What rules of inference are used in this argument? "Noman is an island. Manhattan is an island. Therefore, Man-hattan is not a man."

The rules of inference are;

1. Universal Instantiation

2. Double negation law, or forming the Contra-positive and

3. Modulus tollens

Explanation:

In universal instantiation, an inference is made of the truth of each member of a class, and this is then used to establish the truth about a particular member off the class. For all of a class q, if the class q, is a girl, then the class q, is not a boy. Applying it to the example, If Manhattan is a man, then Manhattan is not an Island.  We now form the contra-positive thus; If Manhattan is an island, then Manhattan is not a man.

Modus tollens is then applied in the last sentence to show that the conditional statement was accepted, the consequent statement was not true, and so the negative of the antecedent can be inferred. So, we conclude that Manhattan is not a man.

an expression designed to call something to mind without mentioning it explicitly; an indirect or passing reference.