D.1. The Primacy of One-to-Many Relations:
I. On a Causal Order of Goods, it is necessary that everything has more than one causes, and it is possible that anything has more than one effects.
II. It is necessary that each need, or disturbance, is satiated by more than one things of good character, and it is possible that each Useful Thing has more than one uses, or serves more than one needs.
Axiomatic Derivation:
1. A Minimum Case of First Order Goods:
1.1. Any human need can be satiated only if it exists, there are useful things, their knowledge and control resides with humans.
1.2. The control of a useful thing implies a useful human action.
1.3. In absence of useful human actions which enable command, or control or the capacity to control (See 6 in Goods), a useful thing cannot acquire good characters.
1.3.1. In modern times several useful actions can be automated, and thus there are only useful actions, and not essentially human actions.
1.4. Following 1.1 to 1.3, two useful things must always be present for satiation of a single human need. (Simplifying distinction between useful action, and useful material objects).
1.5. The logic of 1.4 can be extended to second order since, following Causal Order of Goods, the existence of the first order goods is a need which the useful things at second order serve.
2. General Case of Many Goods:
2.1. The first order of goods are goods because of a human need, their useful properties, knowledge and control of these properties.
2.2. The second order goods are goods because the are useful things which cause the first order of goods to come into existence and humans have the knowledge and control of these.
2.3.If there is only one useful thing at second order, and no useful human action exists to transform it into first order of good, it fails to acquire a good character for human needs.
2.4. Following 2.1 - 3, at least two useful things at second order are required to develop a first order good. (Simplifying distinction between useful action, and useful material objects).
2.6. The same logic extends to even further higher orders.
3. Corollary: Human actions, and inactions are always complementary to the useful things in definition of a Goods.
4. Observation: Empirical regularity exists where more than one useful thing in addition to human actions are combined to form a good.
5. Necessary Case:
Following 1 to 4, we can deduce that it is necessary, due to 4 and if not then 3, that there are always One-To-Many relations between effects and causes i.e. each effect is consequent of more than one causes on a Causal Order of Goods.
6. Corollary: Due to 5 all higher order goods for any given immediate lower order are called Complementary Goods.
7. Observation: Empirical regularity exists where each useful thing serves more than one goods by variation in its Complementary Goods, or in useful actions, or inactions.
7.1. For instance, the same labour of packing fruits can be used to pack vegetables, or with little variation pack most food items. Hence, each action can have alternative uses.
7.2. For instance, the water, useful thing, may be used for drinking to satiate thirst, cooking to satiate hunger, washing cooking utensils for cooking food, hydrating farms for producing vegetables, bathing for satiating body-hygiene, and washing clothes for additional hygiene needs. Hence, each thing can have alternative uses.
8. Possible Case:
Following 7, we can deduce that it is possible that there are One-To-Many relations between cause and effects i.e. each cause may have multiple effects on a Causal Order of Goods because each useful thing can have alternative uses serving alternative needs.
9. Generalizing: Combining 5 and 8, we may deduce the general possibility of a One-To-Many relation between causes and effects.
10. For an elaborate exposition please read further.
Explanations:
I. Necessity of the One-to-Many Relations: When moving from lower order, including human needs, to higher order each lower order is necessarily associated with more than one higher order goods by a causal relation. For instance, bread cannot exist without flour, water, heat, and labour. Flour cannot exist without wheat grain, wheat mill, electricity, and labour. And so on and so forth.
Likewise, we cannot satiate our human need without having control i.e. exerting labour over a useful thing. This holds by definition (See Good for Details). For instance, suppose a most primitive case of drinking water without a glass. We still require our labour to form bowl shapes with our hands to control water. Thus, by definition of Good, and also by our observations, a useful thing and our labour, control, satiates needs.
Note: Because of this necessity of Many Goods for gratification of a single Need, be it human or the production of lower order goods, Menger says that all the multiple goods of immediate higher order required to produce a single good of current order are complementary goods for each other. Absent a single one of them, we cannot produce our goods. Consider examples in Need and Good.
II. Possibility of One-to-Many Relations: When moving from higher to lower order, including human needs, in Causal Order of Goods each higher order may possibly be associated with more than one lower order goods, or needs, by a causal relation. For instance, while water is needed for baking bread, water also is needed for drinking, washing, and bathing etc. Likewise, the wood may be used for fire or for furniture purposes.
The same labourer who has lost his contract in one industry may possibly find a new contract in a different industry. A logistic service supplier may lose contract with one consumer goods company and find a new contract with another company. etc. Certain tools have a wide array of their uses, and certain do not. However, some specialized services, and tools may never find an alternative use. For instance, the skill and knowledge of dentists cannot have alternative uses. Or certain machines can never be used elsewhere because of their special design such as a printing press.
Reference: Menger, Carl (2004). Principles of Economics, Online edition, The Mises Institute, 2004. (Chapter 01 page 58-62 and page 65-67)