(First version from 2004, last version 2019)
Is scientific language part of ordinary language or completely different ?
How do neologisms become part of our scientific and our ordinary language ?
Why do we understand each other rather well although the sender of a language signal understands many concepts in a slightly different way than the receiver of the message ?
Is learning new concepts comparable to children's language learning ?
Is mathematics just another language ?
Are rules of languages applicable to body language, and other forms of signals ?
How does vagueness of our expressions fit in communicating by language ?
I will try to find some answers in this blog, and would be glad to open debate. My preliminary answers are not much more than guesses:
1 - Is scientific language part of ordinary language or completely different ?
Scientific language serves to communicate with all those who learnt the special vocabulary of their science and can use it to understand each other's underlying hypotheses, the topics and the reasoning of their scientific community. Although this may be an artificial language striving to eliminate vagueness to a degree that allows more precision, this is still ordinary language. The difference betwenn scientific and ordinary language is not fundamental but gradual. Only because of this it is possible to learn new words and concepts.
But scientific language is using a specific formal code, the mathematical code. Is mathematics about language ? - I think this is indeed the case, so I will come back to that question later.
2 - How do neologisms become part of our scientific and our ordinary language ?
Neologisms are words introduced into our language to describe objects, things or actions that are new or seen from a new angle. They often enter language before they are fully understood.
There are convergent and divergent neologisms: the convergent ones are used in a way that sharpens borders excluding what lies outside such that the concepts become more precise by narrowing the gap of understanding between sender and receiver; the divergent ones are used in a way that includes ever more meanings such that the concepts become more and more blurred and unprecise. The word "atom" is an example for the convergent, the word "globalization" for the divergent development of meaning.
A special form of neologism is the formal neologism, where the new word or symbol is expressing a new element of formal metalanguage - that is language about language.
3 - Why do we understand each other rather well although the sender of a language signal understands many concepts in a slightly different way than the receiver of the message ?
We understand each other because we observe a principle of sufficiency tolerating some variation of meanings as long as there is sufficient overlapping. How far this overlapping must go depends on the purpose of our communication. If I want to tell somebody how he or she should drive a car the common understanding should be quite precise and underpinned by showing necessary actions and concepts. If I want to win somebody for a monetary contribution against hunger in Africa I only need an emotionally laden photo of a hungry baby - and the wanted effect will be rather immediate even if my opposite number may not know much of the context and the problems of development in Africa.
Communications involves a kind of negotiation about getting to a common understanding of what we are talking about, but the negotiation breaks off in the moment sufficient understanding. There is no need for a more precise definition. So in fact we do not really fully understand each other but it is just enough to enable common action.
There are forms of communication where the goal is mutual openness and sympathy - or even less: just non-aggression. This social communication needs no real understanding, therefore content may be very poor, e.g. when we play the "fine weather today" language game.
4 - Is learning new concepts comparable to children's language learning ?
I guess this may be very similar - however there is some evidence that this may be a different case. Neologisms are spreading in the language group while children learn concepts that are already entrenched in the language group.
5 - Is mathematics just another language ?
Mathematics is definitely a language; and as a highly symbolic language it needs good preparation of all users involved in speaking it. Learning mathematics is learning a language thet can be translated into ordinary language. However, this is not trivial.
To talk about the same in mathematics means that the whole edifice of the underlying theories is always implicitly included even for very shortcut terms of mathematical talking.
6 - Are rules of languages applicable to body language, and other forms of signals ?
Spoken language may be a special case, but there are definitely also forms of language without speech, first of all the symbolic language for deaf people. Language may be a special case of signal giving and signal interpretation; however, spoken language is giving a more unambigeous form of signals than for example body language.
7 - How does vagueness of our expressions fit in communicating by language ?
Vagueness is an essential part of our language. We live in a very limited world - we see only a small part of the electromagnetic spectrum, we hear only a small band of sound waves, we can see forests instead of single trees, we have universals and speak meaningful about them. All of this is only possible if we speak with a certain degree of vagueness.