A strategic assumption allows you to draw a conclusion based on the existence or no-existence of a single interpretation.

– Tautology

Strategic assumption: show that the statement is not a tautology, so assume that the statement is false.

Outcomes:

a) If you find an interpretation under this assumption: the statement is not a tautology; it is either a contradiction or a contingent statement.

b) If you don’t find an interpretation under this assumption, it means you have disproved (proved against) the assumption, so the statement is a tautology.

– Contradiction

Strategic assumption: show that the statement is not a contradiction, so assume the statement is true.

Outcomes:

a) If you find an interpretation under this assumption: the statement is not a contradiction; it is either a tautology or a contingent statement.

b) If you don’t find an interpretation under this assumption, it means you have disproved (proved against) the assumption, so the statement is a contradiction.

– Contingent statement

Use the two assumption tests for tautology and contradiction. If you find an interpretation under the two assumptions, it means the statement is not a tautology nor is it a contradiction, so the statement must be a contingent statement.

– Semantic (in)equivalence

Strategic assumption: connect the statements with a <>operator and assume that the new statement is false.

Outcomes:

a) If you find an interpretation under this assumption: the statements are semantically inequivalent.

b) If you don’t find an interpretation under this assumption, it means you have disproved (proved against) the assumption, so the statements are semantically equivalent.

– (In)consistency

Strategic assumption: try to show that the set of statements is consistent so assume all the statements are true.

Outcomes:

a) If you find an interpretation under this assumption: the set of statements is consistent.

b) If you don’t find an interpretation under this assumption, the set of statements is inconsistent.

– (In)validity

Strategic assumption: try to show that the argument is invalid so assume all the premises are true and the conclusion is false.

Outcomes:

c) If you find an interpretation under this assumption, the argument is invalid.

d) If you don’t find an interpretation under this assumption, the argument is valid.

Note: I will update this post in the near future with some examples.