Critical Reasoning - Examples

An argument with all true premises and a true conclusion, might or might not be deductively valid. Example 1: deductively valid All tigers are felines. All felines are mammals. Therefore all tigers are mammals. Example 2: deductively invalid If I'm over 4' tall, then I'm over 3' tall. I'm over 3' tall. So all I'm over 4' tall . Categorical statement: assertion that some, all, or no members of a certain kind (category) of thing have a certain characteristic The structure of Example 1: All A are B. All B are C. Therefore all A are C. The structure of Example 2 (and 4 and 8): If A then B. B. Therefore A. (fallacy: affirming the consequent) An argument with at least one false premise and a true conclusion might or might not be deductively valid. Example 3: deductively valid If I'm over 3' tall, I'm over 4' tall. I'm over 3' tall. Therefore I'm over 4' tall. Example 4: deductively invalid If I'm over 4' tall then I'm over 8' tall. I'm over 8' tall. So I'm over 4' tall. Example 5: deductively invalid All mammals are animals. All animals are tigers. So all tigers are mammals. Conditional statement: If ___ then … Antecedent: the 'if' part of a conditional. Consequent: the 'then' part of a conditional An argument with at least one false premise and a false conclusion might or might not be deductively valid Example 6: deductively valid All dogs are animals with wings. All animals with wings can fly. So all dogs can fly. Example 7: deductively valid If I am over 9' tall, I'm over 8' tall. I'm over 9' tall. So I'm over 8' tall. Example 8: deductively invalid If I am over 9' tall, I'm over 8' tall. I'm over 8' tall. So I'm over 9' tall. Example 9: deductively invalid All tigers are animals. All animals are snakes. So all snakes are tigers. BUT NO ARGUMENT WITH ALL TRUE PREMISES AND A FALSE CONCLUSION IS DEDUCIVELY VALID. The structure of Example 3 (and 7): If A then B. A. Therefore B. (Modus ponens) Modus ponens is truth-preserving. If you apply this pattern to T premises, the conclusion you thereby infer will be T. Any argument with this structure is valid just because of its structure. Affirming the consequent is not truthpreserving. The structure does NOT GUARANTEE that the conclusion you get by applying this pattern to T premises must be T. The structure of Example 5: All A are B. All B are C. Therefore all A are C. Unlike the structure of example 1, this is an invalid categorical structure, because it is not a truth-preserving structure. NEXT PAGE FOR INDUCTIVE STRENGTH AND WEAKNESS Page 1 of 2 A argument with true premises and a true conclusion might or might not be inductively strong. Example 10: inductively strong Almost all college professors are over 30. I am a college professor. So I am (probably) over 30. Example 11: inductively weak Flipper lives in water. Flipper is a dolphin. Dolphins are mammals. So all mammals live in water. An argument with all true premises and a false conclusion might or might not be inductively strong. Example 16: inductively strong The vast majority of adult females raised in the US are over 5'3". I am an adult female raised in the US. So I'm over 5'3". Example 17: inductively weak I am under 5'2". I am an adult female raised in the US. So most adult females raised in the US are under 5'2". An argument with at least one false premise and a true conclusion might or might not be inductively strong. Example 12: inductively strong The vast majority of women living in the US are college professors. I am a woman living in the US. So I'm a college professor. Example 13: inductively weak I have never taught a philosophy class. So most CSUN faculty have never taught a philosophy class. REMEMBER: An argument with all true premises and a false conclusion might or might not be INDUCTIVELY STRONG BUT an argument with all true premises and a false conclusion CANNOT BE DEDUCTIVELY VALID. An argument with at least one false premise and a false conclusion might or might not be inductively strong. Example 14: inductively strong More than 95% of all CSUN students are less than one foot tall. So it is likely that most students in this class are less than one foot tall. Example 15: inductively weak I own 10 cars. So most people own 10 cars. Also, an argument with whose premises and conclusion have any other combination of truth values (including all true premises and a true conclusion) might or might not be DEDUCTIVELY VALID (and likewise for INDUCTIVELY STRONG). An argument structure is a VALID STRUCTURE if, and only if, it is truthpreserving. Page 2 of 2