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In classical logic, disjunctive syllogism [1] [2] (historically known as modus tollendo ponens (MTP), [3] Latin for "mode that affirms by denying") [4] is a valid argument form which is a syllogism having a disjunctive statement for one of its premises. [5] [6] An example in English: I will choose soup or I will choose salad. I will not choose ...
Disjunctive syllogism (sometimes abbreviated DS) has one of the same characteristics as modus tollens in that it contains a premise, then in a second premise it denies a statement, leading to the conclusion. In Disjunctive Syllogism, the first premise establishes two options.
A syllogism takes the form (note: M – Middle, S – subject, P – predicate.): Major premise: All M are P. Minor premise: All S are M. Conclusion/Consequent: All S are P. The premises and conclusion of a syllogism can be any of four types, which are labeled by letters [14] as follows. The meaning of the letters is given by the table:
Modus ponens is a mixed hypothetical syllogism and is closely related to another valid form of argument, modus tollens. Both have apparently similar but invalid forms: affirming the consequent and denying the antecedent. Constructive dilemma is the disjunctive version of modus ponens. The history of modus ponens goes back to antiquity. [4]
The form of a modus tollens argument is a mixed hypothetical syllogism, with two premises and a conclusion: . If P, then Q. Not Q. Therefore, not P.. The first premise is a conditional ("if-then") claim, such as P implies Q.
Another approach is to reject disjunctive syllogism. From the perspective of dialetheism, it makes perfect sense that disjunctive syllogism should fail. The idea behind this syllogism is that, if ¬ A, then A is excluded and B can be inferred from A ∨ B. However, if A may hold as well as ¬A, then the argument for the inference is weakened.
disjunctive syllogism A form of deductive reasoning that concludes one disjunct must be false if the other is true and a disjunction is given (if P ∨ Q {\displaystyle P\lor Q} and not P {\displaystyle P} , then Q {\displaystyle Q} ).
The source of the fallacy is found in the disjunctive claim in the third premise, i.e. and respectively. The following is an example of a false dilemma with the simple constructive form : (1) "If you tell the truth, you force your friend into a social tragedy; and therefore, are an immoral person".