2.1.2. Useful Things.

D.1. Useful Things: 

I. Given a need, if something has such properties as to cause a transition from disturbance, need, to order, satiation, it is a Useful Thing.

II. From The Primacy of Need Satiation, it follows that certain things in useful quantities and with useful qualities must exist which can cause transition from state of Need to state of Satiation in humans, and these we may call Useful Things.

Axiomatic Derivation:

1. It is tautological, the immediate result of 2.1.0 and 2.1.1 is that such quantities and qualities must exist which can satiate human needs, for an absence of this thwarts needs, debilitates human existence, and that humans strive to gather, or even produce as we can observe, such means which can be useful for their satiation. 

2. Observation: It is implicit in the subsequent writing of Menger in the same chapter, and also it is understood by common observation, that Useful Things Must exist i.e. they do not necessarily exits in advance, and that provisions of nature are transformed into useful things. This is why I have rephrased from "are" used by Menger  in his book to "must" in this axiomatic derivation of the same concept.

Explanation:

E.1. Say if we are hungry and we have bread, this bread is our useful thing. Say we experience hunger, we have no bread but we have flour, water, fire and our labour to bake a bread. Now all of these things and actions are our useful things and actions given our two needs - Hunger, a disturbance in our body, and absence of bread, the means to gratify our hunger which must be prepared.

E.2. Since a useful thing (or action) causes a transition from state of disturbance, need, to state of order, satiation, it always exists in positive quantities, and with certain qualities which can establish the order now disturbed. If we conceive a bread of a certain kind, we also conceive a certain set of qualities of things used in its baking, and their certain quantities, certain actions, and certain order of processes etc. (See Need) 

E.3. Thus, a useful thing has qualities and quantities of certain sorts which can cause a transition from disturbance to order pre-conceived. Accordingly, in our example of baking bread if, for instance, heat of certain amount is absent we would have only a somewhat moist piece of flour - the order we call bread would be disturbed - and if the quality of flour is poor, quality of bread  too would be disturbed - desired order of quality would be disturbed.  

E.4. A distinction requires our attention; A useful thing can exist with or without our knowledge, or command of it. Say an exotic vegetable in market exists, whether or not we have the knowledge of how to cook it, it remains useful for our hunger. The same holds for things we cannot control or of which we have no command. For instance, if by laws of a nation a book which critically evaluates its culture is banned, it remains useful for gratifying intellectual curiosity regardless that we cannot buy it, and read it.

Reference: Menger, Carl (2004). Principles of Economics, Online edition, The Mises Institute, 2004. (Chapter 01 page 52)