What is modus tollens?

Modus tollens (Latin for ‘mode that denies’) is a valid form of logical deduction. It is a conditional form (if-then).

Like in modus ponens, we have an antecedent (p) or condition, and we have a consequent (q) or result. If the antecedent is true, then we assert that the consequent logically follows. However, under MT we deny (or negate) the consequent (recall that under MP we affirm the antecedent). It takes the form:

Premise 1:       If p then q

Premise 2:       Not-q

Conclusion:     Therefore, not-p

For example,

          If it rains then the pavement will be wet.

          The pavement is not wet.

          Therefore, it has not rained.

This is formally valid; that is, if the premises are true then the conclusion necessarily follows.

Contrast this with the following argument which is invalid:

           If it rains then the pavement will be wet.

          The pavement is wet.

          Therefore, it has rained.

Can you work out why this argument is invalid?

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