Ramified Type Theory: Determining Orders/Levels I understand how to determine order in unramified type theory. But, how do you determine order and level in ramified type theory (per Church's interpretation of Russell)? The example given in the Routledge Encyclopedia (Napoleon having the properties of being a general) is unclear to me on how to make the move from having all of the first-order/first-level properties of a general to having a "first-order property of level two." In trying to interpret this entry, it seems as if the class of generals would be of second-order with the second-level property of being a general. And, an individual (first-order) could have the individual properties that make someone a general (first-level) and if all are present than they would have the property of being a general (second-level). Is this the distinction? Levels are for properties and orders are for sets? If I am correct in my interpretation, please let me know as I need to then figure out how ramified type theory would apply in the case of the set of all exponential functions? My guess is that the set of all exponential functions is second-order with the property of being an exponential function (second-level). But, what would be the first level properties in this case?
 A: 
Levels are for properties and orders are for sets? 

No. You can take it all to be about properties. 
One thing we can ask about properties is what they are properties of. The type-1 properties being brave, being wise,  having all the properties of a great general (for example) are properties had by some individual objects, including Napoleon perhaps; the type-2 property being instantiated by exactly three objects (for example) is a property had by some type-1 properties; there are type-3 properties had by type-2 properties, and so on. [I say "type" so as not to tangle with the vocabulary of orders and levels which I'm afraid is not consistently used across all communities -- but also because these are roughly the types of simple type theory.]
Now fix on a particular level(!) in this hierarchy of properties. For simplicity, take type-1 properties (i.e. properties of individuals). We now more finely divide these type-1 properties -- so yes, we are still talking about properties. 
There are, shall we say, basic type-1 properties of individuals -- like being wise, being brave, being a good leader. And then there are shall we say fancy  properties (but still type-1 properties of individuals) that are defined by quantifying over these basic properties -- like having all the basic properties shared by Alexander, Ceasar, Napoleon, Montgomery ... (or having all the basic properties of a great general). And then we can define superfancy properties of individuals defined by quantifying over those latter sort of fancy properties. And so it goes, splitting the type-1 properties into the basic, the fancy, the super-fancy, the super-duper-fancy ... [
It is easy to see why we might think we need to clearly demarcate properties into types (just as we distinguish functions which take objects as arguments from function[al]s which take functions as arguments, and so on). But why -- within a type -- might we suppose that we need to go for a further division into basic, fancy, super-fancy, etc. ? You might at this point find http://plato.stanford.edu/entries/type-theory/ helpful.
