Final answer:
A counterexample for the argument 'No man has wings, and no creature with wings has gills, so no man has gills' can be 'No cat has gills, and no creature with gills has feathers, so no cat has feathers.' While the premises are true, the conclusion is false, demonstrating that the form of the argument could lead to invalid conclusions.
Step-by-step explanation:
To address the student's question regarding a counterexample for the argument 'No man has wings, and no creature with wings has gills, so no man has gills,' we need to find an argument with the same form, where premises are known to be true but the conclusion is false. A counterexample works by demonstrating the invalidity of the original argument. With the structure of the given argument, we must reflect on the logical connections among the premises and the conclusion.
Let's analyze a potential counterexample. Take the following argument: 'No cat has gills, and no creature with gills has feathers, so no cat has feathers.' The premises of this counterexample are true: Cats indeed do not have gills, and fish, which have gills, do not have feathers. However, the conclusion that no cat has feathers is demonstrably false, as there could hypothetically be a mutation or an exotic breed that has feather-like fur. This illustrates that the logical form of the argument is flawed because it is possible to have true premises yet arrive at a false conclusion.
This method of critical thinking is essential in evaluating the validity of deductive arguments. By presenting such a counterexample, we show that the original argument does not have a necessary logical connection among its premises that guarantees the truth of its conclusion. Therefore, it's invalid.
Please note, the mentioned counterexample is purely hypothetical, as all known cat species do not possess feathers. The essence of creating such counterexamples lies in their ability to logically challenge the structure of arguments, rather than to reflect biological facts.