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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 hypothesis of Andreas Cellarius, showing the planetary motions in eccentric and epicyclical orbits. A hypothesis (pl.: hypotheses) is a proposed explanation for a phenomenon. A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess or ...
Statistical hypothesis: A statement about the parameters describing a population (not a sample). Test statistic: A value calculated from a sample without any unknown parameters, often to summarize the sample for comparison purposes.
For example, even though material conditionals with false antecedents are vacuously true, the natural language statement "If 8 is odd, then 3 is prime" is typically judged false. Similarly, any material conditional with a true consequent is itself true, but speakers typically reject sentences such as "If I have a penny in my pocket, then Paris ...
An antecedent is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause. In some contexts the antecedent is called the protasis. [1] Examples: If , then . This is a nonlogical formulation of a hypothetical proposition. In this case, the antecedent is P, and the consequent is Q.
If a statement's negation is false, then the statement is true (and vice versa). If a statement (or its contrapositive) and the inverse (or the converse) are both true or both false, then it is known as a logical biconditional .
Modus tollens is a mixed hypothetical syllogism that takes the form of "If P, then Q. Not Q. Therefore, not P." It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from P implies Q to the negation of Q implies the negation of P is a valid argument.
If P, then Q. P. Therefore, Q. The first premise is a conditional ("if–then") claim, namely that P implies Q. The second premise is an assertion that P, the antecedent of the conditional claim, is the case. From these two premises it can be logically concluded that Q, the consequent of the conditional claim, must be the case as well.