“The Real is therefore simultaneously both the hard impenetrable kernel resisting symbolization and a pure chimerical entity which has in itself no ontological consistency. To use Kripkean terminology, the Real is the rock upon which every attempt at symbolization stumbles, the hard core which remains the same in all possible worlds (symbolic universes); but at the same time its status is thoroughly precarious; it is something that persists only as failed, missed, in a shadow, and dissolves itself as soon as we try to grasp it in its positive nature… like a traumatic event constructed backwards.”

— Slavoj Žižek, book The Sublime Object of Ideology

190
The Sublime Object of Ideology (1989)

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Slavoj Žižek99

Slovene philosopher 1949

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“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 (1882–1944) British astrophysicist

Science and the Unseen World (1929)

“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

“The real is what resists symbolization absolutely.”

Jacques Lacan (1901–1981) French psychoanalyst and psychiatrist

Source: The Seminar of Jacques Lacan: Freud's Papers on Technique

“The symbolic order is striving for a homeostatic balance, but there is in its Kernel, at its very centre, some strange traumatic order - the Thing. Lacan coined a neologism for it: l'extimité - external intimacy, which served as a title for one of Jacques-Alain Miller's Seminars. And what, at this level, is the death drive? Exactly the opposite of the symbolic orderL the possibility of the second death,' the radical annihilation of the symbolic texture through which so-called reality is constructed. They very existence of the symbolic order implies a possibility of its radical effacement, of symbolic death”

Slavoj Žižek book The Sublime Object of Ideology

the the death of the so-called real object in its symbol, but the obliteration of the signifying network itself.
147
The Sublime Object of Ideology (1989)

“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

“The symbol is the tool which gives man his power, and it is the same tool whether the symbols are images or words, mathematical signs or mesons.”

Jacob Bronowski (1908–1974) Polish-born British mathematician

"The Reach of Imagination" (1967)

“The good thing is that all the symbolic elements are gone, and that which really matters – the core – is left.”

Anders Fogh Rasmussen (1953) former Prime Minister of Denmark and NATO secretary general

On the Lisbon Treaty, Jyllands-Posten, 25 June 2007

“Pure mathematics proves itself a royal science both through its content and form, which contains within itself the cause of its being and its methods of proof. For in complete independence mathematics creates for itself the object of which it treats, its magnitudes and laws, its formulas and symbols.”

Christian Heinrich von Dillmann (1829–1899) German educationist

Source: Die Mathematik die Fackelträgerin einer neuen Zeit (Stuttgart, 1889), p. 94.

“There are a number of theorems in ordinary algebra, which, though apparently proved to be true only for symbols representing numbers, admit of a much more extended application. Such theorems depend only on the laws of combination to which the symbols are subject, and are therefore true for all symbols, whatever their nature may be, which are subject to the same laws of combination. The laws with which we have here concern are few in number, and may be stated in the following manner. Let a, b represent two operations, u, v two subjects on which they operate, then the laws are
(1) ab(u) = ba (u),
(2) a(u + v) = a (u) + a (v),
(3) am. an. u = am + n. u.
The first of these laws is called the commutative law, and symbols which are subject to it are called commutative symbols. The second law is called distributive, and the symbols subject to it distributive symbols. The third law is not so much a law of combination of the operation denoted by a, but rather of the operation performed on a, which is indicated by the index affixed to a. It may be conveniently called the law of repetition, since the most obvious and important case of it is that in which m and n are integers, and am therefore indicates the repetition m times of the operation a.”

Duncan Gregory (1813–1844) British mathematician

That these are the laws employed in the demonstration of the principal theorems in Algebra, a slight examination of the processes will easily shew ; but they are not confined to symbols of numbers ; they apply also to the symbol used to denote differentiation. <br class="br"> p. 237 http://books.google.com/books?id=8lQ7AQAAIAAJ&pg=PA237; Highlighted section cited in: George Boole " Mr Boole on a General Method in Analysis http://books.google.com/books?pg=PA225-IA15&id=aGwOAAAAIAAJ&hl," Philosophical Transactions, Vol. 134 (1844), p. 225; Other section (partly) cited in: James Gasser (2000) A Boole Anthology: Recent and Classical Studies in the Logic of George Boole,, p. 52 <br class="br">Examples of the processes of the differential and integral calculus, (1841)

“Symbolical algebra adopts the rules of arithmetical algebra, but removes altogether their restrictions: thus symbolical subtraction differs from the same operation in arithmetical algebra in being possible for all relations of value of the symbols or expressions employed… all the results of arithmetical algebra which are deduced by the application of its rules, and which are general in form, though particular in value, are results likewise of symbolical algebra, where they are general in value as well as in form: thus the product of a^{m} and a^{n}, which is a^{m+n} when m and n are whole numbers, and therefore general in form though particular in value, will be their product likewise when m and n are general in value as well as in form: the series for (a+b)^{n}, determined by the principles of arithmetical algebra, when n is any whole number, if it be exhibited in a general form, without reference to a final term, may be shewn, upon the same principle, to the equivalent series for (a+b)^n, when n is general both in form and value.”

George Peacock (1791–1858) Scottish mathematician

Vol. I: Arithmetical Algebra Preface, p. vi-vii
A Treatise on Algebra (1842)

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