“It remains a real world if there is a background to the symbols — an unknown quantity which the mathematical symbol x stands for. We think we are not wholly cut off from this background. It is to this background that our own personality and consciousness belong, and those spiritual aspects of our nature not to be described by any symbolism … to which mathematical physics has hitherto restricted itself.”

—  Arthur Stanley Eddington

Science and the Unseen World (1929)

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Arthur Stanley Eddington photo
Arthur Stanley Eddington 105
British astrophysicist 1882–1944

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Arthur Stanley Eddington photo

“It is to this background that our own personality and consciousness belong, and those spiritual aspects of our nature not to be described by any symbolism… to which mathematical physics has hitherto restricted itself.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

Science and the Unseen World (1929)
Context: It remains a real world if there is a background to the symbols—an unknown quantity which the mathematical symbol x stands for. We think we are not wholly cut off from this background. It is to this background that our own personality and consciousness belong, and those spiritual aspects of our nature not to be described by any symbolism... to which mathematical physics has hitherto restricted itself.<!--III, p.37-38

Arthur Stanley Eddington photo

“It remains a real world if there is a background to the symbols”

Arthur Stanley Eddington (1882–1944) British astrophysicist

Science and the Unseen World (1929)
Context: It remains a real world if there is a background to the symbols—an unknown quantity which the mathematical symbol x stands for. We think we are not wholly cut off from this background. It is to this background that our own personality and consciousness belong, and those spiritual aspects of our nature not to be described by any symbolism... to which mathematical physics has hitherto restricted itself.<!--III, p.37-38

Arthur Stanley Eddington photo

“We have to build the spiritual world out of symbols taken from our own personality, as we build the scientific world out of the symbols of the mathematician.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

Source: Science and the Unseen World (1929), Ch. VIII, p.82

Arthur Stanley Eddington photo

“If to-day you ask a physicist what he has finally made out the æther or the electron to be, the answer will not be a description in terms of billiard balls or fly-wheels or anything concrete; he will point instead to a number of symbols and a set of mathematical equations which they satisfy. What do the symbols stand for? The mysterious reply is given that physics is indifferent to that; it has no means of probing beneath the symbolism. To understand the phenomena of the physical world it is necessary to know the equations which the symbols obey but not the nature of that which is being symbolised. … this newer outlook has modified the challenge from the material to the spiritual world.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

Science and the Unseen World (1929)

S. I. Hayakawa photo

“SPAN ID=The_process_by>The process by means of which human beings can arbitrarily make certan things stand for other things may be called the symbolic process. Whenever two or more human beings can communicate with each other, they can, by agreement, make anything stand for anything. For example, here are two symbols:
X Y
We can agree to let X stand for buttons and Y for bows; then we can freely change our agreement and let X stand for […] North Korea, and Y for South Korea. We are, as human beings, uniquely free to manufacture and manipulate and assign values to our symbols as we please. Indeed, we can go further by making symbols that stand for symbols. […] This freedom to create symbols of any assigned value and to create symbols that stand for symbols is essential to what we call the symbolic process. </SPAN”

S. I. Hayakawa book Language in Thought and Action

Source: Language in Thought and Action (1949), The Symbolic Process, p. 24

R. G. Collingwood photo

“We can now return to the distinction between language and symbolism. A symbol is language and yet not language. A mathematical or logical or any other kind of symbol is invented to serve a purpose purely scientific; it is supposed to have no emotional expressiveness whatever. But when once a particular symbolism has been taken into use and mastered, it reacquires the emotional expressiveness of language proper. Every mathematician knows this. At the same time, the emotions which mathematicians find expressed in their symbols are not emotions in general, they are the peculiar emotions belonging to mathematical thinking.”

R. G. Collingwood (1889–1943) British historian and philosopher

Source: The Principles of Art (1938), p. 268

Franz Marc photo

“Their thinking has a different aim: To create out of their work symbols for their own time, symbols that belong on the altars of a future spiritual religion, symbols behind which the technical heritage cannot be seen. Scorn and stupidity will be like roses in their path.”

Franz Marc (1880–1916) German painter

1911 - 1914, The 'Savages' of Germany' (1912)

David Deutsch photo

“Reality contains not only evidence, but also the means (such as our minds, and our artefacts) of understanding it. There are mathematical symbols in physical reality. The fact that it is we who put them there does not make them any less physical.”

David Deutsch book The Fabric of Reality

Source: The Fabric of Reality (1997), Ch.3

Hermann Weyl photo

“We now come to a decisive step of mathematical abstraction: we forget about what the symbols stand for… [The mathematician] need not be idle; there are many operations which he may carry out with these symbols, without ever having to look at the things they stand for.”

Hermann Weyl (1885–1955) German mathematician

The Mathematical Way of Thinking (1941)

L. E. J. Brouwer photo

“The viewpoint of the formalist must lead to the conviction that if other symbolic formulas should be substituted for the ones that now represent the fundamental mathematical relations and the mathematical-logical laws, the absence of the sensation of delight, called "consciousness of legitimacy," which might be the result of such substitution would not in the least invalidate its mathematical exactness. To the philosopher or to the anthropologist, but not to the mathematician, belongs the task of investigating why certain systems of symbolic logic rather than others may be effectively projected upon nature. Not to the mathematician, but to the psychologist, belongs the task of explaining why we believe in certain systems of symbolic logic and not in others, in particular why we are averse to the so-called contradictory systems in which the negative as well as the positive of certain propositions are valid.”

L. E. J. Brouwer (1881–1966) Dutch mathematician and logician

as translated by Arnold Dresden from: Brouwer, L. E. J. (1913). Intuitionism and formalism. Bulletin of the American Mathematical Society, 20(2), 81–96. (quote on p. 84)

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