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 ?
Para estos factores el porcentaje de Modus Tollens fue mayor en el grupo de participantes con altas puntuaciones.
I] [flecha diestra] +A) [flecha diestra] A, y como se tiene ~ A, por modus tollens y negacion del condicional se infiere [A.
Lo mismo que con el modus tollens, aqui se aplicaria el silogismo disyuntivo.
As regards the two forms of valid inference, both Brazilian and English children were more accurate with problems involving Modus Ponens than those involving Modus Tollens, replicating results obtained by Dias and Harris, 1988b, Ennis (1976), Evans and Lynch (1973), and Kodroff and Roberge (1975).
Hence, the valid inference Modus Tollens requires more reasoning steps, and so the rule theories predict that it is a more difficult inference.
First, we wanted to verify whether there is task set reconfiguration (Cost of Inference Switch or CIS) between Modus Ponens and Modus Tollens (Experiments 1 and 2).
A [flecha diestra] B R [flecha diestra] Negacion del condicional AiRd [flecha diestra] Negacion del condicional AiA [flecha diestra] Modus Ponens RdA [flecha diestra] Modus Tollens Ri [flecha diestra] Negacion del antecedente Ad [flecha diestra] Afirmacion del consecuente AiAd [flecha A, B [?
Whilst the valid inference modus ponens is almost universally made by untrained reasoners, modus tollens is often withheld (MT rates vary across studies between around 40 per cent and 80 per cent, with a median of about 60 per cent; see Evans et al.
Popper's solution to this formulation of the problem of induction is bold in its simplicity: scientific method is deductive, since it uses modus tollens to refute universal statements.
De acuerdo con una interpretacion de implicacion material del condicional, solo las inferencias Modus Ponens (MP) y Modus Tollens (MT) son inferencias validas, mientras que las inferencias Negacion del Antecedente (NA) y Afirmacion del Consecuente (AC), son inferencias no validas.
The results he achieves might even be employed as parts of a modus tollens against strong scientific realism: if such a realism is assumed, the arguments Melnyk offers do show that RP is plausible; therefore, in order to reject physicalism, the realism grounding it should be disputed.
Logically, two of these arguments are valid, modus ponens (given p and If p then q conclude q) and modus tollens (given not-q and If p then q conclude not-p).