Sufficient Assumption (SA) Cheat Sheet

SUFFICIENT ASSUMPTION (SA) CHEAT SHEET

THE ONLY 3 SA TYPES

• 1. Conditional Chain SA
• 2. Categorical SA
• 3. Multi-Branch Conditional SA

1. CONDITIONAL CHAIN SA

• Definition: Involves all conditional logic, characterized by terms such as “if,” “only if,” “unless,” and “requires.”

• Structure: Premises form ONE chain, and the missing assumption serves to complete this chain.

• Method:

  • Diagram all premises as arrows.
  • Combine the identified premises into one coherent chain.
  • Diagram the conclusion separately.
  • If the conclusion appears in a backward form, flip it to a forward form prior to further analysis.
  • Circle the following after diagramming:
  • Last term of the premise chain
  • Last term of the conclusion
  • The missing assumption can be expressed as:
    $(premise<em>{end} \rightarrow conclusion</em>{end})$

• Example:

  • Premise Chain:
  • unfamiliarcmds → expensivetraining → no_purchase
  • Conclusion Forward:
  • unfamiliarcmds → notsuccessful
  • Missing assumption:
  • $(no<em>purchase \rightarrow not</em>successful)$

2. CATEGORICAL SA

• Definition: Utilizes categories such as “all,” “none,” and “every.” The missing link is what connects these categories.

• Method:

  • Build a chain of categories.
  • Identify the needed category that connects the premises and the conclusion.
  • Supply this missing category link.

• Example:

  • Categories:
  • athlete → muscular → fit
  • Conclusion:
  • athlete → disciplined
  • Missing assumption:
  • $(fit \rightarrow disciplined)$

3. MULTI-BRANCH CONDITIONAL SA

• Definition: Involves multiple conditional arrows that do NOT connect in a single linear chain.

• Method:

  • Diagram all branches separately.
  • Analyze the sufficient side of the conclusion to find the appropriate branch starting with the noted term.
  • Circle the last term of this branch.
  • Circle the necessary term that appears in the conclusion.
  • The missing assumption can be formulated as:
    $(branch<em>{end} \rightarrow conclusion</em>{end})$

• Example:

  • Branches:
  • expand → profit
  • strong_sales → reach
  • succeed → new_customers
  • Conclusion:
  • expand → succeed
  • Missing assumption:
  • $(profit \rightarrow succeed)$

BACKWARD (CONTRAPOSITIVE) CONCLUSIONS

• Identification Criteria: The conclusion can be considered backward if:
  1. It contains a negation that was not used earlier in the argument.
  2. It moves in the opposite direction of the established premises.
• Procedure: Flip the backward conclusion to its forward form before attempting to solve.
• Example:
  • Backward Conclusion:
  • successful → not_UC
  • Forward Form:
  • UC → not_successful

UNIVERSAL HYPERFOCUS RULE

• Circle ONLY the following terms:
  1. Last term reached by the premises, starting from the conclusion.
  2. Necessary term of the conclusion.
• Missing assumption can then be expressed as:
  $(last erm<em>{premise} \rightarrow last erm</em>{conclusion})$

INSTANT IDENTIFICATION TABLE

• If the phrasing includes:
  • “If,” “only if,” “unless,” “requires,” identify this as Conditional Chain SA.
  • “All,” “none,” “every,” “any,” “no,” classify as Categorical SA.
  • Discovering multiple arrows that do not connect signifies Multi-Branch Conditional SA.
  • Encountering a backward or negated conclusion necessitates flipping to derive a Conditional Chain SA.