Valid, True, and Convincing
The school magazine editorial argues: 'All students who attended the extra class passed the exam. Ravi passed the exam. Therefore Ravi attended the extra class.' The editor claims the argument is valid because all three statements are true. A Class XII logic group checks the records: 60 students attended the extra class and 45 passed; 40 students did not attend and 20 passed. There are 100 students in the batch. The editor says: 'The conclusion is true for Ravi, so the argument works.' The group must write a correction note for the magazine. The teacher asks them to distinguish truth, validity, and soundness and to avoid personal remarks.
1. Is the editorial argument valid? Identify its logical form and the fallacy.
Read the worked answer
It is invalid. Its form is: All A are B; R is B; therefore R is A. This is affirming the consequent. The premise says attending implies passing; it does not say passing implies attending. The editor confuses a true conclusion with a valid inference. Even if all three statements are true, the conclusion does not follow from the premises. Validity concerns the form, not the actual truth of the statements.
2. Construct a counterexample with the same form, true premises, and a false conclusion. Then use the numbers to explain why Ravi's passing does not establish that he attended.
Read the worked answer
Counterexample: All dogs are mammals; Tom is a mammal; therefore Tom is a dog. The premises are true and the conclusion is false if Tom is a cat. With the numbers: 65 students passed, 45 attenders and 20 non-attenders. Ravi's passing is compatible with his being among the 20 non-attenders. The data give a probability of about 45/65, roughly 69 per cent, that a passer attended; that is not a deductive proof. The editorial needs the extra premise 'All who passed attended' or direct evidence that Ravi attended.
3. Distinguish truth, validity, and soundness, and state what the editor would need to show for the conclusion to follow.
Read the worked answer
Truth is a property of propositions; validity is a property of argument form-if the premises are true, the conclusion cannot be false; soundness is validity plus true premises. The editorial's premises may be true, but the form is invalid, so the argument is not sound. To show the conclusion, the editor would need a valid form, for example: 'All who passed attended; Ravi passed; therefore Ravi attended,' and evidence for the first premise. Alternatively, the editor could present direct evidence of Ravi's attendance. The correction note should separate the statistical claim from the deductive one.