rigorous-reasoning

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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.

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Added on2026-03-04

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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):

Meta-analysis / Systematic review - Synthesis of multiple studies
Randomized Controlled Trial (RCT) - Controlled experiments
Cohort study - Group follow-up research
Case-control study - Comparative case research
Expert opinion - Professional judgments
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:

Fully understand the opponent's position
Add reasonable premises they may have omitted
Rephrase in the most compelling way
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:

Assume it's true
Derive logical consequences
Show consequences lead to contradiction
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 - 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)