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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.
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. The second premise is an assertion that Q, the consequent of the conditional claim, is not the case.
Of the many and varied argument forms that can possibly be constructed, only very few are valid argument forms. In order to evaluate these forms, statements are put into logical form . Logical form replaces any sentences or ideas with letters to remove any bias from content and allow one to evaluate the argument without any bias due to its ...
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]
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.
Common deductive argument forms are hypothetical syllogism, categorical syllogism, argument by definition, argument based on mathematics, argument from definition. The most reliable forms of logic are modus ponens, modus tollens, and chain arguments because if the premises of the argument are true, then the conclusion necessarily follows. [5]
Examples: The column-14 operator (OR), shows Addition rule : when p =T (the hypothesis selects the first two lines of the table), we see (at column-14) that p ∨ q =T. We can see also that, with the same premise, another conclusions are valid: columns 12, 14 and 15 are T.
hypothetical syllogism A form of logical argument consisting of three propositions: two conditional statements and a conclusion that infers a relationship between the antecedent of the first conditional and the consequent of the second.