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Another valid form of argument is known as constructive dilemma or sometimes just 'dilemma'. It does not leave the user with one statement alone at the end of the argument, instead, it gives an option of two different statements. The first premise gives an option of two different statements.
A mixed hypothetical syllogism has two premises: one conditional statement and one statement that either affirms or denies the antecedent or consequent of that conditional statement. For example, If P, then Q. P. ∴ Q. In this example, the first premise is a conditional statement in which "P" is the antecedent and "Q" is the consequent.
A syllogism (Ancient Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. "Socrates" at the Louvre
A statement can be called valid, i.e. logical truth, in some systems of logic like in Modal logic if the statement is true in all interpretations. In Aristotelian logic statements are not valid per se. Validity refers to entire arguments. The same is true in propositional logic (statements can be true or false but not called valid or invalid).
However, if the latter two statements were switched, the syllogism would be valid: All students carry backpacks. My grandfather is a student. Therefore, my grandfather carries a backpack. In this case, the middle term is the class of students, and the first use clearly refers to 'all students'.
The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that began with the Ancient Greeks. The Ancient Greeks such as Aristotle identified four primary distinct types of categorical proposition and gave them standard forms (now often called A , E , I , and O ).
The name "disjunctive syllogism" derives from its being a syllogism, a three-step argument, and the use of a logical disjunction (any "or" statement.) For example, "P or Q" is a disjunction, where P and Q are called the statement's disjuncts. The rule makes it possible to eliminate a disjunction from a logical proof. It is the rule that
An argument is a series of true or false statements which lead to a true or false conclusion. [3] In the Prior Analytics, Aristotle identifies valid and invalid forms of arguments called syllogisms. A syllogism is an argument that consists of at least three sentences: at least two premises and a conclusion.