Consider this argument: 'All unicorns are blue; Starfire is a unicorn; therefore Starfire is blue.' Both premises are false. Is this argument valid?
ANo — a valid argument must have at least one true premise
BNo — a valid argument must reach a true conclusion
CYes — the conclusion follows necessarily from the premises given the logical form
DYes — but only if we treat the premises as hypothetically true
Validity is entirely about logical structure: can the premises be true while the conclusion is false? This argument has the form of universal instantiation (all Fs are G; x is an F; therefore x is G), which is a valid form. If the premises were true, the conclusion would necessarily be true. Whether the premises are actually true is irrelevant to validity — that's a question of soundness (valid + true premises). Option C captures this correctly. Option D is incorrect because validity is not a conditional claim about hypothetical premises — it is a structural claim that applies regardless.
Question 2 Multiple Choice
Which of the following arguments commits the fallacy of affirming the consequent?
AIf it snows, schools close. Schools are closed. Therefore it snowed.
BIf it snows, schools close. It is snowing. Therefore schools will close.
CIf it snows, schools close. Schools are open. Therefore it is not snowing.
DAll snow days are weekdays. Today is a snow day. Therefore today is a weekday.
Affirming the consequent takes the form: 'If P then Q; Q; therefore P.' Option A fits exactly: P = 'it snows,' Q = 'schools close.' The argument observes Q (schools closed) and concludes P (it snowed). This is invalid because schools might be closed for other reasons (a holiday, a power outage). Option B is valid modus ponens (observing P to conclude Q). Option C is valid modus tollens (observing not-Q to conclude not-P). Option D is valid universal instantiation. The key difference: modus ponens goes P→Q then P, while affirming the consequent goes P→Q then Q — a subtle but critical reversal.
Question 3 True / False
A valid argument guarantees that its conclusion is true.
TTrue
FFalse
Answer: False
Validity only guarantees that IF the premises are true, the conclusion must be true. If one or more premises are false, the conclusion of a valid argument may still be false. For example: 'All fish are mammals; salmon is a fish; therefore salmon is a mammal' is a valid argument with a false conclusion — because the first premise is false. What guarantees a true conclusion is soundness, which requires both validity and actually true premises. Confusing validity with soundness is the most common misunderstanding of what it means for an inference to 'work.'
Question 4 True / False
An argument's validity depends entirely on the logical form of its reasoning, not on whether the sentences in it happen to be about true or real things.
TTrue
FFalse
Answer: True
Validity is purely formal: it is a property of the argument's structure, abstracted from content. You can test an argument form by substituting obviously silly content into it — if the substitution can produce true premises and a false conclusion, the form is invalid. Modus ponens is valid not because of anything about rain or wet ground, but because 'If P then Q; P; therefore Q' is a form that cannot generate a false conclusion from true premises, no matter what you substitute for P and Q. This content-independence is what makes logical forms universally applicable across any domain.
Question 5 Short Answer
What is the difference between a valid argument and a sound argument, and why can a valid argument have a false conclusion?
Think about your answer, then reveal below.
Model answer: A valid argument is one where the conclusion necessarily follows from the premises — if the premises were true, the conclusion could not be false. A sound argument is valid AND has actually true premises. A valid argument can have a false conclusion if one or more of its premises are false, because validity only guarantees the truth-preserving nature of the inference, not the truth of the inputs.
Validity is a conditional guarantee: true premises in → true conclusion out. If you put false premises in, you can get a false conclusion out — through a perfectly valid inference. Soundness is the stronger property that requires both the structure (validity) and the inputs (true premises) to be correct. Recognizing this distinction matters because an argument can appear persuasive due to its valid structure even while containing false premises that contaminate the conclusion. Evaluating an argument requires checking both the structure (validity) and the truth of each premise.