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When we talk mathematics, we may be discussing a secondary language built on the primary language of the nervous system.
--
As quoted in John Von Neumann, 1903-1957' (1958) by John C. Oxtoby and B. J. Pettis, p. 128

 

John von Neumann

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But we have higher mathematics, haven't we? This gives me freedom from my senses. The language of mathematics is even more inborn and universal than the language of music; a mathematical formula is crystal clear and independent of all sense organs. I therefore built a mathematical laboratory, set myself in it as if I were sitting in a car, and moved along with a beam of light.

 

Albert Einstein

 

Of all forms of symbolism, language is the most highly developed, most subtle, and most complicated. It has been pointed out that human beings, by agreement, can make anything stand for anything. Now, human beings have agreed, in the course of centuries of mutual dependency, to let the various noises that they can produce [...] stand for specified happenings in their nervous systems. We call that system of agreements language. For example, we who speak English have been so trained that, when our nervous systems register the presence of a certain kind of animal, we may make the following noise: "That's a cat." Anyone hearing us expects to find that, by looking in the same direction, he will experience a similar event in his nervous system -- one that will lead him to make an almost identical noise. Again, we have been so trained that when we are conscious of wanting food, we make the noise "I'm hungry." (p.26-27)

 

S. I. Hayakawa

 

Human beings do not live in the objective world alone, nor alone in the world of social activity as ordinarily understood, but are very much at the mercy of the particular language which has become the medium of expression for their society. It is quite an illusion to imagine that one adjusts to reality essentially without the use of language and that language is merely an incidental means of solving specific problems of communication or reflection. The fact of the matter is that the ‘real world’ is to a large extent unconsciously built up on the language habits of the group... We see and hear and otherwise experience very largely as we do because the language habits of our community predispose certain choices of interpretation.

 

Steven Pinker

 

The real problem in speech is not precise language. The problem is clear language. The desire is to have the idea clearly communicated to the other person. It is only necessary to be precise when there is some doubt as to the meaning of a phrase, and then the precision should be put in the place where the doubt exists. It is really quite impossible to say anything with absolute precision, unless that thing is so abstracted from the real world as to not represent any real thing. Pure mathematics is just an abstraction from the real world, and pure mathematics does have a special precise language for dealing with its own special and technical subjects. But this precise language is not precise in any sense if you deal with real objects of the world, and it is only pedantic and quite confusing to use it unless there are some special subtleties which have to be carefully distinguished.

 

Richard Feynman

 

Scientific language, which Korzybski used as his model of sane language, is almost exclusively extensional and denotative, or at least tries to be. The language of the mentally ill, most obviously "un-sane," is almost totally intensional and connotative. This is the language that does not correspond to anything "out there," and this is, in fact, how and perhaps even why the user is mentally ill. Korzybski's concern with keeping the conscious "connection" or correspondence between language and verifiable referents is, for all practical purposes, paralleled by the process of psychotherapy. In this process, which is largely "just talk," the purpose is to foster closer and more accurate correspondence between the patient's language and externally verifiable meanings.

 

Alfred Korzybski