“Modus Tollens” Reasoning

“Modus Tollens” is the classical name given to a valid deductive inference of the form:

PREMISE 1: IF proposition P is true, THEN proposition Q is true.
PREMISE 2: Proposition Q is NOT true.
CONCLUSION: Therefore, proposition P is NOT true.

The phrase “Modus Tollens” may be translated from the Latin as “the method of taking away or denying.” (I.M. Copi & C. Cohen, Introduction to Logic, p. 374 (10th ed. 1998).) If the conditional (Premise 1) is true, and the consequent of that conditional (proposition Q) is false (Premise 2), then the antecedent of the conditional (proposition P) must also be false (Conclusion).

But when we model the evidence assessment of a factfinder using our many-valued logic of plausibility, we generalize this argument form to accept degrees of plausibility, not just the “true / false” dichotomy of classical logic.

Legal factfinders seldom have the luxury of deciding which evidentiary assertions in the record are true and which ones false. Rather, they assign degrees of plausibility to such assertions. For example, many factfinders probably use something approaching the seven values of plausibility encoded in the Legal Apprentice™ software: “highly plausible / very plausible / slightly plausible / undecided / slightly implausible / very implausible / highly implausible.” We generalize the “Modus Ponens” structure to work in such a logical system, however: so long as the two premises are plausible to any degree, then the Conclusion is also plausible, but the degree of plausibility of the Conclusion can never be higher than that of the weaker premise. That is, the inference is plausible, but it is only as plausible as its weaker premise.

For an example of “Modus Tollens” in a Vaccine Act decision, go to an illustration from the Howard decision, where you will find clues for analyzing the text, as well as a sample logic tree and a logic diagram for the example:

Image of Modus Ponens Diagram

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