------------| | **Ad Hominem** | Attacking the person instead of the argument | "He's wrong because he's X" | | **Straw Man** | Distorting opponent's argument | Compare with original argument | | **Appeal to Authority** | Citing irrelevant authority | Is the expert qualified in this field? | | **False Dichotomy** | Presenting only 2 options when more exist | Is there a third option? | | **Slippery Slope** | Unproven chain of consequences | Is each step evidenced? | | **Circular Reasoning** | Conclusion embedded in premises | Are premises independent? | | **Post Hoc** | Confusing correlation with causation | Is there a causal mechanism? | | **Hasty Generalization** | Concluding from small sample | Is the sample representative? | | **Appeal to Emotion** | Using emotion instead of logic | Separate emotion from argument | | **Tu Quoque** | "You do it too" | Irrelevant to correctness | ## Scientific Method in Reasoning ### Claim Evaluation Process ``` 1. OBSERVATION └── What claim needs evaluation? 2. HYPOTHESIS ├── H₀ (null): The claim is false └── H₁ (alternative): The claim is true 3. PREDICTION └── If H₁ is true, what do we expect to observe? 4. TESTING ├── Evidence supporting H₁? ├── Evidence refuting H₁? └── Is the evidence falsifiable? 5. CONCLUSION ├── Confidence level? └── Alternative hypotheses? ``` ### Evidence Standards **Evidence hierarchy (strongest to weakest):** 1. **Meta-analysis / Systematic review** - Synthesis of multiple studies 2. **Randomized Controlled Trial (RCT)** - Controlled experiments 3. **Cohort study** - Group follow-up research 4. **Case-control study** - Comparative case research 5. **Expert opinion** - Professional judgments 6. **Anecdotal evidence** - Personal stories (WEAKEST) ### Occam's Razor > Among equivalent explanations, choose the simplest one. **Application:** - Don't multiply entities beyond necessity - Prefer hypotheses with fewer assumptions - Simple ≠ Correct, but it's a good starting point ### Falsifiability Principle (Karl Popper) > A scientific claim must be capable of being refuted. **Test:** - "What evidence would prove this wrong?" - If no answer → Not a scientific claim ## Argument Analysis Process ### Step 1: Reconstruction ``` Input: Raw argument ↓ 1. Identify main conclusion 2. List explicit premises 3. Identify hidden premises 4. Arrange in logical structure ↓ Output: Standardized argument ``` ### Step 2: Evaluate Premises For each premise, ask: - **True?** (Is there supporting evidence?) - **Relevant?** (Does it connect to the conclusion?) - **Sufficient?** (Is it strong enough to infer the conclusion?) ### Step 3: Evaluate Inference - Does the inference follow valid rules? - Are there any formal fallacies? - Does the conclusion follow from the premises? ### Step 4: Consider Counterarguments - Are there counterexamples? - Are there stronger opposing arguments? - Is there additional information that changes the conclusion? ## Thinking Tools ### Steel Man (Opposite of Straw Man) Before critiquing, build the **strongest** version of the opposing argument: 1. Fully understand the opponent's position 2. Add reasonable premises they may have omitted 3. Rephrase in the most compelling way 4. Then critique ### Principle of Charity When an argument can be interpreted multiple ways, choose the most reasonable interpretation before evaluating. ### Reductio ad Absurdum Prove something false by: 1. Assume it's true 2. Derive logical consequences 3. Show consequences lead to contradiction 4. Conclude: The initial assumption is false ### Thought Experiment Construct hypothetical scenarios to test intuitions and explore logical consequences. ## Quick Evaluation Checklist When encountering an argument, check: - [ ] Is the conclusion clearly stated? - [ ] Are all premises listed? - [ ] Do premises have supporting evidence? - [ ] Does inference follow valid rules? - [ ] No formal fallacies? - [ ] No informal fallacies? - [ ] Considered opposing viewpoints? - [ ] Is the claim falsifiable? - [ ] Is evidence strong enough? - [ ] Applied Occam's Razor? ## Applied Example ### Analyzing an Argument **Raw argument:** "AI will replace all jobs because computers are becoming increasingly intelligent." **Reconstruction:** ``` P1: Computers are becoming increasingly intelligent P2: [Hidden] All jobs can be performed by sufficiently intelligent machines P3: [Hidden] This development will continue without limits ───────────────────────────────── C: AI will replace all jobs ``` **Evaluation:** - P1: Partially true, need to quantify "intelligent" - P2: Unproven assumption - are there jobs requiring human elements? - P3: Assumption about the future - are there physical/technical limits? - **Fallacies:** Hasty Generalization, Slippery Slope - **Conclusion:** Weak argument, needs stronger evidence for P2 and P3 ## References For deeper understanding of philosophical foundations, see [references/philosophical-frameworks.md](references/philosophical-frameworks.md) - including: - Classical Logic (Aristotle) - Rationalism (Descartes, Spinoza, Leibniz) - Empiricism (Locke, Hume) - Critical Philosophy (Kant) - Logical Positivism (Vienna Circle) - Philosophy of Science (Karl Popper) - Dialectical Method (Hegel, Marx) - Pragmatism (Peirce, James, Dewey)