Indirect Proof

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Related to Modus tollens: Disjunctive syllogism

indirect proof

[‚in·də‚rekt ′pr¨f]
(mathematics)
A proof of a proposition in which another theorem is first proven from which the given theorem follows.

Indirect Proof

 

the proof in logic of a proposition (thesis), based on the refutation (that is, proof of falsity, proof of negation) of certain other propositions that have certain relations with the thesis.

In what is referred to as partitive indirect proof the thesis is one of the terms of a disjunction (propositions of the form “A1, or A2, or …, or, An”) that is known to be true (or is assumed to have been previously proved); the proof itself consists of refuting all members AI of this disjunction except the one being proved. Apagogic indirect proof, or adversive proof, consists of refuting the negation of the thesis to be proved (”antithesis”). If one assumes the truth (or demonstrableness) of the principle of the excluded middle (“A or not-A”), then apagogic indirect proof may be considered to be a particular case of the partitive method.

References in periodicals archive ?
In this case, the rule of modus tollens (deduce notA from {notB, if A then B}) can be used.
The molecular representation of this pair of conditionals and the pair mentioned in the previous sentence is the same because of modus tollens. We need two molecules to represent conjunction between two elements, and three molecules to represent conjunction between three elements and so on for more elements.
[] No hay suficiente informacion para saberlo b) Planteamiento en Modus Tollens Suponga que la siguiente afirmacion es verdadera en su caso: -- Si estoy bajo fuerte estres creo que me voy a desmoronar.
He nowhere engages with the more technical aspects of formal logic as such, and the only principle repeatedly mentioned though not clearly stated, is modus tollens. No major logician is discussed.
It would appear that they used Popperian style deductive logic in conjunction with the modus tollens. If the class of strong hydrohalic acids contained no oxygen then it could not be the case that oxygen was the essential component of an acid, the observation of one black swan was decisive in this particular instance.
However, List and Pettit's key move, one which is of striking dialectical elegance, is to turn the apparent modus ponens on which this line of thought turns into a modus tollens. In effect, they argue that where we do have collectives whose attitudes are complete and consistent, they cannot be derived from the attitudes of the individuals who make up the collective by means of a well-behaved aggregation function.
One of the most robust results in conditional reasoning is the difference in difficulty of the two valid inferences: Modus Ponens (MP) and Modus Tollens (MT).
The classical schema that describes the HD model can be understood with reference to the modus tollens of classical logic.