On Symbols (1970-1979)

"Any mathematician endowed with a modicum of intellectual honesty will recognise then that in each of his proofs he is capable of giving a meaning to the symbols he uses." (René Thom, "Modern mathematics, does it exist?", 1972)

"Mathematics in itself, as I say, is independent of experience. It begins with the free choice of symbols, to which are freely assigned properties, and it then proceeds to deduce the necessary rational implications of those properties." (Herbert Dingle, "Science at the Crossroads", 1972)

"A physical theory is assigned a literal and objective interpretation by assigning every one of its referential primitive symbols a physical object - entity, property, relation, or event - rather than a mental picture or a human operation." (Mario Bunge, "Philosophy of Physics", 1973)

"The mind reproduces itself by transmitting its symbols to other intermediaries, human and mechanical, than the particular brain that first assembled them." (Lewis Mumford, "Interpretations and Forecasts 1922-1972", 1973)

"Whether or not a given conceptual model or representation of a physical system happens to be picturable, is irrelevant to the semantics of the theory to which it eventually becomes attached. Picturability is a fortunate psychological occurrence, not a scientific necessity. Few of the models that pass for visual representations are picturable anyhow. For one thing, the model may be and usually is constituted by imperceptible items such as unextended particles and invisible fields. True, a model can be given a graphic representation - but so can any idea as long as symbolic or conventional diagrams are allowed. Diagrams, whether representational or symbolic, are meaningless unless attached to some body of theory. On the other hand theories are in no need of diagrams save for psychological purposes. Let us then keep theoretical models apart from visual analogues."  (Mario Bunge, "Philosophy of Physics", 1973)

"The unconscious reveals its meaning imaginatively, through symbols and images, and it speaks [...] a basically mythological language." (Morton Kelsey, "Myth, History & Faith", 1974)

"Models are not intended to either reflect or construct a single objective reality. Rather, their purpose is to simulate some aspect of a possible reality. In NLP, for instance, it is not important whether or not a model is 'true' , but rather that it is 'useful' . In fact, all models can be perceived as symbolic or metaphoric, as opposed to reflective of reality. Whether the description being used is metaphorical or literal, the usefulness of a model depends on the degree to which it allows us to move effectively to the next step in the sequence of transformations connecting deeper structures and surface structures. Instead of 'constructing' reality, models establish a set of functions that serve as a tool or a bridge between deep structures and surface structures. It is this bridge that forms our 'understanding' of reality and allows us to generate new experiences and expressions of reality." (Richard Bandler & John Grinder, "The Structure of Magic", 1975)

"Symbols, formulae and proofs have another hypnotic effect. Because they are not immediately understood, they, like certain jokes, are suspected of holding in some sort of magic embrace the secret of the universe, or at least some of its more hidden parts." (Scott Buchanan, "Poetry and Mathematics", 1975)

"Symbol and myth do bring into awareness infantile, archaic dreads and similar primitive psychic content. This is their regressive aspect. But they also bring out new meaning, new forms, and disclose a reality that was literally not present before, a reality that is not merely subjective but has a second pole which is outside ourselves. This is the progressive side of symbol and myth." (Rollo May, "The Courage to Create", 1975) 

"The most pervasive paradox of the human condition which we see is that the processes which allow us to survive, grow, change, and experience joy are the same processes which allow us to maintain an impoverished model of the world - our ability to manipulate symbols, that is, to create models. So the processes which allow us to accomplish the most extraordinary and unique human activities are the same processes which block our further growth if we commit the error of mistaking the model of the world for reality." (Richard Bandler & John Grinder, "The Structure of Magic", 1975)

"Whenever the Eastern mystics express their knowledge in words - be it with the help of myths, symbols, poetic images or paradoxical statements-they are well aware of the limitations imposed by language and 'linear' thinking. Modern physics has come to take exactly the same attitude with regard to its verbal models and theories. They, too, are only approximate and necessarily inaccurate. They are the counterparts of the Eastern myths, symbols and poetic images, and it is at this level that I shall draw the parallels. The same idea about matter is conveyed, for example, to the Hindu by the cosmic dance of the god Shiva as to the physicist by certain aspects of quantum field theory. Both the dancing god and the physical theory are creations of the mind: models to describe their authors' intuition of reality." (Fritjof Capra, "The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism", 1975)

"The chief difficulty of modern theoretical physics resides not in the fact that it expresses itself almost exclusively in mathematical symbols, but in the psychological difficulty of supposing that complete nonsense can be seriously promulgated and transmitted by persons who have sufficient intelligence of some kind to perform operations in differential and integral calculus […]" (Celia Green, "The Decline and Fall of Science", 1976)

"[…] all our symbols have the same purpose; words are merely the symbols we use most commonly. The function of words in human thought is to stand for things which are not present to the senses, and allow the mind to manipulate them - things, concepts, ideas, everything that does not have a physical reality in front of us now." (Jacob Bronowski, "The Imaginative Mind in Art", 1978) 

"[Human consciousness] depends wholly on our seeing the outside world in such categories. And the problems of consciousness arise from putting reconstitution beside internalization, from our also being able to see ourselves as if we were objects in the outside world. That is in the very nature of language; it is impossible to have a symbolic system without it." (Jacob Bronowski, "The origins of knowledge and imagination", 1978)

"In set theory, perhaps more than in any other branch of mathematics, it is vital to set up a collection of symbolic abbreviations for various logical concepts. Because the basic assumptions of set theory are absolutely minimal, all but the most trivial assertions about sets tend to be logically complex, and a good system of abbreviations helps to make otherwise complex statements."  (Keith Devlin, "Sets, Functions, and Logic: An Introduction to Abstract Mathematics", 1979)