Passing a generic function as parameter
Note: This answer is based on Java 8 and newer. This does not apply to Java 7, as Java 7 does not support Lambda
For starters, your test function is wrong in multiple places:
boolean test(function someSortFunction){//This is not how you pass functions
    int n; //this has to be initialized
    for (int i=0; i&lt;=n ; i++) {//Depending on how n is used, you may have to use &lt; instead of &lt;=
        int[] A = generateArray()//Missing semi-colon
        if (isSorted(someSortFunction(A)) = false) {//Comparing is done with ==, not =
            return false;
        }
    }
    return true;
}

In order to pass a function, you can either use Consumer&lt;Void&gt;, Supplier&lt;Void&gt;, Predicate&lt;Void&gt; or Function&lt;Void, Void&gt; (don't use Void as the type if you have return values)
Supplier defines return type, Consumer defines input type, and function both. Meaning:

Use Predicate when you have a boolean return type with arguments
Use Supplier when you have a return type
Use Consumer when you have an argument
Use Function when you have both an argument and a return value

Since you have both arguments and return types, use Function. The first argument you give it is the argument it receives, and the second is the return type. For an instance, in your case, this would be:
boolean test(Function&lt;int[], int[]&gt; someFunction) 

Using Function requires calling apply to execute the method:
int[] res = someFunction.apply(input);

Before I move on, I'd like to take a second to mention naming conventions. In Java, class names always start with an upper case letter. Instances and functions start with a lower case letter. So your classes would be:
public class ManyFunctions {...}
public class MainClass {...}

Passing methods are not done using someClass.someFunction. In your case, since you are not using static methods, you need to create an instance:
ManyFunctions functions = new ManyFunctions();

now, you pass the functions:
test(functions::mergeSort);

if you make the methods static, you can just skip the instance and use the class name directly:
test(ManyFunctions::mergeSort);

So your class would be:
class MainClass{
    public static void main(String[] args){
        ManyFunctions manyFunctions = new ManyFunctions();
        test(manyFunctions::mergeSort);//Notice the missing &quot;()&quot; and arguments
        test(manyFunctions::otherSort);

    }

    boolean test(Function&lt;int[], int[]&gt; someSortFunction){
        int n = 10;//THIS HAS TO BE INITIALIZED! Otherwise, it won't compile
        for (int i=0; i&lt;=n ; i++) {
            int[] A = generateArray();
            if (isSorted(someSortFunction.apply(A)) == false) {//comparing is done with ==
                return false;
            }
         }
         return true;
    }
}//Don't know if it was a copy-paste problem or not, but you had a missing bracket