![]() But this generalization, unfortunately, is not true. ![]() The above argument about Casey is valid, but it’s not sound. First, it must be valid second, it must have true premises. For an argument to be sound, it must meet two requirements. But not every argument of this form is sound. Premise 2: Casey does not have four legs.Ĭonclusion: Therefore, Casey is not a dog.Īny argument of this form is valid. Premise 1: If Casey is a dog, then Casey has four legs. For example, suppose A = ‘Casey is a dog’ and B = ‘Casey has four legs.’ We can substitute as follows, for a valid argument: Shown schematically, this form of argument looks like this:Īrguments of this form are produced by substituting statements in English for A and for B. The Latin phrase ‘ modus tollens‘, translated literally, means ‘mode of denying’. (A syllogism is any deductive argument with two premises and a conclusion.) Because the form is deductive and has two premises and a conclusion, modus tollens is an example of a syllogism. Unlike modus ponens and modus ponendo tollens, with which it should not be confused, disjunctive syllogism is often not made an explicit rule or axiom of logical systems, as the above arguments can be proven with a combination of reductio ad absurdum and disjunction elimination.ĭisjunctive syllogism holds in classical propositional logic and intuitionistic logic, but not in some paraconsistent logics.Modus tollens is a valid argument form. With the inclusive meaning, one could draw no conclusion from the first two premises of that argument. However, only in the exclusive meaning is the following form valid: Is valid and indifferent between both meanings. The concept of "or" as it exists in the English language is often ambiguous between these two meanings, but the difference is pivotal in evaluating disjunctive arguments.
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