Question about validity of Modus Tollens vs. Denying the Antecedent


What makes denying the antecedent invalid?

Denying the antecedent is invalid because it involves making unjustified conclusions from a conditional (or if-then) statement. A conditional statement claims that if X is true, then Y is true as well. Denying the antecedent occurs when someone concludes from such a conditional that if X is false, then Y is false too.

Is denying the antecedent the same as modus tollens?

While modus tollens denies the consequent of a conditional statement, denying the antecedent denies the antecedent of a conditional statement. Modus tollens (valid) Denying the antecedent (invalid) If p, then q.

Is modus tollens valid or invalid?

Second, modus ponens and modus tollens are universally regarded as valid forms of argument. A valid argument is one in which the premises support the conclusion completely.

Why is modus tollens always valid?

Modus tollens is a valid argument form. Because the form is deductive and has two premises and a conclusion, modus tollens is an example of a syllogism. (A syllogism is any deductive argument with two premises and a conclusion.) The Latin phrase ‘modus tollens’, translated literally, means ‘mode of denying’.

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What is the difference between denying the antecedent and affirming the consequent?

Affirming the Consequent: “If A is true, then B is true. B is true. Therefore, A is true.” Denying the Antecedent: “If A is true, then B is true.

Why is denying the consequent valid?

Like modus ponens, modus tollens is a valid argument form because the truth of the premises guarantees the truth of the conclusion; however, like affirming the consequent, denying the antecedent is an invalid argument form because the truth of the premises does not guarantee the truth of the conclusion.

Can modus tollens have false premises?

Latin for “method of denying.” A rule of inference drawn from the combination of modus ponens and the contrapositive. If q is false, and if p implies q (p q), then p is also false. An error in reasoning.

Modus Ponens Modus Tollens
Therefore, I will wear my sunglasses. Therefore, it is not bright and sunny today.

What is the rule of modus tollens?

Modus tollens 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.

Is denying the consequent valid or invalid?

The opposite statement, denying the consequent, is a valid form of argument. Denying the consequent can be considered a form of abductive reasoning.

Can modus tollens have false premises and true conclusion?

FALSE. A valid argument can have false premises; and it can have a false conclusion. But if a valid argument has all true premises, then it must have a true conclusion.

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Is modus tollens a valid argument form?

Modus tollens is a valid argument form. Affirming the consequent is a valid argument form. An argument of this form—If p, then q; p; therefore, q—is called modus ponens. An argument of this form—If p, then q; not p; therefore, not q—is called modus tollens.

Why is this fallacy called denying the antecedent?

The name denying the antecedent derives from the premise “not P”, which denies the “if” clause of the conditional premise. One way to demonstrate the invalidity of this argument form is with an example that has true premises but an obviously false conclusion.

Is denying the disjunct valid?

To deny a disjunct and affirm the other disjunct as a conclusion is a validating form of argument in propositional logic which is called “disjunctive syllogism”―see the Similar Validating Forms, above.

Can an argument have more than one disjunctive premise?

Can an argument have more than one disjunctive premise? a. Yes, there is no limit to the number of disjunctive premises.

Is modus ponens deductive or inductive?

deductive argument

In propositional logic, modus ponens (/ˈmoʊdəs ˈpoʊnɛnz/; MP), also known as modus ponendo ponens (Latin for “method of putting by placing”) or implication elimination or affirming the antecedent, is a deductive argument form and rule of inference.

Can the same causal factor be both a necessary and a sufficient condition of the effect?

Can the same causal factor be both a necessary and a sufficient condition of the effect? Yes, because some conditions are both necessary and sufficient.