Deductive arguments have FORMAL structure. It is only the formal structure that CAN be valid. Two INVALID forms of argument are:
If P, then Q, Not P, so Not Q (fallacy of denying the antecedent; fallacy because Negating the consequent does not follow from Negating the antecedent)
If P, then Q, Q, so, P (fallacy of affirming the consequent; fallacy because antecedent does not follow from affirming the consequent)
Decide whether the following arguments are valid or invalid:
If the moon is made of green cheese, then there are mice on the moon. The moon is made of green cheese. So, there are mice on the moon.
[ Choose ] invalid fallacy of denying the antecedent invalid fallacy of affirming the consequent valid modus ponens valid modus tollens
If it rains, then the sidewalk will be wet. It did not rain. So, the sidewalk is not wet.
[ Choose ] invalid fallacy of denying the antecedent invalid fallacy of affirming the consequent valid modus ponens valid modus tollens
If our team scores 20 touchdowns in their next game, then they will win. Our team did not score 20 touchdowns in their next game. So, our team will not win.
[ Choose ] invalid fallacy of denying the antecedent invalid fallacy of affirming the consequent valid modus ponens valid modus tollens
If I have a key, then I can open the door. I can open the door. So, I have a key.
[ Choose ] invalid fallacy of denying the antecedent invalid fallacy of affirming the consequent valid modus ponens valid modus tollens
If the sun is shining, then we'll see the enemy coming. The sun is not shining. So, we will not see the enemy coming.
[ Choose ] invalid fallacy of denying the antecedent invalid fallacy of affirming the consequent valid modus ponens valid modus tollens
If the sun is shining, then we'll see the enemy coming. The sun is shining. So, we'll see the enemy coming.
[ Choose ] invalid fallacy of denying the antecedent invalid fallacy of affirming the consequent valid modus ponens valid modus tollens
If our team scores 20 touchdowns in their next game, then they will win. Our team did not win. So, our team did not score 20 touchdowns.
[ Choose ] invalid fallacy of denying the antecedent invalid fallacy of affirming the consequent valid modus ponens valid modus tollens
If the ice sheet in Antarctica melts, then sea level will rise an average of 20 feet. Sea levels have risen an average of 20 feet over the past million years. So, the ice sheet in Antarctic must have melted.
[ Choose ] invalid fallacy of denying the antecedent invalid fallacy of affirming the consequent valid modus ponens valid modus tollens
If P, then Q. Affirm Q. So, P.
[ Choose ] invalid fallacy of denying the antecedent invalid fallacy of affirming the consequent valid modus ponens valid modus tollens
If P, then Q. Deny P. So, Deny Q.
[ Choose ] invalid fallacy of denying the antecedent invalid fallacy of affirming the consequent valid modus ponens valid modus tollens
If P, then Q. P. So. Q.
[ Choose ] invalid fallacy of denying the antecedent invalid fallacy of affirming the consequent valid modus ponens valid modus tollens
If P, then Q. Deny Q. So, Deny P.
If the moon is made of green cheese, then there are mice on the moon. The moon is made of green cheese. So, there are mice on the moon.
This is a If P, then Q, P, so, Q statement. In this statement. This is affriming the antecedent statement that follows a valid inferences even if the premises are false. Hence, this is modes ponens.
Answer. Valid modes ponens.
If it rains, then the sidewalk will be wet. It did not rain. So, the sidewalk is not wet.
This is a " if P, then Q. Not P, the not Q. This is denying the consequent statement an invalid form of drawing inferences. Hence, this is a invalid fallacy of affirming the consequent.
Answer . invalid fallacy of denying the consequent
If our team scores 20 touchdowns in their next game, then they will win. Our team did not score 20 touchdowns in their next game. So, our team will not win.
This is a " If P, then Q. Not P, then not Q" statement, that is denying the consequent fallacy.
Answer. invalid fallacy of denying the consequent
If I have a key, then I can open the door. I can open the door. So, I have a key.
This is "If P, then Q, Q, so, P", that is affriming the consequent, a fallacy.
Answer. invalid fallacy of affirming the consequent
If the sun is shining, then we'll see the enemy coming. The sun is not shining. So, we will not see the enemy coming.
Answer. invalid fallacy of denying the consequent.
If our team scores 20 touchdowns in their next game, then they will win. Our team did not win. So, our team did not score 20 touchdowns.
Answer. Valid modus tollens
If the ice sheet in Antarctica melts, then sea level will rise an average of 20 feet. Sea levels have risen an average of 20 feet over the past million years. So, the ice sheet in Antarctic must have melted.
Answer. invalid fallacy of affirming the consequent
If P, then Q. Affirm Q. So, P.
Answer. invalid fallacy of affirming the consequent
If P, then Q. Deny P. So, Deny Q.
Answer. invalid fallacy of denying the consequent.
If P, then Q. P. So, Q.
Answer. Valid modus ponens.
If P, then Q. Deny Q. So, Deny P
Answer. Valid modus tollens.
Deductive arguments have FORMAL structure. It is only the formal structure that CAN be valid. Two INVALID...
1. Either the Yankees will win the American League pennant or their manager will get fired. 2. The Yankees will not win the American League pennant. ---- 3. Therefore, the manager will get fired. invalid valid denying the antecedent affirming the consequent modus ponens modus tollens disjunctive syllogism reductio ad absurdum do not know if it is sound or unsound