“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

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S. I. Hayakawa 27

American politician 1906–1992

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“ 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."”

S. I. Hayakawa book Language in Thought and Action

</SPAN>
Source: Language in Thought and Action (1949), Language as Symbolism, pp. 26-27

“Let x represent an act of the mind by which we fix our regard upon that portion of time for which the proposition X is true; and let this meaning be understood when it is asserted that x denote the time for which the proposition X is true. (...) We shall term x the representative symbol of the proposition X.”

George Boole (1815–1864) English mathematician, philosopher and logician

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 165; As cited in: James Joseph Sylvester, ‎James Whitbread Lee Glaisher (1910) The Quarterly Journal of Pure and Applied Mathematics. p. 350

“A vice in common can be the ground of a friendship but not a virtue in common. X and Y may be friends because they are both drunkards or womanizers but, if they are both sober and chaste, they are friends for some other reason.”

W. H. Auden book The Dyer's Hand

"Don Juan", p. 403
The Dyer's Hand, and Other Essays (1962)

“Determinism, in the strict sense, is self-contradictory. For if man’s mental processes—specifically, his attempts at reasoning—are not free, if they are determined by environment and heredity, then there is no means of claiming that theory x is true and y is false—since man can have no way of knowing that his mental processes might not be conditioned to force him to believe that x is logical, when in fact it is not.”

Roy A. Childs, Jr. (1949–1992) American libertarian essayist and critic

Source: “Big Business and the Rise of American Statism,” 1969, p. 23

“Essentially, a fuzzy algorithm is an ordered sequence of instructions (like a computer program) in which some of the instructions may contain labels or fuzzy sets, e. g.:
Reduce x slightly if y is very large
Increase x very slightly if y is not very large and not very small
If x is small then stop; otherwise increase x by 2.”

Lotfi A. Zadeh (1921–2017) Electrical engineer and computer scientist

Source: 1970s, Outline of a new approach to the analysis of complex systems and decision processes (1973), p. 30

“Let us conceive, then, of an algebra in which the symbols x, y z etc. admit indifferently of the values 0 and 1, and of these values alone The laws, the axioms, and the processes, of such an Algebra will be identical in their whole extend with the laws, the axioms, and the processes of an Algebra of Logic. Difference of interpretation will alone divide them. Upon this principle the method of the following work is established.”

George Boole (1815–1864) English mathematician, philosopher and logician

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 37; Cited in: William Torrey Harris (1879) The Journal of Speculative Philosophy, p. 109

“Suppose we a certain Number of things exposed, different each from other, as a, b, c, d, e, &c.; The question is, how many ways the order of these may be varied? as, for instance, how many changes may be Rung upon a certain Number of Bells; or, how many ways (by way of Anagram) a certain Number of (different) Letters may be differently ordered?
Alt.1,21) If the thing exposed be but One, as a, it is certain, that the order can be but one. That is 1.
2) If Two be exposed, as a, b, it is also manifest, that they may be taken in a double order, as ab, ba, and no more. That is 1 x 2 = 2. Alt.3
3) If Three be exposed; as a, b, c: Then, beginning with a, the other two b, c, may (by art. 2,) be disposed according to Two different orders, as bc, cb; whence arise Two Changes (or varieties of order) beginning with a as abc, acb: And, in like manner it may be shewed, that there be as many beginning with b; because the other two, a, c, may be so varied, as bac, bca. And again as many beginning with c as cab, cba. And therefore, in all, Three times Two. That is 1 x 2, x 3 = 6.
Alt.34) If Four be exposed as a, b, c, d; Then, beginning with a, the other Three may (by art. preceeding) be disposed six several ways. And (by the same reason) as many beginning with b, and as many beginning with c, and as many beginning with d. And therefore, in all, Four times six, or 24. That is, the Number answering to the case next foregoing, so many times taken as is the Number of things here exposed. That is 1 x 2 x 3, x 4 = 6 x 4 = 24.
5) And in like manner it may be shewed, that this Number 24 Multiplied by 5, that is 120 = 24 x 5 = 1 x 2 x 3 x 4 x 5, is the number of alternations (or changes of order) of Five things exposed. (Or, the Number of Changes on Five Bells.) For each of these five being put in the first place, the other four will (by art. preceeding) admit of 24 varieties, that is, in all, five times 24. And in like manner, this Number 120 Multiplied by 6, shews the Number of Alternations of 6 things exposed; and so onward, by continual Multiplication by the conse quent Numbers 7, 8, 9, &c.;
6) That is, how many so ever of Numbers, in their natural Consecution, beginning from 1, being continually Multiplied, give us the Number of Alternations (or Change of order) of which so many things are capable as is the last of the Numbers so Multiplied. As for instance, the Number of Changes in Ringing Five Bells, is 1 x 2 x 3 x 4 x 5 = 120. In Six Bells, 1 x 2 x 3 x 4 x 5 x 6 = 120 x 6 = 720. In Seven Bells, 720 x 7 = 5040. In Eight Bells, 5040 x 8 = 40320, And so onward, as far as we please.”

John Wallis (1616–1703) English mathematician

Source: A Discourse of Combinations, Alterations, and Aliquot Parts (1685), Ch.II Of Alternations, or the different Change of Order, in any Number of Things proposed.

“The purpose of the mathematical theory of statistics is to deal with the relationship between 2 or more variable quantities without assuming that one is a single-valued mathematical function of the rest. The statistician does not think a certain x will produce a single-valued y; not a causative relation but a correlation. The relationship between x and y will be somewhere within a zone and we have to work out the probability that the point (x,y) will lie in different parts of that zone. The physicist is limited and shrinks the zone into a line. Our treatment will fit all the vagueness of biology, sociology, etc. A very wide science.”

Karl Pearson (1857–1936) English mathematician and biometrician

As quoted by E.S. Pearson, Karl Pearson: An Appreciation of Some Aspects of his Life and Work (1938) and cited in Bernard J. Norton, "Karl Pearson and Statistics: The Social Origins of Scientific Innovation" in Social Studies of Science, Vol. 8, No. 1, Theme Issue: Sociology of Mathematics (Feb.,1978), pp. 3-34.

“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)

“In the abstract world of American economists, equations run both ways; they believe that by changing the sign of a variable from plus to minus or from minus to plus or the price and quantity of x or y, the direction of historical movement can be reversed.”

Robert Gilpin (1930–2018) Political scientist

Source: The Political Economy of International Relations (1987), Chapter Eight, International Finance, p. 336

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S. I. Hayakawa 27

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