disjunctive syllogism

The third Idea is based on the disjunctive syllogism.

Taking together with is a disjunctive syllogism from which we can conclude .

If one is a dialetheist, it makes perfect sense that disjunctive syllogism should fail.

Though each of these principles has been challenged, the most popular approach among logicians is to reject disjunctive syllogism.

This is in reality the disjunctive syllogism.

Another approach is to reject disjunction introduction but keep disjunctive syllogism and transitivity.

The disjunctive syllogism rule may be written in sequent notation:

It is easy to check that this valuation constitutes a counterexample to both explosion and disjunctive syllogism.

Reason, according to ancient philosophers, did not obtain an idea of a perfect God or Ideal from the disjunctive syllogism.

Affirming the disjunct should not be confused with the valid argument known as the disjunctive syllogism.

One allows disjunction introduction, and one allows disjunctive syllogism.

Please observe that the disjunctive syllogism works whether 'or' is considered 'exclusive' or 'inclusive' disjunction.

Occurring in disjunctive syllogisms:

"Formal and Material Consequence, Disjunctive Syllogism and Gamma" in Argumentationstheorie.

Disjunctive syllogism holds in classical propositional logic and intuitionistic logic, but not in some paraconsistent logics.

In propositional logic, disjunctive syllogism (also known as disjunction elimination and or elimination, or abbreviated E), is a valid rule of inference.

Some examples of valid argument forms are modus ponens, modus tollens, disjunctive syllogism, hypothetical syllogism and dilemma.

Hypothetical syllogism is closely related and similar to disjunctive syllogism, in that it is also type of syllogism, and also the name of a rule of inference.

Proof-theoretic paraconsistent logics usually deny the validity of one of the steps necessary for deriving an explosion, typically including disjunctive syllogism, disjunction introduction, and reductio ad absurdum.

The reason this is called "disjunctive syllogism" is that, first, it is a syllogism, a three-step argument, and second, it contains a logical disjunction, which simply means an "or" statement.

In classical logic disjunctive syllogism (historically known as modus tollendo ponens) is a valid argument form which is a syllogism having a disjunctive statement for one of its premises.

Dialethesists solve this problem by rejecting the principle of explosion, and, along with it, at least one of the more basic principles that lead to it, e.g. disjunctive syllogism or transitivity of entailment, or disjunction introduction.

The logical determination of a conception is based upon a disjunctive syllogism, the major of which contains the logical division of the extent of a general conception, the minor limits this extent to a certain part, while the conclusion determines the conception by this part.

Unlike modus ponendo 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 (slightly devious) combination of reductio ad absurdum and disjunction elimination.