Felix Hausdorff used Old Greek words and letters for set theoretical concepts in his book, "Set Theory". But Greeks did not have set theory, so how Felix chose a word from Greek language for an nonexistent concept? Moreover, how a Greek or Latin word can be used for referring to a technology or mathematical concept, one that did not exist in that civilization, and is it a better way to do that rather than using a word from the language you know? It become evident how important is our inherent ability to create references, which are arbitrary in nature, but we want some kind of correlation with the meaning we know with the properties of a concept we are referring to. This, then, tells us that we can create truly arbitrary references, associations, relations, correlations, links between concepts, namely a reference name for an underlying concept.
If we can use a Greek or Latin word to refer to a concept (mathematical, engineering, or any other) that did not exist in their time and still can benefit from these references (we can manipulate them) then we can chose any word from any language to reference that concept. And this brings us to the point that we can conclude that the referenced concept is way more important than the reference word we are using to refer to it.
Our goal is to somehow manipulate concepts and their relationships as a whole using some kind of reference method, using references. Before that we need to understand as completely as we can the underlying inter-correlated concepts - concepts and their relationships, I will call it underlying system. What is the best way to do it? The answer is that they have to be understood in terms of the underlying axioms - we need to be aware of axioms and chosen postulates the underlying system is constructed from. In other words, we expect that underlying system needs to be axiomatized. We can give a best shot to axiomatize it and in many cases this can be a tough task, however, we need to have the best axioms we can come up with. Once the axioms are defined or discovered, postulates that define the underlying system components are discovered and identified we can move on to forming references to it. Then a more abstract step is required. We need to identify the fundamental concepts from which all the system elements are derived or constructed from. For instance, in math it is sets and operations on sets, in set theory it is a set membership relation (element x belongs to set A), in computer engineering is a structure stack and manipulation of it.
When acquiring new knowledge (in mathematics, engineering, or from most other fields) we often have to deal with reference words (references) put out by the authors of the book we are reading. In order to effectively acquire new knowledge, these references need to be masked! We have to cover them with a "cloth" so we can uncover the underlying system, with its axioms and postulates, referenced with now masked word. Then, we replace the masked word with a reference word of our choice. Why the masking is necessary? Because we are inclined to seek the link between the meaning of the reference word we already know, from its everyday use, and somehow use that to describe underlying mathematical, engineering (or other scientific) concept. This in many cases leads to confusion. The reference word can be misguided and misleading to us in our effort to understand the underlying referenced concept. It is misleading because we try to match the everyday meaning of the word with concepts, or their properties, within axiomatized system which is very specific and in many cases disconnected from ordinary word usage. That's why it is more beneficial to use an Old Greek or Latin word for a reference rather than a non-productive metaphor from ordinary word usage. As a matter of fact you can refer to any mathematical concept with randomly chosen strings of letters, like "aadvark12" to describe any mathematical concept, because this reference will not misguide you to seek match between its ordinary use (which it does not exist in this case) and underlying mathematical concept (which, anyway, can be described with set theoretical terms, which in turn can be reduced to the statements 'x belongs to set A', i.e. membership relations.) If the word 'aadvark12' does not exist in a dictionary that does not reduce in any way our understanding of the underlying concept; moreover it prevents us to use everyday word to refer to it and then be misguided. On the other hand, if a word is in the dictionary, it does not mean it is an effective reference to a mathematical concept.
More on this and how to link different axiomatized systems from different fields using Implicative Truth Synthesis and how to recognize and utilize Thought Initiator©, Thought Pusher©, Thought Visitor© mind faculties, in my book, "Yes, You Can!".
