Calculemus Formalization

Calculemus Formalization

When disputes persist due to imprecise language, decompose concepts into precise elements and make reasoning explicit and calculable. Calculemus! - "Let us calculate!" Leibniz dreamed of reducing all disputes to calculation; this skill applies that vision to any situation where verbal confusion blocks resolution.

When to Use

• Disputants are talking past each other using the same words differently
• A debate seems to go in circles without progress
• Key terms are vague or ambiguous
• Reasoning is implicit and needs to be made explicit
• Complex arguments need to be decomposed and evaluated
• You want to identify exactly where disagreement lies

Inputs

The Calculemus Process

Step 1: Identify the Disputed Claim

State precisely what is being disputed. Often disputes are unclear because the claim itself is vague.

Ask: "What exactly is being asserted? What would it mean for this claim to be true or false?"

Step 2: Extract Key Terms

Identify the crucial terms on which the dispute depends.

Look for:

• Abstract nouns (justice, freedom, quality, success)
• Terms used differently by different parties
• Words that seem obvious but are actually ambiguous
• Technical terms that may not be shared

Step 3: Define Precisely

For each key term, provide a precise definition that could be used consistently.

For each term, specify:

• Necessary conditions (what must be present)
• Sufficient conditions (what guarantees the term applies)
• Clear examples and counterexamples
• Quantifiable criteria where possible

Step 4: Make Reasoning Explicit

Reconstruct the argument in explicit logical form.

Format:

Premise 1: [explicit statement]
Premise 2: [explicit statement]
...
Conclusion: [explicit statement]

Check:

• Are all premises stated?
• Is the inference valid (does the conclusion follow)?
• Are there hidden assumptions?

Step 5: Locate the Disagreement

With precise definitions and explicit reasoning, identify exactly where disagreement lies.

Possible locations:

• Definitional: Parties mean different things by key terms
• Factual: Parties disagree about empirical claims
• Logical: Parties disagree about what follows from what
• Evaluative: Parties weight considerations differently

Step 6: Calculate or Decide

Once disagreement is localized:

• If definitional: Negotiate shared definitions or clarify that parties are discussing different things
• If factual: Identify what evidence would resolve it
• If logical: Examine the inference carefully
• If evaluative: Make the value weights explicit and discuss

Workflow

Step 1: Gather and Review Inputs

Collect all relevant information:

• Review the provided data and context
• Identify key parameters and constraints
• Clarify any ambiguities or missing information
• Establish success criteria

Step 2: Analyze the Situation

Perform systematic analysis:

• Identify patterns and relationships
• Evaluate against established frameworks
• Consider multiple perspectives
• Document key findings

Step 3: Generate Recommendations

Create actionable outputs:

• Synthesize insights from analysis
• Prioritize recommendations by impact
• Ensure recommendations are specific and measurable
• Consider implementation feasibility

Output Format

## Calculemus Analysis

### The Dispute
[Precise statement of what is being disputed]

### Key Terms Requiring Definition

| Term | Party A Definition | Party B Definition | Proposed Precise Definition |
|------|-------------------|-------------------|---------------------------|
| [term1] | [how A uses it] | [how B uses it] | [precise definition] |
| [term2] | [how A uses it] | [how B uses it] | [precise definition] |

### Explicit Argument Reconstruction

**Party A's Argument:**

P1: [premise] P2: [premise] C: [conclusion]

**Party B's Argument:**

P1: [premise] P2: [premise] C: [conclusion]

### Hidden Assumptions Identified
- [Assumption 1]
- [Assumption 2]

### Location of Disagreement
| Type | Finding |
|------|---------|
| Definitional | [Where terms are used differently] |
| Factual | [Where empirical claims differ] |
| Logical | [Where inferences differ] |
| Evaluative | [Where values/weights differ] |

### The Calculation
[With precise definitions and explicit reasoning, what follows? Can the dispute be resolved?]

### Resolution Path
[What would resolve the dispute? What evidence, agreement, or clarification is needed?]

Constraints

• Do not oversimplify complex concepts to make them calculable - preserve genuine complexity
• Acknowledge when full formalization is not possible
• Recognize that some disputes are genuinely evaluative and cannot be "calculated"
• Maintain diplomatic courtesy - "If I may propose a precise definition..."
• Be willing to say "this cannot be resolved by calculation alone" when appropriate

Outputs

Primary Output: A structured analysis document that identifies and articulates patterns, insights, and actionable recommendations based on the input data.

Format:

## Analysis: [Topic]

### Key Findings
- [Finding 1]
- [Finding 2]
- [Finding 3]

### Recommendations
1. [Action 1]
2. [Action 2]
3. [Action 3]

Anti-Patterns to Avoid

Examples

Example 1: Growth vs. Profitability Debate

Input: "We're arguing about whether to prioritize user growth or profitability. The debate keeps going in circles."

Output:

Calculemus Analysis

The Dispute

"Should the company prioritize user growth or profitability in the next quarter?"

Key Terms Requiring Definition

Explicit Argument Reconstruction

Party A's Argument (Prioritize Growth):

P1: We are a venture-backed startup with 18 months of runway
P2: Our Series B valuation depends on demonstrating growth trajectory
P3: Profitable-but-slow companies get lower valuations than growing companies
P4: Without a strong Series B, we cannot achieve our mission
C: Therefore, we should prioritize user growth over profitability in Q2

Party B's Argument (Prioritize Profitability):

P1: We have 18 months of runway but macro conditions are uncertain
P2: Companies are getting funded at lower rates than 2021
P3: A company that is profitable, or near-profitable, has more negotiating leverage
P4: Revenue multiples have compressed; fundamentals matter more now
C: Therefore, we should prioritize profitability to reduce existential risk

Hidden Assumptions Identified

• Party A assumes Series B funding environment will reward growth
• Party A assumes 18 months is sufficient to demonstrate growth AND then raise
• Party B assumes funding environment will remain difficult
• Party B assumes profitability signals will matter to investors
• Both assume the choice is binary (not a spectrum)

Location of Disagreement

The Calculation

The dispute is primarily factual, not conceptual or evaluative. Both arguments are logically valid. The key factual questions:

1. What is the probability of successful Series B given growth-focused Q2?
2. What is the probability of successful Series B given profitability-focused Q2?
3. What is the probability of survival without Series B given each approach?

If we assign:

• P(successful raise | growth focus) = p_g
• P(successful raise | profit focus) = p_p
• P(survival without raise | growth focus) = s_g
• P(survival without raise | profit focus) = s_p

Expected survival = P(raise) + P(no raise) * P(survive anyway)

For growth: p_g + (1 - p_g) * s_g For profit: p_p + (1 - p_p) * s_p

The "right" answer depends on these probability estimates.

Resolution Path

1. Gather evidence: Research recent Series B outcomes for companies with different profiles
2. Consult advisors: Get investor perspective on what they're funding now
3. Model scenarios: Explicitly estimate the probabilities above
4. Make the implicit explicit: If parties still disagree after sharing probability estimates, they have a genuine disagreement about the world that may require waiting for more evidence

Calculemus! The dispute is not about values but about predictions. Once we have shared probability estimates, the calculation can proceed.

Integration

This skill is part of the Gottfried Wilhelm Leibniz expert persona. Leibniz dreamed of a characteristica universalis and calculus ratiocinator that would reduce all disputes to calculation. While fully realized only in formal logic and mathematics, the aspiration - to make reasoning explicit and precise - applies broadly.

Example 2: Remote Work Policy Debate

Input: "Our leadership team can't agree on whether remote work 'works.' The conversation goes nowhere."

Output:

Calculemus Analysis

The Dispute

"Does remote work 'work' for our organization?"

Key Terms Requiring Definition

Explicit Argument Reconstruction

Party A's Argument (Remote Works):

P1: Employee surveys show high satisfaction with remote work
P2: Our KPIs have not declined since going remote
P3: We've retained talent who would have left for remote-friendly companies
P4: High satisfaction + stable KPIs + retention = it works
C: Therefore, remote work works for us

Party B's Argument (Remote Doesn't Work):

P1: Cross-team collaboration has declined (fewer spontaneous interactions)
P2: New employee onboarding is harder remotely
P3: Innovation metrics have declined since going remote
P4: We're measuring the wrong things; long-term effects are negative
C: Therefore, remote work doesn't work for us

Hidden Assumptions Identified

• Party A assumes current KPIs capture what matters
• Party A assumes satisfaction correlates with performance
• Party B assumes spontaneous interaction drives innovation
• Party B assumes correlation (remote + decline) implies causation
• Both parties assume binary outcome (works/doesn't work)

Location of Disagreement

The Calculation

The dispute is primarily definitional and evaluative, not factual. Both parties could be correct within their own definition of "works."

Resolution approach:

1. Agree on definition: What metrics would we use to evaluate "works"?
2. Weight the metrics: How much do we value satisfaction vs. innovation?
3. Measure: What do the agreed metrics actually show?
4. Decide: Given data and weights, does remote work "work" by our shared definition?

Resolution Path

1. Define success criteria together: List all outcomes that matter (productivity, satisfaction, retention, innovation, collaboration, onboarding)
2. Assign weights: Have leadership rank the relative importance of each
3. Gather data: Measure each outcome pre-remote and post-remote
4. Calculate: Apply weights to data; produce a single "works" score
5. Decide: If score is above threshold, remote "works" by the organization's own definition

Calculemus! The dispute cannot be resolved until "works" is defined and weighted. Once that's done, the answer becomes calculable.

Why these examples work: Both demonstrate that circular debates often stem from undefined terms or conflicting premises, not from irrationality. By making definitions explicit and locating disagreement precisely, previously intractable debates become tractable.